Hindawi Publishing CorporationISRN Chemical EngineeringVolume 2013 Article ID 591546 17 pageshttpdxdoiorg1011552013591546

Research ArticleKinetics and Product Selectivity (Yield) of Second OrderCompetitive Consecutive Reactions in Fed-Batch Reactor andPlug Flow Reactor

Subash Chandra Bose Selvamony

Process Engineering Arch Pharmalabs Ltd 541A Marol Maroshi Road Andheri (East) Mumbai 400059 India

Correspondence should be addressed to Subash Chandra Bose Selvamony ssubashchangmailcom

Received 27 May 2013 Accepted 19 June 2013

Academic Editors C Chen J A A Gonzalez C-T Hsieh and Y Otsubo

Copyright copy 2013 Subash Chandra Bose Selvamony This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

This literature compares the performance of second order competitive consecutive reaction in Fed-Batch Reactor with that incontinuous Plug Flow Reactor In a kinetic sense this simulation study aims to develop a case for continuous Plug Flow Reactorin pharmaceutical fine chemical and related other chemical industries MATLAB is used to find solutions for the differentialequations The simulation results show that for certain cases of nonelementary scenario product selectivity is higher in PlugFlow Reactor than Fed-Batch Reactor despite the fact that it is the same in both the reactors for elementary reaction The effectof temperature and concentration gradients is beyond the scope of this literature

1 Introduction

Reactions in pharmaceutical (APImdashActive PharmaceuticalIngredients and Drug Intermediates) and fine chemicalindustries are known for their complexities Competitive con-secutive reactions with intermediate product as the desiredproduct are common in these industriesMany such reactionsare conventionally carried out in Fed-Batch (semi-batch)mode wherein one of the reactants is taken in a batchreactor and the other reactant is added over a period oftime (119905

119886 in second s) onto the reactant in the reactor and

maintained for a specific period of time 119905119898

(s) till thereaction gets completed Any choice between the types ofreactors if accompanied by improvement in product yieldwill be industrially significant

2 The Reaction System

The following type of reaction system is a representation ofsecond order competitive consecutive reaction

A + B1198701

997888997888rarr R + C B + R1198702

997888997888rarr S + D (1)

A B R S C and D are various species involved in thereaction

RmdashDesired Product SmdashUndesired Product It shouldbe noted that the species mentioned in the representativechemical equation (1) are not the only chemical componentspresent in the reaction systemMost of the times the reactionsystem would additionally have one or more solvents

The general pattern of concentration-time profile ofcompetitive consecutive reaction of the type shown in (1) inan ideal batch reactor is given in Figure 1 [1] which shows thatif all the reactants are introduced into the reactor at reactioncondition the concentration of the desired product R initiallyrises and goes through a maximum and then it reduceswhereas the concentration of undesired product S keepsrising with timeThe concentration of reactants continuouslydecreases and will become zero at infinite time

As is the case with many industrial operations in Fed-Batch Reactor when we add reactant B on to reactant Ain reactor initially product R forms favorably and this Rreacts further with B to form S After significant extent ofreaction (ie after significant extent of R formation) if wekeep adding B in to the reaction mass the concentration of Rwill be significantly high and that of A will be significantly

2 ISRN Chemical Engineering

002040608

112141618

2

0 1 2 3 4 5 6 7Time (s)

minus1minus02

Con

cent

ratio

n (m

olL

)

Concentration of A Concentration of BConcentration of R Concentration of S

Figure 1 Concentration as a function of time

Reactant Bta (k molmiddotsminus1)NBt

Figure 2 Schematic drawing of Fed-Batch Reactor

less Under this condition with further fresh charge ofB condition for S formation is favored Both modes ofoperations (batch and semibatch or fed batch) would havereacting species concentration so varied with time that aquantitative analysis is imperative to understand the relativesignificance of these two reactors in the light of obtainingmaximum product R yield It has been reported in ChemicalReaction Engineering text book Levenspiel [1] that for anelementary second order competitive consecutive reactionproduct R selectivity is the same in semi-batch (ie Fed-Batch Reactor) and Batch Reactors Efforts have beenmade inthe past to understand the factors affecting product selectivityof competitive consecutive reaction

In the Reaction Engineering text books Levenspiel [1]and Coulson and Richardsonrsquos [2] type of reactors (ie PlugFlow Reactors Mixed Flow reactors or Fed-Batch Reactor)and product selectivity have been discussed especially forcompetitive consecutive reactions

The recent literature on product selectivity of competitiveconsecutive reactions is reported by Shah et al [3 4]which deals with ldquoproduct selectivity with mixing reactionrates and stoichiometryrdquo As the reactions in actual are notnecessarily always elementary [1] it is relevant to simulate the

product selectivity of nonelementary second order competi-tive consecutive reaction schemes

References [5 6] deal with product selectivity andmixingand covering competitive consecutive reaction and competi-tive parallel reactions This shows that identifying the condi-tions for increased product selectivity is an important aspectAt times product selectivity determines the economics ofoperating a plant

In practice Batch reactors unlike FedBatchReactor offerhigher order of nonideality in mixing and heat transfer in theform of significant concentration and temperature gradientsas it (Batch Reactor) has to deal with larger quantities of massand heat energy from the very start of the time 0 secondsThis necessitates the use of Fed-Batch mode of operationspredominantly in Pharmaceuticals and other related indus-tries However the continuous Plug FlowReactors are knownfor their flexibility in offering higher heat transfer area andbettermixing intensitiesOf latemany pieces of literature andpractical works have gone on investigating and implementingcontinuous Plug Flow Reactors in pharmaceutical and otherrelated chemical industries Designs have varied from asimple tube to a static mixer to plate heat exchanger typeof reactors to Microreactors one would see that in piecesof literature [7ndash12] Anderson [7] reports that in lab scale23 yield of desired intermediate product in a specificcompetitive consecutive reaction became 83upon changingthe mode of reaction from semi-batch to continuous plugflow Brechtelsbauer and Ricard [8] report that static mixerbased continuous Plug Flow Reactor gave a better productyield due to good turbulent and heat transfer characteristicsThe major challenge in implementing Plug Flow Reactor inPharmaceuticals and related other industries is in identifyingthe right reaction kinetics [13]

The primary aim of this simulation work is to find outa kinetic scenario in which continuous Plug Flow Reactorwould yield higher desired product than that the conven-tional Fed-Batch Reactor would yield Also this paper aimsto provide a practical method to pick among the simulatedreaction models the schemes which would be kineticallyfavored in Plug Flow Reactor

The rate equations governing the chemical reaction sys-tem given in (1) is as follows [1]

119903A = minus 1198701119862119886

A119862119887

B

119903B = minus 1198701119862119886

A119862119887

B minus 1198702119862119888

B119862119889

R

119903R = 1198701119862119886

A119862119887

B minus 1198702119862119888

B119862119889

R

119903S = 1198702119862119888

B119862119889

R

(2)

The exponents a b c and d represent the order of the reactionwith respect to each of the reacting species When 119886 = 119887 =119888 = 119889 = 1 the reaction becomes an elementary second orderreaction Values other than 1 for any of the exponents makethe reaction nonelementary Here the analysis is limited tosecond order reactions hence 119886 + 119887 = 119888 + 119889 = 2 [1]

ISRN Chemical Engineering 3

FA0

CA0

FA

CAF

FAF

FA + dFA

Figure 3 Schematic drawing of Plug Flow Reactor

Table 1 Molecular weights

Molecular weight of A 750000 Molecular weight of R 468750Molecular weight of B 187500 Molecular weight of C 468750Total (1st reactionreactants) 937500 Total (1st reaction

products) 937500

Molecular weight of R 468750 Molecular weight of S 328125Molecular weight of B 187500 Molecular weight of D 328125Total (2nd reactionreactants) 656250 Total (2nd reaction

products) 656250

3 The Fed-Batch Reactor (Reactor-1)

Reactant A is taken in the reactor whereas reactant B isadded continuously over reactant A (see Figure 2) It is tobe noted that component B is added (no output flow term)whereas component A is taken inside the reactor (no inputflow term and no output flow term) Hence material balancefor components A and B must be written separately Materialbalance pattern of all other products is similar to that ofcomponent A

For Species A

Input = Output + Disappearance by Reaction

+ Accumulation

0 = 0 + (minus119903A) 119881 + (119889119873A119889119905)

(minus1

119881) sdot (119889119873A119889119905) = minus119903A

(3)

For Species B

Input = Output + Disappearance by Reaction

+ Accumulation

(119873B119905119905119886

) = 0 + (minus119903B) 119881 + (119889119873B119889119905)

(minus1

119881)(119889119873B119889119905) = minus119903B minus (

119873B119905119881119905119886

)

(4)

From (3) to (4) we can mathematically describe thereaction system in ideal Fed-Batch Reactor as follows119889119873A119889119905

= (minus1

119881)1198701119873119886

A119873119887

B 0 lt 119905 le 119905119886 + 119905119898

119889119873B119889119905= (minus1

119881)1198701119873119886

A119873119887

B minus (1

119881)1198702119873119888

B119873119889

R +119873B119905119905119886

0 lt 119905 le 119905119886

119889119873B119889119905= (minus1

119881)1198701119873119886

A119873119887

B minus (1

119881)1198702119873119888

B119873119889

R 119905119886 lt 119905 le 119905119886+119898

119889119873R119889119905= (1

119881)1198701119873119886

A119873119887

B minus (1

119881)1198702119873119888

B119873119889

R 0 lt 119905 le 119905119886+119898

119889119873S119889119905= (1

119881)1198702119873119888

B119873119889

R 0 lt 119905 le 119905119886+119898

119881 =119905119881119886119905

119905119886

+ (119881119905minus 119881119886119905) 0 lt 119905 le 119905

119886

119881 = 119881119905 119905119886lt 119905 le 119905

119886+119898

(5)

The sets of equations (5) represent in the second orderconsecutive competitive reaction in Fed-Batch Reactor

4 The Plug Flow Reactor (Reactor-2) (SeeFigure 3)

Thematerial (ie chemical) balance equations for a Plug FlowReactor can be written as follows [1]

Input = Output + Disappearance by reaction+ Accumulation

(6)

119865A = 119865A + 119889119865A + (minus119903A sdot 119889V) (7)

(minus119889119865A119889V) = minus119903A (8)

(minus119889119862AV

1015840

119889V) = minus119903A (9)

Space time in Plug Flow Reactor 119905lowast = VV1015840When volumetric flow rate is constant 119889119905lowast = 119889VV1015840 (8)

becomes as follows

(minus119889119862A119889119905lowast) = minus119903A (10)

From (7) to (10) we can mathematically describe thereaction system in ideal Plug Flow Reactor as follows

119889119862A119889119905lowast= minus 119870

1119862119886

A119862119887

B

119889119862B119889119905lowast= minus 119870

1119862119886

A119862119887

B minus 1198702119862119888

B119862119889

R

119889119862R119889119905lowast= 1198701119862119886

A119862119887

B minus 1198702119862119888

B119862119889

R

119889119862S119889119905lowast= 1198702119862119888

B119862119889

R

(11)

5 Simulation Plan

Solutions to the set of equations in (5) and (11) will enable oneto analyze the performance of reaction system in Fed BatchReactor and continuous Plug flow Reactor respectively

The main aim of this literature is to carry out thepreviouslymentioned analysis for an arbitrary still practicallyrelevant reaction system

4 ISRN Chemical Engineering

Table 2 (a) Reactor-1 (Fed-Batch Scheme 1 Part 1) (b) Reactor-2 (Plug Flow Scheme 1 Part 1) (c) Reactor-1 (Fed-Batch Scheme 1 Part2) (d) Reactor-2 (Plug Flow Scheme 1 Part 2) (e) Reactor-1 (Fed-Batch Scheme 1 Part 3) (f) Reactor-2 (Plug Flow Scheme 1 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 129 2132 0027 000 184 0801 8623600 129 2132 0027 000 184 08 8624

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1291 2132 0026 1119864 minus 26 1838 0803 861460 1291 2132 0026 000 1838 0803 8614

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 129 2132 0027 2119864 minus 06 184 08 8624900 129 2132 0027 1119864 minus 06 184 08 86241800 129 2132 0027 9119864 minus 07 184 08 8624900 129 2132 0027 1E minus 06 184 08 8624900 129 2132 0027 1E minus 06 184 08 8624

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1313 2133 0027 0061 184 08 8625360 1296 2132 0027 0016 184 08 8624720 129 2132 0027 4119864 minus 04 184 08 8624240 1313 2133 0027 0061 184 08 8625240 1313 2133 0027 0061 184 08 8625

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 106 2127 0027 0002 2454 0186 1151900 106 2127 0027 0001 2454 0186 1151

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1117 2128 0027 0152 2454 0186 1151360 1086 2127 0027 007 2454 0186 1151

Rate constant values are assumed with three individualscenarios first one with ratio of119870

1to1198702considered as 10 and

1198701considered as 100sdotLitresdotmolminus1sdotsminus1 the second one with the

same ratio of11987011198702but with the119870

1as 01 Litresdotmolminus1sdotsminus1 and

the third one with the ratio of 11987011198702considered as 50 with

the1198701considered as 01 Litresdotmolminus1sdotsminus1

Totally nine different sets of exponents (ie a b c d)have been considered such that the overall order of reactionremains two Hence there are 9 sets of reactions schemeseach scheme is analyzed for the mentioned 3 sets of kineticconstants Molecular weight of each of the componentsinvolved in the reaction is considered in consistent with thestoichiometry given in (1) The values are given in Table 1

In this study the molecular weights are used to convertmoles into Kg and vice versa (molecular weight values arearbitrary in Table 1)

Total solvent quantity considered is 2m3 Quantity ofsolvent m3 used to make a stream of reactant A is called Sol

R Quantity of solvent m3 used to make a stream of reactantB is called Sol A For the ensuing simulations amount ofsolvent used in both the reacting streams is same that is SolA(Sol A + Sol R) = 05 unless specified otherwise in therespective calculationoutput datagraphsTableThe effect ofrelative concentration of both the streams on kinetics is nottreated at length however few cases with Sol A(Sol R + SolA) = 025 and 075 have been simulated to indicate the changein reaction selectivity with change in relative concentration ofreactant streams

As the reaction considered is in liquid phase constantvolume reaction system is supposed except for the volumechange due to addition of the solution of second component(reactant B) in to the solution of 1st component (reactant A)in the Fed-Batch Reactor There is no volume change dueto reaction Volumetric flow rate in Plug Flow Reactor isconsidered constantThe volume in liters constituted by eachof the starting materials (A and B) is assumed 05 times theweight in kg of the respective components

ISRN Chemical Engineering 5

005

115

225

3

0 100 200 300 400 500 600 700Con

cent

ratio

n (m

olL

)

Time (s)minus05

(a)

0

05

1

15

2

25

0 100 200 300 400 500 600 700Time (s)

Volu

me (

m3)

(b)

002040608

112141618

0 05 1 15 2 25 3 35

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(c)

0

05

1

15

2

25

3

0 500 1000 1500 2000 2500C

once

ntra

tion

(mol

L)

Time (s)minus05

(d)

002040608

112141618

0 100 200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(e)

0

05

1

15

2

25

3

0 500 1000 1500 2000 2500

Con

cent

ratio

n (m

olL

)

Time (s)minus05

(f)

002040608

1121416

0 100

AB

RS

200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(g)

Figure 4 (a) Concentration as a function of time Fed-Batch Reactor (Scheme 1 Part 1 Case 1 119905119886= 60 s 119905

119898= 600 s (see Scheme 1

in Supplementary Material available online at httpdxdoiorg1011552013591546) (b) Volume as a function of time Fed-Batch Reactor(Scheme 1 Part 1 Case-1 119905

119886= 60 s 119905

119898= 600 s) (c) Concentration as a function of time Plug Flow Reactor (Scheme 1 Part 1 119905end = 6 s for

brevity graph is plotted for 3 s only) (d) Concentration as a function of time Fed-Batch Reactor (Scheme 1 Part 2 119905119886= 900 s 119905

119898= 1200 s)

(e) Concentration as a function of time Plug Flow Reactor (Scheme 1 Part 2 119905end = 360 s) (f) Concentration as a function of time Fed-BatchReactor (Scheme 1 Part 3 119905

119886= 900 s 119905

119898= 1200 s) (g) Concentration as a function of time Plug Flow Reactor (Scheme 1 Part 3 119905end = 360 s)

6 ISRN Chemical Engineering

0

05

1

15

2

25

3

0 100 200 300 400 500 600 700

Con

cent

ratio

n (m

olL

)

Time (s)minus05

(a)

0

02

04

06

08

1

12

14

16

0 05 1 15 2 25 3 35

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(b)

0

05

1

15

2

25

3

0 500 1000 1500 2000 2500

Con

cent

ratio

n (m

olL

)

Time (s)minus05

AB

RS

(c)

0

02

04

06

08

1

12

14

16

0 100 200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)

AB

RS

(d)

Figure 5 (a) Concentration as a function of time Fed-Batch Reactor (Scheme 2 Part 1 119905119886= 60 s 119905

119898= 600 s) (b) Concentration as a function

of time Plug Flow Reactor (Scheme 2 Part 1 119905end = 6 s for brevity graph is plotted for 3 s only) (c) Concentration as a function of timeFed-Batch Reactor (Scheme 2 Part 2 119905

119886= 900 s 119905

119898= 1200 s) (d) Concentration as a function of time Plug Flow Reactor (Scheme 2 Part 2

119905end = 360 s)

The quantity of A used in the entire study is 200Kgs Incase of Fed batch reactor the simulation has been done forvarious addition time of streamB reactionmaintenance timeis chosen such that further change in concentration profileis practically absent The constancy of concentration profiletowards the end of 119905

119898can be observed in the concentration

profiles obtained from MATLAB Also 119905119898

is maintainedconstant for a given set of 119870

11198702in order to make the

comparative study relevant In case of Plug Flow Reactor thesimulation is done for different reaction end time as differentcase The reaction time 119905end in Plug Flow Reactor refers tospace time

In case of Fed-Batch Reactor the addition rate is consid-ered constant across the entire addition time

The reaction is run in both the reactors for a specifiedextent of conversion that is 99 of reactant A conversionis the reaction end point For a prechosen 119905

119886 119905119898 and 119905end the

99 conversion of reactant A is ensured by adjusting the totalmoles of reactant B that is by adjusting 119873B119905119873A119905 final 99conversion of reactant A is achieved for predefined cases of 119905

119886

(s) 119905119898(s) and 119905end (s)

The previously mentioned assumptions and basis havebeen considered keeping in mind that the actual reactionscenarios in the industry can be understood and interpretedin the light of the conclusions arrived at in this simulationstudy

The concentration profiles given in the subsequent sec-tions are intended only to showcase the pattern of thecorresponding reaction scheme The quantitative details ofsuch graphs are given in the tables for the respective cases

6 Simulation Accuracy

Solution to the previouslymentioned simultaneous nonlineardifferential equations ((5) and (11)) has been obtained by thesoftware MATLAB which entailed its default Explicit Runge-Kutta (45) Variable step (Dormand-Prince Pair) methodThe calculation tolerance has been set at a default 01with step limits adjusted such that step limits n and n10seconds would return the final results matching up to 3decimal points When the gap between reactor-1 and reactor-2 results narrowsbecomes more significant towards arriving

ISRN Chemical Engineering 7

112

211

37 115

3

116

7

117

3

118

1

118

5

101

3 103

210

52

105

9

106

1

106

2

106

3

106

3

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 6 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 2 Part 2)

at a conclusion tolerance is squeezed further to 001 withthe same step limit criteria as done for the simulation withtolerance 01

7 Simulation (Scheme 1 119886 = 119887 = 119888 = 119889 = 1 ieElementary Reaction)

71 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 In Tables 2(a) and 2(b) simulation results for two

cases have been captured Figures 4(a) and 4(c) are sampleconcentration profiles of reaction species in ideal Fed Batchand ideal Plug Flow Reactor Figure 4(b) is the graphicalrepresentation of reaction volume in Fed-Batch Reactor

It can be observed in Figure 4(a) that with 119905119898= 600 s

further concentration change (reaction) is negligible As theaddition rate of reagent B considered in this simulation studyis constant the fed batch volume increases linearly till 119905 =119905119886 During Reaction maintenance time 119905

119898 the Fed-Batch

volume remains constant

72 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Figures 4(d) and 4(e) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

In Tables 2(c) and 2(d) results for all simulated cases havebeen captured and the data lines (rows) 4 and 5 correspondto the fraction Sol A(Sol A + Sol R) = 025 and 075respectively

73 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and

1198702= 0002 Figures 4(f) and 4(g) are sample concentration

profiles of reaction species in ideal Fed Batch and ideal PlugFlow Reactors

In Tables 2(e) and 2(f) simulation results for two caseshave been captured

Tables 2(a) to 2(f) show that elementary reaction of thetype given in (1) yields the same amount of desired product infed batch reactor and Plug Flow Reactor Moreover the yield

values in Part 2 remain the same as those in Part 1 That isbecause119870

11198702values remain the same in both Part 1 and Part

2 even though the individual 1198701and 119870

2values are different

It is to be noted that in Part 3 yield values are different fromthat in Part 1 and Part 2That is because119870

11198702value in Part 3

is different from those in Part 1 and Part 2 The change in therelative concentration of both the reacting streams (as shownin Table 2(c) rows 2 4 and 5 and Table 2(d) rows 1 4 and 5)does not have any effect on the yield

8 Simulation (Scheme 2 119886 = 119887 = 1 119888 = 15 119889 =05 Nonelementary)

81 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 Figures 5(a) and 5(b) are sample concentration

profiles of reaction species in ideal Fed Batch and ideal PlugFlow Reactors

In Tables 3(a) and 3(b) simulation results for two casessimulated have been captured

82 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Figures 5(c) and 5(d) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

In Tables 3(c) and 3(d) and Figure 6 results for all thesimulated cases have been captured The data lines (rows) 4and 5 in Tables 3(c) and 3(d) correspond to the fraction SolA(Sol A + Sol R) = 025 and 075 respectively

The yield values for varying reaction times are capturedin Figure 6

83 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 In Tables 3(e) and 3(f) simulation results for two caseshave been captured

Tables 3(a) and 3(f) and Figure 6 show that this nonelementary reaction yields higher desired product in Fed-Batch Reactor than in Continuous Plug Flow Reactor

In Figure 6 the Plug Flow Reactor yield initially increaseswith the increase in reaction time (ie lengthier reactor pipe)consequently 119873B119905119873A119905 value decreases as shown in Tables3(c) and 3(d) (ie reduced consumption of Reactant B)However the Plug Flow Reactor yield saturates out belowFed-Batch Reactor yield Overall the Fed Batch Reactoryields higher product R than Plug Flow Reactor even thoughthere is a very marginal change in yield for the change in therelative concentration of reacting streams (Table 3(c) rows 24 and 5) in Fed Batch Reactor

9 Simulation (Scheme 3 119886 = 119887 = 1 119888 = 05 119889 =15 Nonelementary)

91 Part 1 (Cases 1 and 2)1198701= 100119870

11198702= 10 and119870

2= 10

In Tables 4(a) and 4(b) simulation results for two cases havebeen captured

Figures 7(a) and 7(b) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

8 ISRN Chemical Engineering

Table 3 (a) Reactor-1 (Fed-Batch Scheme 2 Part 1) (b) Reactor-2 (Plug Flow Scheme 2 Part 1) (c) Reactor-1 (Fed-Batch Scheme 2 Part2) (d) Reactor-2 (Plug Flow Scheme 2 Part 2) (e) Reactor-1 (Fed-Batch Scheme 2 Part 3) (f) Reactor-2 (Plug Flow Scheme 2 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1005 2132 0027 000 2598 0042 122600 0996 2125 0027 000 2625 0015 123

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 113 2128 0027 6119864 minus 06 2267 04 106360 113 2128 0027 3119864 minus 35 2267 04 1063

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1072 2127 0027 0005 2425 0215 1137900 1059 2166 0027 0004 2459 0181 11531800 1048 2126 0027 0004 2491 0149 1167900 1061 2127 0027 0004 2456 0184 1151900 1058 2126 0027 0004 2463 0177 1154

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1221 2131 0027 0135 216 048 1013360 118 2129 0027 0068 2202 0438 1032720 1145 2129 0027 0018 2244 0396 1052240 1221 2131 0027 0135 216 048 1013240 1221 2131 0027 0135 216 048 1013

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1009 2125 0027 0008 2599 0041 1218900 1006 2125 0027 0008 2605 0035 1221

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1094 2127 0027 0083 2545 0095 1193360 1058 2126 0027 0097 2555 0085 1198

92 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 4(c) and 4(d) and Figure 8 results for othersimulated cases have been captured

The last two data lines (rows) in Tables 4(c) and 4(d)correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

Figures 7(c) and 7(d) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

The yield values for varying reaction times are capturedin Figure 8

93 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 InTables 4(e) and 4(f) simulation results for two caseshave been captured

Tables 4(a)ndash4(f) and Figure 8 show that this non elemen-tary reaction yields higher desired product R in Plug FlowReactor than in Fed-Batch Reactor

It is to be noted that the reduced addition time in FedBatch Reactor results in increased product yield Howeverin actual practice heat transfer and other limitations of thereactor vessel could possibly determine the minimum addi-tion time beyond which addition time cannot be reduced Sothe Fed Batch reactor yield is limited

It is to be further noted that there is a marginal changein the yield in Fed Batch reactor with the change in relativeconcentration of reacting streams (Table 4(c) rows 2 4 and5) However this variation is too low to catch up with PlugFlow Reactor yield

10 Simulations (for the Rest of the Schemes)

101 (Scheme 4 119886 = 05 119887 = 15 119888 = 05 119889 = 15Nonelementary)

1011 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and 119870

2=

10 See Tables 5(a) and 5(b)

ISRN Chemical Engineering 9

Table 4 (a) Reactor-1 (Fed-Batch Scheme 3 Part 1) (b) Reactor-2 (Plug Flow Scheme 3 Part 1) (c) Reactor-1 (Fed-Batch Scheme 3 Part2) (d) Reactor-2 (Plug Flow Scheme 3 Part 2) (e) Reactor-1 (Fed-Batch Scheme 3 Part 3) (f) Reactor-2 (Plug Flow Scheme 3 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1909 2148 0027 000 019 245 9600 195 2149 0027 000 0079 2561 4

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1448 2136 0027 3119864 minus 08 1419 12 665260 1447 2136 0027 3119864 minus 05 142 12 6657

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1598 214 0027 5119864 minus 13 1019 1621 4776900 1661 2142 0027 3119864 minus 13 0851 1789 39891800 1722 2143 0027 7119864 minus 13 0687 1953 3222900 1655 2141 0027 1119864 minus 12 0868 1772 4067900 1668 2142 0027 1119864 minus 12 0833 1807 3905

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1448 2136 0027 4119864 minus 12 1419 1221 6652360 1448 2136 0027 4119864 minus 12 1419 1221 6652720 1448 2136 0027 4119864 minus 12 1419 1221 6652240 1448 2136 0027 4E minus 12 1419 1221 6652240 1448 2136 0027 4E minus 12 1419 1221 6652

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1214 213 0027 0000 2043 0597 9575900 1251 2131 0027 0000 1943 0697 9107

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1172 2129 0027 0071 2227 0413 1044360 1163 2129 0027 0003 2182 0458 1023

1012 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 The data lines (rows) 4 and 5 in Tables 5(c) and 5(d)correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 9

1013 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 (See Tables 5(e) and 5(f)) Tables 5(a)ndash5(f) and Figure 9show that this non elementary reaction yields higher desiredproduct in Plug Flow Reactor than in Fed-Batch Reactor

As in Scheme 3 the reduced addition time in Fed BatchReactor results in increased product yield However in actualpractice heat transfer and other limitations of the reactorvessel could possibly determine the minimum addition timebeyond which addition time cannot be reduced So the FedBatch reactor yield is limited

Themarginal change in the yield in FedBatch reactorwithrelative concentration of reacting streams (Table 5(c) rows 24 and 5) may be noted However this variation is too low tocatch up with Plug Flow Reactor yield

102 (Scheme 5 119886 = 15 119887 = 05 119888 = 05 119889 = 15Nonelementary)

1021 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 6(a) and 6(b)

1022 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 119870

2=

001 In Table 6(c) and 6(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1023 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 119870

2=

0002 (See Tables 6(e) and 6(f)) Tables 6(a)ndash6(f) show that

10 ISRN Chemical Engineering

0

05

1

15

2

25

3

0 100 200 300 400 500 600 700

Con

cent

ratio

n (m

olL

)

Time (s)minus05

(a)

002040608

112141618

2

0 05 1 15 2 25 3 35

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(b)

0

05

1

15

2

25

3

0 500 1000 1500 2000 2500Time (s)minus05

Con

cent

ratio

n (m

olL

)

AB

RS

(c)

002040608

112141618

2

0 100

AB

RS

200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(d)

Figure 7 (a) Concentration as a function of time Fed-Batch Reactor (Scheme 3 Part 1 119905119886= 60 s 119905

119898= 600 s) (b) Concentration as a function

of time Plug Flow Reactor (Scheme 3 Part 1 119905end = 6 s for brevity graph is plotted for 3 s only) (c) Concentration as a function of timeFed-Batch Reactor (Scheme 3 Part 2 119905

119886= 900 s 119905

119898= 1200 s) (d) Concentration as a function of time Plug Flow Reactor (Scheme 3 Part 2

119905end = 360 s)

this type of nonelementary reaction yields the same amountof desired product in fed batch reactor and in Plug FlowReactor Moreover the yield values in Part 2 remain the sameas those in Part 1 That is because 119870

11198702values remain the

same in both Part 1 and Part 2 even though the individual1198701and119870

2values are different It is to be noted that in Part 3

yield values are different from that in Part 1 and Part 2That isbecause 119870

11198702value in Part 3 is different from those in Part

1 and Part 2The change in the relative concentration of both the

reacting streams (as shown in Table 6(c) rows 2 4 and 5 andTable 6(d) rows 1 4 and 5) does not have any effect on theyield

103 (Scheme 6 119886 = 05 119887 = 15 119888 = 15 119889 = 05Nonelementary)

1031 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 7(a) and 7(b)

1032 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 7(c) and 7(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1033 Part 3 (Cases 1 and 2)1198701= 01119870

11198702= 50 and119870

2=

0002 (See Tables 7(e) and 7(f)) Tables 7(a)ndash7(f) show thatthis type of nonelementary reaction also behaves similar toelementary reaction and nonelementary reaction Scheme 5with respect to product selectivity that is the yield is the samein both the reactors The change in the relative concentrationof both the reacting streams (as shown in Table 7(c) rows 24 and 5 and Table 7(d) rows 1 4 and 5) does not have anyeffect on the yield

104 (Scheme 7 119886 = 15 119887 = 05 119888 = 15 119889 = 05Nonelementary)

1041 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 8(a) and 8(b)

ISRN Chemical Engineering 11

Table 5 (a) Reactor-1 (Fed-Batch Scheme 4 Part 1) (b) Reactor-2 (Plug Flow Scheme 4 Part 1) (c) Reactor-1 (Fed-Batch Scheme 4 Part2) (d) Reactor-2 (Plug Flow Scheme 4 Part 2) (e) Reactor-1 (Fed-Batch Scheme 4 Part 3) (f) Reactor-2 (Plug Flow Scheme 4 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1927 2148 0027 000 0141 2499 7600 1961 2149 0027 000 005 259 2

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1313 2133 0027 6119864 minus 08 1778 09 833460 1313 2667 0027 6119864 minus 08 1778 09 8334

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1562 2139 0027 000 1113 1527 5219900 1654 2141 0027 1119864 minus 10 0869 1771 40751800 1733 2143 0027 6119864 minus 13 0658 1982 3085900 1646 2141 0027 1E minus 12 0868 175 4171900 1662 2142 0027 1E minus 10 0848 1792 3974

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1313 2133 0027 000 1778 0862 8334360 1313 2133 0027 000 1778 0862 8334720 1313 2133 0027 8119864 minus 12 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1203 213 0027 7119864 minus 11 2071 0569 971900 1265 2132 0027 6119864 minus 11 1907 0733 894

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 2997 2128 0027 0021 2304 0336 108360 1124 2128 0027 000 2284 0356 107

609

477

6

398

9

322

2

746

266

52

665

2

665

2

0 500 1000 1500 2000ta or tend (s)

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 8 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 3 Part 2)

ta or tend (s)

741

521

9

407

5

308

5

857

1

8334

833

4

833

4

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 9 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 4 Part 2)

12 ISRN Chemical Engineering

Table 6 (a) Reactor-1 (Fed-Batch Scheme 5 Part 1) (b) Reactor-2 (Plug Flow Scheme 5 Part 2) (c) Reactor-1 (Fed-Batch Scheme 5 Part2) (d) Reactor-2 (Plug Flow Scheme 5 Part 2) (e) Reactor-1 (Fed-Batch Scheme 5 Part 2) (f) Reactor-2 (Plug Flow Scheme 5 Part 2)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1664 2142 0027 000 0843 1797 3954600 1664 2149 0027 000 0843 1797 3954

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1664 2142 0027 6119864 minus 09 0843 18 395460 1664 2142 0027 6119864 minus 09 0843 18 3954

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1664 2142 0027 1119864 minus 10 0844 1796 3956900 1664 2142 0027 1119864 minus 10 0843 1797 39541800 1664 2142 0027 1119864 minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1794 2145 0027 0348 0843 1797 3954360 1672 2142 0027 0022 0844 1796 3954720 1664 2142 0027 000 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 124 2131 0027 7119864 minus 11 1973 0667 9249900 124 2131 0027 7119864 minus 11 1973 0667 9248

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1442 2136 0027 0537 1973 0667 9247360 1277 2132 0027 0099 1973 0667 9248

116

211

79

119

5

120

7

121

2

121

8

122

500

280

6 101

5

104

9

105

1

105

1

105

1

105

1

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 10 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 7 Part 2)

1042 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 8(c) and 8(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 10

1043 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 8(c) and 8(d)) Tables 7(a)ndash

7(d) and Figure 10 show that this non elementary reactionyields higher desired product in Fed-Batch Reactor than inContinuous Plug Flow Reactor

As in Scheme 2 the Plug Flow Reactor yield initiallyincreases with the increase in reaction time (ie lengthierreactor pipe) consequently 119873B119905119873A119905 value decreases asshown in Table 8(d) (ie reduced consumption of ReactantB) However the Plug Flow Reactor yield saturates out below

ISRN Chemical Engineering 13

Table 7 (a) Reactor-1 (Fed-Batch Scheme 6 Part 1) (b) Reactor-2 (Plug Flow Scheme 6 Part 1) (c) Reactor-1 (Fed-Batch Scheme 6 Part2) (d) Reactor-2 (Plug Flow Scheme 6 Part 2) (e) Reactor-1 (Fed-Batch Scheme 6 Part 3) (f) Reactor-2 (Plug Flow Scheme 6 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1121 2128 0027 000 229 035 1073600 1121 2128 0027 000 229 035 1073

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1121 2128 0027 4119864 minus 04 229 04 107360 1121 2128 0027 5119864 minus 06 229 04 1073

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7119864 minus 03 229 035 10731800 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1152 2129 0027 0083 229 035 1073360 1139 2128 0027 0048 229 035 1073720 1128 2128 0027 0017 229 035 1073240 1152 2129 0027 0083 229 035 1073240 1152 2129 0027 0083 229 035 1073

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1022 2126 0027 0012 2568 0073 1204900 1022 2126 0027 0012 2567 0072 1203

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1058 2126 0027 0108 2567 0072 1204360 1042 2126 0027 0066 2568 0073 1204

Fed-Batch Reactor yield (Figure 10) Overall the Fed BatchReactor yields higher product R than Plug Flow Reactor eventhough there is a verymarginal change in yield for the changein the relative concentration of reacting streams (Table 8(c)rows 2 4 and 5)

105 (Scheme 8 a = 05 b = 15 c = 1 d = 1 Nonelementary)

1051 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 9(a) and 9(b)

1052 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 9(c) and 9(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 11

1053 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 9(e) and 9(f)) Tables 9(a)ndash9(f)

and Figure 11 show that this non elementary reaction yieldshigher desired product in Plug Flow Reactor than in Fed-Batch Reactor Also the yield in Fed batch reactor decreaseswith addition time

As in Scheme 3 and Scheme 4 the reduced additiontime in Fed Batch Reactor results in increased productyield However in actual practice heat transfer and otherlimitations of the reactor vessel could possibly determine theminimum addition time beyond which addition time cannotbe reduced So the Fed Batch reactor yield is limited

It is to be noted that there is amarginal change in the yieldin Fed Batch reactor with relative concentration of reacting

14 ISRN Chemical Engineering

Table 8 (a) Reactor-1 (Fed-Batch Scheme 7 Part 1) (b) Reactor-2 (Plug Flow Scheme 7 Part 1) (c) Reactor-1 (Fed-Batch Scheme 7 Part2) (d) Reactor-2 (Plug Flow Scheme 7 Part 2) (e) Reactor-1 (Fed-Batch Scheme 7 Part 3) (f) Reactor-2 (Plug Flow Scheme 7 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 0992 2125 0026 000 2636 0004 1236600 099 2125 0027 000 264 8119864 minus 05 1237

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1139 2128 0027 2119864 minus 11 2242 04 105160 1139 2128 0027 2119864 minus 11 2242 04 1051

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1037 2126 0027 5119864 minus 04 2515 0125 1179900 1024 2126 0027 3119864 minus 04 2548 0092 11951800 1014 2125 0027 1119864 minus 04 2576 0064 1207900 1025 2126 0027 3E minus 04 2547 0093 1194900 1024 2126 0027 3E minus 04 255 009 1195

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1757 2144 0027 0472 1067 1573 5002360 1397 2135 0027 0165 172 092 806720 1176 2129 0027 0021 2166 0474 1015240 1757 2144 0027 0472 1067 1573 5002240 1757 2144 0027 0472 1067 1573 5002

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 0998 2125 0027 0001 2619 0021 1228900 0996 2125 0027 9119864 minus 04 2624 0016 1230

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1372 2134 0027 0687 2309 0331 1082360 115 2129 0027 0258 2472 0168 1159

913

3

827

768

696

999

1

965

595

8

955

1

955

0 500 1000 1500 2000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 11 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 8 Part 2)

80 847 91

2

985 101

4

105

3

107

2

452

5 586 694

9

701

701

701

701

701

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 12 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 9 Part 2)

ISRN Chemical Engineering 15

Table 9 (a) Reactor-1 (Fed-Batch Scheme 8 Part 1) (b) Reactor-2 (Plug Flow Scheme 8 Part 1) (c) Reactor-1 (Fed-Batch Scheme 8 Part2) (d) Reactor-2 (Plug Flow Scheme 8 Part 2) (e) Reactor-1 (Fed-Batch Scheme 8 Part 3) (f) Reactor-2 (Plug Flow Scheme 8 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 176 2144 0027 000 0588 2052 275600 1892 2147 0027 000 0234 2406 110

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1216 213 0027 3119864 minus 26 2037 06 95560 1216 213 0027 0000 2037 06 955

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1318 2133 0027 6119864 minus 06 1765 0875 827900 1366 2124 0027 9119864 minus 06 1638 1002 7681800 1423 2136 0027 2119864 minus 05 1485 1155 696900 1359 2134 0027 8E minus 06 1656 0984 776900 1374 2667 0027 1E minus 05 1615 1025 757

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1218 213 0027 0029 206 058 9655360 1216 213 0027 0008 2044 0596 958720 1216 213 0027 2119864 minus 04 2038 0602 9551240 1218 213 0027 0029 206 058 9655240 1218 213 0027 0029 206 058 9655

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1078 2127 0027 0003 2408 0232 1129900 109 2127 0027 0002 2376 0264 1114

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1076 2127 0027 0087 2498 0142 1171360 1065 2127 0027 0046 2486 0154 1166

streams (Table 9(c) rows 2 4 and 5) However this variationis too low to catch up with Plug Flow Reactor yield

106 (Scheme 9 119886 = 15 119887 = 05 119888 = 1 and 119889 = 1Nonelementary)

1061 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 10(a) and 10(b)

1062 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Theyield values for varying reaction times are capturedin Figure 12

In Tables 10(c) and 10(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1063 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 Tables 10(a)ndash10(f) and Figure 12 show that

this nonelementary reaction yields higher desired productin Fed-Batch Reactor than in Continuous Plug Flow Reac-tor

As in Scheme 2 and Scheme 7 the Plug Flow Reactoryield initially increases with the increase in reaction time(ie lengthier reactor pipe) consequently 119873B119905119873A119905 valuedecreases (ie reduced consumption of Reactant B) How-ever the Plug Flow Reactor yield saturates out below Fed-Batch Reactor yield (Figure 12)

Overall the Fed Batch Reactor yields higher product Rthan Plug Flow Reactor even though there is a very marginalchange in yield for the change in the relative concentration ofreacting streams (Table 10(c) rows 2 4 and 5) in Fed-BatchReactor

16 ISRN Chemical Engineering

Table 10 (a) Reactor-1 (Fed-Batch Scheme 9 Part 1) (b) Reactor-2 (Plug Flow Scheme 9 Part 1) (c) Reactor-1 (Fed-Batch Scheme 9 Part2) (d) Reactor-2 (Plug Flow Scheme 9 Part 2) (e) Reactor-1 (Fed-Batch Scheme 9 Part 3) (f) Reactor-2 (Plug Flow Scheme 9 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1019 2125 0027 000 2564 0077 1202600 0994 2125 0027 000 263 1119864 minus 02 1233

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1419 2135 0027 2119864 minus 11 1497 11 701560 1419 2135 0027 2119864 minus 11 1497 11 7015

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1302 2133 0027 4119864 minus 15 1807 0833 847900 125 2131 0027 4119864 minus 15 1946 0694 9121800 1192 213 0027 4119864 minus 15 2101 0539 985900 1254 2131 0027 4E minus 15 1936 0704 907900 1246 2131 0027 4E minus 15 1957 0683 917

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1771 2144 0027 0408 0965 1675 4525360 1544 2139 0027 0088 1251 1389 586720 1425 2136 0027 0001 1482 1158 6949240 1771 2144 0027 0408 0965 1675 4525240 1771 2144 0027 0408 0965 1675 4525

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 104 2667 0027 1119864 minus 06 2506 0134 1175900 1034 2126 0027 4119864 minus 15 2523 0117 1183

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 14 2135 0027 0624 217 047 1017360 1191 213 0027 0202 2307 0333 1081

Table 11 Summary of results

Schemenumber

119886 119887 119888 119889 Favored reactorRelationship

between 119886 119887 119888 and119889

1 1 1 1 1 Both equally 119886 + 119888 = 119887 + 119889

2 1 1 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

3 1 1 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

4 05 15 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

5 15 05 05 15 Both equally 119886 + 119888 = 119887 + 119889

6 05 15 15 05 Both equally 119886 + 119888 = 119887 + 119889

7 15 05 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

8 05 15 1 1 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

9 15 05 1 1 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

11 Conclusion

Under the simulated conditions elementary Second ordercompetitive consecutive reactions of the type mentioned in(1) yield the same amount of intermediate product R in bothideal fed batch and ideal Plug Flow Reactors for a constantconversion (99) of limiting reactant A Yield and selectivityof the product depends only on119870

11198702in both the reactors

However of the 8 nonelementary scenarios simulatedthree (Schemes 3 4 and 8) favor Plug Flow Reactor and threeother (Schemes 2 7 and 9) favor Fed Batch Reactor Twoothers (Schemes 5 and 6) like elementary reaction yield thesame in both Plug Flow Reactor and Fed batch reactor

Among the schemes simulated previously (Schemes 1 to9) the schemes giving increased yield R with reduced addi-tion time in Fed batch reactor favor Plug Flow Reactor andthe schemes giving increased yield with increased addition

ISRN Chemical Engineering 17

time in fed batch reactor favor Fed batch reactor This couldwell be a practical reckoner to screen the potential candidateamong the simulated schemes for Plug Flow Reactor eventhough this idea is only with respect to suitability of kineticparameters

The relationship between the exponents 119886 119887 119888 and 119889 andthe favourable reactor found in the simulation as shown inTable 11 is noteworthy

Nomenclature

1198701 Rate constant of reaction between A and

B in Litresdotmolminus1sdotsminus1K2 Rate constant of 2nd reaction between R

and B in Litresdotmolminus1sdotsminus1t Time s119905119886 Reactant B addition time in Fed Batch

Reactor s119905119898 Reaction mass maintenance time in Fed

Batch Reactor stlowast Space time in Plug Flow Reactor stend Space time for which each case of plug

flow rector simulation has been done s119903119909 Rate of change of species ldquoxrdquo

(molsdotLitreminus1sdotsminus1) ldquoxrdquo is representative ofspecies A B R S C and D

119862119909= 119873119909119881 Concentration molsdotLitreminus1 of any species

say ldquoxrdquoV Reaction volume m3119873119909 Number of Kg moles of species ldquoxrdquo k mol

NB119905 Total Kg moles of reactant B used inreaction k mol

NA119905 Total kg moles of reactant A used inreaction k mol

119881119886119905 Volume of stream containing reactant B

m3119881119905 Total volume of contents including

streams of reactant A and reactant B m3v Plug Flow Reactor volume m3v1015840 Volumetric flow rate m3s119865119909 Molar flow rate (k molsdotsminus1) of species ldquoxrdquo

which is representative of species A B RS C and D

NB119905NA119905 Ratio of total moles of B to total moles ofA taken for the reaction

119873119909119865 Final kg moles of the species ldquoxrdquo k mol

WR Weight kg of total intermediate (desired)product formed at the end of reaction inFed Batch Reactor and at the end of agiven space time in the Plug Flow Reactor

Acknowledgment

The author would like to thank Chandra Kanth Terupally ofPlanck Technical Hyderabad India for providing adequatesupport in MATLAB Programming

References

[1] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1998

[2] J F Richardson and D G Peacock Coulson and RichardsonrsquosChemical Engineering Chemical and Biochemical Reactors andProcess Control Butterworth-Heinemann Boston Mass USA3rd edition 1994

[3] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart I model developmentrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 750162 16pages 2012

[4] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart II design protocolsrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 65432113 pages 2012

[5] J R Bourne ldquoMixing and the selectivity of chemical reactionsrdquoOrganic Process Research andDevelopment vol 7 no 4 pp 471ndash508 2003

[6] J Bałdyga J R Bourne and S J Hearn ldquoInteraction betweenchemical reactions and mixing on various scalesrdquo ChemicalEngineering Science vol 52 no 4 pp 457ndash466 1997

[7] N G Anderson ldquoPractical use of continuous processing indeveloping and scaling up laboratory processesrdquo Organic Pro-cess Research and Development vol 5 no 6 pp 613ndash621 2001

[8] C Brechtelsbauer and F Ricard ldquoReaction engineering evalua-tion and utilization of static mixer technology for the synthesisof pharmaceuticalsrdquoOrganic Process Research andDevelopmentvol 5 no 6 pp 646ndash651 2001

[9] Z Anxionnaz M Cabassud C Gourdon and P Tochon ldquoHeatexchangerreactors (HEX reactors) concepts technologiesstate-of-the-artrdquo Chemical Engineering and Processing vol 47no 12 pp 2029ndash2050 2008

[10] P Barthe C Guermeur O Lobet et al ldquoContinuous multi-injection reactor for multipurpose productionmdashpart Irdquo Chem-ical Engineering and Technology vol 31 no 8 pp 1146ndash11542008

[11] M Patel and G Gasparini ldquoReactor technology flow reactorsand dynamic mixingrdquo Specialty Chemicals Magazine 2009

[12] X W Ni ldquoContinuous oscilatory baffled reactor technologyrdquoin Innovations in Pharmaceutical TechnologymdashManufacturingpp 90ndash96 2006 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=392

[13] L Proctor ldquoContinuous chemical processingrdquo in Innovationsin Pharmaceutical Technology pp 84ndash88 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=290

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International Journal of

2 ISRN Chemical Engineering

002040608

112141618

2

0 1 2 3 4 5 6 7Time (s)

minus1minus02

Con

cent

ratio

n (m

olL

)

Concentration of A Concentration of BConcentration of R Concentration of S

Figure 1 Concentration as a function of time

Reactant Bta (k molmiddotsminus1)NBt

Figure 2 Schematic drawing of Fed-Batch Reactor

less Under this condition with further fresh charge ofB condition for S formation is favored Both modes ofoperations (batch and semibatch or fed batch) would havereacting species concentration so varied with time that aquantitative analysis is imperative to understand the relativesignificance of these two reactors in the light of obtainingmaximum product R yield It has been reported in ChemicalReaction Engineering text book Levenspiel [1] that for anelementary second order competitive consecutive reactionproduct R selectivity is the same in semi-batch (ie Fed-Batch Reactor) and Batch Reactors Efforts have beenmade inthe past to understand the factors affecting product selectivityof competitive consecutive reaction

In the Reaction Engineering text books Levenspiel [1]and Coulson and Richardsonrsquos [2] type of reactors (ie PlugFlow Reactors Mixed Flow reactors or Fed-Batch Reactor)and product selectivity have been discussed especially forcompetitive consecutive reactions

The recent literature on product selectivity of competitiveconsecutive reactions is reported by Shah et al [3 4]which deals with ldquoproduct selectivity with mixing reactionrates and stoichiometryrdquo As the reactions in actual are notnecessarily always elementary [1] it is relevant to simulate the

product selectivity of nonelementary second order competi-tive consecutive reaction schemes

References [5 6] deal with product selectivity andmixingand covering competitive consecutive reaction and competi-tive parallel reactions This shows that identifying the condi-tions for increased product selectivity is an important aspectAt times product selectivity determines the economics ofoperating a plant

In practice Batch reactors unlike FedBatchReactor offerhigher order of nonideality in mixing and heat transfer in theform of significant concentration and temperature gradientsas it (Batch Reactor) has to deal with larger quantities of massand heat energy from the very start of the time 0 secondsThis necessitates the use of Fed-Batch mode of operationspredominantly in Pharmaceuticals and other related indus-tries However the continuous Plug FlowReactors are knownfor their flexibility in offering higher heat transfer area andbettermixing intensitiesOf latemany pieces of literature andpractical works have gone on investigating and implementingcontinuous Plug Flow Reactors in pharmaceutical and otherrelated chemical industries Designs have varied from asimple tube to a static mixer to plate heat exchanger typeof reactors to Microreactors one would see that in piecesof literature [7ndash12] Anderson [7] reports that in lab scale23 yield of desired intermediate product in a specificcompetitive consecutive reaction became 83upon changingthe mode of reaction from semi-batch to continuous plugflow Brechtelsbauer and Ricard [8] report that static mixerbased continuous Plug Flow Reactor gave a better productyield due to good turbulent and heat transfer characteristicsThe major challenge in implementing Plug Flow Reactor inPharmaceuticals and related other industries is in identifyingthe right reaction kinetics [13]

The primary aim of this simulation work is to find outa kinetic scenario in which continuous Plug Flow Reactorwould yield higher desired product than that the conven-tional Fed-Batch Reactor would yield Also this paper aimsto provide a practical method to pick among the simulatedreaction models the schemes which would be kineticallyfavored in Plug Flow Reactor

The rate equations governing the chemical reaction sys-tem given in (1) is as follows [1]

119903A = minus 1198701119862119886

A119862119887

B

119903B = minus 1198701119862119886

A119862119887

B minus 1198702119862119888

B119862119889

R

119903R = 1198701119862119886

A119862119887

B minus 1198702119862119888

B119862119889

R

119903S = 1198702119862119888

B119862119889

R

(2)

The exponents a b c and d represent the order of the reactionwith respect to each of the reacting species When 119886 = 119887 =119888 = 119889 = 1 the reaction becomes an elementary second orderreaction Values other than 1 for any of the exponents makethe reaction nonelementary Here the analysis is limited tosecond order reactions hence 119886 + 119887 = 119888 + 119889 = 2 [1]

ISRN Chemical Engineering 3

FA0

CA0

FA

CAF

FAF

FA + dFA

Figure 3 Schematic drawing of Plug Flow Reactor

Table 1 Molecular weights

Molecular weight of A 750000 Molecular weight of R 468750Molecular weight of B 187500 Molecular weight of C 468750Total (1st reactionreactants) 937500 Total (1st reaction

products) 937500

Molecular weight of R 468750 Molecular weight of S 328125Molecular weight of B 187500 Molecular weight of D 328125Total (2nd reactionreactants) 656250 Total (2nd reaction

products) 656250

3 The Fed-Batch Reactor (Reactor-1)

Reactant A is taken in the reactor whereas reactant B isadded continuously over reactant A (see Figure 2) It is tobe noted that component B is added (no output flow term)whereas component A is taken inside the reactor (no inputflow term and no output flow term) Hence material balancefor components A and B must be written separately Materialbalance pattern of all other products is similar to that ofcomponent A

For Species A

Input = Output + Disappearance by Reaction

+ Accumulation

0 = 0 + (minus119903A) 119881 + (119889119873A119889119905)

(minus1

119881) sdot (119889119873A119889119905) = minus119903A

(3)

For Species B

Input = Output + Disappearance by Reaction

+ Accumulation

(119873B119905119905119886

) = 0 + (minus119903B) 119881 + (119889119873B119889119905)

(minus1

119881)(119889119873B119889119905) = minus119903B minus (

119873B119905119881119905119886

)

(4)

From (3) to (4) we can mathematically describe thereaction system in ideal Fed-Batch Reactor as follows119889119873A119889119905

= (minus1

119881)1198701119873119886

A119873119887

B 0 lt 119905 le 119905119886 + 119905119898

119889119873B119889119905= (minus1

119881)1198701119873119886

A119873119887

B minus (1

119881)1198702119873119888

B119873119889

R +119873B119905119905119886

0 lt 119905 le 119905119886

119889119873B119889119905= (minus1

119881)1198701119873119886

A119873119887

B minus (1

119881)1198702119873119888

B119873119889

R 119905119886 lt 119905 le 119905119886+119898

119889119873R119889119905= (1

119881)1198701119873119886

A119873119887

B minus (1

119881)1198702119873119888

B119873119889

R 0 lt 119905 le 119905119886+119898

119889119873S119889119905= (1

119881)1198702119873119888

B119873119889

R 0 lt 119905 le 119905119886+119898

119881 =119905119881119886119905

119905119886

+ (119881119905minus 119881119886119905) 0 lt 119905 le 119905

119886

119881 = 119881119905 119905119886lt 119905 le 119905

119886+119898

(5)

The sets of equations (5) represent in the second orderconsecutive competitive reaction in Fed-Batch Reactor

4 The Plug Flow Reactor (Reactor-2) (SeeFigure 3)

Thematerial (ie chemical) balance equations for a Plug FlowReactor can be written as follows [1]

Input = Output + Disappearance by reaction+ Accumulation

(6)

119865A = 119865A + 119889119865A + (minus119903A sdot 119889V) (7)

(minus119889119865A119889V) = minus119903A (8)

(minus119889119862AV

1015840

119889V) = minus119903A (9)

Space time in Plug Flow Reactor 119905lowast = VV1015840When volumetric flow rate is constant 119889119905lowast = 119889VV1015840 (8)

becomes as follows

(minus119889119862A119889119905lowast) = minus119903A (10)

From (7) to (10) we can mathematically describe thereaction system in ideal Plug Flow Reactor as follows

119889119862A119889119905lowast= minus 119870

1119862119886

A119862119887

B

119889119862B119889119905lowast= minus 119870

1119862119886

A119862119887

B minus 1198702119862119888

B119862119889

R

119889119862R119889119905lowast= 1198701119862119886

A119862119887

B minus 1198702119862119888

B119862119889

R

119889119862S119889119905lowast= 1198702119862119888

B119862119889

R

(11)

5 Simulation Plan

Solutions to the set of equations in (5) and (11) will enable oneto analyze the performance of reaction system in Fed BatchReactor and continuous Plug flow Reactor respectively

The main aim of this literature is to carry out thepreviouslymentioned analysis for an arbitrary still practicallyrelevant reaction system

4 ISRN Chemical Engineering

Table 2 (a) Reactor-1 (Fed-Batch Scheme 1 Part 1) (b) Reactor-2 (Plug Flow Scheme 1 Part 1) (c) Reactor-1 (Fed-Batch Scheme 1 Part2) (d) Reactor-2 (Plug Flow Scheme 1 Part 2) (e) Reactor-1 (Fed-Batch Scheme 1 Part 3) (f) Reactor-2 (Plug Flow Scheme 1 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 129 2132 0027 000 184 0801 8623600 129 2132 0027 000 184 08 8624

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1291 2132 0026 1119864 minus 26 1838 0803 861460 1291 2132 0026 000 1838 0803 8614

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 129 2132 0027 2119864 minus 06 184 08 8624900 129 2132 0027 1119864 minus 06 184 08 86241800 129 2132 0027 9119864 minus 07 184 08 8624900 129 2132 0027 1E minus 06 184 08 8624900 129 2132 0027 1E minus 06 184 08 8624

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1313 2133 0027 0061 184 08 8625360 1296 2132 0027 0016 184 08 8624720 129 2132 0027 4119864 minus 04 184 08 8624240 1313 2133 0027 0061 184 08 8625240 1313 2133 0027 0061 184 08 8625

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 106 2127 0027 0002 2454 0186 1151900 106 2127 0027 0001 2454 0186 1151

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1117 2128 0027 0152 2454 0186 1151360 1086 2127 0027 007 2454 0186 1151

Rate constant values are assumed with three individualscenarios first one with ratio of119870

1to1198702considered as 10 and

1198701considered as 100sdotLitresdotmolminus1sdotsminus1 the second one with the

same ratio of11987011198702but with the119870

1as 01 Litresdotmolminus1sdotsminus1 and

the third one with the ratio of 11987011198702considered as 50 with

the1198701considered as 01 Litresdotmolminus1sdotsminus1

Totally nine different sets of exponents (ie a b c d)have been considered such that the overall order of reactionremains two Hence there are 9 sets of reactions schemeseach scheme is analyzed for the mentioned 3 sets of kineticconstants Molecular weight of each of the componentsinvolved in the reaction is considered in consistent with thestoichiometry given in (1) The values are given in Table 1

In this study the molecular weights are used to convertmoles into Kg and vice versa (molecular weight values arearbitrary in Table 1)

Total solvent quantity considered is 2m3 Quantity ofsolvent m3 used to make a stream of reactant A is called Sol

R Quantity of solvent m3 used to make a stream of reactantB is called Sol A For the ensuing simulations amount ofsolvent used in both the reacting streams is same that is SolA(Sol A + Sol R) = 05 unless specified otherwise in therespective calculationoutput datagraphsTableThe effect ofrelative concentration of both the streams on kinetics is nottreated at length however few cases with Sol A(Sol R + SolA) = 025 and 075 have been simulated to indicate the changein reaction selectivity with change in relative concentration ofreactant streams

As the reaction considered is in liquid phase constantvolume reaction system is supposed except for the volumechange due to addition of the solution of second component(reactant B) in to the solution of 1st component (reactant A)in the Fed-Batch Reactor There is no volume change dueto reaction Volumetric flow rate in Plug Flow Reactor isconsidered constantThe volume in liters constituted by eachof the starting materials (A and B) is assumed 05 times theweight in kg of the respective components

ISRN Chemical Engineering 5

005

115

225

3

0 100 200 300 400 500 600 700Con

cent

ratio

n (m

olL

)

Time (s)minus05

(a)

0

05

1

15

2

25

0 100 200 300 400 500 600 700Time (s)

Volu

me (

m3)

(b)

002040608

112141618

0 05 1 15 2 25 3 35

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(c)

0

05

1

15

2

25

3

0 500 1000 1500 2000 2500C

once

ntra

tion

(mol

L)

Time (s)minus05

(d)

002040608

112141618

0 100 200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(e)

0

05

1

15

2

25

3

0 500 1000 1500 2000 2500

Con

cent

ratio

n (m

olL

)

Time (s)minus05

(f)

002040608

1121416

0 100

AB

RS

200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(g)

Figure 4 (a) Concentration as a function of time Fed-Batch Reactor (Scheme 1 Part 1 Case 1 119905119886= 60 s 119905

119898= 600 s (see Scheme 1

in Supplementary Material available online at httpdxdoiorg1011552013591546) (b) Volume as a function of time Fed-Batch Reactor(Scheme 1 Part 1 Case-1 119905

119886= 60 s 119905

119898= 600 s) (c) Concentration as a function of time Plug Flow Reactor (Scheme 1 Part 1 119905end = 6 s for

brevity graph is plotted for 3 s only) (d) Concentration as a function of time Fed-Batch Reactor (Scheme 1 Part 2 119905119886= 900 s 119905

119898= 1200 s)

(e) Concentration as a function of time Plug Flow Reactor (Scheme 1 Part 2 119905end = 360 s) (f) Concentration as a function of time Fed-BatchReactor (Scheme 1 Part 3 119905

119886= 900 s 119905

119898= 1200 s) (g) Concentration as a function of time Plug Flow Reactor (Scheme 1 Part 3 119905end = 360 s)

6 ISRN Chemical Engineering

0

05

1

15

2

25

3

0 100 200 300 400 500 600 700

Con

cent

ratio

n (m

olL

)

Time (s)minus05

(a)

0

02

04

06

08

1

12

14

16

0 05 1 15 2 25 3 35

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(b)

0

05

1

15

2

25

3

0 500 1000 1500 2000 2500

Con

cent

ratio

n (m

olL

)

Time (s)minus05

AB

RS

(c)

0

02

04

06

08

1

12

14

16

0 100 200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)

AB

RS

(d)

Figure 5 (a) Concentration as a function of time Fed-Batch Reactor (Scheme 2 Part 1 119905119886= 60 s 119905

119898= 600 s) (b) Concentration as a function

of time Plug Flow Reactor (Scheme 2 Part 1 119905end = 6 s for brevity graph is plotted for 3 s only) (c) Concentration as a function of timeFed-Batch Reactor (Scheme 2 Part 2 119905

119886= 900 s 119905

119898= 1200 s) (d) Concentration as a function of time Plug Flow Reactor (Scheme 2 Part 2

119905end = 360 s)

The quantity of A used in the entire study is 200Kgs Incase of Fed batch reactor the simulation has been done forvarious addition time of streamB reactionmaintenance timeis chosen such that further change in concentration profileis practically absent The constancy of concentration profiletowards the end of 119905

119898can be observed in the concentration

profiles obtained from MATLAB Also 119905119898

is maintainedconstant for a given set of 119870

11198702in order to make the

comparative study relevant In case of Plug Flow Reactor thesimulation is done for different reaction end time as differentcase The reaction time 119905end in Plug Flow Reactor refers tospace time

In case of Fed-Batch Reactor the addition rate is consid-ered constant across the entire addition time

The reaction is run in both the reactors for a specifiedextent of conversion that is 99 of reactant A conversionis the reaction end point For a prechosen 119905

119886 119905119898 and 119905end the

99 conversion of reactant A is ensured by adjusting the totalmoles of reactant B that is by adjusting 119873B119905119873A119905 final 99conversion of reactant A is achieved for predefined cases of 119905

119886

(s) 119905119898(s) and 119905end (s)

The previously mentioned assumptions and basis havebeen considered keeping in mind that the actual reactionscenarios in the industry can be understood and interpretedin the light of the conclusions arrived at in this simulationstudy

The concentration profiles given in the subsequent sec-tions are intended only to showcase the pattern of thecorresponding reaction scheme The quantitative details ofsuch graphs are given in the tables for the respective cases

6 Simulation Accuracy

Solution to the previouslymentioned simultaneous nonlineardifferential equations ((5) and (11)) has been obtained by thesoftware MATLAB which entailed its default Explicit Runge-Kutta (45) Variable step (Dormand-Prince Pair) methodThe calculation tolerance has been set at a default 01with step limits adjusted such that step limits n and n10seconds would return the final results matching up to 3decimal points When the gap between reactor-1 and reactor-2 results narrowsbecomes more significant towards arriving

ISRN Chemical Engineering 7

112

211

37 115

3

116

7

117

3

118

1

118

5

101

3 103

210

52

105

9

106

1

106

2

106

3

106

3

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 6 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 2 Part 2)

at a conclusion tolerance is squeezed further to 001 withthe same step limit criteria as done for the simulation withtolerance 01

7 Simulation (Scheme 1 119886 = 119887 = 119888 = 119889 = 1 ieElementary Reaction)

71 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 In Tables 2(a) and 2(b) simulation results for two

cases have been captured Figures 4(a) and 4(c) are sampleconcentration profiles of reaction species in ideal Fed Batchand ideal Plug Flow Reactor Figure 4(b) is the graphicalrepresentation of reaction volume in Fed-Batch Reactor

It can be observed in Figure 4(a) that with 119905119898= 600 s

further concentration change (reaction) is negligible As theaddition rate of reagent B considered in this simulation studyis constant the fed batch volume increases linearly till 119905 =119905119886 During Reaction maintenance time 119905

119898 the Fed-Batch

volume remains constant

72 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Figures 4(d) and 4(e) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

In Tables 2(c) and 2(d) results for all simulated cases havebeen captured and the data lines (rows) 4 and 5 correspondto the fraction Sol A(Sol A + Sol R) = 025 and 075respectively

73 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and

1198702= 0002 Figures 4(f) and 4(g) are sample concentration

profiles of reaction species in ideal Fed Batch and ideal PlugFlow Reactors

In Tables 2(e) and 2(f) simulation results for two caseshave been captured

Tables 2(a) to 2(f) show that elementary reaction of thetype given in (1) yields the same amount of desired product infed batch reactor and Plug Flow Reactor Moreover the yield

values in Part 2 remain the same as those in Part 1 That isbecause119870

11198702values remain the same in both Part 1 and Part

2 even though the individual 1198701and 119870

2values are different

It is to be noted that in Part 3 yield values are different fromthat in Part 1 and Part 2That is because119870

11198702value in Part 3

is different from those in Part 1 and Part 2 The change in therelative concentration of both the reacting streams (as shownin Table 2(c) rows 2 4 and 5 and Table 2(d) rows 1 4 and 5)does not have any effect on the yield

8 Simulation (Scheme 2 119886 = 119887 = 1 119888 = 15 119889 =05 Nonelementary)

81 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 Figures 5(a) and 5(b) are sample concentration

profiles of reaction species in ideal Fed Batch and ideal PlugFlow Reactors

In Tables 3(a) and 3(b) simulation results for two casessimulated have been captured

82 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Figures 5(c) and 5(d) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

In Tables 3(c) and 3(d) and Figure 6 results for all thesimulated cases have been captured The data lines (rows) 4and 5 in Tables 3(c) and 3(d) correspond to the fraction SolA(Sol A + Sol R) = 025 and 075 respectively

The yield values for varying reaction times are capturedin Figure 6

83 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 In Tables 3(e) and 3(f) simulation results for two caseshave been captured

Tables 3(a) and 3(f) and Figure 6 show that this nonelementary reaction yields higher desired product in Fed-Batch Reactor than in Continuous Plug Flow Reactor

In Figure 6 the Plug Flow Reactor yield initially increaseswith the increase in reaction time (ie lengthier reactor pipe)consequently 119873B119905119873A119905 value decreases as shown in Tables3(c) and 3(d) (ie reduced consumption of Reactant B)However the Plug Flow Reactor yield saturates out belowFed-Batch Reactor yield Overall the Fed Batch Reactoryields higher product R than Plug Flow Reactor even thoughthere is a very marginal change in yield for the change in therelative concentration of reacting streams (Table 3(c) rows 24 and 5) in Fed Batch Reactor

9 Simulation (Scheme 3 119886 = 119887 = 1 119888 = 05 119889 =15 Nonelementary)

91 Part 1 (Cases 1 and 2)1198701= 100119870

11198702= 10 and119870

2= 10

In Tables 4(a) and 4(b) simulation results for two cases havebeen captured

Figures 7(a) and 7(b) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

8 ISRN Chemical Engineering

Table 3 (a) Reactor-1 (Fed-Batch Scheme 2 Part 1) (b) Reactor-2 (Plug Flow Scheme 2 Part 1) (c) Reactor-1 (Fed-Batch Scheme 2 Part2) (d) Reactor-2 (Plug Flow Scheme 2 Part 2) (e) Reactor-1 (Fed-Batch Scheme 2 Part 3) (f) Reactor-2 (Plug Flow Scheme 2 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1005 2132 0027 000 2598 0042 122600 0996 2125 0027 000 2625 0015 123

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 113 2128 0027 6119864 minus 06 2267 04 106360 113 2128 0027 3119864 minus 35 2267 04 1063

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1072 2127 0027 0005 2425 0215 1137900 1059 2166 0027 0004 2459 0181 11531800 1048 2126 0027 0004 2491 0149 1167900 1061 2127 0027 0004 2456 0184 1151900 1058 2126 0027 0004 2463 0177 1154

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1221 2131 0027 0135 216 048 1013360 118 2129 0027 0068 2202 0438 1032720 1145 2129 0027 0018 2244 0396 1052240 1221 2131 0027 0135 216 048 1013240 1221 2131 0027 0135 216 048 1013

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1009 2125 0027 0008 2599 0041 1218900 1006 2125 0027 0008 2605 0035 1221

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1094 2127 0027 0083 2545 0095 1193360 1058 2126 0027 0097 2555 0085 1198

92 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 4(c) and 4(d) and Figure 8 results for othersimulated cases have been captured

The last two data lines (rows) in Tables 4(c) and 4(d)correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

Figures 7(c) and 7(d) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

The yield values for varying reaction times are capturedin Figure 8

93 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 InTables 4(e) and 4(f) simulation results for two caseshave been captured

Tables 4(a)ndash4(f) and Figure 8 show that this non elemen-tary reaction yields higher desired product R in Plug FlowReactor than in Fed-Batch Reactor

It is to be noted that the reduced addition time in FedBatch Reactor results in increased product yield Howeverin actual practice heat transfer and other limitations of thereactor vessel could possibly determine the minimum addi-tion time beyond which addition time cannot be reduced Sothe Fed Batch reactor yield is limited

It is to be further noted that there is a marginal changein the yield in Fed Batch reactor with the change in relativeconcentration of reacting streams (Table 4(c) rows 2 4 and5) However this variation is too low to catch up with PlugFlow Reactor yield

10 Simulations (for the Rest of the Schemes)

101 (Scheme 4 119886 = 05 119887 = 15 119888 = 05 119889 = 15Nonelementary)

1011 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and 119870

2=

10 See Tables 5(a) and 5(b)

ISRN Chemical Engineering 9

Table 4 (a) Reactor-1 (Fed-Batch Scheme 3 Part 1) (b) Reactor-2 (Plug Flow Scheme 3 Part 1) (c) Reactor-1 (Fed-Batch Scheme 3 Part2) (d) Reactor-2 (Plug Flow Scheme 3 Part 2) (e) Reactor-1 (Fed-Batch Scheme 3 Part 3) (f) Reactor-2 (Plug Flow Scheme 3 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1909 2148 0027 000 019 245 9600 195 2149 0027 000 0079 2561 4

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1448 2136 0027 3119864 minus 08 1419 12 665260 1447 2136 0027 3119864 minus 05 142 12 6657

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1598 214 0027 5119864 minus 13 1019 1621 4776900 1661 2142 0027 3119864 minus 13 0851 1789 39891800 1722 2143 0027 7119864 minus 13 0687 1953 3222900 1655 2141 0027 1119864 minus 12 0868 1772 4067900 1668 2142 0027 1119864 minus 12 0833 1807 3905

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1448 2136 0027 4119864 minus 12 1419 1221 6652360 1448 2136 0027 4119864 minus 12 1419 1221 6652720 1448 2136 0027 4119864 minus 12 1419 1221 6652240 1448 2136 0027 4E minus 12 1419 1221 6652240 1448 2136 0027 4E minus 12 1419 1221 6652

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1214 213 0027 0000 2043 0597 9575900 1251 2131 0027 0000 1943 0697 9107

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1172 2129 0027 0071 2227 0413 1044360 1163 2129 0027 0003 2182 0458 1023

1012 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 The data lines (rows) 4 and 5 in Tables 5(c) and 5(d)correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 9

1013 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 (See Tables 5(e) and 5(f)) Tables 5(a)ndash5(f) and Figure 9show that this non elementary reaction yields higher desiredproduct in Plug Flow Reactor than in Fed-Batch Reactor

As in Scheme 3 the reduced addition time in Fed BatchReactor results in increased product yield However in actualpractice heat transfer and other limitations of the reactorvessel could possibly determine the minimum addition timebeyond which addition time cannot be reduced So the FedBatch reactor yield is limited

Themarginal change in the yield in FedBatch reactorwithrelative concentration of reacting streams (Table 5(c) rows 24 and 5) may be noted However this variation is too low tocatch up with Plug Flow Reactor yield

102 (Scheme 5 119886 = 15 119887 = 05 119888 = 05 119889 = 15Nonelementary)

1021 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 6(a) and 6(b)

1022 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 119870

2=

001 In Table 6(c) and 6(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1023 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 119870

2=

0002 (See Tables 6(e) and 6(f)) Tables 6(a)ndash6(f) show that

10 ISRN Chemical Engineering

0

05

1

15

2

25

3

0 100 200 300 400 500 600 700

Con

cent

ratio

n (m

olL

)

Time (s)minus05

(a)

002040608

112141618

2

0 05 1 15 2 25 3 35

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(b)

0

05

1

15

2

25

3

0 500 1000 1500 2000 2500Time (s)minus05

Con

cent

ratio

n (m

olL

)

AB

RS

(c)

002040608

112141618

2

0 100

AB

RS

200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(d)

Figure 7 (a) Concentration as a function of time Fed-Batch Reactor (Scheme 3 Part 1 119905119886= 60 s 119905

119898= 600 s) (b) Concentration as a function

of time Plug Flow Reactor (Scheme 3 Part 1 119905end = 6 s for brevity graph is plotted for 3 s only) (c) Concentration as a function of timeFed-Batch Reactor (Scheme 3 Part 2 119905

119886= 900 s 119905

119898= 1200 s) (d) Concentration as a function of time Plug Flow Reactor (Scheme 3 Part 2

119905end = 360 s)

this type of nonelementary reaction yields the same amountof desired product in fed batch reactor and in Plug FlowReactor Moreover the yield values in Part 2 remain the sameas those in Part 1 That is because 119870

11198702values remain the

same in both Part 1 and Part 2 even though the individual1198701and119870

2values are different It is to be noted that in Part 3

yield values are different from that in Part 1 and Part 2That isbecause 119870

11198702value in Part 3 is different from those in Part

1 and Part 2The change in the relative concentration of both the

reacting streams (as shown in Table 6(c) rows 2 4 and 5 andTable 6(d) rows 1 4 and 5) does not have any effect on theyield

103 (Scheme 6 119886 = 05 119887 = 15 119888 = 15 119889 = 05Nonelementary)

1031 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 7(a) and 7(b)

1032 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 7(c) and 7(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1033 Part 3 (Cases 1 and 2)1198701= 01119870

11198702= 50 and119870

2=

0002 (See Tables 7(e) and 7(f)) Tables 7(a)ndash7(f) show thatthis type of nonelementary reaction also behaves similar toelementary reaction and nonelementary reaction Scheme 5with respect to product selectivity that is the yield is the samein both the reactors The change in the relative concentrationof both the reacting streams (as shown in Table 7(c) rows 24 and 5 and Table 7(d) rows 1 4 and 5) does not have anyeffect on the yield

104 (Scheme 7 119886 = 15 119887 = 05 119888 = 15 119889 = 05Nonelementary)

1041 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 8(a) and 8(b)

ISRN Chemical Engineering 11

Table 5 (a) Reactor-1 (Fed-Batch Scheme 4 Part 1) (b) Reactor-2 (Plug Flow Scheme 4 Part 1) (c) Reactor-1 (Fed-Batch Scheme 4 Part2) (d) Reactor-2 (Plug Flow Scheme 4 Part 2) (e) Reactor-1 (Fed-Batch Scheme 4 Part 3) (f) Reactor-2 (Plug Flow Scheme 4 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1927 2148 0027 000 0141 2499 7600 1961 2149 0027 000 005 259 2

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1313 2133 0027 6119864 minus 08 1778 09 833460 1313 2667 0027 6119864 minus 08 1778 09 8334

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1562 2139 0027 000 1113 1527 5219900 1654 2141 0027 1119864 minus 10 0869 1771 40751800 1733 2143 0027 6119864 minus 13 0658 1982 3085900 1646 2141 0027 1E minus 12 0868 175 4171900 1662 2142 0027 1E minus 10 0848 1792 3974

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1313 2133 0027 000 1778 0862 8334360 1313 2133 0027 000 1778 0862 8334720 1313 2133 0027 8119864 minus 12 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1203 213 0027 7119864 minus 11 2071 0569 971900 1265 2132 0027 6119864 minus 11 1907 0733 894

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 2997 2128 0027 0021 2304 0336 108360 1124 2128 0027 000 2284 0356 107

609

477

6

398

9

322

2

746

266

52

665

2

665

2

0 500 1000 1500 2000ta or tend (s)

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 8 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 3 Part 2)

ta or tend (s)

741

521

9

407

5

308

5

857

1

8334

833

4

833

4

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 9 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 4 Part 2)

12 ISRN Chemical Engineering

Table 6 (a) Reactor-1 (Fed-Batch Scheme 5 Part 1) (b) Reactor-2 (Plug Flow Scheme 5 Part 2) (c) Reactor-1 (Fed-Batch Scheme 5 Part2) (d) Reactor-2 (Plug Flow Scheme 5 Part 2) (e) Reactor-1 (Fed-Batch Scheme 5 Part 2) (f) Reactor-2 (Plug Flow Scheme 5 Part 2)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1664 2142 0027 000 0843 1797 3954600 1664 2149 0027 000 0843 1797 3954

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1664 2142 0027 6119864 minus 09 0843 18 395460 1664 2142 0027 6119864 minus 09 0843 18 3954

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1664 2142 0027 1119864 minus 10 0844 1796 3956900 1664 2142 0027 1119864 minus 10 0843 1797 39541800 1664 2142 0027 1119864 minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1794 2145 0027 0348 0843 1797 3954360 1672 2142 0027 0022 0844 1796 3954720 1664 2142 0027 000 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 124 2131 0027 7119864 minus 11 1973 0667 9249900 124 2131 0027 7119864 minus 11 1973 0667 9248

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1442 2136 0027 0537 1973 0667 9247360 1277 2132 0027 0099 1973 0667 9248

116

211

79

119

5

120

7

121

2

121

8

122

500

280

6 101

5

104

9

105

1

105

1

105

1

105

1

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 10 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 7 Part 2)

1042 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 8(c) and 8(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 10

1043 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 8(c) and 8(d)) Tables 7(a)ndash

7(d) and Figure 10 show that this non elementary reactionyields higher desired product in Fed-Batch Reactor than inContinuous Plug Flow Reactor

As in Scheme 2 the Plug Flow Reactor yield initiallyincreases with the increase in reaction time (ie lengthierreactor pipe) consequently 119873B119905119873A119905 value decreases asshown in Table 8(d) (ie reduced consumption of ReactantB) However the Plug Flow Reactor yield saturates out below

ISRN Chemical Engineering 13

Table 7 (a) Reactor-1 (Fed-Batch Scheme 6 Part 1) (b) Reactor-2 (Plug Flow Scheme 6 Part 1) (c) Reactor-1 (Fed-Batch Scheme 6 Part2) (d) Reactor-2 (Plug Flow Scheme 6 Part 2) (e) Reactor-1 (Fed-Batch Scheme 6 Part 3) (f) Reactor-2 (Plug Flow Scheme 6 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1121 2128 0027 000 229 035 1073600 1121 2128 0027 000 229 035 1073

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1121 2128 0027 4119864 minus 04 229 04 107360 1121 2128 0027 5119864 minus 06 229 04 1073

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7119864 minus 03 229 035 10731800 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1152 2129 0027 0083 229 035 1073360 1139 2128 0027 0048 229 035 1073720 1128 2128 0027 0017 229 035 1073240 1152 2129 0027 0083 229 035 1073240 1152 2129 0027 0083 229 035 1073

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1022 2126 0027 0012 2568 0073 1204900 1022 2126 0027 0012 2567 0072 1203

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1058 2126 0027 0108 2567 0072 1204360 1042 2126 0027 0066 2568 0073 1204

Fed-Batch Reactor yield (Figure 10) Overall the Fed BatchReactor yields higher product R than Plug Flow Reactor eventhough there is a verymarginal change in yield for the changein the relative concentration of reacting streams (Table 8(c)rows 2 4 and 5)

105 (Scheme 8 a = 05 b = 15 c = 1 d = 1 Nonelementary)

1051 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 9(a) and 9(b)

1052 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 9(c) and 9(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 11

1053 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 9(e) and 9(f)) Tables 9(a)ndash9(f)

and Figure 11 show that this non elementary reaction yieldshigher desired product in Plug Flow Reactor than in Fed-Batch Reactor Also the yield in Fed batch reactor decreaseswith addition time

As in Scheme 3 and Scheme 4 the reduced additiontime in Fed Batch Reactor results in increased productyield However in actual practice heat transfer and otherlimitations of the reactor vessel could possibly determine theminimum addition time beyond which addition time cannotbe reduced So the Fed Batch reactor yield is limited

It is to be noted that there is amarginal change in the yieldin Fed Batch reactor with relative concentration of reacting

14 ISRN Chemical Engineering

Table 8 (a) Reactor-1 (Fed-Batch Scheme 7 Part 1) (b) Reactor-2 (Plug Flow Scheme 7 Part 1) (c) Reactor-1 (Fed-Batch Scheme 7 Part2) (d) Reactor-2 (Plug Flow Scheme 7 Part 2) (e) Reactor-1 (Fed-Batch Scheme 7 Part 3) (f) Reactor-2 (Plug Flow Scheme 7 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 0992 2125 0026 000 2636 0004 1236600 099 2125 0027 000 264 8119864 minus 05 1237

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1139 2128 0027 2119864 minus 11 2242 04 105160 1139 2128 0027 2119864 minus 11 2242 04 1051

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1037 2126 0027 5119864 minus 04 2515 0125 1179900 1024 2126 0027 3119864 minus 04 2548 0092 11951800 1014 2125 0027 1119864 minus 04 2576 0064 1207900 1025 2126 0027 3E minus 04 2547 0093 1194900 1024 2126 0027 3E minus 04 255 009 1195

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1757 2144 0027 0472 1067 1573 5002360 1397 2135 0027 0165 172 092 806720 1176 2129 0027 0021 2166 0474 1015240 1757 2144 0027 0472 1067 1573 5002240 1757 2144 0027 0472 1067 1573 5002

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 0998 2125 0027 0001 2619 0021 1228900 0996 2125 0027 9119864 minus 04 2624 0016 1230

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1372 2134 0027 0687 2309 0331 1082360 115 2129 0027 0258 2472 0168 1159

913

3

827

768

696

999

1

965

595

8

955

1

955

0 500 1000 1500 2000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 11 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 8 Part 2)

80 847 91

2

985 101

4

105

3

107

2

452

5 586 694

9

701

701

701

701

701

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 12 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 9 Part 2)

ISRN Chemical Engineering 15

Table 9 (a) Reactor-1 (Fed-Batch Scheme 8 Part 1) (b) Reactor-2 (Plug Flow Scheme 8 Part 1) (c) Reactor-1 (Fed-Batch Scheme 8 Part2) (d) Reactor-2 (Plug Flow Scheme 8 Part 2) (e) Reactor-1 (Fed-Batch Scheme 8 Part 3) (f) Reactor-2 (Plug Flow Scheme 8 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 176 2144 0027 000 0588 2052 275600 1892 2147 0027 000 0234 2406 110

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1216 213 0027 3119864 minus 26 2037 06 95560 1216 213 0027 0000 2037 06 955

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1318 2133 0027 6119864 minus 06 1765 0875 827900 1366 2124 0027 9119864 minus 06 1638 1002 7681800 1423 2136 0027 2119864 minus 05 1485 1155 696900 1359 2134 0027 8E minus 06 1656 0984 776900 1374 2667 0027 1E minus 05 1615 1025 757

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1218 213 0027 0029 206 058 9655360 1216 213 0027 0008 2044 0596 958720 1216 213 0027 2119864 minus 04 2038 0602 9551240 1218 213 0027 0029 206 058 9655240 1218 213 0027 0029 206 058 9655

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1078 2127 0027 0003 2408 0232 1129900 109 2127 0027 0002 2376 0264 1114

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1076 2127 0027 0087 2498 0142 1171360 1065 2127 0027 0046 2486 0154 1166

streams (Table 9(c) rows 2 4 and 5) However this variationis too low to catch up with Plug Flow Reactor yield

106 (Scheme 9 119886 = 15 119887 = 05 119888 = 1 and 119889 = 1Nonelementary)

1061 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 10(a) and 10(b)

1062 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Theyield values for varying reaction times are capturedin Figure 12

In Tables 10(c) and 10(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1063 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 Tables 10(a)ndash10(f) and Figure 12 show that

this nonelementary reaction yields higher desired productin Fed-Batch Reactor than in Continuous Plug Flow Reac-tor

As in Scheme 2 and Scheme 7 the Plug Flow Reactoryield initially increases with the increase in reaction time(ie lengthier reactor pipe) consequently 119873B119905119873A119905 valuedecreases (ie reduced consumption of Reactant B) How-ever the Plug Flow Reactor yield saturates out below Fed-Batch Reactor yield (Figure 12)

Overall the Fed Batch Reactor yields higher product Rthan Plug Flow Reactor even though there is a very marginalchange in yield for the change in the relative concentration ofreacting streams (Table 10(c) rows 2 4 and 5) in Fed-BatchReactor

16 ISRN Chemical Engineering

Table 10 (a) Reactor-1 (Fed-Batch Scheme 9 Part 1) (b) Reactor-2 (Plug Flow Scheme 9 Part 1) (c) Reactor-1 (Fed-Batch Scheme 9 Part2) (d) Reactor-2 (Plug Flow Scheme 9 Part 2) (e) Reactor-1 (Fed-Batch Scheme 9 Part 3) (f) Reactor-2 (Plug Flow Scheme 9 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1019 2125 0027 000 2564 0077 1202600 0994 2125 0027 000 263 1119864 minus 02 1233

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1419 2135 0027 2119864 minus 11 1497 11 701560 1419 2135 0027 2119864 minus 11 1497 11 7015

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1302 2133 0027 4119864 minus 15 1807 0833 847900 125 2131 0027 4119864 minus 15 1946 0694 9121800 1192 213 0027 4119864 minus 15 2101 0539 985900 1254 2131 0027 4E minus 15 1936 0704 907900 1246 2131 0027 4E minus 15 1957 0683 917

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1771 2144 0027 0408 0965 1675 4525360 1544 2139 0027 0088 1251 1389 586720 1425 2136 0027 0001 1482 1158 6949240 1771 2144 0027 0408 0965 1675 4525240 1771 2144 0027 0408 0965 1675 4525

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 104 2667 0027 1119864 minus 06 2506 0134 1175900 1034 2126 0027 4119864 minus 15 2523 0117 1183

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 14 2135 0027 0624 217 047 1017360 1191 213 0027 0202 2307 0333 1081

Table 11 Summary of results

Schemenumber

119886 119887 119888 119889 Favored reactorRelationship

between 119886 119887 119888 and119889

1 1 1 1 1 Both equally 119886 + 119888 = 119887 + 119889

2 1 1 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

3 1 1 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

4 05 15 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

5 15 05 05 15 Both equally 119886 + 119888 = 119887 + 119889

6 05 15 15 05 Both equally 119886 + 119888 = 119887 + 119889

7 15 05 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

8 05 15 1 1 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

9 15 05 1 1 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

11 Conclusion

Under the simulated conditions elementary Second ordercompetitive consecutive reactions of the type mentioned in(1) yield the same amount of intermediate product R in bothideal fed batch and ideal Plug Flow Reactors for a constantconversion (99) of limiting reactant A Yield and selectivityof the product depends only on119870

11198702in both the reactors

However of the 8 nonelementary scenarios simulatedthree (Schemes 3 4 and 8) favor Plug Flow Reactor and threeother (Schemes 2 7 and 9) favor Fed Batch Reactor Twoothers (Schemes 5 and 6) like elementary reaction yield thesame in both Plug Flow Reactor and Fed batch reactor

Among the schemes simulated previously (Schemes 1 to9) the schemes giving increased yield R with reduced addi-tion time in Fed batch reactor favor Plug Flow Reactor andthe schemes giving increased yield with increased addition

ISRN Chemical Engineering 17

time in fed batch reactor favor Fed batch reactor This couldwell be a practical reckoner to screen the potential candidateamong the simulated schemes for Plug Flow Reactor eventhough this idea is only with respect to suitability of kineticparameters

The relationship between the exponents 119886 119887 119888 and 119889 andthe favourable reactor found in the simulation as shown inTable 11 is noteworthy

Nomenclature

1198701 Rate constant of reaction between A and

B in Litresdotmolminus1sdotsminus1K2 Rate constant of 2nd reaction between R

and B in Litresdotmolminus1sdotsminus1t Time s119905119886 Reactant B addition time in Fed Batch

Reactor s119905119898 Reaction mass maintenance time in Fed

Batch Reactor stlowast Space time in Plug Flow Reactor stend Space time for which each case of plug

flow rector simulation has been done s119903119909 Rate of change of species ldquoxrdquo

(molsdotLitreminus1sdotsminus1) ldquoxrdquo is representative ofspecies A B R S C and D

119862119909= 119873119909119881 Concentration molsdotLitreminus1 of any species

say ldquoxrdquoV Reaction volume m3119873119909 Number of Kg moles of species ldquoxrdquo k mol

NB119905 Total Kg moles of reactant B used inreaction k mol

NA119905 Total kg moles of reactant A used inreaction k mol

119881119886119905 Volume of stream containing reactant B

m3119881119905 Total volume of contents including

streams of reactant A and reactant B m3v Plug Flow Reactor volume m3v1015840 Volumetric flow rate m3s119865119909 Molar flow rate (k molsdotsminus1) of species ldquoxrdquo

which is representative of species A B RS C and D

NB119905NA119905 Ratio of total moles of B to total moles ofA taken for the reaction

119873119909119865 Final kg moles of the species ldquoxrdquo k mol

WR Weight kg of total intermediate (desired)product formed at the end of reaction inFed Batch Reactor and at the end of agiven space time in the Plug Flow Reactor

Acknowledgment

The author would like to thank Chandra Kanth Terupally ofPlanck Technical Hyderabad India for providing adequatesupport in MATLAB Programming

References

[1] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1998

[2] J F Richardson and D G Peacock Coulson and RichardsonrsquosChemical Engineering Chemical and Biochemical Reactors andProcess Control Butterworth-Heinemann Boston Mass USA3rd edition 1994

[3] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart I model developmentrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 750162 16pages 2012

[4] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart II design protocolsrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 65432113 pages 2012

[5] J R Bourne ldquoMixing and the selectivity of chemical reactionsrdquoOrganic Process Research andDevelopment vol 7 no 4 pp 471ndash508 2003

[6] J Bałdyga J R Bourne and S J Hearn ldquoInteraction betweenchemical reactions and mixing on various scalesrdquo ChemicalEngineering Science vol 52 no 4 pp 457ndash466 1997

[7] N G Anderson ldquoPractical use of continuous processing indeveloping and scaling up laboratory processesrdquo Organic Pro-cess Research and Development vol 5 no 6 pp 613ndash621 2001

[8] C Brechtelsbauer and F Ricard ldquoReaction engineering evalua-tion and utilization of static mixer technology for the synthesisof pharmaceuticalsrdquoOrganic Process Research andDevelopmentvol 5 no 6 pp 646ndash651 2001

[9] Z Anxionnaz M Cabassud C Gourdon and P Tochon ldquoHeatexchangerreactors (HEX reactors) concepts technologiesstate-of-the-artrdquo Chemical Engineering and Processing vol 47no 12 pp 2029ndash2050 2008

[10] P Barthe C Guermeur O Lobet et al ldquoContinuous multi-injection reactor for multipurpose productionmdashpart Irdquo Chem-ical Engineering and Technology vol 31 no 8 pp 1146ndash11542008

[11] M Patel and G Gasparini ldquoReactor technology flow reactorsand dynamic mixingrdquo Specialty Chemicals Magazine 2009

[12] X W Ni ldquoContinuous oscilatory baffled reactor technologyrdquoin Innovations in Pharmaceutical TechnologymdashManufacturingpp 90ndash96 2006 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=392

[13] L Proctor ldquoContinuous chemical processingrdquo in Innovationsin Pharmaceutical Technology pp 84ndash88 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=290

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ISRN Chemical Engineering 3

FA0

CA0

FA

CAF

FAF

FA + dFA

Figure 3 Schematic drawing of Plug Flow Reactor

Table 1 Molecular weights

Molecular weight of A 750000 Molecular weight of R 468750Molecular weight of B 187500 Molecular weight of C 468750Total (1st reactionreactants) 937500 Total (1st reaction

products) 937500

Molecular weight of R 468750 Molecular weight of S 328125Molecular weight of B 187500 Molecular weight of D 328125Total (2nd reactionreactants) 656250 Total (2nd reaction

products) 656250

3 The Fed-Batch Reactor (Reactor-1)

Reactant A is taken in the reactor whereas reactant B isadded continuously over reactant A (see Figure 2) It is tobe noted that component B is added (no output flow term)whereas component A is taken inside the reactor (no inputflow term and no output flow term) Hence material balancefor components A and B must be written separately Materialbalance pattern of all other products is similar to that ofcomponent A

For Species A

Input = Output + Disappearance by Reaction

+ Accumulation

0 = 0 + (minus119903A) 119881 + (119889119873A119889119905)

(minus1

119881) sdot (119889119873A119889119905) = minus119903A

(3)

For Species B

Input = Output + Disappearance by Reaction

+ Accumulation

(119873B119905119905119886

) = 0 + (minus119903B) 119881 + (119889119873B119889119905)

(minus1

119881)(119889119873B119889119905) = minus119903B minus (

119873B119905119881119905119886

)

(4)

From (3) to (4) we can mathematically describe thereaction system in ideal Fed-Batch Reactor as follows119889119873A119889119905

= (minus1

119881)1198701119873119886

A119873119887

B 0 lt 119905 le 119905119886 + 119905119898

119889119873B119889119905= (minus1

119881)1198701119873119886

A119873119887

B minus (1

119881)1198702119873119888

B119873119889

R +119873B119905119905119886

0 lt 119905 le 119905119886

119889119873B119889119905= (minus1

119881)1198701119873119886

A119873119887

B minus (1

119881)1198702119873119888

B119873119889

R 119905119886 lt 119905 le 119905119886+119898

119889119873R119889119905= (1

119881)1198701119873119886

A119873119887

B minus (1

119881)1198702119873119888

B119873119889

R 0 lt 119905 le 119905119886+119898

119889119873S119889119905= (1

119881)1198702119873119888

B119873119889

R 0 lt 119905 le 119905119886+119898

119881 =119905119881119886119905

119905119886

+ (119881119905minus 119881119886119905) 0 lt 119905 le 119905

119886

119881 = 119881119905 119905119886lt 119905 le 119905

119886+119898

(5)

The sets of equations (5) represent in the second orderconsecutive competitive reaction in Fed-Batch Reactor

4 The Plug Flow Reactor (Reactor-2) (SeeFigure 3)

Thematerial (ie chemical) balance equations for a Plug FlowReactor can be written as follows [1]

Input = Output + Disappearance by reaction+ Accumulation

(6)

119865A = 119865A + 119889119865A + (minus119903A sdot 119889V) (7)

(minus119889119865A119889V) = minus119903A (8)

(minus119889119862AV

1015840

119889V) = minus119903A (9)

Space time in Plug Flow Reactor 119905lowast = VV1015840When volumetric flow rate is constant 119889119905lowast = 119889VV1015840 (8)

becomes as follows

(minus119889119862A119889119905lowast) = minus119903A (10)

From (7) to (10) we can mathematically describe thereaction system in ideal Plug Flow Reactor as follows

119889119862A119889119905lowast= minus 119870

1119862119886

A119862119887

B

119889119862B119889119905lowast= minus 119870

1119862119886

A119862119887

B minus 1198702119862119888

B119862119889

R

119889119862R119889119905lowast= 1198701119862119886

A119862119887

B minus 1198702119862119888

B119862119889

R

119889119862S119889119905lowast= 1198702119862119888

B119862119889

R

(11)

5 Simulation Plan

Solutions to the set of equations in (5) and (11) will enable oneto analyze the performance of reaction system in Fed BatchReactor and continuous Plug flow Reactor respectively

The main aim of this literature is to carry out thepreviouslymentioned analysis for an arbitrary still practicallyrelevant reaction system

4 ISRN Chemical Engineering

Table 2 (a) Reactor-1 (Fed-Batch Scheme 1 Part 1) (b) Reactor-2 (Plug Flow Scheme 1 Part 1) (c) Reactor-1 (Fed-Batch Scheme 1 Part2) (d) Reactor-2 (Plug Flow Scheme 1 Part 2) (e) Reactor-1 (Fed-Batch Scheme 1 Part 3) (f) Reactor-2 (Plug Flow Scheme 1 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 129 2132 0027 000 184 0801 8623600 129 2132 0027 000 184 08 8624

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1291 2132 0026 1119864 minus 26 1838 0803 861460 1291 2132 0026 000 1838 0803 8614

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 129 2132 0027 2119864 minus 06 184 08 8624900 129 2132 0027 1119864 minus 06 184 08 86241800 129 2132 0027 9119864 minus 07 184 08 8624900 129 2132 0027 1E minus 06 184 08 8624900 129 2132 0027 1E minus 06 184 08 8624

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1313 2133 0027 0061 184 08 8625360 1296 2132 0027 0016 184 08 8624720 129 2132 0027 4119864 minus 04 184 08 8624240 1313 2133 0027 0061 184 08 8625240 1313 2133 0027 0061 184 08 8625

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 106 2127 0027 0002 2454 0186 1151900 106 2127 0027 0001 2454 0186 1151

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1117 2128 0027 0152 2454 0186 1151360 1086 2127 0027 007 2454 0186 1151

Rate constant values are assumed with three individualscenarios first one with ratio of119870

1to1198702considered as 10 and

1198701considered as 100sdotLitresdotmolminus1sdotsminus1 the second one with the

same ratio of11987011198702but with the119870

1as 01 Litresdotmolminus1sdotsminus1 and

the third one with the ratio of 11987011198702considered as 50 with

the1198701considered as 01 Litresdotmolminus1sdotsminus1

Totally nine different sets of exponents (ie a b c d)have been considered such that the overall order of reactionremains two Hence there are 9 sets of reactions schemeseach scheme is analyzed for the mentioned 3 sets of kineticconstants Molecular weight of each of the componentsinvolved in the reaction is considered in consistent with thestoichiometry given in (1) The values are given in Table 1

In this study the molecular weights are used to convertmoles into Kg and vice versa (molecular weight values arearbitrary in Table 1)

Total solvent quantity considered is 2m3 Quantity ofsolvent m3 used to make a stream of reactant A is called Sol

R Quantity of solvent m3 used to make a stream of reactantB is called Sol A For the ensuing simulations amount ofsolvent used in both the reacting streams is same that is SolA(Sol A + Sol R) = 05 unless specified otherwise in therespective calculationoutput datagraphsTableThe effect ofrelative concentration of both the streams on kinetics is nottreated at length however few cases with Sol A(Sol R + SolA) = 025 and 075 have been simulated to indicate the changein reaction selectivity with change in relative concentration ofreactant streams

As the reaction considered is in liquid phase constantvolume reaction system is supposed except for the volumechange due to addition of the solution of second component(reactant B) in to the solution of 1st component (reactant A)in the Fed-Batch Reactor There is no volume change dueto reaction Volumetric flow rate in Plug Flow Reactor isconsidered constantThe volume in liters constituted by eachof the starting materials (A and B) is assumed 05 times theweight in kg of the respective components

ISRN Chemical Engineering 5

005

115

225

3

0 100 200 300 400 500 600 700Con

cent

ratio

n (m

olL

)

Time (s)minus05

(a)

0

05

1

15

2

25

0 100 200 300 400 500 600 700Time (s)

Volu

me (

m3)

(b)

002040608

112141618

0 05 1 15 2 25 3 35

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cent

ratio

n (m

olL

)

Time (s)minus02

(c)

0

05

1

15

2

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0 500 1000 1500 2000 2500C

once

ntra

tion

(mol

L)

Time (s)minus05

(d)

002040608

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0 100 200 300 400

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cent

ratio

n (m

olL

)

Time (s)minus02

(e)

0

05

1

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0 500 1000 1500 2000 2500

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cent

ratio

n (m

olL

)

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(f)

002040608

1121416

0 100

AB

RS

200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(g)

Figure 4 (a) Concentration as a function of time Fed-Batch Reactor (Scheme 1 Part 1 Case 1 119905119886= 60 s 119905

119898= 600 s (see Scheme 1

in Supplementary Material available online at httpdxdoiorg1011552013591546) (b) Volume as a function of time Fed-Batch Reactor(Scheme 1 Part 1 Case-1 119905

119886= 60 s 119905

119898= 600 s) (c) Concentration as a function of time Plug Flow Reactor (Scheme 1 Part 1 119905end = 6 s for

brevity graph is plotted for 3 s only) (d) Concentration as a function of time Fed-Batch Reactor (Scheme 1 Part 2 119905119886= 900 s 119905

119898= 1200 s)

(e) Concentration as a function of time Plug Flow Reactor (Scheme 1 Part 2 119905end = 360 s) (f) Concentration as a function of time Fed-BatchReactor (Scheme 1 Part 3 119905

119886= 900 s 119905

119898= 1200 s) (g) Concentration as a function of time Plug Flow Reactor (Scheme 1 Part 3 119905end = 360 s)

6 ISRN Chemical Engineering

0

05

1

15

2

25

3

0 100 200 300 400 500 600 700

Con

cent

ratio

n (m

olL

)

Time (s)minus05

(a)

0

02

04

06

08

1

12

14

16

0 05 1 15 2 25 3 35

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(b)

0

05

1

15

2

25

3

0 500 1000 1500 2000 2500

Con

cent

ratio

n (m

olL

)

Time (s)minus05

AB

RS

(c)

0

02

04

06

08

1

12

14

16

0 100 200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)

AB

RS

(d)

Figure 5 (a) Concentration as a function of time Fed-Batch Reactor (Scheme 2 Part 1 119905119886= 60 s 119905

119898= 600 s) (b) Concentration as a function

of time Plug Flow Reactor (Scheme 2 Part 1 119905end = 6 s for brevity graph is plotted for 3 s only) (c) Concentration as a function of timeFed-Batch Reactor (Scheme 2 Part 2 119905

119886= 900 s 119905

119898= 1200 s) (d) Concentration as a function of time Plug Flow Reactor (Scheme 2 Part 2

119905end = 360 s)

The quantity of A used in the entire study is 200Kgs Incase of Fed batch reactor the simulation has been done forvarious addition time of streamB reactionmaintenance timeis chosen such that further change in concentration profileis practically absent The constancy of concentration profiletowards the end of 119905

119898can be observed in the concentration

profiles obtained from MATLAB Also 119905119898

is maintainedconstant for a given set of 119870

11198702in order to make the

comparative study relevant In case of Plug Flow Reactor thesimulation is done for different reaction end time as differentcase The reaction time 119905end in Plug Flow Reactor refers tospace time

In case of Fed-Batch Reactor the addition rate is consid-ered constant across the entire addition time

The reaction is run in both the reactors for a specifiedextent of conversion that is 99 of reactant A conversionis the reaction end point For a prechosen 119905

119886 119905119898 and 119905end the

99 conversion of reactant A is ensured by adjusting the totalmoles of reactant B that is by adjusting 119873B119905119873A119905 final 99conversion of reactant A is achieved for predefined cases of 119905

119886

(s) 119905119898(s) and 119905end (s)

The previously mentioned assumptions and basis havebeen considered keeping in mind that the actual reactionscenarios in the industry can be understood and interpretedin the light of the conclusions arrived at in this simulationstudy

The concentration profiles given in the subsequent sec-tions are intended only to showcase the pattern of thecorresponding reaction scheme The quantitative details ofsuch graphs are given in the tables for the respective cases

6 Simulation Accuracy

Solution to the previouslymentioned simultaneous nonlineardifferential equations ((5) and (11)) has been obtained by thesoftware MATLAB which entailed its default Explicit Runge-Kutta (45) Variable step (Dormand-Prince Pair) methodThe calculation tolerance has been set at a default 01with step limits adjusted such that step limits n and n10seconds would return the final results matching up to 3decimal points When the gap between reactor-1 and reactor-2 results narrowsbecomes more significant towards arriving

ISRN Chemical Engineering 7

112

211

37 115

3

116

7

117

3

118

1

118

5

101

3 103

210

52

105

9

106

1

106

2

106

3

106

3

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 6 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 2 Part 2)

at a conclusion tolerance is squeezed further to 001 withthe same step limit criteria as done for the simulation withtolerance 01

7 Simulation (Scheme 1 119886 = 119887 = 119888 = 119889 = 1 ieElementary Reaction)

71 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 In Tables 2(a) and 2(b) simulation results for two

cases have been captured Figures 4(a) and 4(c) are sampleconcentration profiles of reaction species in ideal Fed Batchand ideal Plug Flow Reactor Figure 4(b) is the graphicalrepresentation of reaction volume in Fed-Batch Reactor

It can be observed in Figure 4(a) that with 119905119898= 600 s

further concentration change (reaction) is negligible As theaddition rate of reagent B considered in this simulation studyis constant the fed batch volume increases linearly till 119905 =119905119886 During Reaction maintenance time 119905

119898 the Fed-Batch

volume remains constant

72 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Figures 4(d) and 4(e) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

In Tables 2(c) and 2(d) results for all simulated cases havebeen captured and the data lines (rows) 4 and 5 correspondto the fraction Sol A(Sol A + Sol R) = 025 and 075respectively

73 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and

1198702= 0002 Figures 4(f) and 4(g) are sample concentration

profiles of reaction species in ideal Fed Batch and ideal PlugFlow Reactors

In Tables 2(e) and 2(f) simulation results for two caseshave been captured

Tables 2(a) to 2(f) show that elementary reaction of thetype given in (1) yields the same amount of desired product infed batch reactor and Plug Flow Reactor Moreover the yield

values in Part 2 remain the same as those in Part 1 That isbecause119870

11198702values remain the same in both Part 1 and Part

2 even though the individual 1198701and 119870

2values are different

It is to be noted that in Part 3 yield values are different fromthat in Part 1 and Part 2That is because119870

11198702value in Part 3

is different from those in Part 1 and Part 2 The change in therelative concentration of both the reacting streams (as shownin Table 2(c) rows 2 4 and 5 and Table 2(d) rows 1 4 and 5)does not have any effect on the yield

8 Simulation (Scheme 2 119886 = 119887 = 1 119888 = 15 119889 =05 Nonelementary)

81 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 Figures 5(a) and 5(b) are sample concentration

profiles of reaction species in ideal Fed Batch and ideal PlugFlow Reactors

In Tables 3(a) and 3(b) simulation results for two casessimulated have been captured

82 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Figures 5(c) and 5(d) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

In Tables 3(c) and 3(d) and Figure 6 results for all thesimulated cases have been captured The data lines (rows) 4and 5 in Tables 3(c) and 3(d) correspond to the fraction SolA(Sol A + Sol R) = 025 and 075 respectively

The yield values for varying reaction times are capturedin Figure 6

83 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 In Tables 3(e) and 3(f) simulation results for two caseshave been captured

Tables 3(a) and 3(f) and Figure 6 show that this nonelementary reaction yields higher desired product in Fed-Batch Reactor than in Continuous Plug Flow Reactor

In Figure 6 the Plug Flow Reactor yield initially increaseswith the increase in reaction time (ie lengthier reactor pipe)consequently 119873B119905119873A119905 value decreases as shown in Tables3(c) and 3(d) (ie reduced consumption of Reactant B)However the Plug Flow Reactor yield saturates out belowFed-Batch Reactor yield Overall the Fed Batch Reactoryields higher product R than Plug Flow Reactor even thoughthere is a very marginal change in yield for the change in therelative concentration of reacting streams (Table 3(c) rows 24 and 5) in Fed Batch Reactor

9 Simulation (Scheme 3 119886 = 119887 = 1 119888 = 05 119889 =15 Nonelementary)

91 Part 1 (Cases 1 and 2)1198701= 100119870

11198702= 10 and119870

2= 10

In Tables 4(a) and 4(b) simulation results for two cases havebeen captured

Figures 7(a) and 7(b) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

8 ISRN Chemical Engineering

Table 3 (a) Reactor-1 (Fed-Batch Scheme 2 Part 1) (b) Reactor-2 (Plug Flow Scheme 2 Part 1) (c) Reactor-1 (Fed-Batch Scheme 2 Part2) (d) Reactor-2 (Plug Flow Scheme 2 Part 2) (e) Reactor-1 (Fed-Batch Scheme 2 Part 3) (f) Reactor-2 (Plug Flow Scheme 2 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1005 2132 0027 000 2598 0042 122600 0996 2125 0027 000 2625 0015 123

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 113 2128 0027 6119864 minus 06 2267 04 106360 113 2128 0027 3119864 minus 35 2267 04 1063

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1072 2127 0027 0005 2425 0215 1137900 1059 2166 0027 0004 2459 0181 11531800 1048 2126 0027 0004 2491 0149 1167900 1061 2127 0027 0004 2456 0184 1151900 1058 2126 0027 0004 2463 0177 1154

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1221 2131 0027 0135 216 048 1013360 118 2129 0027 0068 2202 0438 1032720 1145 2129 0027 0018 2244 0396 1052240 1221 2131 0027 0135 216 048 1013240 1221 2131 0027 0135 216 048 1013

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1009 2125 0027 0008 2599 0041 1218900 1006 2125 0027 0008 2605 0035 1221

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1094 2127 0027 0083 2545 0095 1193360 1058 2126 0027 0097 2555 0085 1198

92 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 4(c) and 4(d) and Figure 8 results for othersimulated cases have been captured

The last two data lines (rows) in Tables 4(c) and 4(d)correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

Figures 7(c) and 7(d) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

The yield values for varying reaction times are capturedin Figure 8

93 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 InTables 4(e) and 4(f) simulation results for two caseshave been captured

Tables 4(a)ndash4(f) and Figure 8 show that this non elemen-tary reaction yields higher desired product R in Plug FlowReactor than in Fed-Batch Reactor

It is to be noted that the reduced addition time in FedBatch Reactor results in increased product yield Howeverin actual practice heat transfer and other limitations of thereactor vessel could possibly determine the minimum addi-tion time beyond which addition time cannot be reduced Sothe Fed Batch reactor yield is limited

It is to be further noted that there is a marginal changein the yield in Fed Batch reactor with the change in relativeconcentration of reacting streams (Table 4(c) rows 2 4 and5) However this variation is too low to catch up with PlugFlow Reactor yield

10 Simulations (for the Rest of the Schemes)

101 (Scheme 4 119886 = 05 119887 = 15 119888 = 05 119889 = 15Nonelementary)

1011 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and 119870

2=

10 See Tables 5(a) and 5(b)

ISRN Chemical Engineering 9

Table 4 (a) Reactor-1 (Fed-Batch Scheme 3 Part 1) (b) Reactor-2 (Plug Flow Scheme 3 Part 1) (c) Reactor-1 (Fed-Batch Scheme 3 Part2) (d) Reactor-2 (Plug Flow Scheme 3 Part 2) (e) Reactor-1 (Fed-Batch Scheme 3 Part 3) (f) Reactor-2 (Plug Flow Scheme 3 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1909 2148 0027 000 019 245 9600 195 2149 0027 000 0079 2561 4

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1448 2136 0027 3119864 minus 08 1419 12 665260 1447 2136 0027 3119864 minus 05 142 12 6657

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1598 214 0027 5119864 minus 13 1019 1621 4776900 1661 2142 0027 3119864 minus 13 0851 1789 39891800 1722 2143 0027 7119864 minus 13 0687 1953 3222900 1655 2141 0027 1119864 minus 12 0868 1772 4067900 1668 2142 0027 1119864 minus 12 0833 1807 3905

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1448 2136 0027 4119864 minus 12 1419 1221 6652360 1448 2136 0027 4119864 minus 12 1419 1221 6652720 1448 2136 0027 4119864 minus 12 1419 1221 6652240 1448 2136 0027 4E minus 12 1419 1221 6652240 1448 2136 0027 4E minus 12 1419 1221 6652

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1214 213 0027 0000 2043 0597 9575900 1251 2131 0027 0000 1943 0697 9107

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1172 2129 0027 0071 2227 0413 1044360 1163 2129 0027 0003 2182 0458 1023

1012 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 The data lines (rows) 4 and 5 in Tables 5(c) and 5(d)correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 9

1013 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 (See Tables 5(e) and 5(f)) Tables 5(a)ndash5(f) and Figure 9show that this non elementary reaction yields higher desiredproduct in Plug Flow Reactor than in Fed-Batch Reactor

As in Scheme 3 the reduced addition time in Fed BatchReactor results in increased product yield However in actualpractice heat transfer and other limitations of the reactorvessel could possibly determine the minimum addition timebeyond which addition time cannot be reduced So the FedBatch reactor yield is limited

Themarginal change in the yield in FedBatch reactorwithrelative concentration of reacting streams (Table 5(c) rows 24 and 5) may be noted However this variation is too low tocatch up with Plug Flow Reactor yield

102 (Scheme 5 119886 = 15 119887 = 05 119888 = 05 119889 = 15Nonelementary)

1021 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 6(a) and 6(b)

1022 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 119870

2=

001 In Table 6(c) and 6(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1023 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 119870

2=

0002 (See Tables 6(e) and 6(f)) Tables 6(a)ndash6(f) show that

10 ISRN Chemical Engineering

0

05

1

15

2

25

3

0 100 200 300 400 500 600 700

Con

cent

ratio

n (m

olL

)

Time (s)minus05

(a)

002040608

112141618

2

0 05 1 15 2 25 3 35

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(b)

0

05

1

15

2

25

3

0 500 1000 1500 2000 2500Time (s)minus05

Con

cent

ratio

n (m

olL

)

AB

RS

(c)

002040608

112141618

2

0 100

AB

RS

200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(d)

Figure 7 (a) Concentration as a function of time Fed-Batch Reactor (Scheme 3 Part 1 119905119886= 60 s 119905

119898= 600 s) (b) Concentration as a function

of time Plug Flow Reactor (Scheme 3 Part 1 119905end = 6 s for brevity graph is plotted for 3 s only) (c) Concentration as a function of timeFed-Batch Reactor (Scheme 3 Part 2 119905

119886= 900 s 119905

119898= 1200 s) (d) Concentration as a function of time Plug Flow Reactor (Scheme 3 Part 2

119905end = 360 s)

this type of nonelementary reaction yields the same amountof desired product in fed batch reactor and in Plug FlowReactor Moreover the yield values in Part 2 remain the sameas those in Part 1 That is because 119870

11198702values remain the

same in both Part 1 and Part 2 even though the individual1198701and119870

2values are different It is to be noted that in Part 3

yield values are different from that in Part 1 and Part 2That isbecause 119870

11198702value in Part 3 is different from those in Part

1 and Part 2The change in the relative concentration of both the

reacting streams (as shown in Table 6(c) rows 2 4 and 5 andTable 6(d) rows 1 4 and 5) does not have any effect on theyield

103 (Scheme 6 119886 = 05 119887 = 15 119888 = 15 119889 = 05Nonelementary)

1031 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 7(a) and 7(b)

1032 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 7(c) and 7(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1033 Part 3 (Cases 1 and 2)1198701= 01119870

11198702= 50 and119870

2=

0002 (See Tables 7(e) and 7(f)) Tables 7(a)ndash7(f) show thatthis type of nonelementary reaction also behaves similar toelementary reaction and nonelementary reaction Scheme 5with respect to product selectivity that is the yield is the samein both the reactors The change in the relative concentrationof both the reacting streams (as shown in Table 7(c) rows 24 and 5 and Table 7(d) rows 1 4 and 5) does not have anyeffect on the yield

104 (Scheme 7 119886 = 15 119887 = 05 119888 = 15 119889 = 05Nonelementary)

1041 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 8(a) and 8(b)

ISRN Chemical Engineering 11

Table 5 (a) Reactor-1 (Fed-Batch Scheme 4 Part 1) (b) Reactor-2 (Plug Flow Scheme 4 Part 1) (c) Reactor-1 (Fed-Batch Scheme 4 Part2) (d) Reactor-2 (Plug Flow Scheme 4 Part 2) (e) Reactor-1 (Fed-Batch Scheme 4 Part 3) (f) Reactor-2 (Plug Flow Scheme 4 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1927 2148 0027 000 0141 2499 7600 1961 2149 0027 000 005 259 2

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1313 2133 0027 6119864 minus 08 1778 09 833460 1313 2667 0027 6119864 minus 08 1778 09 8334

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1562 2139 0027 000 1113 1527 5219900 1654 2141 0027 1119864 minus 10 0869 1771 40751800 1733 2143 0027 6119864 minus 13 0658 1982 3085900 1646 2141 0027 1E minus 12 0868 175 4171900 1662 2142 0027 1E minus 10 0848 1792 3974

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1313 2133 0027 000 1778 0862 8334360 1313 2133 0027 000 1778 0862 8334720 1313 2133 0027 8119864 minus 12 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1203 213 0027 7119864 minus 11 2071 0569 971900 1265 2132 0027 6119864 minus 11 1907 0733 894

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 2997 2128 0027 0021 2304 0336 108360 1124 2128 0027 000 2284 0356 107

609

477

6

398

9

322

2

746

266

52

665

2

665

2

0 500 1000 1500 2000ta or tend (s)

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 8 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 3 Part 2)

ta or tend (s)

741

521

9

407

5

308

5

857

1

8334

833

4

833

4

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 9 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 4 Part 2)

12 ISRN Chemical Engineering

Table 6 (a) Reactor-1 (Fed-Batch Scheme 5 Part 1) (b) Reactor-2 (Plug Flow Scheme 5 Part 2) (c) Reactor-1 (Fed-Batch Scheme 5 Part2) (d) Reactor-2 (Plug Flow Scheme 5 Part 2) (e) Reactor-1 (Fed-Batch Scheme 5 Part 2) (f) Reactor-2 (Plug Flow Scheme 5 Part 2)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1664 2142 0027 000 0843 1797 3954600 1664 2149 0027 000 0843 1797 3954

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1664 2142 0027 6119864 minus 09 0843 18 395460 1664 2142 0027 6119864 minus 09 0843 18 3954

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1664 2142 0027 1119864 minus 10 0844 1796 3956900 1664 2142 0027 1119864 minus 10 0843 1797 39541800 1664 2142 0027 1119864 minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1794 2145 0027 0348 0843 1797 3954360 1672 2142 0027 0022 0844 1796 3954720 1664 2142 0027 000 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 124 2131 0027 7119864 minus 11 1973 0667 9249900 124 2131 0027 7119864 minus 11 1973 0667 9248

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1442 2136 0027 0537 1973 0667 9247360 1277 2132 0027 0099 1973 0667 9248

116

211

79

119

5

120

7

121

2

121

8

122

500

280

6 101

5

104

9

105

1

105

1

105

1

105

1

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 10 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 7 Part 2)

1042 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 8(c) and 8(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 10

1043 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 8(c) and 8(d)) Tables 7(a)ndash

7(d) and Figure 10 show that this non elementary reactionyields higher desired product in Fed-Batch Reactor than inContinuous Plug Flow Reactor

As in Scheme 2 the Plug Flow Reactor yield initiallyincreases with the increase in reaction time (ie lengthierreactor pipe) consequently 119873B119905119873A119905 value decreases asshown in Table 8(d) (ie reduced consumption of ReactantB) However the Plug Flow Reactor yield saturates out below

ISRN Chemical Engineering 13

Table 7 (a) Reactor-1 (Fed-Batch Scheme 6 Part 1) (b) Reactor-2 (Plug Flow Scheme 6 Part 1) (c) Reactor-1 (Fed-Batch Scheme 6 Part2) (d) Reactor-2 (Plug Flow Scheme 6 Part 2) (e) Reactor-1 (Fed-Batch Scheme 6 Part 3) (f) Reactor-2 (Plug Flow Scheme 6 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1121 2128 0027 000 229 035 1073600 1121 2128 0027 000 229 035 1073

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1121 2128 0027 4119864 minus 04 229 04 107360 1121 2128 0027 5119864 minus 06 229 04 1073

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7119864 minus 03 229 035 10731800 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1152 2129 0027 0083 229 035 1073360 1139 2128 0027 0048 229 035 1073720 1128 2128 0027 0017 229 035 1073240 1152 2129 0027 0083 229 035 1073240 1152 2129 0027 0083 229 035 1073

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1022 2126 0027 0012 2568 0073 1204900 1022 2126 0027 0012 2567 0072 1203

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1058 2126 0027 0108 2567 0072 1204360 1042 2126 0027 0066 2568 0073 1204

Fed-Batch Reactor yield (Figure 10) Overall the Fed BatchReactor yields higher product R than Plug Flow Reactor eventhough there is a verymarginal change in yield for the changein the relative concentration of reacting streams (Table 8(c)rows 2 4 and 5)

105 (Scheme 8 a = 05 b = 15 c = 1 d = 1 Nonelementary)

1051 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 9(a) and 9(b)

1052 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 9(c) and 9(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 11

1053 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 9(e) and 9(f)) Tables 9(a)ndash9(f)

and Figure 11 show that this non elementary reaction yieldshigher desired product in Plug Flow Reactor than in Fed-Batch Reactor Also the yield in Fed batch reactor decreaseswith addition time

As in Scheme 3 and Scheme 4 the reduced additiontime in Fed Batch Reactor results in increased productyield However in actual practice heat transfer and otherlimitations of the reactor vessel could possibly determine theminimum addition time beyond which addition time cannotbe reduced So the Fed Batch reactor yield is limited

It is to be noted that there is amarginal change in the yieldin Fed Batch reactor with relative concentration of reacting

14 ISRN Chemical Engineering

Table 8 (a) Reactor-1 (Fed-Batch Scheme 7 Part 1) (b) Reactor-2 (Plug Flow Scheme 7 Part 1) (c) Reactor-1 (Fed-Batch Scheme 7 Part2) (d) Reactor-2 (Plug Flow Scheme 7 Part 2) (e) Reactor-1 (Fed-Batch Scheme 7 Part 3) (f) Reactor-2 (Plug Flow Scheme 7 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 0992 2125 0026 000 2636 0004 1236600 099 2125 0027 000 264 8119864 minus 05 1237

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1139 2128 0027 2119864 minus 11 2242 04 105160 1139 2128 0027 2119864 minus 11 2242 04 1051

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1037 2126 0027 5119864 minus 04 2515 0125 1179900 1024 2126 0027 3119864 minus 04 2548 0092 11951800 1014 2125 0027 1119864 minus 04 2576 0064 1207900 1025 2126 0027 3E minus 04 2547 0093 1194900 1024 2126 0027 3E minus 04 255 009 1195

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1757 2144 0027 0472 1067 1573 5002360 1397 2135 0027 0165 172 092 806720 1176 2129 0027 0021 2166 0474 1015240 1757 2144 0027 0472 1067 1573 5002240 1757 2144 0027 0472 1067 1573 5002

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 0998 2125 0027 0001 2619 0021 1228900 0996 2125 0027 9119864 minus 04 2624 0016 1230

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1372 2134 0027 0687 2309 0331 1082360 115 2129 0027 0258 2472 0168 1159

913

3

827

768

696

999

1

965

595

8

955

1

955

0 500 1000 1500 2000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 11 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 8 Part 2)

80 847 91

2

985 101

4

105

3

107

2

452

5 586 694

9

701

701

701

701

701

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 12 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 9 Part 2)

ISRN Chemical Engineering 15

Table 9 (a) Reactor-1 (Fed-Batch Scheme 8 Part 1) (b) Reactor-2 (Plug Flow Scheme 8 Part 1) (c) Reactor-1 (Fed-Batch Scheme 8 Part2) (d) Reactor-2 (Plug Flow Scheme 8 Part 2) (e) Reactor-1 (Fed-Batch Scheme 8 Part 3) (f) Reactor-2 (Plug Flow Scheme 8 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 176 2144 0027 000 0588 2052 275600 1892 2147 0027 000 0234 2406 110

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1216 213 0027 3119864 minus 26 2037 06 95560 1216 213 0027 0000 2037 06 955

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1318 2133 0027 6119864 minus 06 1765 0875 827900 1366 2124 0027 9119864 minus 06 1638 1002 7681800 1423 2136 0027 2119864 minus 05 1485 1155 696900 1359 2134 0027 8E minus 06 1656 0984 776900 1374 2667 0027 1E minus 05 1615 1025 757

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1218 213 0027 0029 206 058 9655360 1216 213 0027 0008 2044 0596 958720 1216 213 0027 2119864 minus 04 2038 0602 9551240 1218 213 0027 0029 206 058 9655240 1218 213 0027 0029 206 058 9655

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1078 2127 0027 0003 2408 0232 1129900 109 2127 0027 0002 2376 0264 1114

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1076 2127 0027 0087 2498 0142 1171360 1065 2127 0027 0046 2486 0154 1166

streams (Table 9(c) rows 2 4 and 5) However this variationis too low to catch up with Plug Flow Reactor yield

106 (Scheme 9 119886 = 15 119887 = 05 119888 = 1 and 119889 = 1Nonelementary)

1061 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 10(a) and 10(b)

1062 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Theyield values for varying reaction times are capturedin Figure 12

In Tables 10(c) and 10(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1063 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 Tables 10(a)ndash10(f) and Figure 12 show that

this nonelementary reaction yields higher desired productin Fed-Batch Reactor than in Continuous Plug Flow Reac-tor

As in Scheme 2 and Scheme 7 the Plug Flow Reactoryield initially increases with the increase in reaction time(ie lengthier reactor pipe) consequently 119873B119905119873A119905 valuedecreases (ie reduced consumption of Reactant B) How-ever the Plug Flow Reactor yield saturates out below Fed-Batch Reactor yield (Figure 12)

Overall the Fed Batch Reactor yields higher product Rthan Plug Flow Reactor even though there is a very marginalchange in yield for the change in the relative concentration ofreacting streams (Table 10(c) rows 2 4 and 5) in Fed-BatchReactor

16 ISRN Chemical Engineering

Table 10 (a) Reactor-1 (Fed-Batch Scheme 9 Part 1) (b) Reactor-2 (Plug Flow Scheme 9 Part 1) (c) Reactor-1 (Fed-Batch Scheme 9 Part2) (d) Reactor-2 (Plug Flow Scheme 9 Part 2) (e) Reactor-1 (Fed-Batch Scheme 9 Part 3) (f) Reactor-2 (Plug Flow Scheme 9 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1019 2125 0027 000 2564 0077 1202600 0994 2125 0027 000 263 1119864 minus 02 1233

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1419 2135 0027 2119864 minus 11 1497 11 701560 1419 2135 0027 2119864 minus 11 1497 11 7015

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1302 2133 0027 4119864 minus 15 1807 0833 847900 125 2131 0027 4119864 minus 15 1946 0694 9121800 1192 213 0027 4119864 minus 15 2101 0539 985900 1254 2131 0027 4E minus 15 1936 0704 907900 1246 2131 0027 4E minus 15 1957 0683 917

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1771 2144 0027 0408 0965 1675 4525360 1544 2139 0027 0088 1251 1389 586720 1425 2136 0027 0001 1482 1158 6949240 1771 2144 0027 0408 0965 1675 4525240 1771 2144 0027 0408 0965 1675 4525

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 104 2667 0027 1119864 minus 06 2506 0134 1175900 1034 2126 0027 4119864 minus 15 2523 0117 1183

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 14 2135 0027 0624 217 047 1017360 1191 213 0027 0202 2307 0333 1081

Table 11 Summary of results

Schemenumber

119886 119887 119888 119889 Favored reactorRelationship

between 119886 119887 119888 and119889

1 1 1 1 1 Both equally 119886 + 119888 = 119887 + 119889

2 1 1 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

3 1 1 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

4 05 15 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

5 15 05 05 15 Both equally 119886 + 119888 = 119887 + 119889

6 05 15 15 05 Both equally 119886 + 119888 = 119887 + 119889

7 15 05 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

8 05 15 1 1 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

9 15 05 1 1 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

11 Conclusion

Under the simulated conditions elementary Second ordercompetitive consecutive reactions of the type mentioned in(1) yield the same amount of intermediate product R in bothideal fed batch and ideal Plug Flow Reactors for a constantconversion (99) of limiting reactant A Yield and selectivityof the product depends only on119870

11198702in both the reactors

However of the 8 nonelementary scenarios simulatedthree (Schemes 3 4 and 8) favor Plug Flow Reactor and threeother (Schemes 2 7 and 9) favor Fed Batch Reactor Twoothers (Schemes 5 and 6) like elementary reaction yield thesame in both Plug Flow Reactor and Fed batch reactor

Among the schemes simulated previously (Schemes 1 to9) the schemes giving increased yield R with reduced addi-tion time in Fed batch reactor favor Plug Flow Reactor andthe schemes giving increased yield with increased addition

ISRN Chemical Engineering 17

time in fed batch reactor favor Fed batch reactor This couldwell be a practical reckoner to screen the potential candidateamong the simulated schemes for Plug Flow Reactor eventhough this idea is only with respect to suitability of kineticparameters

The relationship between the exponents 119886 119887 119888 and 119889 andthe favourable reactor found in the simulation as shown inTable 11 is noteworthy

Nomenclature

1198701 Rate constant of reaction between A and

B in Litresdotmolminus1sdotsminus1K2 Rate constant of 2nd reaction between R

and B in Litresdotmolminus1sdotsminus1t Time s119905119886 Reactant B addition time in Fed Batch

Reactor s119905119898 Reaction mass maintenance time in Fed

Batch Reactor stlowast Space time in Plug Flow Reactor stend Space time for which each case of plug

flow rector simulation has been done s119903119909 Rate of change of species ldquoxrdquo

(molsdotLitreminus1sdotsminus1) ldquoxrdquo is representative ofspecies A B R S C and D

119862119909= 119873119909119881 Concentration molsdotLitreminus1 of any species

say ldquoxrdquoV Reaction volume m3119873119909 Number of Kg moles of species ldquoxrdquo k mol

NB119905 Total Kg moles of reactant B used inreaction k mol

NA119905 Total kg moles of reactant A used inreaction k mol

119881119886119905 Volume of stream containing reactant B

m3119881119905 Total volume of contents including

streams of reactant A and reactant B m3v Plug Flow Reactor volume m3v1015840 Volumetric flow rate m3s119865119909 Molar flow rate (k molsdotsminus1) of species ldquoxrdquo

which is representative of species A B RS C and D

NB119905NA119905 Ratio of total moles of B to total moles ofA taken for the reaction

119873119909119865 Final kg moles of the species ldquoxrdquo k mol

WR Weight kg of total intermediate (desired)product formed at the end of reaction inFed Batch Reactor and at the end of agiven space time in the Plug Flow Reactor

Acknowledgment

The author would like to thank Chandra Kanth Terupally ofPlanck Technical Hyderabad India for providing adequatesupport in MATLAB Programming

References

[1] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1998

[2] J F Richardson and D G Peacock Coulson and RichardsonrsquosChemical Engineering Chemical and Biochemical Reactors andProcess Control Butterworth-Heinemann Boston Mass USA3rd edition 1994

[3] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart I model developmentrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 750162 16pages 2012

[4] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart II design protocolsrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 65432113 pages 2012

[5] J R Bourne ldquoMixing and the selectivity of chemical reactionsrdquoOrganic Process Research andDevelopment vol 7 no 4 pp 471ndash508 2003

[6] J Bałdyga J R Bourne and S J Hearn ldquoInteraction betweenchemical reactions and mixing on various scalesrdquo ChemicalEngineering Science vol 52 no 4 pp 457ndash466 1997

[7] N G Anderson ldquoPractical use of continuous processing indeveloping and scaling up laboratory processesrdquo Organic Pro-cess Research and Development vol 5 no 6 pp 613ndash621 2001

[8] C Brechtelsbauer and F Ricard ldquoReaction engineering evalua-tion and utilization of static mixer technology for the synthesisof pharmaceuticalsrdquoOrganic Process Research andDevelopmentvol 5 no 6 pp 646ndash651 2001

[9] Z Anxionnaz M Cabassud C Gourdon and P Tochon ldquoHeatexchangerreactors (HEX reactors) concepts technologiesstate-of-the-artrdquo Chemical Engineering and Processing vol 47no 12 pp 2029ndash2050 2008

[10] P Barthe C Guermeur O Lobet et al ldquoContinuous multi-injection reactor for multipurpose productionmdashpart Irdquo Chem-ical Engineering and Technology vol 31 no 8 pp 1146ndash11542008

[11] M Patel and G Gasparini ldquoReactor technology flow reactorsand dynamic mixingrdquo Specialty Chemicals Magazine 2009

[12] X W Ni ldquoContinuous oscilatory baffled reactor technologyrdquoin Innovations in Pharmaceutical TechnologymdashManufacturingpp 90ndash96 2006 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=392

[13] L Proctor ldquoContinuous chemical processingrdquo in Innovationsin Pharmaceutical Technology pp 84ndash88 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=290

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4 ISRN Chemical Engineering

Table 2 (a) Reactor-1 (Fed-Batch Scheme 1 Part 1) (b) Reactor-2 (Plug Flow Scheme 1 Part 1) (c) Reactor-1 (Fed-Batch Scheme 1 Part2) (d) Reactor-2 (Plug Flow Scheme 1 Part 2) (e) Reactor-1 (Fed-Batch Scheme 1 Part 3) (f) Reactor-2 (Plug Flow Scheme 1 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 129 2132 0027 000 184 0801 8623600 129 2132 0027 000 184 08 8624

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1291 2132 0026 1119864 minus 26 1838 0803 861460 1291 2132 0026 000 1838 0803 8614

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 129 2132 0027 2119864 minus 06 184 08 8624900 129 2132 0027 1119864 minus 06 184 08 86241800 129 2132 0027 9119864 minus 07 184 08 8624900 129 2132 0027 1E minus 06 184 08 8624900 129 2132 0027 1E minus 06 184 08 8624

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1313 2133 0027 0061 184 08 8625360 1296 2132 0027 0016 184 08 8624720 129 2132 0027 4119864 minus 04 184 08 8624240 1313 2133 0027 0061 184 08 8625240 1313 2133 0027 0061 184 08 8625

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 106 2127 0027 0002 2454 0186 1151900 106 2127 0027 0001 2454 0186 1151

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1117 2128 0027 0152 2454 0186 1151360 1086 2127 0027 007 2454 0186 1151

Rate constant values are assumed with three individualscenarios first one with ratio of119870

1to1198702considered as 10 and

1198701considered as 100sdotLitresdotmolminus1sdotsminus1 the second one with the

same ratio of11987011198702but with the119870

1as 01 Litresdotmolminus1sdotsminus1 and

the third one with the ratio of 11987011198702considered as 50 with

the1198701considered as 01 Litresdotmolminus1sdotsminus1

Totally nine different sets of exponents (ie a b c d)have been considered such that the overall order of reactionremains two Hence there are 9 sets of reactions schemeseach scheme is analyzed for the mentioned 3 sets of kineticconstants Molecular weight of each of the componentsinvolved in the reaction is considered in consistent with thestoichiometry given in (1) The values are given in Table 1

In this study the molecular weights are used to convertmoles into Kg and vice versa (molecular weight values arearbitrary in Table 1)

Total solvent quantity considered is 2m3 Quantity ofsolvent m3 used to make a stream of reactant A is called Sol

R Quantity of solvent m3 used to make a stream of reactantB is called Sol A For the ensuing simulations amount ofsolvent used in both the reacting streams is same that is SolA(Sol A + Sol R) = 05 unless specified otherwise in therespective calculationoutput datagraphsTableThe effect ofrelative concentration of both the streams on kinetics is nottreated at length however few cases with Sol A(Sol R + SolA) = 025 and 075 have been simulated to indicate the changein reaction selectivity with change in relative concentration ofreactant streams

As the reaction considered is in liquid phase constantvolume reaction system is supposed except for the volumechange due to addition of the solution of second component(reactant B) in to the solution of 1st component (reactant A)in the Fed-Batch Reactor There is no volume change dueto reaction Volumetric flow rate in Plug Flow Reactor isconsidered constantThe volume in liters constituted by eachof the starting materials (A and B) is assumed 05 times theweight in kg of the respective components

ISRN Chemical Engineering 5

005

115

225

3

0 100 200 300 400 500 600 700Con

cent

ratio

n (m

olL

)

Time (s)minus05

(a)

0

05

1

15

2

25

0 100 200 300 400 500 600 700Time (s)

Volu

me (

m3)

(b)

002040608

112141618

0 05 1 15 2 25 3 35

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cent

ratio

n (m

olL

)

Time (s)minus02

(c)

0

05

1

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0 500 1000 1500 2000 2500C

once

ntra

tion

(mol

L)

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(d)

002040608

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0 100 200 300 400

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n (m

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(e)

0

05

1

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0 500 1000 1500 2000 2500

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cent

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)

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(f)

002040608

1121416

0 100

AB

RS

200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(g)

Figure 4 (a) Concentration as a function of time Fed-Batch Reactor (Scheme 1 Part 1 Case 1 119905119886= 60 s 119905

119898= 600 s (see Scheme 1

in Supplementary Material available online at httpdxdoiorg1011552013591546) (b) Volume as a function of time Fed-Batch Reactor(Scheme 1 Part 1 Case-1 119905

119886= 60 s 119905

119898= 600 s) (c) Concentration as a function of time Plug Flow Reactor (Scheme 1 Part 1 119905end = 6 s for

brevity graph is plotted for 3 s only) (d) Concentration as a function of time Fed-Batch Reactor (Scheme 1 Part 2 119905119886= 900 s 119905

119898= 1200 s)

(e) Concentration as a function of time Plug Flow Reactor (Scheme 1 Part 2 119905end = 360 s) (f) Concentration as a function of time Fed-BatchReactor (Scheme 1 Part 3 119905

119886= 900 s 119905

119898= 1200 s) (g) Concentration as a function of time Plug Flow Reactor (Scheme 1 Part 3 119905end = 360 s)

6 ISRN Chemical Engineering

0

05

1

15

2

25

3

0 100 200 300 400 500 600 700

Con

cent

ratio

n (m

olL

)

Time (s)minus05

(a)

0

02

04

06

08

1

12

14

16

0 05 1 15 2 25 3 35

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(b)

0

05

1

15

2

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0 500 1000 1500 2000 2500

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cent

ratio

n (m

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)

Time (s)minus05

AB

RS

(c)

0

02

04

06

08

1

12

14

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0 100 200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)

AB

RS

(d)

Figure 5 (a) Concentration as a function of time Fed-Batch Reactor (Scheme 2 Part 1 119905119886= 60 s 119905

119898= 600 s) (b) Concentration as a function

of time Plug Flow Reactor (Scheme 2 Part 1 119905end = 6 s for brevity graph is plotted for 3 s only) (c) Concentration as a function of timeFed-Batch Reactor (Scheme 2 Part 2 119905

119886= 900 s 119905

119898= 1200 s) (d) Concentration as a function of time Plug Flow Reactor (Scheme 2 Part 2

119905end = 360 s)

The quantity of A used in the entire study is 200Kgs Incase of Fed batch reactor the simulation has been done forvarious addition time of streamB reactionmaintenance timeis chosen such that further change in concentration profileis practically absent The constancy of concentration profiletowards the end of 119905

119898can be observed in the concentration

profiles obtained from MATLAB Also 119905119898

is maintainedconstant for a given set of 119870

11198702in order to make the

comparative study relevant In case of Plug Flow Reactor thesimulation is done for different reaction end time as differentcase The reaction time 119905end in Plug Flow Reactor refers tospace time

In case of Fed-Batch Reactor the addition rate is consid-ered constant across the entire addition time

The reaction is run in both the reactors for a specifiedextent of conversion that is 99 of reactant A conversionis the reaction end point For a prechosen 119905

119886 119905119898 and 119905end the

99 conversion of reactant A is ensured by adjusting the totalmoles of reactant B that is by adjusting 119873B119905119873A119905 final 99conversion of reactant A is achieved for predefined cases of 119905

119886

(s) 119905119898(s) and 119905end (s)

The previously mentioned assumptions and basis havebeen considered keeping in mind that the actual reactionscenarios in the industry can be understood and interpretedin the light of the conclusions arrived at in this simulationstudy

The concentration profiles given in the subsequent sec-tions are intended only to showcase the pattern of thecorresponding reaction scheme The quantitative details ofsuch graphs are given in the tables for the respective cases

6 Simulation Accuracy

Solution to the previouslymentioned simultaneous nonlineardifferential equations ((5) and (11)) has been obtained by thesoftware MATLAB which entailed its default Explicit Runge-Kutta (45) Variable step (Dormand-Prince Pair) methodThe calculation tolerance has been set at a default 01with step limits adjusted such that step limits n and n10seconds would return the final results matching up to 3decimal points When the gap between reactor-1 and reactor-2 results narrowsbecomes more significant towards arriving

ISRN Chemical Engineering 7

112

211

37 115

3

116

7

117

3

118

1

118

5

101

3 103

210

52

105

9

106

1

106

2

106

3

106

3

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 6 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 2 Part 2)

at a conclusion tolerance is squeezed further to 001 withthe same step limit criteria as done for the simulation withtolerance 01

7 Simulation (Scheme 1 119886 = 119887 = 119888 = 119889 = 1 ieElementary Reaction)

71 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 In Tables 2(a) and 2(b) simulation results for two

cases have been captured Figures 4(a) and 4(c) are sampleconcentration profiles of reaction species in ideal Fed Batchand ideal Plug Flow Reactor Figure 4(b) is the graphicalrepresentation of reaction volume in Fed-Batch Reactor

It can be observed in Figure 4(a) that with 119905119898= 600 s

further concentration change (reaction) is negligible As theaddition rate of reagent B considered in this simulation studyis constant the fed batch volume increases linearly till 119905 =119905119886 During Reaction maintenance time 119905

119898 the Fed-Batch

volume remains constant

72 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Figures 4(d) and 4(e) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

In Tables 2(c) and 2(d) results for all simulated cases havebeen captured and the data lines (rows) 4 and 5 correspondto the fraction Sol A(Sol A + Sol R) = 025 and 075respectively

73 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and

1198702= 0002 Figures 4(f) and 4(g) are sample concentration

profiles of reaction species in ideal Fed Batch and ideal PlugFlow Reactors

In Tables 2(e) and 2(f) simulation results for two caseshave been captured

Tables 2(a) to 2(f) show that elementary reaction of thetype given in (1) yields the same amount of desired product infed batch reactor and Plug Flow Reactor Moreover the yield

values in Part 2 remain the same as those in Part 1 That isbecause119870

11198702values remain the same in both Part 1 and Part

2 even though the individual 1198701and 119870

2values are different

It is to be noted that in Part 3 yield values are different fromthat in Part 1 and Part 2That is because119870

11198702value in Part 3

is different from those in Part 1 and Part 2 The change in therelative concentration of both the reacting streams (as shownin Table 2(c) rows 2 4 and 5 and Table 2(d) rows 1 4 and 5)does not have any effect on the yield

8 Simulation (Scheme 2 119886 = 119887 = 1 119888 = 15 119889 =05 Nonelementary)

81 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 Figures 5(a) and 5(b) are sample concentration

profiles of reaction species in ideal Fed Batch and ideal PlugFlow Reactors

In Tables 3(a) and 3(b) simulation results for two casessimulated have been captured

82 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Figures 5(c) and 5(d) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

In Tables 3(c) and 3(d) and Figure 6 results for all thesimulated cases have been captured The data lines (rows) 4and 5 in Tables 3(c) and 3(d) correspond to the fraction SolA(Sol A + Sol R) = 025 and 075 respectively

The yield values for varying reaction times are capturedin Figure 6

83 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 In Tables 3(e) and 3(f) simulation results for two caseshave been captured

Tables 3(a) and 3(f) and Figure 6 show that this nonelementary reaction yields higher desired product in Fed-Batch Reactor than in Continuous Plug Flow Reactor

In Figure 6 the Plug Flow Reactor yield initially increaseswith the increase in reaction time (ie lengthier reactor pipe)consequently 119873B119905119873A119905 value decreases as shown in Tables3(c) and 3(d) (ie reduced consumption of Reactant B)However the Plug Flow Reactor yield saturates out belowFed-Batch Reactor yield Overall the Fed Batch Reactoryields higher product R than Plug Flow Reactor even thoughthere is a very marginal change in yield for the change in therelative concentration of reacting streams (Table 3(c) rows 24 and 5) in Fed Batch Reactor

9 Simulation (Scheme 3 119886 = 119887 = 1 119888 = 05 119889 =15 Nonelementary)

91 Part 1 (Cases 1 and 2)1198701= 100119870

11198702= 10 and119870

2= 10

In Tables 4(a) and 4(b) simulation results for two cases havebeen captured

Figures 7(a) and 7(b) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

8 ISRN Chemical Engineering

Table 3 (a) Reactor-1 (Fed-Batch Scheme 2 Part 1) (b) Reactor-2 (Plug Flow Scheme 2 Part 1) (c) Reactor-1 (Fed-Batch Scheme 2 Part2) (d) Reactor-2 (Plug Flow Scheme 2 Part 2) (e) Reactor-1 (Fed-Batch Scheme 2 Part 3) (f) Reactor-2 (Plug Flow Scheme 2 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1005 2132 0027 000 2598 0042 122600 0996 2125 0027 000 2625 0015 123

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 113 2128 0027 6119864 minus 06 2267 04 106360 113 2128 0027 3119864 minus 35 2267 04 1063

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1072 2127 0027 0005 2425 0215 1137900 1059 2166 0027 0004 2459 0181 11531800 1048 2126 0027 0004 2491 0149 1167900 1061 2127 0027 0004 2456 0184 1151900 1058 2126 0027 0004 2463 0177 1154

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1221 2131 0027 0135 216 048 1013360 118 2129 0027 0068 2202 0438 1032720 1145 2129 0027 0018 2244 0396 1052240 1221 2131 0027 0135 216 048 1013240 1221 2131 0027 0135 216 048 1013

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1009 2125 0027 0008 2599 0041 1218900 1006 2125 0027 0008 2605 0035 1221

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1094 2127 0027 0083 2545 0095 1193360 1058 2126 0027 0097 2555 0085 1198

92 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 4(c) and 4(d) and Figure 8 results for othersimulated cases have been captured

The last two data lines (rows) in Tables 4(c) and 4(d)correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

Figures 7(c) and 7(d) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

The yield values for varying reaction times are capturedin Figure 8

93 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 InTables 4(e) and 4(f) simulation results for two caseshave been captured

Tables 4(a)ndash4(f) and Figure 8 show that this non elemen-tary reaction yields higher desired product R in Plug FlowReactor than in Fed-Batch Reactor

It is to be noted that the reduced addition time in FedBatch Reactor results in increased product yield Howeverin actual practice heat transfer and other limitations of thereactor vessel could possibly determine the minimum addi-tion time beyond which addition time cannot be reduced Sothe Fed Batch reactor yield is limited

It is to be further noted that there is a marginal changein the yield in Fed Batch reactor with the change in relativeconcentration of reacting streams (Table 4(c) rows 2 4 and5) However this variation is too low to catch up with PlugFlow Reactor yield

10 Simulations (for the Rest of the Schemes)

101 (Scheme 4 119886 = 05 119887 = 15 119888 = 05 119889 = 15Nonelementary)

1011 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and 119870

2=

10 See Tables 5(a) and 5(b)

ISRN Chemical Engineering 9

Table 4 (a) Reactor-1 (Fed-Batch Scheme 3 Part 1) (b) Reactor-2 (Plug Flow Scheme 3 Part 1) (c) Reactor-1 (Fed-Batch Scheme 3 Part2) (d) Reactor-2 (Plug Flow Scheme 3 Part 2) (e) Reactor-1 (Fed-Batch Scheme 3 Part 3) (f) Reactor-2 (Plug Flow Scheme 3 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1909 2148 0027 000 019 245 9600 195 2149 0027 000 0079 2561 4

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1448 2136 0027 3119864 minus 08 1419 12 665260 1447 2136 0027 3119864 minus 05 142 12 6657

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1598 214 0027 5119864 minus 13 1019 1621 4776900 1661 2142 0027 3119864 minus 13 0851 1789 39891800 1722 2143 0027 7119864 minus 13 0687 1953 3222900 1655 2141 0027 1119864 minus 12 0868 1772 4067900 1668 2142 0027 1119864 minus 12 0833 1807 3905

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1448 2136 0027 4119864 minus 12 1419 1221 6652360 1448 2136 0027 4119864 minus 12 1419 1221 6652720 1448 2136 0027 4119864 minus 12 1419 1221 6652240 1448 2136 0027 4E minus 12 1419 1221 6652240 1448 2136 0027 4E minus 12 1419 1221 6652

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1214 213 0027 0000 2043 0597 9575900 1251 2131 0027 0000 1943 0697 9107

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1172 2129 0027 0071 2227 0413 1044360 1163 2129 0027 0003 2182 0458 1023

1012 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 The data lines (rows) 4 and 5 in Tables 5(c) and 5(d)correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 9

1013 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 (See Tables 5(e) and 5(f)) Tables 5(a)ndash5(f) and Figure 9show that this non elementary reaction yields higher desiredproduct in Plug Flow Reactor than in Fed-Batch Reactor

As in Scheme 3 the reduced addition time in Fed BatchReactor results in increased product yield However in actualpractice heat transfer and other limitations of the reactorvessel could possibly determine the minimum addition timebeyond which addition time cannot be reduced So the FedBatch reactor yield is limited

Themarginal change in the yield in FedBatch reactorwithrelative concentration of reacting streams (Table 5(c) rows 24 and 5) may be noted However this variation is too low tocatch up with Plug Flow Reactor yield

102 (Scheme 5 119886 = 15 119887 = 05 119888 = 05 119889 = 15Nonelementary)

1021 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 6(a) and 6(b)

1022 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 119870

2=

001 In Table 6(c) and 6(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1023 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 119870

2=

0002 (See Tables 6(e) and 6(f)) Tables 6(a)ndash6(f) show that

10 ISRN Chemical Engineering

0

05

1

15

2

25

3

0 100 200 300 400 500 600 700

Con

cent

ratio

n (m

olL

)

Time (s)minus05

(a)

002040608

112141618

2

0 05 1 15 2 25 3 35

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(b)

0

05

1

15

2

25

3

0 500 1000 1500 2000 2500Time (s)minus05

Con

cent

ratio

n (m

olL

)

AB

RS

(c)

002040608

112141618

2

0 100

AB

RS

200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(d)

Figure 7 (a) Concentration as a function of time Fed-Batch Reactor (Scheme 3 Part 1 119905119886= 60 s 119905

119898= 600 s) (b) Concentration as a function

of time Plug Flow Reactor (Scheme 3 Part 1 119905end = 6 s for brevity graph is plotted for 3 s only) (c) Concentration as a function of timeFed-Batch Reactor (Scheme 3 Part 2 119905

119886= 900 s 119905

119898= 1200 s) (d) Concentration as a function of time Plug Flow Reactor (Scheme 3 Part 2

119905end = 360 s)

this type of nonelementary reaction yields the same amountof desired product in fed batch reactor and in Plug FlowReactor Moreover the yield values in Part 2 remain the sameas those in Part 1 That is because 119870

11198702values remain the

same in both Part 1 and Part 2 even though the individual1198701and119870

2values are different It is to be noted that in Part 3

yield values are different from that in Part 1 and Part 2That isbecause 119870

11198702value in Part 3 is different from those in Part

1 and Part 2The change in the relative concentration of both the

reacting streams (as shown in Table 6(c) rows 2 4 and 5 andTable 6(d) rows 1 4 and 5) does not have any effect on theyield

103 (Scheme 6 119886 = 05 119887 = 15 119888 = 15 119889 = 05Nonelementary)

1031 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 7(a) and 7(b)

1032 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 7(c) and 7(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1033 Part 3 (Cases 1 and 2)1198701= 01119870

11198702= 50 and119870

2=

0002 (See Tables 7(e) and 7(f)) Tables 7(a)ndash7(f) show thatthis type of nonelementary reaction also behaves similar toelementary reaction and nonelementary reaction Scheme 5with respect to product selectivity that is the yield is the samein both the reactors The change in the relative concentrationof both the reacting streams (as shown in Table 7(c) rows 24 and 5 and Table 7(d) rows 1 4 and 5) does not have anyeffect on the yield

104 (Scheme 7 119886 = 15 119887 = 05 119888 = 15 119889 = 05Nonelementary)

1041 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 8(a) and 8(b)

ISRN Chemical Engineering 11

Table 5 (a) Reactor-1 (Fed-Batch Scheme 4 Part 1) (b) Reactor-2 (Plug Flow Scheme 4 Part 1) (c) Reactor-1 (Fed-Batch Scheme 4 Part2) (d) Reactor-2 (Plug Flow Scheme 4 Part 2) (e) Reactor-1 (Fed-Batch Scheme 4 Part 3) (f) Reactor-2 (Plug Flow Scheme 4 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1927 2148 0027 000 0141 2499 7600 1961 2149 0027 000 005 259 2

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1313 2133 0027 6119864 minus 08 1778 09 833460 1313 2667 0027 6119864 minus 08 1778 09 8334

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1562 2139 0027 000 1113 1527 5219900 1654 2141 0027 1119864 minus 10 0869 1771 40751800 1733 2143 0027 6119864 minus 13 0658 1982 3085900 1646 2141 0027 1E minus 12 0868 175 4171900 1662 2142 0027 1E minus 10 0848 1792 3974

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1313 2133 0027 000 1778 0862 8334360 1313 2133 0027 000 1778 0862 8334720 1313 2133 0027 8119864 minus 12 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1203 213 0027 7119864 minus 11 2071 0569 971900 1265 2132 0027 6119864 minus 11 1907 0733 894

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 2997 2128 0027 0021 2304 0336 108360 1124 2128 0027 000 2284 0356 107

609

477

6

398

9

322

2

746

266

52

665

2

665

2

0 500 1000 1500 2000ta or tend (s)

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 8 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 3 Part 2)

ta or tend (s)

741

521

9

407

5

308

5

857

1

8334

833

4

833

4

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 9 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 4 Part 2)

12 ISRN Chemical Engineering

Table 6 (a) Reactor-1 (Fed-Batch Scheme 5 Part 1) (b) Reactor-2 (Plug Flow Scheme 5 Part 2) (c) Reactor-1 (Fed-Batch Scheme 5 Part2) (d) Reactor-2 (Plug Flow Scheme 5 Part 2) (e) Reactor-1 (Fed-Batch Scheme 5 Part 2) (f) Reactor-2 (Plug Flow Scheme 5 Part 2)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1664 2142 0027 000 0843 1797 3954600 1664 2149 0027 000 0843 1797 3954

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1664 2142 0027 6119864 minus 09 0843 18 395460 1664 2142 0027 6119864 minus 09 0843 18 3954

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1664 2142 0027 1119864 minus 10 0844 1796 3956900 1664 2142 0027 1119864 minus 10 0843 1797 39541800 1664 2142 0027 1119864 minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1794 2145 0027 0348 0843 1797 3954360 1672 2142 0027 0022 0844 1796 3954720 1664 2142 0027 000 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 124 2131 0027 7119864 minus 11 1973 0667 9249900 124 2131 0027 7119864 minus 11 1973 0667 9248

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1442 2136 0027 0537 1973 0667 9247360 1277 2132 0027 0099 1973 0667 9248

116

211

79

119

5

120

7

121

2

121

8

122

500

280

6 101

5

104

9

105

1

105

1

105

1

105

1

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 10 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 7 Part 2)

1042 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 8(c) and 8(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 10

1043 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 8(c) and 8(d)) Tables 7(a)ndash

7(d) and Figure 10 show that this non elementary reactionyields higher desired product in Fed-Batch Reactor than inContinuous Plug Flow Reactor

As in Scheme 2 the Plug Flow Reactor yield initiallyincreases with the increase in reaction time (ie lengthierreactor pipe) consequently 119873B119905119873A119905 value decreases asshown in Table 8(d) (ie reduced consumption of ReactantB) However the Plug Flow Reactor yield saturates out below

ISRN Chemical Engineering 13

Table 7 (a) Reactor-1 (Fed-Batch Scheme 6 Part 1) (b) Reactor-2 (Plug Flow Scheme 6 Part 1) (c) Reactor-1 (Fed-Batch Scheme 6 Part2) (d) Reactor-2 (Plug Flow Scheme 6 Part 2) (e) Reactor-1 (Fed-Batch Scheme 6 Part 3) (f) Reactor-2 (Plug Flow Scheme 6 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1121 2128 0027 000 229 035 1073600 1121 2128 0027 000 229 035 1073

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1121 2128 0027 4119864 minus 04 229 04 107360 1121 2128 0027 5119864 minus 06 229 04 1073

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7119864 minus 03 229 035 10731800 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1152 2129 0027 0083 229 035 1073360 1139 2128 0027 0048 229 035 1073720 1128 2128 0027 0017 229 035 1073240 1152 2129 0027 0083 229 035 1073240 1152 2129 0027 0083 229 035 1073

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1022 2126 0027 0012 2568 0073 1204900 1022 2126 0027 0012 2567 0072 1203

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1058 2126 0027 0108 2567 0072 1204360 1042 2126 0027 0066 2568 0073 1204

Fed-Batch Reactor yield (Figure 10) Overall the Fed BatchReactor yields higher product R than Plug Flow Reactor eventhough there is a verymarginal change in yield for the changein the relative concentration of reacting streams (Table 8(c)rows 2 4 and 5)

105 (Scheme 8 a = 05 b = 15 c = 1 d = 1 Nonelementary)

1051 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 9(a) and 9(b)

1052 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 9(c) and 9(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 11

1053 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 9(e) and 9(f)) Tables 9(a)ndash9(f)

and Figure 11 show that this non elementary reaction yieldshigher desired product in Plug Flow Reactor than in Fed-Batch Reactor Also the yield in Fed batch reactor decreaseswith addition time

As in Scheme 3 and Scheme 4 the reduced additiontime in Fed Batch Reactor results in increased productyield However in actual practice heat transfer and otherlimitations of the reactor vessel could possibly determine theminimum addition time beyond which addition time cannotbe reduced So the Fed Batch reactor yield is limited

It is to be noted that there is amarginal change in the yieldin Fed Batch reactor with relative concentration of reacting

14 ISRN Chemical Engineering

Table 8 (a) Reactor-1 (Fed-Batch Scheme 7 Part 1) (b) Reactor-2 (Plug Flow Scheme 7 Part 1) (c) Reactor-1 (Fed-Batch Scheme 7 Part2) (d) Reactor-2 (Plug Flow Scheme 7 Part 2) (e) Reactor-1 (Fed-Batch Scheme 7 Part 3) (f) Reactor-2 (Plug Flow Scheme 7 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 0992 2125 0026 000 2636 0004 1236600 099 2125 0027 000 264 8119864 minus 05 1237

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1139 2128 0027 2119864 minus 11 2242 04 105160 1139 2128 0027 2119864 minus 11 2242 04 1051

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1037 2126 0027 5119864 minus 04 2515 0125 1179900 1024 2126 0027 3119864 minus 04 2548 0092 11951800 1014 2125 0027 1119864 minus 04 2576 0064 1207900 1025 2126 0027 3E minus 04 2547 0093 1194900 1024 2126 0027 3E minus 04 255 009 1195

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1757 2144 0027 0472 1067 1573 5002360 1397 2135 0027 0165 172 092 806720 1176 2129 0027 0021 2166 0474 1015240 1757 2144 0027 0472 1067 1573 5002240 1757 2144 0027 0472 1067 1573 5002

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 0998 2125 0027 0001 2619 0021 1228900 0996 2125 0027 9119864 minus 04 2624 0016 1230

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1372 2134 0027 0687 2309 0331 1082360 115 2129 0027 0258 2472 0168 1159

913

3

827

768

696

999

1

965

595

8

955

1

955

0 500 1000 1500 2000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 11 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 8 Part 2)

80 847 91

2

985 101

4

105

3

107

2

452

5 586 694

9

701

701

701

701

701

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 12 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 9 Part 2)

ISRN Chemical Engineering 15

Table 9 (a) Reactor-1 (Fed-Batch Scheme 8 Part 1) (b) Reactor-2 (Plug Flow Scheme 8 Part 1) (c) Reactor-1 (Fed-Batch Scheme 8 Part2) (d) Reactor-2 (Plug Flow Scheme 8 Part 2) (e) Reactor-1 (Fed-Batch Scheme 8 Part 3) (f) Reactor-2 (Plug Flow Scheme 8 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 176 2144 0027 000 0588 2052 275600 1892 2147 0027 000 0234 2406 110

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1216 213 0027 3119864 minus 26 2037 06 95560 1216 213 0027 0000 2037 06 955

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1318 2133 0027 6119864 minus 06 1765 0875 827900 1366 2124 0027 9119864 minus 06 1638 1002 7681800 1423 2136 0027 2119864 minus 05 1485 1155 696900 1359 2134 0027 8E minus 06 1656 0984 776900 1374 2667 0027 1E minus 05 1615 1025 757

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1218 213 0027 0029 206 058 9655360 1216 213 0027 0008 2044 0596 958720 1216 213 0027 2119864 minus 04 2038 0602 9551240 1218 213 0027 0029 206 058 9655240 1218 213 0027 0029 206 058 9655

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1078 2127 0027 0003 2408 0232 1129900 109 2127 0027 0002 2376 0264 1114

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1076 2127 0027 0087 2498 0142 1171360 1065 2127 0027 0046 2486 0154 1166

streams (Table 9(c) rows 2 4 and 5) However this variationis too low to catch up with Plug Flow Reactor yield

106 (Scheme 9 119886 = 15 119887 = 05 119888 = 1 and 119889 = 1Nonelementary)

1061 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 10(a) and 10(b)

1062 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Theyield values for varying reaction times are capturedin Figure 12

In Tables 10(c) and 10(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1063 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 Tables 10(a)ndash10(f) and Figure 12 show that

this nonelementary reaction yields higher desired productin Fed-Batch Reactor than in Continuous Plug Flow Reac-tor

As in Scheme 2 and Scheme 7 the Plug Flow Reactoryield initially increases with the increase in reaction time(ie lengthier reactor pipe) consequently 119873B119905119873A119905 valuedecreases (ie reduced consumption of Reactant B) How-ever the Plug Flow Reactor yield saturates out below Fed-Batch Reactor yield (Figure 12)

Overall the Fed Batch Reactor yields higher product Rthan Plug Flow Reactor even though there is a very marginalchange in yield for the change in the relative concentration ofreacting streams (Table 10(c) rows 2 4 and 5) in Fed-BatchReactor

16 ISRN Chemical Engineering

Table 10 (a) Reactor-1 (Fed-Batch Scheme 9 Part 1) (b) Reactor-2 (Plug Flow Scheme 9 Part 1) (c) Reactor-1 (Fed-Batch Scheme 9 Part2) (d) Reactor-2 (Plug Flow Scheme 9 Part 2) (e) Reactor-1 (Fed-Batch Scheme 9 Part 3) (f) Reactor-2 (Plug Flow Scheme 9 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1019 2125 0027 000 2564 0077 1202600 0994 2125 0027 000 263 1119864 minus 02 1233

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1419 2135 0027 2119864 minus 11 1497 11 701560 1419 2135 0027 2119864 minus 11 1497 11 7015

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1302 2133 0027 4119864 minus 15 1807 0833 847900 125 2131 0027 4119864 minus 15 1946 0694 9121800 1192 213 0027 4119864 minus 15 2101 0539 985900 1254 2131 0027 4E minus 15 1936 0704 907900 1246 2131 0027 4E minus 15 1957 0683 917

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1771 2144 0027 0408 0965 1675 4525360 1544 2139 0027 0088 1251 1389 586720 1425 2136 0027 0001 1482 1158 6949240 1771 2144 0027 0408 0965 1675 4525240 1771 2144 0027 0408 0965 1675 4525

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 104 2667 0027 1119864 minus 06 2506 0134 1175900 1034 2126 0027 4119864 minus 15 2523 0117 1183

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 14 2135 0027 0624 217 047 1017360 1191 213 0027 0202 2307 0333 1081

Table 11 Summary of results

Schemenumber

119886 119887 119888 119889 Favored reactorRelationship

between 119886 119887 119888 and119889

1 1 1 1 1 Both equally 119886 + 119888 = 119887 + 119889

2 1 1 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

3 1 1 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

4 05 15 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

5 15 05 05 15 Both equally 119886 + 119888 = 119887 + 119889

6 05 15 15 05 Both equally 119886 + 119888 = 119887 + 119889

7 15 05 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

8 05 15 1 1 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

9 15 05 1 1 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

11 Conclusion

Under the simulated conditions elementary Second ordercompetitive consecutive reactions of the type mentioned in(1) yield the same amount of intermediate product R in bothideal fed batch and ideal Plug Flow Reactors for a constantconversion (99) of limiting reactant A Yield and selectivityof the product depends only on119870

11198702in both the reactors

However of the 8 nonelementary scenarios simulatedthree (Schemes 3 4 and 8) favor Plug Flow Reactor and threeother (Schemes 2 7 and 9) favor Fed Batch Reactor Twoothers (Schemes 5 and 6) like elementary reaction yield thesame in both Plug Flow Reactor and Fed batch reactor

Among the schemes simulated previously (Schemes 1 to9) the schemes giving increased yield R with reduced addi-tion time in Fed batch reactor favor Plug Flow Reactor andthe schemes giving increased yield with increased addition

ISRN Chemical Engineering 17

time in fed batch reactor favor Fed batch reactor This couldwell be a practical reckoner to screen the potential candidateamong the simulated schemes for Plug Flow Reactor eventhough this idea is only with respect to suitability of kineticparameters

The relationship between the exponents 119886 119887 119888 and 119889 andthe favourable reactor found in the simulation as shown inTable 11 is noteworthy

Nomenclature

1198701 Rate constant of reaction between A and

B in Litresdotmolminus1sdotsminus1K2 Rate constant of 2nd reaction between R

and B in Litresdotmolminus1sdotsminus1t Time s119905119886 Reactant B addition time in Fed Batch

Reactor s119905119898 Reaction mass maintenance time in Fed

Batch Reactor stlowast Space time in Plug Flow Reactor stend Space time for which each case of plug

flow rector simulation has been done s119903119909 Rate of change of species ldquoxrdquo

(molsdotLitreminus1sdotsminus1) ldquoxrdquo is representative ofspecies A B R S C and D

119862119909= 119873119909119881 Concentration molsdotLitreminus1 of any species

say ldquoxrdquoV Reaction volume m3119873119909 Number of Kg moles of species ldquoxrdquo k mol

NB119905 Total Kg moles of reactant B used inreaction k mol

NA119905 Total kg moles of reactant A used inreaction k mol

119881119886119905 Volume of stream containing reactant B

m3119881119905 Total volume of contents including

streams of reactant A and reactant B m3v Plug Flow Reactor volume m3v1015840 Volumetric flow rate m3s119865119909 Molar flow rate (k molsdotsminus1) of species ldquoxrdquo

which is representative of species A B RS C and D

NB119905NA119905 Ratio of total moles of B to total moles ofA taken for the reaction

119873119909119865 Final kg moles of the species ldquoxrdquo k mol

WR Weight kg of total intermediate (desired)product formed at the end of reaction inFed Batch Reactor and at the end of agiven space time in the Plug Flow Reactor

Acknowledgment

The author would like to thank Chandra Kanth Terupally ofPlanck Technical Hyderabad India for providing adequatesupport in MATLAB Programming

References

[1] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1998

[2] J F Richardson and D G Peacock Coulson and RichardsonrsquosChemical Engineering Chemical and Biochemical Reactors andProcess Control Butterworth-Heinemann Boston Mass USA3rd edition 1994

[3] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart I model developmentrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 750162 16pages 2012

[4] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart II design protocolsrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 65432113 pages 2012

[5] J R Bourne ldquoMixing and the selectivity of chemical reactionsrdquoOrganic Process Research andDevelopment vol 7 no 4 pp 471ndash508 2003

[6] J Bałdyga J R Bourne and S J Hearn ldquoInteraction betweenchemical reactions and mixing on various scalesrdquo ChemicalEngineering Science vol 52 no 4 pp 457ndash466 1997

[7] N G Anderson ldquoPractical use of continuous processing indeveloping and scaling up laboratory processesrdquo Organic Pro-cess Research and Development vol 5 no 6 pp 613ndash621 2001

[8] C Brechtelsbauer and F Ricard ldquoReaction engineering evalua-tion and utilization of static mixer technology for the synthesisof pharmaceuticalsrdquoOrganic Process Research andDevelopmentvol 5 no 6 pp 646ndash651 2001

[9] Z Anxionnaz M Cabassud C Gourdon and P Tochon ldquoHeatexchangerreactors (HEX reactors) concepts technologiesstate-of-the-artrdquo Chemical Engineering and Processing vol 47no 12 pp 2029ndash2050 2008

[10] P Barthe C Guermeur O Lobet et al ldquoContinuous multi-injection reactor for multipurpose productionmdashpart Irdquo Chem-ical Engineering and Technology vol 31 no 8 pp 1146ndash11542008

[11] M Patel and G Gasparini ldquoReactor technology flow reactorsand dynamic mixingrdquo Specialty Chemicals Magazine 2009

[12] X W Ni ldquoContinuous oscilatory baffled reactor technologyrdquoin Innovations in Pharmaceutical TechnologymdashManufacturingpp 90ndash96 2006 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=392

[13] L Proctor ldquoContinuous chemical processingrdquo in Innovationsin Pharmaceutical Technology pp 84ndash88 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=290

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ISRN Chemical Engineering 5

005

115

225

3

0 100 200 300 400 500 600 700Con

cent

ratio

n (m

olL

)

Time (s)minus05

(a)

0

05

1

15

2

25

0 100 200 300 400 500 600 700Time (s)

Volu

me (

m3)

(b)

002040608

112141618

0 05 1 15 2 25 3 35

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(c)

0

05

1

15

2

25

3

0 500 1000 1500 2000 2500C

once

ntra

tion

(mol

L)

Time (s)minus05

(d)

002040608

112141618

0 100 200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(e)

0

05

1

15

2

25

3

0 500 1000 1500 2000 2500

Con

cent

ratio

n (m

olL

)

Time (s)minus05

(f)

002040608

1121416

0 100

AB

RS

200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(g)

Figure 4 (a) Concentration as a function of time Fed-Batch Reactor (Scheme 1 Part 1 Case 1 119905119886= 60 s 119905

119898= 600 s (see Scheme 1

in Supplementary Material available online at httpdxdoiorg1011552013591546) (b) Volume as a function of time Fed-Batch Reactor(Scheme 1 Part 1 Case-1 119905

119886= 60 s 119905

119898= 600 s) (c) Concentration as a function of time Plug Flow Reactor (Scheme 1 Part 1 119905end = 6 s for

brevity graph is plotted for 3 s only) (d) Concentration as a function of time Fed-Batch Reactor (Scheme 1 Part 2 119905119886= 900 s 119905

119898= 1200 s)

(e) Concentration as a function of time Plug Flow Reactor (Scheme 1 Part 2 119905end = 360 s) (f) Concentration as a function of time Fed-BatchReactor (Scheme 1 Part 3 119905

119886= 900 s 119905

119898= 1200 s) (g) Concentration as a function of time Plug Flow Reactor (Scheme 1 Part 3 119905end = 360 s)

6 ISRN Chemical Engineering

0

05

1

15

2

25

3

0 100 200 300 400 500 600 700

Con

cent

ratio

n (m

olL

)

Time (s)minus05

(a)

0

02

04

06

08

1

12

14

16

0 05 1 15 2 25 3 35

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(b)

0

05

1

15

2

25

3

0 500 1000 1500 2000 2500

Con

cent

ratio

n (m

olL

)

Time (s)minus05

AB

RS

(c)

0

02

04

06

08

1

12

14

16

0 100 200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)

AB

RS

(d)

Figure 5 (a) Concentration as a function of time Fed-Batch Reactor (Scheme 2 Part 1 119905119886= 60 s 119905

119898= 600 s) (b) Concentration as a function

of time Plug Flow Reactor (Scheme 2 Part 1 119905end = 6 s for brevity graph is plotted for 3 s only) (c) Concentration as a function of timeFed-Batch Reactor (Scheme 2 Part 2 119905

119886= 900 s 119905

119898= 1200 s) (d) Concentration as a function of time Plug Flow Reactor (Scheme 2 Part 2

119905end = 360 s)

The quantity of A used in the entire study is 200Kgs Incase of Fed batch reactor the simulation has been done forvarious addition time of streamB reactionmaintenance timeis chosen such that further change in concentration profileis practically absent The constancy of concentration profiletowards the end of 119905

119898can be observed in the concentration

profiles obtained from MATLAB Also 119905119898

is maintainedconstant for a given set of 119870

11198702in order to make the

comparative study relevant In case of Plug Flow Reactor thesimulation is done for different reaction end time as differentcase The reaction time 119905end in Plug Flow Reactor refers tospace time

In case of Fed-Batch Reactor the addition rate is consid-ered constant across the entire addition time

The reaction is run in both the reactors for a specifiedextent of conversion that is 99 of reactant A conversionis the reaction end point For a prechosen 119905

119886 119905119898 and 119905end the

99 conversion of reactant A is ensured by adjusting the totalmoles of reactant B that is by adjusting 119873B119905119873A119905 final 99conversion of reactant A is achieved for predefined cases of 119905

119886

(s) 119905119898(s) and 119905end (s)

The previously mentioned assumptions and basis havebeen considered keeping in mind that the actual reactionscenarios in the industry can be understood and interpretedin the light of the conclusions arrived at in this simulationstudy

The concentration profiles given in the subsequent sec-tions are intended only to showcase the pattern of thecorresponding reaction scheme The quantitative details ofsuch graphs are given in the tables for the respective cases

6 Simulation Accuracy

Solution to the previouslymentioned simultaneous nonlineardifferential equations ((5) and (11)) has been obtained by thesoftware MATLAB which entailed its default Explicit Runge-Kutta (45) Variable step (Dormand-Prince Pair) methodThe calculation tolerance has been set at a default 01with step limits adjusted such that step limits n and n10seconds would return the final results matching up to 3decimal points When the gap between reactor-1 and reactor-2 results narrowsbecomes more significant towards arriving

ISRN Chemical Engineering 7

112

211

37 115

3

116

7

117

3

118

1

118

5

101

3 103

210

52

105

9

106

1

106

2

106

3

106

3

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 6 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 2 Part 2)

at a conclusion tolerance is squeezed further to 001 withthe same step limit criteria as done for the simulation withtolerance 01

7 Simulation (Scheme 1 119886 = 119887 = 119888 = 119889 = 1 ieElementary Reaction)

71 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 In Tables 2(a) and 2(b) simulation results for two

cases have been captured Figures 4(a) and 4(c) are sampleconcentration profiles of reaction species in ideal Fed Batchand ideal Plug Flow Reactor Figure 4(b) is the graphicalrepresentation of reaction volume in Fed-Batch Reactor

It can be observed in Figure 4(a) that with 119905119898= 600 s

further concentration change (reaction) is negligible As theaddition rate of reagent B considered in this simulation studyis constant the fed batch volume increases linearly till 119905 =119905119886 During Reaction maintenance time 119905

119898 the Fed-Batch

volume remains constant

72 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Figures 4(d) and 4(e) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

In Tables 2(c) and 2(d) results for all simulated cases havebeen captured and the data lines (rows) 4 and 5 correspondto the fraction Sol A(Sol A + Sol R) = 025 and 075respectively

73 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and

1198702= 0002 Figures 4(f) and 4(g) are sample concentration

profiles of reaction species in ideal Fed Batch and ideal PlugFlow Reactors

In Tables 2(e) and 2(f) simulation results for two caseshave been captured

Tables 2(a) to 2(f) show that elementary reaction of thetype given in (1) yields the same amount of desired product infed batch reactor and Plug Flow Reactor Moreover the yield

values in Part 2 remain the same as those in Part 1 That isbecause119870

11198702values remain the same in both Part 1 and Part

2 even though the individual 1198701and 119870

2values are different

It is to be noted that in Part 3 yield values are different fromthat in Part 1 and Part 2That is because119870

11198702value in Part 3

is different from those in Part 1 and Part 2 The change in therelative concentration of both the reacting streams (as shownin Table 2(c) rows 2 4 and 5 and Table 2(d) rows 1 4 and 5)does not have any effect on the yield

8 Simulation (Scheme 2 119886 = 119887 = 1 119888 = 15 119889 =05 Nonelementary)

81 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 Figures 5(a) and 5(b) are sample concentration

profiles of reaction species in ideal Fed Batch and ideal PlugFlow Reactors

In Tables 3(a) and 3(b) simulation results for two casessimulated have been captured

82 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Figures 5(c) and 5(d) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

In Tables 3(c) and 3(d) and Figure 6 results for all thesimulated cases have been captured The data lines (rows) 4and 5 in Tables 3(c) and 3(d) correspond to the fraction SolA(Sol A + Sol R) = 025 and 075 respectively

The yield values for varying reaction times are capturedin Figure 6

83 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 In Tables 3(e) and 3(f) simulation results for two caseshave been captured

Tables 3(a) and 3(f) and Figure 6 show that this nonelementary reaction yields higher desired product in Fed-Batch Reactor than in Continuous Plug Flow Reactor

In Figure 6 the Plug Flow Reactor yield initially increaseswith the increase in reaction time (ie lengthier reactor pipe)consequently 119873B119905119873A119905 value decreases as shown in Tables3(c) and 3(d) (ie reduced consumption of Reactant B)However the Plug Flow Reactor yield saturates out belowFed-Batch Reactor yield Overall the Fed Batch Reactoryields higher product R than Plug Flow Reactor even thoughthere is a very marginal change in yield for the change in therelative concentration of reacting streams (Table 3(c) rows 24 and 5) in Fed Batch Reactor

9 Simulation (Scheme 3 119886 = 119887 = 1 119888 = 05 119889 =15 Nonelementary)

91 Part 1 (Cases 1 and 2)1198701= 100119870

11198702= 10 and119870

2= 10

In Tables 4(a) and 4(b) simulation results for two cases havebeen captured

Figures 7(a) and 7(b) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

8 ISRN Chemical Engineering

Table 3 (a) Reactor-1 (Fed-Batch Scheme 2 Part 1) (b) Reactor-2 (Plug Flow Scheme 2 Part 1) (c) Reactor-1 (Fed-Batch Scheme 2 Part2) (d) Reactor-2 (Plug Flow Scheme 2 Part 2) (e) Reactor-1 (Fed-Batch Scheme 2 Part 3) (f) Reactor-2 (Plug Flow Scheme 2 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1005 2132 0027 000 2598 0042 122600 0996 2125 0027 000 2625 0015 123

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 113 2128 0027 6119864 minus 06 2267 04 106360 113 2128 0027 3119864 minus 35 2267 04 1063

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1072 2127 0027 0005 2425 0215 1137900 1059 2166 0027 0004 2459 0181 11531800 1048 2126 0027 0004 2491 0149 1167900 1061 2127 0027 0004 2456 0184 1151900 1058 2126 0027 0004 2463 0177 1154

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1221 2131 0027 0135 216 048 1013360 118 2129 0027 0068 2202 0438 1032720 1145 2129 0027 0018 2244 0396 1052240 1221 2131 0027 0135 216 048 1013240 1221 2131 0027 0135 216 048 1013

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1009 2125 0027 0008 2599 0041 1218900 1006 2125 0027 0008 2605 0035 1221

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1094 2127 0027 0083 2545 0095 1193360 1058 2126 0027 0097 2555 0085 1198

92 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 4(c) and 4(d) and Figure 8 results for othersimulated cases have been captured

The last two data lines (rows) in Tables 4(c) and 4(d)correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

Figures 7(c) and 7(d) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

The yield values for varying reaction times are capturedin Figure 8

93 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 InTables 4(e) and 4(f) simulation results for two caseshave been captured

Tables 4(a)ndash4(f) and Figure 8 show that this non elemen-tary reaction yields higher desired product R in Plug FlowReactor than in Fed-Batch Reactor

It is to be noted that the reduced addition time in FedBatch Reactor results in increased product yield Howeverin actual practice heat transfer and other limitations of thereactor vessel could possibly determine the minimum addi-tion time beyond which addition time cannot be reduced Sothe Fed Batch reactor yield is limited

It is to be further noted that there is a marginal changein the yield in Fed Batch reactor with the change in relativeconcentration of reacting streams (Table 4(c) rows 2 4 and5) However this variation is too low to catch up with PlugFlow Reactor yield

10 Simulations (for the Rest of the Schemes)

101 (Scheme 4 119886 = 05 119887 = 15 119888 = 05 119889 = 15Nonelementary)

1011 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and 119870

2=

10 See Tables 5(a) and 5(b)

ISRN Chemical Engineering 9

Table 4 (a) Reactor-1 (Fed-Batch Scheme 3 Part 1) (b) Reactor-2 (Plug Flow Scheme 3 Part 1) (c) Reactor-1 (Fed-Batch Scheme 3 Part2) (d) Reactor-2 (Plug Flow Scheme 3 Part 2) (e) Reactor-1 (Fed-Batch Scheme 3 Part 3) (f) Reactor-2 (Plug Flow Scheme 3 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1909 2148 0027 000 019 245 9600 195 2149 0027 000 0079 2561 4

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1448 2136 0027 3119864 minus 08 1419 12 665260 1447 2136 0027 3119864 minus 05 142 12 6657

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1598 214 0027 5119864 minus 13 1019 1621 4776900 1661 2142 0027 3119864 minus 13 0851 1789 39891800 1722 2143 0027 7119864 minus 13 0687 1953 3222900 1655 2141 0027 1119864 minus 12 0868 1772 4067900 1668 2142 0027 1119864 minus 12 0833 1807 3905

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1448 2136 0027 4119864 minus 12 1419 1221 6652360 1448 2136 0027 4119864 minus 12 1419 1221 6652720 1448 2136 0027 4119864 minus 12 1419 1221 6652240 1448 2136 0027 4E minus 12 1419 1221 6652240 1448 2136 0027 4E minus 12 1419 1221 6652

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1214 213 0027 0000 2043 0597 9575900 1251 2131 0027 0000 1943 0697 9107

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1172 2129 0027 0071 2227 0413 1044360 1163 2129 0027 0003 2182 0458 1023

1012 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 The data lines (rows) 4 and 5 in Tables 5(c) and 5(d)correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 9

1013 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 (See Tables 5(e) and 5(f)) Tables 5(a)ndash5(f) and Figure 9show that this non elementary reaction yields higher desiredproduct in Plug Flow Reactor than in Fed-Batch Reactor

As in Scheme 3 the reduced addition time in Fed BatchReactor results in increased product yield However in actualpractice heat transfer and other limitations of the reactorvessel could possibly determine the minimum addition timebeyond which addition time cannot be reduced So the FedBatch reactor yield is limited

Themarginal change in the yield in FedBatch reactorwithrelative concentration of reacting streams (Table 5(c) rows 24 and 5) may be noted However this variation is too low tocatch up with Plug Flow Reactor yield

102 (Scheme 5 119886 = 15 119887 = 05 119888 = 05 119889 = 15Nonelementary)

1021 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 6(a) and 6(b)

1022 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 119870

2=

001 In Table 6(c) and 6(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1023 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 119870

2=

0002 (See Tables 6(e) and 6(f)) Tables 6(a)ndash6(f) show that

10 ISRN Chemical Engineering

0

05

1

15

2

25

3

0 100 200 300 400 500 600 700

Con

cent

ratio

n (m

olL

)

Time (s)minus05

(a)

002040608

112141618

2

0 05 1 15 2 25 3 35

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(b)

0

05

1

15

2

25

3

0 500 1000 1500 2000 2500Time (s)minus05

Con

cent

ratio

n (m

olL

)

AB

RS

(c)

002040608

112141618

2

0 100

AB

RS

200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(d)

Figure 7 (a) Concentration as a function of time Fed-Batch Reactor (Scheme 3 Part 1 119905119886= 60 s 119905

119898= 600 s) (b) Concentration as a function

of time Plug Flow Reactor (Scheme 3 Part 1 119905end = 6 s for brevity graph is plotted for 3 s only) (c) Concentration as a function of timeFed-Batch Reactor (Scheme 3 Part 2 119905

119886= 900 s 119905

119898= 1200 s) (d) Concentration as a function of time Plug Flow Reactor (Scheme 3 Part 2

119905end = 360 s)

this type of nonelementary reaction yields the same amountof desired product in fed batch reactor and in Plug FlowReactor Moreover the yield values in Part 2 remain the sameas those in Part 1 That is because 119870

11198702values remain the

same in both Part 1 and Part 2 even though the individual1198701and119870

2values are different It is to be noted that in Part 3

yield values are different from that in Part 1 and Part 2That isbecause 119870

11198702value in Part 3 is different from those in Part

1 and Part 2The change in the relative concentration of both the

reacting streams (as shown in Table 6(c) rows 2 4 and 5 andTable 6(d) rows 1 4 and 5) does not have any effect on theyield

103 (Scheme 6 119886 = 05 119887 = 15 119888 = 15 119889 = 05Nonelementary)

1031 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 7(a) and 7(b)

1032 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 7(c) and 7(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1033 Part 3 (Cases 1 and 2)1198701= 01119870

11198702= 50 and119870

2=

0002 (See Tables 7(e) and 7(f)) Tables 7(a)ndash7(f) show thatthis type of nonelementary reaction also behaves similar toelementary reaction and nonelementary reaction Scheme 5with respect to product selectivity that is the yield is the samein both the reactors The change in the relative concentrationof both the reacting streams (as shown in Table 7(c) rows 24 and 5 and Table 7(d) rows 1 4 and 5) does not have anyeffect on the yield

104 (Scheme 7 119886 = 15 119887 = 05 119888 = 15 119889 = 05Nonelementary)

1041 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 8(a) and 8(b)

ISRN Chemical Engineering 11

Table 5 (a) Reactor-1 (Fed-Batch Scheme 4 Part 1) (b) Reactor-2 (Plug Flow Scheme 4 Part 1) (c) Reactor-1 (Fed-Batch Scheme 4 Part2) (d) Reactor-2 (Plug Flow Scheme 4 Part 2) (e) Reactor-1 (Fed-Batch Scheme 4 Part 3) (f) Reactor-2 (Plug Flow Scheme 4 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1927 2148 0027 000 0141 2499 7600 1961 2149 0027 000 005 259 2

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1313 2133 0027 6119864 minus 08 1778 09 833460 1313 2667 0027 6119864 minus 08 1778 09 8334

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1562 2139 0027 000 1113 1527 5219900 1654 2141 0027 1119864 minus 10 0869 1771 40751800 1733 2143 0027 6119864 minus 13 0658 1982 3085900 1646 2141 0027 1E minus 12 0868 175 4171900 1662 2142 0027 1E minus 10 0848 1792 3974

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1313 2133 0027 000 1778 0862 8334360 1313 2133 0027 000 1778 0862 8334720 1313 2133 0027 8119864 minus 12 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1203 213 0027 7119864 minus 11 2071 0569 971900 1265 2132 0027 6119864 minus 11 1907 0733 894

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 2997 2128 0027 0021 2304 0336 108360 1124 2128 0027 000 2284 0356 107

609

477

6

398

9

322

2

746

266

52

665

2

665

2

0 500 1000 1500 2000ta or tend (s)

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 8 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 3 Part 2)

ta or tend (s)

741

521

9

407

5

308

5

857

1

8334

833

4

833

4

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 9 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 4 Part 2)

12 ISRN Chemical Engineering

Table 6 (a) Reactor-1 (Fed-Batch Scheme 5 Part 1) (b) Reactor-2 (Plug Flow Scheme 5 Part 2) (c) Reactor-1 (Fed-Batch Scheme 5 Part2) (d) Reactor-2 (Plug Flow Scheme 5 Part 2) (e) Reactor-1 (Fed-Batch Scheme 5 Part 2) (f) Reactor-2 (Plug Flow Scheme 5 Part 2)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1664 2142 0027 000 0843 1797 3954600 1664 2149 0027 000 0843 1797 3954

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1664 2142 0027 6119864 minus 09 0843 18 395460 1664 2142 0027 6119864 minus 09 0843 18 3954

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1664 2142 0027 1119864 minus 10 0844 1796 3956900 1664 2142 0027 1119864 minus 10 0843 1797 39541800 1664 2142 0027 1119864 minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1794 2145 0027 0348 0843 1797 3954360 1672 2142 0027 0022 0844 1796 3954720 1664 2142 0027 000 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 124 2131 0027 7119864 minus 11 1973 0667 9249900 124 2131 0027 7119864 minus 11 1973 0667 9248

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1442 2136 0027 0537 1973 0667 9247360 1277 2132 0027 0099 1973 0667 9248

116

211

79

119

5

120

7

121

2

121

8

122

500

280

6 101

5

104

9

105

1

105

1

105

1

105

1

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 10 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 7 Part 2)

1042 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 8(c) and 8(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 10

1043 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 8(c) and 8(d)) Tables 7(a)ndash

7(d) and Figure 10 show that this non elementary reactionyields higher desired product in Fed-Batch Reactor than inContinuous Plug Flow Reactor

As in Scheme 2 the Plug Flow Reactor yield initiallyincreases with the increase in reaction time (ie lengthierreactor pipe) consequently 119873B119905119873A119905 value decreases asshown in Table 8(d) (ie reduced consumption of ReactantB) However the Plug Flow Reactor yield saturates out below

ISRN Chemical Engineering 13

Table 7 (a) Reactor-1 (Fed-Batch Scheme 6 Part 1) (b) Reactor-2 (Plug Flow Scheme 6 Part 1) (c) Reactor-1 (Fed-Batch Scheme 6 Part2) (d) Reactor-2 (Plug Flow Scheme 6 Part 2) (e) Reactor-1 (Fed-Batch Scheme 6 Part 3) (f) Reactor-2 (Plug Flow Scheme 6 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1121 2128 0027 000 229 035 1073600 1121 2128 0027 000 229 035 1073

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1121 2128 0027 4119864 minus 04 229 04 107360 1121 2128 0027 5119864 minus 06 229 04 1073

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7119864 minus 03 229 035 10731800 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1152 2129 0027 0083 229 035 1073360 1139 2128 0027 0048 229 035 1073720 1128 2128 0027 0017 229 035 1073240 1152 2129 0027 0083 229 035 1073240 1152 2129 0027 0083 229 035 1073

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1022 2126 0027 0012 2568 0073 1204900 1022 2126 0027 0012 2567 0072 1203

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1058 2126 0027 0108 2567 0072 1204360 1042 2126 0027 0066 2568 0073 1204

Fed-Batch Reactor yield (Figure 10) Overall the Fed BatchReactor yields higher product R than Plug Flow Reactor eventhough there is a verymarginal change in yield for the changein the relative concentration of reacting streams (Table 8(c)rows 2 4 and 5)

105 (Scheme 8 a = 05 b = 15 c = 1 d = 1 Nonelementary)

1051 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 9(a) and 9(b)

1052 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 9(c) and 9(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 11

1053 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 9(e) and 9(f)) Tables 9(a)ndash9(f)

and Figure 11 show that this non elementary reaction yieldshigher desired product in Plug Flow Reactor than in Fed-Batch Reactor Also the yield in Fed batch reactor decreaseswith addition time

As in Scheme 3 and Scheme 4 the reduced additiontime in Fed Batch Reactor results in increased productyield However in actual practice heat transfer and otherlimitations of the reactor vessel could possibly determine theminimum addition time beyond which addition time cannotbe reduced So the Fed Batch reactor yield is limited

It is to be noted that there is amarginal change in the yieldin Fed Batch reactor with relative concentration of reacting

14 ISRN Chemical Engineering

Table 8 (a) Reactor-1 (Fed-Batch Scheme 7 Part 1) (b) Reactor-2 (Plug Flow Scheme 7 Part 1) (c) Reactor-1 (Fed-Batch Scheme 7 Part2) (d) Reactor-2 (Plug Flow Scheme 7 Part 2) (e) Reactor-1 (Fed-Batch Scheme 7 Part 3) (f) Reactor-2 (Plug Flow Scheme 7 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 0992 2125 0026 000 2636 0004 1236600 099 2125 0027 000 264 8119864 minus 05 1237

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1139 2128 0027 2119864 minus 11 2242 04 105160 1139 2128 0027 2119864 minus 11 2242 04 1051

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1037 2126 0027 5119864 minus 04 2515 0125 1179900 1024 2126 0027 3119864 minus 04 2548 0092 11951800 1014 2125 0027 1119864 minus 04 2576 0064 1207900 1025 2126 0027 3E minus 04 2547 0093 1194900 1024 2126 0027 3E minus 04 255 009 1195

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1757 2144 0027 0472 1067 1573 5002360 1397 2135 0027 0165 172 092 806720 1176 2129 0027 0021 2166 0474 1015240 1757 2144 0027 0472 1067 1573 5002240 1757 2144 0027 0472 1067 1573 5002

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 0998 2125 0027 0001 2619 0021 1228900 0996 2125 0027 9119864 minus 04 2624 0016 1230

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1372 2134 0027 0687 2309 0331 1082360 115 2129 0027 0258 2472 0168 1159

913

3

827

768

696

999

1

965

595

8

955

1

955

0 500 1000 1500 2000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 11 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 8 Part 2)

80 847 91

2

985 101

4

105

3

107

2

452

5 586 694

9

701

701

701

701

701

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 12 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 9 Part 2)

ISRN Chemical Engineering 15

Table 9 (a) Reactor-1 (Fed-Batch Scheme 8 Part 1) (b) Reactor-2 (Plug Flow Scheme 8 Part 1) (c) Reactor-1 (Fed-Batch Scheme 8 Part2) (d) Reactor-2 (Plug Flow Scheme 8 Part 2) (e) Reactor-1 (Fed-Batch Scheme 8 Part 3) (f) Reactor-2 (Plug Flow Scheme 8 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 176 2144 0027 000 0588 2052 275600 1892 2147 0027 000 0234 2406 110

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1216 213 0027 3119864 minus 26 2037 06 95560 1216 213 0027 0000 2037 06 955

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1318 2133 0027 6119864 minus 06 1765 0875 827900 1366 2124 0027 9119864 minus 06 1638 1002 7681800 1423 2136 0027 2119864 minus 05 1485 1155 696900 1359 2134 0027 8E minus 06 1656 0984 776900 1374 2667 0027 1E minus 05 1615 1025 757

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1218 213 0027 0029 206 058 9655360 1216 213 0027 0008 2044 0596 958720 1216 213 0027 2119864 minus 04 2038 0602 9551240 1218 213 0027 0029 206 058 9655240 1218 213 0027 0029 206 058 9655

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1078 2127 0027 0003 2408 0232 1129900 109 2127 0027 0002 2376 0264 1114

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1076 2127 0027 0087 2498 0142 1171360 1065 2127 0027 0046 2486 0154 1166

streams (Table 9(c) rows 2 4 and 5) However this variationis too low to catch up with Plug Flow Reactor yield

106 (Scheme 9 119886 = 15 119887 = 05 119888 = 1 and 119889 = 1Nonelementary)

1061 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 10(a) and 10(b)

1062 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Theyield values for varying reaction times are capturedin Figure 12

In Tables 10(c) and 10(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1063 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 Tables 10(a)ndash10(f) and Figure 12 show that

this nonelementary reaction yields higher desired productin Fed-Batch Reactor than in Continuous Plug Flow Reac-tor

As in Scheme 2 and Scheme 7 the Plug Flow Reactoryield initially increases with the increase in reaction time(ie lengthier reactor pipe) consequently 119873B119905119873A119905 valuedecreases (ie reduced consumption of Reactant B) How-ever the Plug Flow Reactor yield saturates out below Fed-Batch Reactor yield (Figure 12)

Overall the Fed Batch Reactor yields higher product Rthan Plug Flow Reactor even though there is a very marginalchange in yield for the change in the relative concentration ofreacting streams (Table 10(c) rows 2 4 and 5) in Fed-BatchReactor

16 ISRN Chemical Engineering

Table 10 (a) Reactor-1 (Fed-Batch Scheme 9 Part 1) (b) Reactor-2 (Plug Flow Scheme 9 Part 1) (c) Reactor-1 (Fed-Batch Scheme 9 Part2) (d) Reactor-2 (Plug Flow Scheme 9 Part 2) (e) Reactor-1 (Fed-Batch Scheme 9 Part 3) (f) Reactor-2 (Plug Flow Scheme 9 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1019 2125 0027 000 2564 0077 1202600 0994 2125 0027 000 263 1119864 minus 02 1233

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1419 2135 0027 2119864 minus 11 1497 11 701560 1419 2135 0027 2119864 minus 11 1497 11 7015

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1302 2133 0027 4119864 minus 15 1807 0833 847900 125 2131 0027 4119864 minus 15 1946 0694 9121800 1192 213 0027 4119864 minus 15 2101 0539 985900 1254 2131 0027 4E minus 15 1936 0704 907900 1246 2131 0027 4E minus 15 1957 0683 917

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1771 2144 0027 0408 0965 1675 4525360 1544 2139 0027 0088 1251 1389 586720 1425 2136 0027 0001 1482 1158 6949240 1771 2144 0027 0408 0965 1675 4525240 1771 2144 0027 0408 0965 1675 4525

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 104 2667 0027 1119864 minus 06 2506 0134 1175900 1034 2126 0027 4119864 minus 15 2523 0117 1183

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 14 2135 0027 0624 217 047 1017360 1191 213 0027 0202 2307 0333 1081

Table 11 Summary of results

Schemenumber

119886 119887 119888 119889 Favored reactorRelationship

between 119886 119887 119888 and119889

1 1 1 1 1 Both equally 119886 + 119888 = 119887 + 119889

2 1 1 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

3 1 1 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

4 05 15 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

5 15 05 05 15 Both equally 119886 + 119888 = 119887 + 119889

6 05 15 15 05 Both equally 119886 + 119888 = 119887 + 119889

7 15 05 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

8 05 15 1 1 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

9 15 05 1 1 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

11 Conclusion

Under the simulated conditions elementary Second ordercompetitive consecutive reactions of the type mentioned in(1) yield the same amount of intermediate product R in bothideal fed batch and ideal Plug Flow Reactors for a constantconversion (99) of limiting reactant A Yield and selectivityof the product depends only on119870

11198702in both the reactors

However of the 8 nonelementary scenarios simulatedthree (Schemes 3 4 and 8) favor Plug Flow Reactor and threeother (Schemes 2 7 and 9) favor Fed Batch Reactor Twoothers (Schemes 5 and 6) like elementary reaction yield thesame in both Plug Flow Reactor and Fed batch reactor

Among the schemes simulated previously (Schemes 1 to9) the schemes giving increased yield R with reduced addi-tion time in Fed batch reactor favor Plug Flow Reactor andthe schemes giving increased yield with increased addition

ISRN Chemical Engineering 17

time in fed batch reactor favor Fed batch reactor This couldwell be a practical reckoner to screen the potential candidateamong the simulated schemes for Plug Flow Reactor eventhough this idea is only with respect to suitability of kineticparameters

The relationship between the exponents 119886 119887 119888 and 119889 andthe favourable reactor found in the simulation as shown inTable 11 is noteworthy

Nomenclature

1198701 Rate constant of reaction between A and

B in Litresdotmolminus1sdotsminus1K2 Rate constant of 2nd reaction between R

and B in Litresdotmolminus1sdotsminus1t Time s119905119886 Reactant B addition time in Fed Batch

Reactor s119905119898 Reaction mass maintenance time in Fed

Batch Reactor stlowast Space time in Plug Flow Reactor stend Space time for which each case of plug

flow rector simulation has been done s119903119909 Rate of change of species ldquoxrdquo

(molsdotLitreminus1sdotsminus1) ldquoxrdquo is representative ofspecies A B R S C and D

119862119909= 119873119909119881 Concentration molsdotLitreminus1 of any species

say ldquoxrdquoV Reaction volume m3119873119909 Number of Kg moles of species ldquoxrdquo k mol

NB119905 Total Kg moles of reactant B used inreaction k mol

NA119905 Total kg moles of reactant A used inreaction k mol

119881119886119905 Volume of stream containing reactant B

m3119881119905 Total volume of contents including

streams of reactant A and reactant B m3v Plug Flow Reactor volume m3v1015840 Volumetric flow rate m3s119865119909 Molar flow rate (k molsdotsminus1) of species ldquoxrdquo

which is representative of species A B RS C and D

NB119905NA119905 Ratio of total moles of B to total moles ofA taken for the reaction

119873119909119865 Final kg moles of the species ldquoxrdquo k mol

WR Weight kg of total intermediate (desired)product formed at the end of reaction inFed Batch Reactor and at the end of agiven space time in the Plug Flow Reactor

Acknowledgment

The author would like to thank Chandra Kanth Terupally ofPlanck Technical Hyderabad India for providing adequatesupport in MATLAB Programming

References

[1] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1998

[2] J F Richardson and D G Peacock Coulson and RichardsonrsquosChemical Engineering Chemical and Biochemical Reactors andProcess Control Butterworth-Heinemann Boston Mass USA3rd edition 1994

[3] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart I model developmentrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 750162 16pages 2012

[4] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart II design protocolsrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 65432113 pages 2012

[5] J R Bourne ldquoMixing and the selectivity of chemical reactionsrdquoOrganic Process Research andDevelopment vol 7 no 4 pp 471ndash508 2003

[6] J Bałdyga J R Bourne and S J Hearn ldquoInteraction betweenchemical reactions and mixing on various scalesrdquo ChemicalEngineering Science vol 52 no 4 pp 457ndash466 1997

[7] N G Anderson ldquoPractical use of continuous processing indeveloping and scaling up laboratory processesrdquo Organic Pro-cess Research and Development vol 5 no 6 pp 613ndash621 2001

[8] C Brechtelsbauer and F Ricard ldquoReaction engineering evalua-tion and utilization of static mixer technology for the synthesisof pharmaceuticalsrdquoOrganic Process Research andDevelopmentvol 5 no 6 pp 646ndash651 2001

[9] Z Anxionnaz M Cabassud C Gourdon and P Tochon ldquoHeatexchangerreactors (HEX reactors) concepts technologiesstate-of-the-artrdquo Chemical Engineering and Processing vol 47no 12 pp 2029ndash2050 2008

[10] P Barthe C Guermeur O Lobet et al ldquoContinuous multi-injection reactor for multipurpose productionmdashpart Irdquo Chem-ical Engineering and Technology vol 31 no 8 pp 1146ndash11542008

[11] M Patel and G Gasparini ldquoReactor technology flow reactorsand dynamic mixingrdquo Specialty Chemicals Magazine 2009

[12] X W Ni ldquoContinuous oscilatory baffled reactor technologyrdquoin Innovations in Pharmaceutical TechnologymdashManufacturingpp 90ndash96 2006 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=392

[13] L Proctor ldquoContinuous chemical processingrdquo in Innovationsin Pharmaceutical Technology pp 84ndash88 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=290

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6 ISRN Chemical Engineering

0

05

1

15

2

25

3

0 100 200 300 400 500 600 700

Con

cent

ratio

n (m

olL

)

Time (s)minus05

(a)

0

02

04

06

08

1

12

14

16

0 05 1 15 2 25 3 35

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(b)

0

05

1

15

2

25

3

0 500 1000 1500 2000 2500

Con

cent

ratio

n (m

olL

)

Time (s)minus05

AB

RS

(c)

0

02

04

06

08

1

12

14

16

0 100 200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)

AB

RS

(d)

Figure 5 (a) Concentration as a function of time Fed-Batch Reactor (Scheme 2 Part 1 119905119886= 60 s 119905

119898= 600 s) (b) Concentration as a function

of time Plug Flow Reactor (Scheme 2 Part 1 119905end = 6 s for brevity graph is plotted for 3 s only) (c) Concentration as a function of timeFed-Batch Reactor (Scheme 2 Part 2 119905

119886= 900 s 119905

119898= 1200 s) (d) Concentration as a function of time Plug Flow Reactor (Scheme 2 Part 2

119905end = 360 s)

The quantity of A used in the entire study is 200Kgs Incase of Fed batch reactor the simulation has been done forvarious addition time of streamB reactionmaintenance timeis chosen such that further change in concentration profileis practically absent The constancy of concentration profiletowards the end of 119905

119898can be observed in the concentration

profiles obtained from MATLAB Also 119905119898

is maintainedconstant for a given set of 119870

11198702in order to make the

comparative study relevant In case of Plug Flow Reactor thesimulation is done for different reaction end time as differentcase The reaction time 119905end in Plug Flow Reactor refers tospace time

In case of Fed-Batch Reactor the addition rate is consid-ered constant across the entire addition time

The reaction is run in both the reactors for a specifiedextent of conversion that is 99 of reactant A conversionis the reaction end point For a prechosen 119905

119886 119905119898 and 119905end the

99 conversion of reactant A is ensured by adjusting the totalmoles of reactant B that is by adjusting 119873B119905119873A119905 final 99conversion of reactant A is achieved for predefined cases of 119905

119886

(s) 119905119898(s) and 119905end (s)

The previously mentioned assumptions and basis havebeen considered keeping in mind that the actual reactionscenarios in the industry can be understood and interpretedin the light of the conclusions arrived at in this simulationstudy

The concentration profiles given in the subsequent sec-tions are intended only to showcase the pattern of thecorresponding reaction scheme The quantitative details ofsuch graphs are given in the tables for the respective cases

6 Simulation Accuracy

Solution to the previouslymentioned simultaneous nonlineardifferential equations ((5) and (11)) has been obtained by thesoftware MATLAB which entailed its default Explicit Runge-Kutta (45) Variable step (Dormand-Prince Pair) methodThe calculation tolerance has been set at a default 01with step limits adjusted such that step limits n and n10seconds would return the final results matching up to 3decimal points When the gap between reactor-1 and reactor-2 results narrowsbecomes more significant towards arriving

ISRN Chemical Engineering 7

112

211

37 115

3

116

7

117

3

118

1

118

5

101

3 103

210

52

105

9

106

1

106

2

106

3

106

3

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 6 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 2 Part 2)

at a conclusion tolerance is squeezed further to 001 withthe same step limit criteria as done for the simulation withtolerance 01

7 Simulation (Scheme 1 119886 = 119887 = 119888 = 119889 = 1 ieElementary Reaction)

71 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 In Tables 2(a) and 2(b) simulation results for two

cases have been captured Figures 4(a) and 4(c) are sampleconcentration profiles of reaction species in ideal Fed Batchand ideal Plug Flow Reactor Figure 4(b) is the graphicalrepresentation of reaction volume in Fed-Batch Reactor

It can be observed in Figure 4(a) that with 119905119898= 600 s

further concentration change (reaction) is negligible As theaddition rate of reagent B considered in this simulation studyis constant the fed batch volume increases linearly till 119905 =119905119886 During Reaction maintenance time 119905

119898 the Fed-Batch

volume remains constant

72 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Figures 4(d) and 4(e) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

In Tables 2(c) and 2(d) results for all simulated cases havebeen captured and the data lines (rows) 4 and 5 correspondto the fraction Sol A(Sol A + Sol R) = 025 and 075respectively

73 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and

1198702= 0002 Figures 4(f) and 4(g) are sample concentration

profiles of reaction species in ideal Fed Batch and ideal PlugFlow Reactors

In Tables 2(e) and 2(f) simulation results for two caseshave been captured

Tables 2(a) to 2(f) show that elementary reaction of thetype given in (1) yields the same amount of desired product infed batch reactor and Plug Flow Reactor Moreover the yield

values in Part 2 remain the same as those in Part 1 That isbecause119870

11198702values remain the same in both Part 1 and Part

2 even though the individual 1198701and 119870

2values are different

It is to be noted that in Part 3 yield values are different fromthat in Part 1 and Part 2That is because119870

11198702value in Part 3

is different from those in Part 1 and Part 2 The change in therelative concentration of both the reacting streams (as shownin Table 2(c) rows 2 4 and 5 and Table 2(d) rows 1 4 and 5)does not have any effect on the yield

8 Simulation (Scheme 2 119886 = 119887 = 1 119888 = 15 119889 =05 Nonelementary)

81 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 Figures 5(a) and 5(b) are sample concentration

profiles of reaction species in ideal Fed Batch and ideal PlugFlow Reactors

In Tables 3(a) and 3(b) simulation results for two casessimulated have been captured

82 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Figures 5(c) and 5(d) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

In Tables 3(c) and 3(d) and Figure 6 results for all thesimulated cases have been captured The data lines (rows) 4and 5 in Tables 3(c) and 3(d) correspond to the fraction SolA(Sol A + Sol R) = 025 and 075 respectively

The yield values for varying reaction times are capturedin Figure 6

83 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 In Tables 3(e) and 3(f) simulation results for two caseshave been captured

Tables 3(a) and 3(f) and Figure 6 show that this nonelementary reaction yields higher desired product in Fed-Batch Reactor than in Continuous Plug Flow Reactor

In Figure 6 the Plug Flow Reactor yield initially increaseswith the increase in reaction time (ie lengthier reactor pipe)consequently 119873B119905119873A119905 value decreases as shown in Tables3(c) and 3(d) (ie reduced consumption of Reactant B)However the Plug Flow Reactor yield saturates out belowFed-Batch Reactor yield Overall the Fed Batch Reactoryields higher product R than Plug Flow Reactor even thoughthere is a very marginal change in yield for the change in therelative concentration of reacting streams (Table 3(c) rows 24 and 5) in Fed Batch Reactor

9 Simulation (Scheme 3 119886 = 119887 = 1 119888 = 05 119889 =15 Nonelementary)

91 Part 1 (Cases 1 and 2)1198701= 100119870

11198702= 10 and119870

2= 10

In Tables 4(a) and 4(b) simulation results for two cases havebeen captured

Figures 7(a) and 7(b) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

8 ISRN Chemical Engineering

Table 3 (a) Reactor-1 (Fed-Batch Scheme 2 Part 1) (b) Reactor-2 (Plug Flow Scheme 2 Part 1) (c) Reactor-1 (Fed-Batch Scheme 2 Part2) (d) Reactor-2 (Plug Flow Scheme 2 Part 2) (e) Reactor-1 (Fed-Batch Scheme 2 Part 3) (f) Reactor-2 (Plug Flow Scheme 2 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1005 2132 0027 000 2598 0042 122600 0996 2125 0027 000 2625 0015 123

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 113 2128 0027 6119864 minus 06 2267 04 106360 113 2128 0027 3119864 minus 35 2267 04 1063

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1072 2127 0027 0005 2425 0215 1137900 1059 2166 0027 0004 2459 0181 11531800 1048 2126 0027 0004 2491 0149 1167900 1061 2127 0027 0004 2456 0184 1151900 1058 2126 0027 0004 2463 0177 1154

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1221 2131 0027 0135 216 048 1013360 118 2129 0027 0068 2202 0438 1032720 1145 2129 0027 0018 2244 0396 1052240 1221 2131 0027 0135 216 048 1013240 1221 2131 0027 0135 216 048 1013

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1009 2125 0027 0008 2599 0041 1218900 1006 2125 0027 0008 2605 0035 1221

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1094 2127 0027 0083 2545 0095 1193360 1058 2126 0027 0097 2555 0085 1198

92 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 4(c) and 4(d) and Figure 8 results for othersimulated cases have been captured

The last two data lines (rows) in Tables 4(c) and 4(d)correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

Figures 7(c) and 7(d) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

The yield values for varying reaction times are capturedin Figure 8

93 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 InTables 4(e) and 4(f) simulation results for two caseshave been captured

Tables 4(a)ndash4(f) and Figure 8 show that this non elemen-tary reaction yields higher desired product R in Plug FlowReactor than in Fed-Batch Reactor

It is to be noted that the reduced addition time in FedBatch Reactor results in increased product yield Howeverin actual practice heat transfer and other limitations of thereactor vessel could possibly determine the minimum addi-tion time beyond which addition time cannot be reduced Sothe Fed Batch reactor yield is limited

It is to be further noted that there is a marginal changein the yield in Fed Batch reactor with the change in relativeconcentration of reacting streams (Table 4(c) rows 2 4 and5) However this variation is too low to catch up with PlugFlow Reactor yield

10 Simulations (for the Rest of the Schemes)

101 (Scheme 4 119886 = 05 119887 = 15 119888 = 05 119889 = 15Nonelementary)

1011 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and 119870

2=

10 See Tables 5(a) and 5(b)

ISRN Chemical Engineering 9

Table 4 (a) Reactor-1 (Fed-Batch Scheme 3 Part 1) (b) Reactor-2 (Plug Flow Scheme 3 Part 1) (c) Reactor-1 (Fed-Batch Scheme 3 Part2) (d) Reactor-2 (Plug Flow Scheme 3 Part 2) (e) Reactor-1 (Fed-Batch Scheme 3 Part 3) (f) Reactor-2 (Plug Flow Scheme 3 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1909 2148 0027 000 019 245 9600 195 2149 0027 000 0079 2561 4

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1448 2136 0027 3119864 minus 08 1419 12 665260 1447 2136 0027 3119864 minus 05 142 12 6657

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1598 214 0027 5119864 minus 13 1019 1621 4776900 1661 2142 0027 3119864 minus 13 0851 1789 39891800 1722 2143 0027 7119864 minus 13 0687 1953 3222900 1655 2141 0027 1119864 minus 12 0868 1772 4067900 1668 2142 0027 1119864 minus 12 0833 1807 3905

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1448 2136 0027 4119864 minus 12 1419 1221 6652360 1448 2136 0027 4119864 minus 12 1419 1221 6652720 1448 2136 0027 4119864 minus 12 1419 1221 6652240 1448 2136 0027 4E minus 12 1419 1221 6652240 1448 2136 0027 4E minus 12 1419 1221 6652

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1214 213 0027 0000 2043 0597 9575900 1251 2131 0027 0000 1943 0697 9107

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1172 2129 0027 0071 2227 0413 1044360 1163 2129 0027 0003 2182 0458 1023

1012 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 The data lines (rows) 4 and 5 in Tables 5(c) and 5(d)correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 9

1013 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 (See Tables 5(e) and 5(f)) Tables 5(a)ndash5(f) and Figure 9show that this non elementary reaction yields higher desiredproduct in Plug Flow Reactor than in Fed-Batch Reactor

As in Scheme 3 the reduced addition time in Fed BatchReactor results in increased product yield However in actualpractice heat transfer and other limitations of the reactorvessel could possibly determine the minimum addition timebeyond which addition time cannot be reduced So the FedBatch reactor yield is limited

Themarginal change in the yield in FedBatch reactorwithrelative concentration of reacting streams (Table 5(c) rows 24 and 5) may be noted However this variation is too low tocatch up with Plug Flow Reactor yield

102 (Scheme 5 119886 = 15 119887 = 05 119888 = 05 119889 = 15Nonelementary)

1021 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 6(a) and 6(b)

1022 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 119870

2=

001 In Table 6(c) and 6(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1023 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 119870

2=

0002 (See Tables 6(e) and 6(f)) Tables 6(a)ndash6(f) show that

10 ISRN Chemical Engineering

0

05

1

15

2

25

3

0 100 200 300 400 500 600 700

Con

cent

ratio

n (m

olL

)

Time (s)minus05

(a)

002040608

112141618

2

0 05 1 15 2 25 3 35

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(b)

0

05

1

15

2

25

3

0 500 1000 1500 2000 2500Time (s)minus05

Con

cent

ratio

n (m

olL

)

AB

RS

(c)

002040608

112141618

2

0 100

AB

RS

200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(d)

Figure 7 (a) Concentration as a function of time Fed-Batch Reactor (Scheme 3 Part 1 119905119886= 60 s 119905

119898= 600 s) (b) Concentration as a function

of time Plug Flow Reactor (Scheme 3 Part 1 119905end = 6 s for brevity graph is plotted for 3 s only) (c) Concentration as a function of timeFed-Batch Reactor (Scheme 3 Part 2 119905

119886= 900 s 119905

119898= 1200 s) (d) Concentration as a function of time Plug Flow Reactor (Scheme 3 Part 2

119905end = 360 s)

this type of nonelementary reaction yields the same amountof desired product in fed batch reactor and in Plug FlowReactor Moreover the yield values in Part 2 remain the sameas those in Part 1 That is because 119870

11198702values remain the

same in both Part 1 and Part 2 even though the individual1198701and119870

2values are different It is to be noted that in Part 3

yield values are different from that in Part 1 and Part 2That isbecause 119870

11198702value in Part 3 is different from those in Part

1 and Part 2The change in the relative concentration of both the

reacting streams (as shown in Table 6(c) rows 2 4 and 5 andTable 6(d) rows 1 4 and 5) does not have any effect on theyield

103 (Scheme 6 119886 = 05 119887 = 15 119888 = 15 119889 = 05Nonelementary)

1031 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 7(a) and 7(b)

1032 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 7(c) and 7(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1033 Part 3 (Cases 1 and 2)1198701= 01119870

11198702= 50 and119870

2=

0002 (See Tables 7(e) and 7(f)) Tables 7(a)ndash7(f) show thatthis type of nonelementary reaction also behaves similar toelementary reaction and nonelementary reaction Scheme 5with respect to product selectivity that is the yield is the samein both the reactors The change in the relative concentrationof both the reacting streams (as shown in Table 7(c) rows 24 and 5 and Table 7(d) rows 1 4 and 5) does not have anyeffect on the yield

104 (Scheme 7 119886 = 15 119887 = 05 119888 = 15 119889 = 05Nonelementary)

1041 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 8(a) and 8(b)

ISRN Chemical Engineering 11

Table 5 (a) Reactor-1 (Fed-Batch Scheme 4 Part 1) (b) Reactor-2 (Plug Flow Scheme 4 Part 1) (c) Reactor-1 (Fed-Batch Scheme 4 Part2) (d) Reactor-2 (Plug Flow Scheme 4 Part 2) (e) Reactor-1 (Fed-Batch Scheme 4 Part 3) (f) Reactor-2 (Plug Flow Scheme 4 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1927 2148 0027 000 0141 2499 7600 1961 2149 0027 000 005 259 2

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1313 2133 0027 6119864 minus 08 1778 09 833460 1313 2667 0027 6119864 minus 08 1778 09 8334

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1562 2139 0027 000 1113 1527 5219900 1654 2141 0027 1119864 minus 10 0869 1771 40751800 1733 2143 0027 6119864 minus 13 0658 1982 3085900 1646 2141 0027 1E minus 12 0868 175 4171900 1662 2142 0027 1E minus 10 0848 1792 3974

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1313 2133 0027 000 1778 0862 8334360 1313 2133 0027 000 1778 0862 8334720 1313 2133 0027 8119864 minus 12 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1203 213 0027 7119864 minus 11 2071 0569 971900 1265 2132 0027 6119864 minus 11 1907 0733 894

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 2997 2128 0027 0021 2304 0336 108360 1124 2128 0027 000 2284 0356 107

609

477

6

398

9

322

2

746

266

52

665

2

665

2

0 500 1000 1500 2000ta or tend (s)

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 8 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 3 Part 2)

ta or tend (s)

741

521

9

407

5

308

5

857

1

8334

833

4

833

4

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 9 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 4 Part 2)

12 ISRN Chemical Engineering

Table 6 (a) Reactor-1 (Fed-Batch Scheme 5 Part 1) (b) Reactor-2 (Plug Flow Scheme 5 Part 2) (c) Reactor-1 (Fed-Batch Scheme 5 Part2) (d) Reactor-2 (Plug Flow Scheme 5 Part 2) (e) Reactor-1 (Fed-Batch Scheme 5 Part 2) (f) Reactor-2 (Plug Flow Scheme 5 Part 2)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1664 2142 0027 000 0843 1797 3954600 1664 2149 0027 000 0843 1797 3954

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1664 2142 0027 6119864 minus 09 0843 18 395460 1664 2142 0027 6119864 minus 09 0843 18 3954

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1664 2142 0027 1119864 minus 10 0844 1796 3956900 1664 2142 0027 1119864 minus 10 0843 1797 39541800 1664 2142 0027 1119864 minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1794 2145 0027 0348 0843 1797 3954360 1672 2142 0027 0022 0844 1796 3954720 1664 2142 0027 000 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 124 2131 0027 7119864 minus 11 1973 0667 9249900 124 2131 0027 7119864 minus 11 1973 0667 9248

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1442 2136 0027 0537 1973 0667 9247360 1277 2132 0027 0099 1973 0667 9248

116

211

79

119

5

120

7

121

2

121

8

122

500

280

6 101

5

104

9

105

1

105

1

105

1

105

1

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 10 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 7 Part 2)

1042 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 8(c) and 8(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 10

1043 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 8(c) and 8(d)) Tables 7(a)ndash

7(d) and Figure 10 show that this non elementary reactionyields higher desired product in Fed-Batch Reactor than inContinuous Plug Flow Reactor

As in Scheme 2 the Plug Flow Reactor yield initiallyincreases with the increase in reaction time (ie lengthierreactor pipe) consequently 119873B119905119873A119905 value decreases asshown in Table 8(d) (ie reduced consumption of ReactantB) However the Plug Flow Reactor yield saturates out below

ISRN Chemical Engineering 13

Table 7 (a) Reactor-1 (Fed-Batch Scheme 6 Part 1) (b) Reactor-2 (Plug Flow Scheme 6 Part 1) (c) Reactor-1 (Fed-Batch Scheme 6 Part2) (d) Reactor-2 (Plug Flow Scheme 6 Part 2) (e) Reactor-1 (Fed-Batch Scheme 6 Part 3) (f) Reactor-2 (Plug Flow Scheme 6 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1121 2128 0027 000 229 035 1073600 1121 2128 0027 000 229 035 1073

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1121 2128 0027 4119864 minus 04 229 04 107360 1121 2128 0027 5119864 minus 06 229 04 1073

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7119864 minus 03 229 035 10731800 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1152 2129 0027 0083 229 035 1073360 1139 2128 0027 0048 229 035 1073720 1128 2128 0027 0017 229 035 1073240 1152 2129 0027 0083 229 035 1073240 1152 2129 0027 0083 229 035 1073

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1022 2126 0027 0012 2568 0073 1204900 1022 2126 0027 0012 2567 0072 1203

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1058 2126 0027 0108 2567 0072 1204360 1042 2126 0027 0066 2568 0073 1204

Fed-Batch Reactor yield (Figure 10) Overall the Fed BatchReactor yields higher product R than Plug Flow Reactor eventhough there is a verymarginal change in yield for the changein the relative concentration of reacting streams (Table 8(c)rows 2 4 and 5)

105 (Scheme 8 a = 05 b = 15 c = 1 d = 1 Nonelementary)

1051 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 9(a) and 9(b)

1052 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 9(c) and 9(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 11

1053 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 9(e) and 9(f)) Tables 9(a)ndash9(f)

and Figure 11 show that this non elementary reaction yieldshigher desired product in Plug Flow Reactor than in Fed-Batch Reactor Also the yield in Fed batch reactor decreaseswith addition time

As in Scheme 3 and Scheme 4 the reduced additiontime in Fed Batch Reactor results in increased productyield However in actual practice heat transfer and otherlimitations of the reactor vessel could possibly determine theminimum addition time beyond which addition time cannotbe reduced So the Fed Batch reactor yield is limited

It is to be noted that there is amarginal change in the yieldin Fed Batch reactor with relative concentration of reacting

14 ISRN Chemical Engineering

Table 8 (a) Reactor-1 (Fed-Batch Scheme 7 Part 1) (b) Reactor-2 (Plug Flow Scheme 7 Part 1) (c) Reactor-1 (Fed-Batch Scheme 7 Part2) (d) Reactor-2 (Plug Flow Scheme 7 Part 2) (e) Reactor-1 (Fed-Batch Scheme 7 Part 3) (f) Reactor-2 (Plug Flow Scheme 7 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 0992 2125 0026 000 2636 0004 1236600 099 2125 0027 000 264 8119864 minus 05 1237

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1139 2128 0027 2119864 minus 11 2242 04 105160 1139 2128 0027 2119864 minus 11 2242 04 1051

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1037 2126 0027 5119864 minus 04 2515 0125 1179900 1024 2126 0027 3119864 minus 04 2548 0092 11951800 1014 2125 0027 1119864 minus 04 2576 0064 1207900 1025 2126 0027 3E minus 04 2547 0093 1194900 1024 2126 0027 3E minus 04 255 009 1195

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1757 2144 0027 0472 1067 1573 5002360 1397 2135 0027 0165 172 092 806720 1176 2129 0027 0021 2166 0474 1015240 1757 2144 0027 0472 1067 1573 5002240 1757 2144 0027 0472 1067 1573 5002

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 0998 2125 0027 0001 2619 0021 1228900 0996 2125 0027 9119864 minus 04 2624 0016 1230

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1372 2134 0027 0687 2309 0331 1082360 115 2129 0027 0258 2472 0168 1159

913

3

827

768

696

999

1

965

595

8

955

1

955

0 500 1000 1500 2000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 11 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 8 Part 2)

80 847 91

2

985 101

4

105

3

107

2

452

5 586 694

9

701

701

701

701

701

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 12 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 9 Part 2)

ISRN Chemical Engineering 15

Table 9 (a) Reactor-1 (Fed-Batch Scheme 8 Part 1) (b) Reactor-2 (Plug Flow Scheme 8 Part 1) (c) Reactor-1 (Fed-Batch Scheme 8 Part2) (d) Reactor-2 (Plug Flow Scheme 8 Part 2) (e) Reactor-1 (Fed-Batch Scheme 8 Part 3) (f) Reactor-2 (Plug Flow Scheme 8 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 176 2144 0027 000 0588 2052 275600 1892 2147 0027 000 0234 2406 110

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1216 213 0027 3119864 minus 26 2037 06 95560 1216 213 0027 0000 2037 06 955

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1318 2133 0027 6119864 minus 06 1765 0875 827900 1366 2124 0027 9119864 minus 06 1638 1002 7681800 1423 2136 0027 2119864 minus 05 1485 1155 696900 1359 2134 0027 8E minus 06 1656 0984 776900 1374 2667 0027 1E minus 05 1615 1025 757

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1218 213 0027 0029 206 058 9655360 1216 213 0027 0008 2044 0596 958720 1216 213 0027 2119864 minus 04 2038 0602 9551240 1218 213 0027 0029 206 058 9655240 1218 213 0027 0029 206 058 9655

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1078 2127 0027 0003 2408 0232 1129900 109 2127 0027 0002 2376 0264 1114

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1076 2127 0027 0087 2498 0142 1171360 1065 2127 0027 0046 2486 0154 1166

streams (Table 9(c) rows 2 4 and 5) However this variationis too low to catch up with Plug Flow Reactor yield

106 (Scheme 9 119886 = 15 119887 = 05 119888 = 1 and 119889 = 1Nonelementary)

1061 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 10(a) and 10(b)

1062 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Theyield values for varying reaction times are capturedin Figure 12

In Tables 10(c) and 10(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1063 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 Tables 10(a)ndash10(f) and Figure 12 show that

this nonelementary reaction yields higher desired productin Fed-Batch Reactor than in Continuous Plug Flow Reac-tor

As in Scheme 2 and Scheme 7 the Plug Flow Reactoryield initially increases with the increase in reaction time(ie lengthier reactor pipe) consequently 119873B119905119873A119905 valuedecreases (ie reduced consumption of Reactant B) How-ever the Plug Flow Reactor yield saturates out below Fed-Batch Reactor yield (Figure 12)

Overall the Fed Batch Reactor yields higher product Rthan Plug Flow Reactor even though there is a very marginalchange in yield for the change in the relative concentration ofreacting streams (Table 10(c) rows 2 4 and 5) in Fed-BatchReactor

16 ISRN Chemical Engineering

Table 10 (a) Reactor-1 (Fed-Batch Scheme 9 Part 1) (b) Reactor-2 (Plug Flow Scheme 9 Part 1) (c) Reactor-1 (Fed-Batch Scheme 9 Part2) (d) Reactor-2 (Plug Flow Scheme 9 Part 2) (e) Reactor-1 (Fed-Batch Scheme 9 Part 3) (f) Reactor-2 (Plug Flow Scheme 9 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1019 2125 0027 000 2564 0077 1202600 0994 2125 0027 000 263 1119864 minus 02 1233

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1419 2135 0027 2119864 minus 11 1497 11 701560 1419 2135 0027 2119864 minus 11 1497 11 7015

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1302 2133 0027 4119864 minus 15 1807 0833 847900 125 2131 0027 4119864 minus 15 1946 0694 9121800 1192 213 0027 4119864 minus 15 2101 0539 985900 1254 2131 0027 4E minus 15 1936 0704 907900 1246 2131 0027 4E minus 15 1957 0683 917

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1771 2144 0027 0408 0965 1675 4525360 1544 2139 0027 0088 1251 1389 586720 1425 2136 0027 0001 1482 1158 6949240 1771 2144 0027 0408 0965 1675 4525240 1771 2144 0027 0408 0965 1675 4525

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 104 2667 0027 1119864 minus 06 2506 0134 1175900 1034 2126 0027 4119864 minus 15 2523 0117 1183

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 14 2135 0027 0624 217 047 1017360 1191 213 0027 0202 2307 0333 1081

Table 11 Summary of results

Schemenumber

119886 119887 119888 119889 Favored reactorRelationship

between 119886 119887 119888 and119889

1 1 1 1 1 Both equally 119886 + 119888 = 119887 + 119889

2 1 1 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

3 1 1 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

4 05 15 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

5 15 05 05 15 Both equally 119886 + 119888 = 119887 + 119889

6 05 15 15 05 Both equally 119886 + 119888 = 119887 + 119889

7 15 05 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

8 05 15 1 1 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

9 15 05 1 1 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

11 Conclusion

Under the simulated conditions elementary Second ordercompetitive consecutive reactions of the type mentioned in(1) yield the same amount of intermediate product R in bothideal fed batch and ideal Plug Flow Reactors for a constantconversion (99) of limiting reactant A Yield and selectivityof the product depends only on119870

11198702in both the reactors

However of the 8 nonelementary scenarios simulatedthree (Schemes 3 4 and 8) favor Plug Flow Reactor and threeother (Schemes 2 7 and 9) favor Fed Batch Reactor Twoothers (Schemes 5 and 6) like elementary reaction yield thesame in both Plug Flow Reactor and Fed batch reactor

Among the schemes simulated previously (Schemes 1 to9) the schemes giving increased yield R with reduced addi-tion time in Fed batch reactor favor Plug Flow Reactor andthe schemes giving increased yield with increased addition

ISRN Chemical Engineering 17

time in fed batch reactor favor Fed batch reactor This couldwell be a practical reckoner to screen the potential candidateamong the simulated schemes for Plug Flow Reactor eventhough this idea is only with respect to suitability of kineticparameters

The relationship between the exponents 119886 119887 119888 and 119889 andthe favourable reactor found in the simulation as shown inTable 11 is noteworthy

Nomenclature

1198701 Rate constant of reaction between A and

B in Litresdotmolminus1sdotsminus1K2 Rate constant of 2nd reaction between R

and B in Litresdotmolminus1sdotsminus1t Time s119905119886 Reactant B addition time in Fed Batch

Reactor s119905119898 Reaction mass maintenance time in Fed

Batch Reactor stlowast Space time in Plug Flow Reactor stend Space time for which each case of plug

flow rector simulation has been done s119903119909 Rate of change of species ldquoxrdquo

(molsdotLitreminus1sdotsminus1) ldquoxrdquo is representative ofspecies A B R S C and D

119862119909= 119873119909119881 Concentration molsdotLitreminus1 of any species

say ldquoxrdquoV Reaction volume m3119873119909 Number of Kg moles of species ldquoxrdquo k mol

NB119905 Total Kg moles of reactant B used inreaction k mol

NA119905 Total kg moles of reactant A used inreaction k mol

119881119886119905 Volume of stream containing reactant B

m3119881119905 Total volume of contents including

streams of reactant A and reactant B m3v Plug Flow Reactor volume m3v1015840 Volumetric flow rate m3s119865119909 Molar flow rate (k molsdotsminus1) of species ldquoxrdquo

which is representative of species A B RS C and D

NB119905NA119905 Ratio of total moles of B to total moles ofA taken for the reaction

119873119909119865 Final kg moles of the species ldquoxrdquo k mol

WR Weight kg of total intermediate (desired)product formed at the end of reaction inFed Batch Reactor and at the end of agiven space time in the Plug Flow Reactor

Acknowledgment

The author would like to thank Chandra Kanth Terupally ofPlanck Technical Hyderabad India for providing adequatesupport in MATLAB Programming

References

[1] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1998

[2] J F Richardson and D G Peacock Coulson and RichardsonrsquosChemical Engineering Chemical and Biochemical Reactors andProcess Control Butterworth-Heinemann Boston Mass USA3rd edition 1994

[3] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart I model developmentrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 750162 16pages 2012

[4] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart II design protocolsrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 65432113 pages 2012

[5] J R Bourne ldquoMixing and the selectivity of chemical reactionsrdquoOrganic Process Research andDevelopment vol 7 no 4 pp 471ndash508 2003

[6] J Bałdyga J R Bourne and S J Hearn ldquoInteraction betweenchemical reactions and mixing on various scalesrdquo ChemicalEngineering Science vol 52 no 4 pp 457ndash466 1997

[7] N G Anderson ldquoPractical use of continuous processing indeveloping and scaling up laboratory processesrdquo Organic Pro-cess Research and Development vol 5 no 6 pp 613ndash621 2001

[8] C Brechtelsbauer and F Ricard ldquoReaction engineering evalua-tion and utilization of static mixer technology for the synthesisof pharmaceuticalsrdquoOrganic Process Research andDevelopmentvol 5 no 6 pp 646ndash651 2001

[9] Z Anxionnaz M Cabassud C Gourdon and P Tochon ldquoHeatexchangerreactors (HEX reactors) concepts technologiesstate-of-the-artrdquo Chemical Engineering and Processing vol 47no 12 pp 2029ndash2050 2008

[10] P Barthe C Guermeur O Lobet et al ldquoContinuous multi-injection reactor for multipurpose productionmdashpart Irdquo Chem-ical Engineering and Technology vol 31 no 8 pp 1146ndash11542008

[11] M Patel and G Gasparini ldquoReactor technology flow reactorsand dynamic mixingrdquo Specialty Chemicals Magazine 2009

[12] X W Ni ldquoContinuous oscilatory baffled reactor technologyrdquoin Innovations in Pharmaceutical TechnologymdashManufacturingpp 90ndash96 2006 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=392

[13] L Proctor ldquoContinuous chemical processingrdquo in Innovationsin Pharmaceutical Technology pp 84ndash88 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=290

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ISRN Chemical Engineering 7

112

211

37 115

3

116

7

117

3

118

1

118

5

101

3 103

210

52

105

9

106

1

106

2

106

3

106

3

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 6 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 2 Part 2)

at a conclusion tolerance is squeezed further to 001 withthe same step limit criteria as done for the simulation withtolerance 01

7 Simulation (Scheme 1 119886 = 119887 = 119888 = 119889 = 1 ieElementary Reaction)

71 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 In Tables 2(a) and 2(b) simulation results for two

cases have been captured Figures 4(a) and 4(c) are sampleconcentration profiles of reaction species in ideal Fed Batchand ideal Plug Flow Reactor Figure 4(b) is the graphicalrepresentation of reaction volume in Fed-Batch Reactor

It can be observed in Figure 4(a) that with 119905119898= 600 s

further concentration change (reaction) is negligible As theaddition rate of reagent B considered in this simulation studyis constant the fed batch volume increases linearly till 119905 =119905119886 During Reaction maintenance time 119905

119898 the Fed-Batch

volume remains constant

72 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Figures 4(d) and 4(e) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

In Tables 2(c) and 2(d) results for all simulated cases havebeen captured and the data lines (rows) 4 and 5 correspondto the fraction Sol A(Sol A + Sol R) = 025 and 075respectively

73 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and

1198702= 0002 Figures 4(f) and 4(g) are sample concentration

profiles of reaction species in ideal Fed Batch and ideal PlugFlow Reactors

In Tables 2(e) and 2(f) simulation results for two caseshave been captured

Tables 2(a) to 2(f) show that elementary reaction of thetype given in (1) yields the same amount of desired product infed batch reactor and Plug Flow Reactor Moreover the yield

values in Part 2 remain the same as those in Part 1 That isbecause119870

11198702values remain the same in both Part 1 and Part

2 even though the individual 1198701and 119870

2values are different

It is to be noted that in Part 3 yield values are different fromthat in Part 1 and Part 2That is because119870

11198702value in Part 3

is different from those in Part 1 and Part 2 The change in therelative concentration of both the reacting streams (as shownin Table 2(c) rows 2 4 and 5 and Table 2(d) rows 1 4 and 5)does not have any effect on the yield

8 Simulation (Scheme 2 119886 = 119887 = 1 119888 = 15 119889 =05 Nonelementary)

81 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 Figures 5(a) and 5(b) are sample concentration

profiles of reaction species in ideal Fed Batch and ideal PlugFlow Reactors

In Tables 3(a) and 3(b) simulation results for two casessimulated have been captured

82 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Figures 5(c) and 5(d) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

In Tables 3(c) and 3(d) and Figure 6 results for all thesimulated cases have been captured The data lines (rows) 4and 5 in Tables 3(c) and 3(d) correspond to the fraction SolA(Sol A + Sol R) = 025 and 075 respectively

The yield values for varying reaction times are capturedin Figure 6

83 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 In Tables 3(e) and 3(f) simulation results for two caseshave been captured

Tables 3(a) and 3(f) and Figure 6 show that this nonelementary reaction yields higher desired product in Fed-Batch Reactor than in Continuous Plug Flow Reactor

In Figure 6 the Plug Flow Reactor yield initially increaseswith the increase in reaction time (ie lengthier reactor pipe)consequently 119873B119905119873A119905 value decreases as shown in Tables3(c) and 3(d) (ie reduced consumption of Reactant B)However the Plug Flow Reactor yield saturates out belowFed-Batch Reactor yield Overall the Fed Batch Reactoryields higher product R than Plug Flow Reactor even thoughthere is a very marginal change in yield for the change in therelative concentration of reacting streams (Table 3(c) rows 24 and 5) in Fed Batch Reactor

9 Simulation (Scheme 3 119886 = 119887 = 1 119888 = 05 119889 =15 Nonelementary)

91 Part 1 (Cases 1 and 2)1198701= 100119870

11198702= 10 and119870

2= 10

In Tables 4(a) and 4(b) simulation results for two cases havebeen captured

Figures 7(a) and 7(b) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

8 ISRN Chemical Engineering

Table 3 (a) Reactor-1 (Fed-Batch Scheme 2 Part 1) (b) Reactor-2 (Plug Flow Scheme 2 Part 1) (c) Reactor-1 (Fed-Batch Scheme 2 Part2) (d) Reactor-2 (Plug Flow Scheme 2 Part 2) (e) Reactor-1 (Fed-Batch Scheme 2 Part 3) (f) Reactor-2 (Plug Flow Scheme 2 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1005 2132 0027 000 2598 0042 122600 0996 2125 0027 000 2625 0015 123

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 113 2128 0027 6119864 minus 06 2267 04 106360 113 2128 0027 3119864 minus 35 2267 04 1063

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1072 2127 0027 0005 2425 0215 1137900 1059 2166 0027 0004 2459 0181 11531800 1048 2126 0027 0004 2491 0149 1167900 1061 2127 0027 0004 2456 0184 1151900 1058 2126 0027 0004 2463 0177 1154

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1221 2131 0027 0135 216 048 1013360 118 2129 0027 0068 2202 0438 1032720 1145 2129 0027 0018 2244 0396 1052240 1221 2131 0027 0135 216 048 1013240 1221 2131 0027 0135 216 048 1013

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1009 2125 0027 0008 2599 0041 1218900 1006 2125 0027 0008 2605 0035 1221

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1094 2127 0027 0083 2545 0095 1193360 1058 2126 0027 0097 2555 0085 1198

92 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 4(c) and 4(d) and Figure 8 results for othersimulated cases have been captured

The last two data lines (rows) in Tables 4(c) and 4(d)correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

Figures 7(c) and 7(d) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

The yield values for varying reaction times are capturedin Figure 8

93 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 InTables 4(e) and 4(f) simulation results for two caseshave been captured

Tables 4(a)ndash4(f) and Figure 8 show that this non elemen-tary reaction yields higher desired product R in Plug FlowReactor than in Fed-Batch Reactor

It is to be noted that the reduced addition time in FedBatch Reactor results in increased product yield Howeverin actual practice heat transfer and other limitations of thereactor vessel could possibly determine the minimum addi-tion time beyond which addition time cannot be reduced Sothe Fed Batch reactor yield is limited

It is to be further noted that there is a marginal changein the yield in Fed Batch reactor with the change in relativeconcentration of reacting streams (Table 4(c) rows 2 4 and5) However this variation is too low to catch up with PlugFlow Reactor yield

10 Simulations (for the Rest of the Schemes)

101 (Scheme 4 119886 = 05 119887 = 15 119888 = 05 119889 = 15Nonelementary)

1011 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and 119870

2=

10 See Tables 5(a) and 5(b)

ISRN Chemical Engineering 9

Table 4 (a) Reactor-1 (Fed-Batch Scheme 3 Part 1) (b) Reactor-2 (Plug Flow Scheme 3 Part 1) (c) Reactor-1 (Fed-Batch Scheme 3 Part2) (d) Reactor-2 (Plug Flow Scheme 3 Part 2) (e) Reactor-1 (Fed-Batch Scheme 3 Part 3) (f) Reactor-2 (Plug Flow Scheme 3 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1909 2148 0027 000 019 245 9600 195 2149 0027 000 0079 2561 4

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1448 2136 0027 3119864 minus 08 1419 12 665260 1447 2136 0027 3119864 minus 05 142 12 6657

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1598 214 0027 5119864 minus 13 1019 1621 4776900 1661 2142 0027 3119864 minus 13 0851 1789 39891800 1722 2143 0027 7119864 minus 13 0687 1953 3222900 1655 2141 0027 1119864 minus 12 0868 1772 4067900 1668 2142 0027 1119864 minus 12 0833 1807 3905

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1448 2136 0027 4119864 minus 12 1419 1221 6652360 1448 2136 0027 4119864 minus 12 1419 1221 6652720 1448 2136 0027 4119864 minus 12 1419 1221 6652240 1448 2136 0027 4E minus 12 1419 1221 6652240 1448 2136 0027 4E minus 12 1419 1221 6652

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1214 213 0027 0000 2043 0597 9575900 1251 2131 0027 0000 1943 0697 9107

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1172 2129 0027 0071 2227 0413 1044360 1163 2129 0027 0003 2182 0458 1023

1012 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 The data lines (rows) 4 and 5 in Tables 5(c) and 5(d)correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 9

1013 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 (See Tables 5(e) and 5(f)) Tables 5(a)ndash5(f) and Figure 9show that this non elementary reaction yields higher desiredproduct in Plug Flow Reactor than in Fed-Batch Reactor

As in Scheme 3 the reduced addition time in Fed BatchReactor results in increased product yield However in actualpractice heat transfer and other limitations of the reactorvessel could possibly determine the minimum addition timebeyond which addition time cannot be reduced So the FedBatch reactor yield is limited

Themarginal change in the yield in FedBatch reactorwithrelative concentration of reacting streams (Table 5(c) rows 24 and 5) may be noted However this variation is too low tocatch up with Plug Flow Reactor yield

102 (Scheme 5 119886 = 15 119887 = 05 119888 = 05 119889 = 15Nonelementary)

1021 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 6(a) and 6(b)

1022 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 119870

2=

001 In Table 6(c) and 6(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1023 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 119870

2=

0002 (See Tables 6(e) and 6(f)) Tables 6(a)ndash6(f) show that

10 ISRN Chemical Engineering

0

05

1

15

2

25

3

0 100 200 300 400 500 600 700

Con

cent

ratio

n (m

olL

)

Time (s)minus05

(a)

002040608

112141618

2

0 05 1 15 2 25 3 35

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(b)

0

05

1

15

2

25

3

0 500 1000 1500 2000 2500Time (s)minus05

Con

cent

ratio

n (m

olL

)

AB

RS

(c)

002040608

112141618

2

0 100

AB

RS

200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(d)

Figure 7 (a) Concentration as a function of time Fed-Batch Reactor (Scheme 3 Part 1 119905119886= 60 s 119905

119898= 600 s) (b) Concentration as a function

of time Plug Flow Reactor (Scheme 3 Part 1 119905end = 6 s for brevity graph is plotted for 3 s only) (c) Concentration as a function of timeFed-Batch Reactor (Scheme 3 Part 2 119905

119886= 900 s 119905

119898= 1200 s) (d) Concentration as a function of time Plug Flow Reactor (Scheme 3 Part 2

119905end = 360 s)

this type of nonelementary reaction yields the same amountof desired product in fed batch reactor and in Plug FlowReactor Moreover the yield values in Part 2 remain the sameas those in Part 1 That is because 119870

11198702values remain the

same in both Part 1 and Part 2 even though the individual1198701and119870

2values are different It is to be noted that in Part 3

yield values are different from that in Part 1 and Part 2That isbecause 119870

11198702value in Part 3 is different from those in Part

1 and Part 2The change in the relative concentration of both the

reacting streams (as shown in Table 6(c) rows 2 4 and 5 andTable 6(d) rows 1 4 and 5) does not have any effect on theyield

103 (Scheme 6 119886 = 05 119887 = 15 119888 = 15 119889 = 05Nonelementary)

1031 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 7(a) and 7(b)

1032 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 7(c) and 7(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1033 Part 3 (Cases 1 and 2)1198701= 01119870

11198702= 50 and119870

2=

0002 (See Tables 7(e) and 7(f)) Tables 7(a)ndash7(f) show thatthis type of nonelementary reaction also behaves similar toelementary reaction and nonelementary reaction Scheme 5with respect to product selectivity that is the yield is the samein both the reactors The change in the relative concentrationof both the reacting streams (as shown in Table 7(c) rows 24 and 5 and Table 7(d) rows 1 4 and 5) does not have anyeffect on the yield

104 (Scheme 7 119886 = 15 119887 = 05 119888 = 15 119889 = 05Nonelementary)

1041 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 8(a) and 8(b)

ISRN Chemical Engineering 11

Table 5 (a) Reactor-1 (Fed-Batch Scheme 4 Part 1) (b) Reactor-2 (Plug Flow Scheme 4 Part 1) (c) Reactor-1 (Fed-Batch Scheme 4 Part2) (d) Reactor-2 (Plug Flow Scheme 4 Part 2) (e) Reactor-1 (Fed-Batch Scheme 4 Part 3) (f) Reactor-2 (Plug Flow Scheme 4 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1927 2148 0027 000 0141 2499 7600 1961 2149 0027 000 005 259 2

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1313 2133 0027 6119864 minus 08 1778 09 833460 1313 2667 0027 6119864 minus 08 1778 09 8334

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1562 2139 0027 000 1113 1527 5219900 1654 2141 0027 1119864 minus 10 0869 1771 40751800 1733 2143 0027 6119864 minus 13 0658 1982 3085900 1646 2141 0027 1E minus 12 0868 175 4171900 1662 2142 0027 1E minus 10 0848 1792 3974

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1313 2133 0027 000 1778 0862 8334360 1313 2133 0027 000 1778 0862 8334720 1313 2133 0027 8119864 minus 12 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1203 213 0027 7119864 minus 11 2071 0569 971900 1265 2132 0027 6119864 minus 11 1907 0733 894

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 2997 2128 0027 0021 2304 0336 108360 1124 2128 0027 000 2284 0356 107

609

477

6

398

9

322

2

746

266

52

665

2

665

2

0 500 1000 1500 2000ta or tend (s)

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 8 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 3 Part 2)

ta or tend (s)

741

521

9

407

5

308

5

857

1

8334

833

4

833

4

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 9 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 4 Part 2)

12 ISRN Chemical Engineering

Table 6 (a) Reactor-1 (Fed-Batch Scheme 5 Part 1) (b) Reactor-2 (Plug Flow Scheme 5 Part 2) (c) Reactor-1 (Fed-Batch Scheme 5 Part2) (d) Reactor-2 (Plug Flow Scheme 5 Part 2) (e) Reactor-1 (Fed-Batch Scheme 5 Part 2) (f) Reactor-2 (Plug Flow Scheme 5 Part 2)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1664 2142 0027 000 0843 1797 3954600 1664 2149 0027 000 0843 1797 3954

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1664 2142 0027 6119864 minus 09 0843 18 395460 1664 2142 0027 6119864 minus 09 0843 18 3954

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1664 2142 0027 1119864 minus 10 0844 1796 3956900 1664 2142 0027 1119864 minus 10 0843 1797 39541800 1664 2142 0027 1119864 minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1794 2145 0027 0348 0843 1797 3954360 1672 2142 0027 0022 0844 1796 3954720 1664 2142 0027 000 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 124 2131 0027 7119864 minus 11 1973 0667 9249900 124 2131 0027 7119864 minus 11 1973 0667 9248

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1442 2136 0027 0537 1973 0667 9247360 1277 2132 0027 0099 1973 0667 9248

116

211

79

119

5

120

7

121

2

121

8

122

500

280

6 101

5

104

9

105

1

105

1

105

1

105

1

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 10 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 7 Part 2)

1042 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 8(c) and 8(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 10

1043 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 8(c) and 8(d)) Tables 7(a)ndash

7(d) and Figure 10 show that this non elementary reactionyields higher desired product in Fed-Batch Reactor than inContinuous Plug Flow Reactor

As in Scheme 2 the Plug Flow Reactor yield initiallyincreases with the increase in reaction time (ie lengthierreactor pipe) consequently 119873B119905119873A119905 value decreases asshown in Table 8(d) (ie reduced consumption of ReactantB) However the Plug Flow Reactor yield saturates out below

ISRN Chemical Engineering 13

Table 7 (a) Reactor-1 (Fed-Batch Scheme 6 Part 1) (b) Reactor-2 (Plug Flow Scheme 6 Part 1) (c) Reactor-1 (Fed-Batch Scheme 6 Part2) (d) Reactor-2 (Plug Flow Scheme 6 Part 2) (e) Reactor-1 (Fed-Batch Scheme 6 Part 3) (f) Reactor-2 (Plug Flow Scheme 6 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1121 2128 0027 000 229 035 1073600 1121 2128 0027 000 229 035 1073

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1121 2128 0027 4119864 minus 04 229 04 107360 1121 2128 0027 5119864 minus 06 229 04 1073

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7119864 minus 03 229 035 10731800 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1152 2129 0027 0083 229 035 1073360 1139 2128 0027 0048 229 035 1073720 1128 2128 0027 0017 229 035 1073240 1152 2129 0027 0083 229 035 1073240 1152 2129 0027 0083 229 035 1073

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1022 2126 0027 0012 2568 0073 1204900 1022 2126 0027 0012 2567 0072 1203

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1058 2126 0027 0108 2567 0072 1204360 1042 2126 0027 0066 2568 0073 1204

Fed-Batch Reactor yield (Figure 10) Overall the Fed BatchReactor yields higher product R than Plug Flow Reactor eventhough there is a verymarginal change in yield for the changein the relative concentration of reacting streams (Table 8(c)rows 2 4 and 5)

105 (Scheme 8 a = 05 b = 15 c = 1 d = 1 Nonelementary)

1051 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 9(a) and 9(b)

1052 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 9(c) and 9(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 11

1053 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 9(e) and 9(f)) Tables 9(a)ndash9(f)

and Figure 11 show that this non elementary reaction yieldshigher desired product in Plug Flow Reactor than in Fed-Batch Reactor Also the yield in Fed batch reactor decreaseswith addition time

As in Scheme 3 and Scheme 4 the reduced additiontime in Fed Batch Reactor results in increased productyield However in actual practice heat transfer and otherlimitations of the reactor vessel could possibly determine theminimum addition time beyond which addition time cannotbe reduced So the Fed Batch reactor yield is limited

It is to be noted that there is amarginal change in the yieldin Fed Batch reactor with relative concentration of reacting

14 ISRN Chemical Engineering

Table 8 (a) Reactor-1 (Fed-Batch Scheme 7 Part 1) (b) Reactor-2 (Plug Flow Scheme 7 Part 1) (c) Reactor-1 (Fed-Batch Scheme 7 Part2) (d) Reactor-2 (Plug Flow Scheme 7 Part 2) (e) Reactor-1 (Fed-Batch Scheme 7 Part 3) (f) Reactor-2 (Plug Flow Scheme 7 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 0992 2125 0026 000 2636 0004 1236600 099 2125 0027 000 264 8119864 minus 05 1237

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1139 2128 0027 2119864 minus 11 2242 04 105160 1139 2128 0027 2119864 minus 11 2242 04 1051

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1037 2126 0027 5119864 minus 04 2515 0125 1179900 1024 2126 0027 3119864 minus 04 2548 0092 11951800 1014 2125 0027 1119864 minus 04 2576 0064 1207900 1025 2126 0027 3E minus 04 2547 0093 1194900 1024 2126 0027 3E minus 04 255 009 1195

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1757 2144 0027 0472 1067 1573 5002360 1397 2135 0027 0165 172 092 806720 1176 2129 0027 0021 2166 0474 1015240 1757 2144 0027 0472 1067 1573 5002240 1757 2144 0027 0472 1067 1573 5002

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 0998 2125 0027 0001 2619 0021 1228900 0996 2125 0027 9119864 minus 04 2624 0016 1230

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1372 2134 0027 0687 2309 0331 1082360 115 2129 0027 0258 2472 0168 1159

913

3

827

768

696

999

1

965

595

8

955

1

955

0 500 1000 1500 2000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 11 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 8 Part 2)

80 847 91

2

985 101

4

105

3

107

2

452

5 586 694

9

701

701

701

701

701

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 12 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 9 Part 2)

ISRN Chemical Engineering 15

Table 9 (a) Reactor-1 (Fed-Batch Scheme 8 Part 1) (b) Reactor-2 (Plug Flow Scheme 8 Part 1) (c) Reactor-1 (Fed-Batch Scheme 8 Part2) (d) Reactor-2 (Plug Flow Scheme 8 Part 2) (e) Reactor-1 (Fed-Batch Scheme 8 Part 3) (f) Reactor-2 (Plug Flow Scheme 8 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 176 2144 0027 000 0588 2052 275600 1892 2147 0027 000 0234 2406 110

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1216 213 0027 3119864 minus 26 2037 06 95560 1216 213 0027 0000 2037 06 955

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1318 2133 0027 6119864 minus 06 1765 0875 827900 1366 2124 0027 9119864 minus 06 1638 1002 7681800 1423 2136 0027 2119864 minus 05 1485 1155 696900 1359 2134 0027 8E minus 06 1656 0984 776900 1374 2667 0027 1E minus 05 1615 1025 757

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1218 213 0027 0029 206 058 9655360 1216 213 0027 0008 2044 0596 958720 1216 213 0027 2119864 minus 04 2038 0602 9551240 1218 213 0027 0029 206 058 9655240 1218 213 0027 0029 206 058 9655

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1078 2127 0027 0003 2408 0232 1129900 109 2127 0027 0002 2376 0264 1114

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1076 2127 0027 0087 2498 0142 1171360 1065 2127 0027 0046 2486 0154 1166

streams (Table 9(c) rows 2 4 and 5) However this variationis too low to catch up with Plug Flow Reactor yield

106 (Scheme 9 119886 = 15 119887 = 05 119888 = 1 and 119889 = 1Nonelementary)

1061 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 10(a) and 10(b)

1062 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Theyield values for varying reaction times are capturedin Figure 12

In Tables 10(c) and 10(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1063 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 Tables 10(a)ndash10(f) and Figure 12 show that

this nonelementary reaction yields higher desired productin Fed-Batch Reactor than in Continuous Plug Flow Reac-tor

As in Scheme 2 and Scheme 7 the Plug Flow Reactoryield initially increases with the increase in reaction time(ie lengthier reactor pipe) consequently 119873B119905119873A119905 valuedecreases (ie reduced consumption of Reactant B) How-ever the Plug Flow Reactor yield saturates out below Fed-Batch Reactor yield (Figure 12)

Overall the Fed Batch Reactor yields higher product Rthan Plug Flow Reactor even though there is a very marginalchange in yield for the change in the relative concentration ofreacting streams (Table 10(c) rows 2 4 and 5) in Fed-BatchReactor

16 ISRN Chemical Engineering

Table 10 (a) Reactor-1 (Fed-Batch Scheme 9 Part 1) (b) Reactor-2 (Plug Flow Scheme 9 Part 1) (c) Reactor-1 (Fed-Batch Scheme 9 Part2) (d) Reactor-2 (Plug Flow Scheme 9 Part 2) (e) Reactor-1 (Fed-Batch Scheme 9 Part 3) (f) Reactor-2 (Plug Flow Scheme 9 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1019 2125 0027 000 2564 0077 1202600 0994 2125 0027 000 263 1119864 minus 02 1233

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1419 2135 0027 2119864 minus 11 1497 11 701560 1419 2135 0027 2119864 minus 11 1497 11 7015

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1302 2133 0027 4119864 minus 15 1807 0833 847900 125 2131 0027 4119864 minus 15 1946 0694 9121800 1192 213 0027 4119864 minus 15 2101 0539 985900 1254 2131 0027 4E minus 15 1936 0704 907900 1246 2131 0027 4E minus 15 1957 0683 917

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1771 2144 0027 0408 0965 1675 4525360 1544 2139 0027 0088 1251 1389 586720 1425 2136 0027 0001 1482 1158 6949240 1771 2144 0027 0408 0965 1675 4525240 1771 2144 0027 0408 0965 1675 4525

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 104 2667 0027 1119864 minus 06 2506 0134 1175900 1034 2126 0027 4119864 minus 15 2523 0117 1183

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 14 2135 0027 0624 217 047 1017360 1191 213 0027 0202 2307 0333 1081

Table 11 Summary of results

Schemenumber

119886 119887 119888 119889 Favored reactorRelationship

between 119886 119887 119888 and119889

1 1 1 1 1 Both equally 119886 + 119888 = 119887 + 119889

2 1 1 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

3 1 1 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

4 05 15 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

5 15 05 05 15 Both equally 119886 + 119888 = 119887 + 119889

6 05 15 15 05 Both equally 119886 + 119888 = 119887 + 119889

7 15 05 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

8 05 15 1 1 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

9 15 05 1 1 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

11 Conclusion

Under the simulated conditions elementary Second ordercompetitive consecutive reactions of the type mentioned in(1) yield the same amount of intermediate product R in bothideal fed batch and ideal Plug Flow Reactors for a constantconversion (99) of limiting reactant A Yield and selectivityof the product depends only on119870

11198702in both the reactors

However of the 8 nonelementary scenarios simulatedthree (Schemes 3 4 and 8) favor Plug Flow Reactor and threeother (Schemes 2 7 and 9) favor Fed Batch Reactor Twoothers (Schemes 5 and 6) like elementary reaction yield thesame in both Plug Flow Reactor and Fed batch reactor

Among the schemes simulated previously (Schemes 1 to9) the schemes giving increased yield R with reduced addi-tion time in Fed batch reactor favor Plug Flow Reactor andthe schemes giving increased yield with increased addition

ISRN Chemical Engineering 17

time in fed batch reactor favor Fed batch reactor This couldwell be a practical reckoner to screen the potential candidateamong the simulated schemes for Plug Flow Reactor eventhough this idea is only with respect to suitability of kineticparameters

The relationship between the exponents 119886 119887 119888 and 119889 andthe favourable reactor found in the simulation as shown inTable 11 is noteworthy

Nomenclature

1198701 Rate constant of reaction between A and

B in Litresdotmolminus1sdotsminus1K2 Rate constant of 2nd reaction between R

and B in Litresdotmolminus1sdotsminus1t Time s119905119886 Reactant B addition time in Fed Batch

Reactor s119905119898 Reaction mass maintenance time in Fed

Batch Reactor stlowast Space time in Plug Flow Reactor stend Space time for which each case of plug

flow rector simulation has been done s119903119909 Rate of change of species ldquoxrdquo

(molsdotLitreminus1sdotsminus1) ldquoxrdquo is representative ofspecies A B R S C and D

119862119909= 119873119909119881 Concentration molsdotLitreminus1 of any species

say ldquoxrdquoV Reaction volume m3119873119909 Number of Kg moles of species ldquoxrdquo k mol

NB119905 Total Kg moles of reactant B used inreaction k mol

NA119905 Total kg moles of reactant A used inreaction k mol

119881119886119905 Volume of stream containing reactant B

m3119881119905 Total volume of contents including

streams of reactant A and reactant B m3v Plug Flow Reactor volume m3v1015840 Volumetric flow rate m3s119865119909 Molar flow rate (k molsdotsminus1) of species ldquoxrdquo

which is representative of species A B RS C and D

NB119905NA119905 Ratio of total moles of B to total moles ofA taken for the reaction

119873119909119865 Final kg moles of the species ldquoxrdquo k mol

WR Weight kg of total intermediate (desired)product formed at the end of reaction inFed Batch Reactor and at the end of agiven space time in the Plug Flow Reactor

Acknowledgment

The author would like to thank Chandra Kanth Terupally ofPlanck Technical Hyderabad India for providing adequatesupport in MATLAB Programming

References

[1] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1998

[2] J F Richardson and D G Peacock Coulson and RichardsonrsquosChemical Engineering Chemical and Biochemical Reactors andProcess Control Butterworth-Heinemann Boston Mass USA3rd edition 1994

[3] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart I model developmentrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 750162 16pages 2012

[4] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart II design protocolsrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 65432113 pages 2012

[5] J R Bourne ldquoMixing and the selectivity of chemical reactionsrdquoOrganic Process Research andDevelopment vol 7 no 4 pp 471ndash508 2003

[6] J Bałdyga J R Bourne and S J Hearn ldquoInteraction betweenchemical reactions and mixing on various scalesrdquo ChemicalEngineering Science vol 52 no 4 pp 457ndash466 1997

[7] N G Anderson ldquoPractical use of continuous processing indeveloping and scaling up laboratory processesrdquo Organic Pro-cess Research and Development vol 5 no 6 pp 613ndash621 2001

[8] C Brechtelsbauer and F Ricard ldquoReaction engineering evalua-tion and utilization of static mixer technology for the synthesisof pharmaceuticalsrdquoOrganic Process Research andDevelopmentvol 5 no 6 pp 646ndash651 2001

[9] Z Anxionnaz M Cabassud C Gourdon and P Tochon ldquoHeatexchangerreactors (HEX reactors) concepts technologiesstate-of-the-artrdquo Chemical Engineering and Processing vol 47no 12 pp 2029ndash2050 2008

[10] P Barthe C Guermeur O Lobet et al ldquoContinuous multi-injection reactor for multipurpose productionmdashpart Irdquo Chem-ical Engineering and Technology vol 31 no 8 pp 1146ndash11542008

[11] M Patel and G Gasparini ldquoReactor technology flow reactorsand dynamic mixingrdquo Specialty Chemicals Magazine 2009

[12] X W Ni ldquoContinuous oscilatory baffled reactor technologyrdquoin Innovations in Pharmaceutical TechnologymdashManufacturingpp 90ndash96 2006 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=392

[13] L Proctor ldquoContinuous chemical processingrdquo in Innovationsin Pharmaceutical Technology pp 84ndash88 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=290

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8 ISRN Chemical Engineering

Table 3 (a) Reactor-1 (Fed-Batch Scheme 2 Part 1) (b) Reactor-2 (Plug Flow Scheme 2 Part 1) (c) Reactor-1 (Fed-Batch Scheme 2 Part2) (d) Reactor-2 (Plug Flow Scheme 2 Part 2) (e) Reactor-1 (Fed-Batch Scheme 2 Part 3) (f) Reactor-2 (Plug Flow Scheme 2 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1005 2132 0027 000 2598 0042 122600 0996 2125 0027 000 2625 0015 123

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 113 2128 0027 6119864 minus 06 2267 04 106360 113 2128 0027 3119864 minus 35 2267 04 1063

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1072 2127 0027 0005 2425 0215 1137900 1059 2166 0027 0004 2459 0181 11531800 1048 2126 0027 0004 2491 0149 1167900 1061 2127 0027 0004 2456 0184 1151900 1058 2126 0027 0004 2463 0177 1154

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1221 2131 0027 0135 216 048 1013360 118 2129 0027 0068 2202 0438 1032720 1145 2129 0027 0018 2244 0396 1052240 1221 2131 0027 0135 216 048 1013240 1221 2131 0027 0135 216 048 1013

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1009 2125 0027 0008 2599 0041 1218900 1006 2125 0027 0008 2605 0035 1221

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1094 2127 0027 0083 2545 0095 1193360 1058 2126 0027 0097 2555 0085 1198

92 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 4(c) and 4(d) and Figure 8 results for othersimulated cases have been captured

The last two data lines (rows) in Tables 4(c) and 4(d)correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

Figures 7(c) and 7(d) are sample concentration profilesof reaction species in ideal Fed Batch and ideal Plug FlowReactors

The yield values for varying reaction times are capturedin Figure 8

93 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 InTables 4(e) and 4(f) simulation results for two caseshave been captured

Tables 4(a)ndash4(f) and Figure 8 show that this non elemen-tary reaction yields higher desired product R in Plug FlowReactor than in Fed-Batch Reactor

It is to be noted that the reduced addition time in FedBatch Reactor results in increased product yield Howeverin actual practice heat transfer and other limitations of thereactor vessel could possibly determine the minimum addi-tion time beyond which addition time cannot be reduced Sothe Fed Batch reactor yield is limited

It is to be further noted that there is a marginal changein the yield in Fed Batch reactor with the change in relativeconcentration of reacting streams (Table 4(c) rows 2 4 and5) However this variation is too low to catch up with PlugFlow Reactor yield

10 Simulations (for the Rest of the Schemes)

101 (Scheme 4 119886 = 05 119887 = 15 119888 = 05 119889 = 15Nonelementary)

1011 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and 119870

2=

10 See Tables 5(a) and 5(b)

ISRN Chemical Engineering 9

Table 4 (a) Reactor-1 (Fed-Batch Scheme 3 Part 1) (b) Reactor-2 (Plug Flow Scheme 3 Part 1) (c) Reactor-1 (Fed-Batch Scheme 3 Part2) (d) Reactor-2 (Plug Flow Scheme 3 Part 2) (e) Reactor-1 (Fed-Batch Scheme 3 Part 3) (f) Reactor-2 (Plug Flow Scheme 3 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1909 2148 0027 000 019 245 9600 195 2149 0027 000 0079 2561 4

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1448 2136 0027 3119864 minus 08 1419 12 665260 1447 2136 0027 3119864 minus 05 142 12 6657

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1598 214 0027 5119864 minus 13 1019 1621 4776900 1661 2142 0027 3119864 minus 13 0851 1789 39891800 1722 2143 0027 7119864 minus 13 0687 1953 3222900 1655 2141 0027 1119864 minus 12 0868 1772 4067900 1668 2142 0027 1119864 minus 12 0833 1807 3905

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1448 2136 0027 4119864 minus 12 1419 1221 6652360 1448 2136 0027 4119864 minus 12 1419 1221 6652720 1448 2136 0027 4119864 minus 12 1419 1221 6652240 1448 2136 0027 4E minus 12 1419 1221 6652240 1448 2136 0027 4E minus 12 1419 1221 6652

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1214 213 0027 0000 2043 0597 9575900 1251 2131 0027 0000 1943 0697 9107

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1172 2129 0027 0071 2227 0413 1044360 1163 2129 0027 0003 2182 0458 1023

1012 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 The data lines (rows) 4 and 5 in Tables 5(c) and 5(d)correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 9

1013 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 (See Tables 5(e) and 5(f)) Tables 5(a)ndash5(f) and Figure 9show that this non elementary reaction yields higher desiredproduct in Plug Flow Reactor than in Fed-Batch Reactor

As in Scheme 3 the reduced addition time in Fed BatchReactor results in increased product yield However in actualpractice heat transfer and other limitations of the reactorvessel could possibly determine the minimum addition timebeyond which addition time cannot be reduced So the FedBatch reactor yield is limited

Themarginal change in the yield in FedBatch reactorwithrelative concentration of reacting streams (Table 5(c) rows 24 and 5) may be noted However this variation is too low tocatch up with Plug Flow Reactor yield

102 (Scheme 5 119886 = 15 119887 = 05 119888 = 05 119889 = 15Nonelementary)

1021 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 6(a) and 6(b)

1022 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 119870

2=

001 In Table 6(c) and 6(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1023 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 119870

2=

0002 (See Tables 6(e) and 6(f)) Tables 6(a)ndash6(f) show that

10 ISRN Chemical Engineering

0

05

1

15

2

25

3

0 100 200 300 400 500 600 700

Con

cent

ratio

n (m

olL

)

Time (s)minus05

(a)

002040608

112141618

2

0 05 1 15 2 25 3 35

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(b)

0

05

1

15

2

25

3

0 500 1000 1500 2000 2500Time (s)minus05

Con

cent

ratio

n (m

olL

)

AB

RS

(c)

002040608

112141618

2

0 100

AB

RS

200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(d)

Figure 7 (a) Concentration as a function of time Fed-Batch Reactor (Scheme 3 Part 1 119905119886= 60 s 119905

119898= 600 s) (b) Concentration as a function

of time Plug Flow Reactor (Scheme 3 Part 1 119905end = 6 s for brevity graph is plotted for 3 s only) (c) Concentration as a function of timeFed-Batch Reactor (Scheme 3 Part 2 119905

119886= 900 s 119905

119898= 1200 s) (d) Concentration as a function of time Plug Flow Reactor (Scheme 3 Part 2

119905end = 360 s)

this type of nonelementary reaction yields the same amountof desired product in fed batch reactor and in Plug FlowReactor Moreover the yield values in Part 2 remain the sameas those in Part 1 That is because 119870

11198702values remain the

same in both Part 1 and Part 2 even though the individual1198701and119870

2values are different It is to be noted that in Part 3

yield values are different from that in Part 1 and Part 2That isbecause 119870

11198702value in Part 3 is different from those in Part

1 and Part 2The change in the relative concentration of both the

reacting streams (as shown in Table 6(c) rows 2 4 and 5 andTable 6(d) rows 1 4 and 5) does not have any effect on theyield

103 (Scheme 6 119886 = 05 119887 = 15 119888 = 15 119889 = 05Nonelementary)

1031 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 7(a) and 7(b)

1032 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 7(c) and 7(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1033 Part 3 (Cases 1 and 2)1198701= 01119870

11198702= 50 and119870

2=

0002 (See Tables 7(e) and 7(f)) Tables 7(a)ndash7(f) show thatthis type of nonelementary reaction also behaves similar toelementary reaction and nonelementary reaction Scheme 5with respect to product selectivity that is the yield is the samein both the reactors The change in the relative concentrationof both the reacting streams (as shown in Table 7(c) rows 24 and 5 and Table 7(d) rows 1 4 and 5) does not have anyeffect on the yield

104 (Scheme 7 119886 = 15 119887 = 05 119888 = 15 119889 = 05Nonelementary)

1041 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 8(a) and 8(b)

ISRN Chemical Engineering 11

Table 5 (a) Reactor-1 (Fed-Batch Scheme 4 Part 1) (b) Reactor-2 (Plug Flow Scheme 4 Part 1) (c) Reactor-1 (Fed-Batch Scheme 4 Part2) (d) Reactor-2 (Plug Flow Scheme 4 Part 2) (e) Reactor-1 (Fed-Batch Scheme 4 Part 3) (f) Reactor-2 (Plug Flow Scheme 4 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1927 2148 0027 000 0141 2499 7600 1961 2149 0027 000 005 259 2

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1313 2133 0027 6119864 minus 08 1778 09 833460 1313 2667 0027 6119864 minus 08 1778 09 8334

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1562 2139 0027 000 1113 1527 5219900 1654 2141 0027 1119864 minus 10 0869 1771 40751800 1733 2143 0027 6119864 minus 13 0658 1982 3085900 1646 2141 0027 1E minus 12 0868 175 4171900 1662 2142 0027 1E minus 10 0848 1792 3974

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1313 2133 0027 000 1778 0862 8334360 1313 2133 0027 000 1778 0862 8334720 1313 2133 0027 8119864 minus 12 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1203 213 0027 7119864 minus 11 2071 0569 971900 1265 2132 0027 6119864 minus 11 1907 0733 894

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 2997 2128 0027 0021 2304 0336 108360 1124 2128 0027 000 2284 0356 107

609

477

6

398

9

322

2

746

266

52

665

2

665

2

0 500 1000 1500 2000ta or tend (s)

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 8 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 3 Part 2)

ta or tend (s)

741

521

9

407

5

308

5

857

1

8334

833

4

833

4

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 9 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 4 Part 2)

12 ISRN Chemical Engineering

Table 6 (a) Reactor-1 (Fed-Batch Scheme 5 Part 1) (b) Reactor-2 (Plug Flow Scheme 5 Part 2) (c) Reactor-1 (Fed-Batch Scheme 5 Part2) (d) Reactor-2 (Plug Flow Scheme 5 Part 2) (e) Reactor-1 (Fed-Batch Scheme 5 Part 2) (f) Reactor-2 (Plug Flow Scheme 5 Part 2)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1664 2142 0027 000 0843 1797 3954600 1664 2149 0027 000 0843 1797 3954

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1664 2142 0027 6119864 minus 09 0843 18 395460 1664 2142 0027 6119864 minus 09 0843 18 3954

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1664 2142 0027 1119864 minus 10 0844 1796 3956900 1664 2142 0027 1119864 minus 10 0843 1797 39541800 1664 2142 0027 1119864 minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1794 2145 0027 0348 0843 1797 3954360 1672 2142 0027 0022 0844 1796 3954720 1664 2142 0027 000 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 124 2131 0027 7119864 minus 11 1973 0667 9249900 124 2131 0027 7119864 minus 11 1973 0667 9248

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1442 2136 0027 0537 1973 0667 9247360 1277 2132 0027 0099 1973 0667 9248

116

211

79

119

5

120

7

121

2

121

8

122

500

280

6 101

5

104

9

105

1

105

1

105

1

105

1

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 10 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 7 Part 2)

1042 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 8(c) and 8(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 10

1043 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 8(c) and 8(d)) Tables 7(a)ndash

7(d) and Figure 10 show that this non elementary reactionyields higher desired product in Fed-Batch Reactor than inContinuous Plug Flow Reactor

As in Scheme 2 the Plug Flow Reactor yield initiallyincreases with the increase in reaction time (ie lengthierreactor pipe) consequently 119873B119905119873A119905 value decreases asshown in Table 8(d) (ie reduced consumption of ReactantB) However the Plug Flow Reactor yield saturates out below

ISRN Chemical Engineering 13

Table 7 (a) Reactor-1 (Fed-Batch Scheme 6 Part 1) (b) Reactor-2 (Plug Flow Scheme 6 Part 1) (c) Reactor-1 (Fed-Batch Scheme 6 Part2) (d) Reactor-2 (Plug Flow Scheme 6 Part 2) (e) Reactor-1 (Fed-Batch Scheme 6 Part 3) (f) Reactor-2 (Plug Flow Scheme 6 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1121 2128 0027 000 229 035 1073600 1121 2128 0027 000 229 035 1073

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1121 2128 0027 4119864 minus 04 229 04 107360 1121 2128 0027 5119864 minus 06 229 04 1073

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7119864 minus 03 229 035 10731800 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1152 2129 0027 0083 229 035 1073360 1139 2128 0027 0048 229 035 1073720 1128 2128 0027 0017 229 035 1073240 1152 2129 0027 0083 229 035 1073240 1152 2129 0027 0083 229 035 1073

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1022 2126 0027 0012 2568 0073 1204900 1022 2126 0027 0012 2567 0072 1203

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1058 2126 0027 0108 2567 0072 1204360 1042 2126 0027 0066 2568 0073 1204

Fed-Batch Reactor yield (Figure 10) Overall the Fed BatchReactor yields higher product R than Plug Flow Reactor eventhough there is a verymarginal change in yield for the changein the relative concentration of reacting streams (Table 8(c)rows 2 4 and 5)

105 (Scheme 8 a = 05 b = 15 c = 1 d = 1 Nonelementary)

1051 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 9(a) and 9(b)

1052 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 9(c) and 9(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 11

1053 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 9(e) and 9(f)) Tables 9(a)ndash9(f)

and Figure 11 show that this non elementary reaction yieldshigher desired product in Plug Flow Reactor than in Fed-Batch Reactor Also the yield in Fed batch reactor decreaseswith addition time

As in Scheme 3 and Scheme 4 the reduced additiontime in Fed Batch Reactor results in increased productyield However in actual practice heat transfer and otherlimitations of the reactor vessel could possibly determine theminimum addition time beyond which addition time cannotbe reduced So the Fed Batch reactor yield is limited

It is to be noted that there is amarginal change in the yieldin Fed Batch reactor with relative concentration of reacting

14 ISRN Chemical Engineering

Table 8 (a) Reactor-1 (Fed-Batch Scheme 7 Part 1) (b) Reactor-2 (Plug Flow Scheme 7 Part 1) (c) Reactor-1 (Fed-Batch Scheme 7 Part2) (d) Reactor-2 (Plug Flow Scheme 7 Part 2) (e) Reactor-1 (Fed-Batch Scheme 7 Part 3) (f) Reactor-2 (Plug Flow Scheme 7 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 0992 2125 0026 000 2636 0004 1236600 099 2125 0027 000 264 8119864 minus 05 1237

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1139 2128 0027 2119864 minus 11 2242 04 105160 1139 2128 0027 2119864 minus 11 2242 04 1051

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1037 2126 0027 5119864 minus 04 2515 0125 1179900 1024 2126 0027 3119864 minus 04 2548 0092 11951800 1014 2125 0027 1119864 minus 04 2576 0064 1207900 1025 2126 0027 3E minus 04 2547 0093 1194900 1024 2126 0027 3E minus 04 255 009 1195

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1757 2144 0027 0472 1067 1573 5002360 1397 2135 0027 0165 172 092 806720 1176 2129 0027 0021 2166 0474 1015240 1757 2144 0027 0472 1067 1573 5002240 1757 2144 0027 0472 1067 1573 5002

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 0998 2125 0027 0001 2619 0021 1228900 0996 2125 0027 9119864 minus 04 2624 0016 1230

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1372 2134 0027 0687 2309 0331 1082360 115 2129 0027 0258 2472 0168 1159

913

3

827

768

696

999

1

965

595

8

955

1

955

0 500 1000 1500 2000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 11 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 8 Part 2)

80 847 91

2

985 101

4

105

3

107

2

452

5 586 694

9

701

701

701

701

701

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 12 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 9 Part 2)

ISRN Chemical Engineering 15

Table 9 (a) Reactor-1 (Fed-Batch Scheme 8 Part 1) (b) Reactor-2 (Plug Flow Scheme 8 Part 1) (c) Reactor-1 (Fed-Batch Scheme 8 Part2) (d) Reactor-2 (Plug Flow Scheme 8 Part 2) (e) Reactor-1 (Fed-Batch Scheme 8 Part 3) (f) Reactor-2 (Plug Flow Scheme 8 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 176 2144 0027 000 0588 2052 275600 1892 2147 0027 000 0234 2406 110

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1216 213 0027 3119864 minus 26 2037 06 95560 1216 213 0027 0000 2037 06 955

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1318 2133 0027 6119864 minus 06 1765 0875 827900 1366 2124 0027 9119864 minus 06 1638 1002 7681800 1423 2136 0027 2119864 minus 05 1485 1155 696900 1359 2134 0027 8E minus 06 1656 0984 776900 1374 2667 0027 1E minus 05 1615 1025 757

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1218 213 0027 0029 206 058 9655360 1216 213 0027 0008 2044 0596 958720 1216 213 0027 2119864 minus 04 2038 0602 9551240 1218 213 0027 0029 206 058 9655240 1218 213 0027 0029 206 058 9655

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1078 2127 0027 0003 2408 0232 1129900 109 2127 0027 0002 2376 0264 1114

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1076 2127 0027 0087 2498 0142 1171360 1065 2127 0027 0046 2486 0154 1166

streams (Table 9(c) rows 2 4 and 5) However this variationis too low to catch up with Plug Flow Reactor yield

106 (Scheme 9 119886 = 15 119887 = 05 119888 = 1 and 119889 = 1Nonelementary)

1061 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 10(a) and 10(b)

1062 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Theyield values for varying reaction times are capturedin Figure 12

In Tables 10(c) and 10(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1063 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 Tables 10(a)ndash10(f) and Figure 12 show that

this nonelementary reaction yields higher desired productin Fed-Batch Reactor than in Continuous Plug Flow Reac-tor

As in Scheme 2 and Scheme 7 the Plug Flow Reactoryield initially increases with the increase in reaction time(ie lengthier reactor pipe) consequently 119873B119905119873A119905 valuedecreases (ie reduced consumption of Reactant B) How-ever the Plug Flow Reactor yield saturates out below Fed-Batch Reactor yield (Figure 12)

Overall the Fed Batch Reactor yields higher product Rthan Plug Flow Reactor even though there is a very marginalchange in yield for the change in the relative concentration ofreacting streams (Table 10(c) rows 2 4 and 5) in Fed-BatchReactor

16 ISRN Chemical Engineering

Table 10 (a) Reactor-1 (Fed-Batch Scheme 9 Part 1) (b) Reactor-2 (Plug Flow Scheme 9 Part 1) (c) Reactor-1 (Fed-Batch Scheme 9 Part2) (d) Reactor-2 (Plug Flow Scheme 9 Part 2) (e) Reactor-1 (Fed-Batch Scheme 9 Part 3) (f) Reactor-2 (Plug Flow Scheme 9 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1019 2125 0027 000 2564 0077 1202600 0994 2125 0027 000 263 1119864 minus 02 1233

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1419 2135 0027 2119864 minus 11 1497 11 701560 1419 2135 0027 2119864 minus 11 1497 11 7015

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1302 2133 0027 4119864 minus 15 1807 0833 847900 125 2131 0027 4119864 minus 15 1946 0694 9121800 1192 213 0027 4119864 minus 15 2101 0539 985900 1254 2131 0027 4E minus 15 1936 0704 907900 1246 2131 0027 4E minus 15 1957 0683 917

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1771 2144 0027 0408 0965 1675 4525360 1544 2139 0027 0088 1251 1389 586720 1425 2136 0027 0001 1482 1158 6949240 1771 2144 0027 0408 0965 1675 4525240 1771 2144 0027 0408 0965 1675 4525

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 104 2667 0027 1119864 minus 06 2506 0134 1175900 1034 2126 0027 4119864 minus 15 2523 0117 1183

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 14 2135 0027 0624 217 047 1017360 1191 213 0027 0202 2307 0333 1081

Table 11 Summary of results

Schemenumber

119886 119887 119888 119889 Favored reactorRelationship

between 119886 119887 119888 and119889

1 1 1 1 1 Both equally 119886 + 119888 = 119887 + 119889

2 1 1 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

3 1 1 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

4 05 15 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

5 15 05 05 15 Both equally 119886 + 119888 = 119887 + 119889

6 05 15 15 05 Both equally 119886 + 119888 = 119887 + 119889

7 15 05 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

8 05 15 1 1 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

9 15 05 1 1 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

11 Conclusion

Under the simulated conditions elementary Second ordercompetitive consecutive reactions of the type mentioned in(1) yield the same amount of intermediate product R in bothideal fed batch and ideal Plug Flow Reactors for a constantconversion (99) of limiting reactant A Yield and selectivityof the product depends only on119870

11198702in both the reactors

However of the 8 nonelementary scenarios simulatedthree (Schemes 3 4 and 8) favor Plug Flow Reactor and threeother (Schemes 2 7 and 9) favor Fed Batch Reactor Twoothers (Schemes 5 and 6) like elementary reaction yield thesame in both Plug Flow Reactor and Fed batch reactor

Among the schemes simulated previously (Schemes 1 to9) the schemes giving increased yield R with reduced addi-tion time in Fed batch reactor favor Plug Flow Reactor andthe schemes giving increased yield with increased addition

ISRN Chemical Engineering 17

time in fed batch reactor favor Fed batch reactor This couldwell be a practical reckoner to screen the potential candidateamong the simulated schemes for Plug Flow Reactor eventhough this idea is only with respect to suitability of kineticparameters

The relationship between the exponents 119886 119887 119888 and 119889 andthe favourable reactor found in the simulation as shown inTable 11 is noteworthy

Nomenclature

1198701 Rate constant of reaction between A and

B in Litresdotmolminus1sdotsminus1K2 Rate constant of 2nd reaction between R

and B in Litresdotmolminus1sdotsminus1t Time s119905119886 Reactant B addition time in Fed Batch

Reactor s119905119898 Reaction mass maintenance time in Fed

Batch Reactor stlowast Space time in Plug Flow Reactor stend Space time for which each case of plug

flow rector simulation has been done s119903119909 Rate of change of species ldquoxrdquo

(molsdotLitreminus1sdotsminus1) ldquoxrdquo is representative ofspecies A B R S C and D

119862119909= 119873119909119881 Concentration molsdotLitreminus1 of any species

say ldquoxrdquoV Reaction volume m3119873119909 Number of Kg moles of species ldquoxrdquo k mol

NB119905 Total Kg moles of reactant B used inreaction k mol

NA119905 Total kg moles of reactant A used inreaction k mol

119881119886119905 Volume of stream containing reactant B

m3119881119905 Total volume of contents including

streams of reactant A and reactant B m3v Plug Flow Reactor volume m3v1015840 Volumetric flow rate m3s119865119909 Molar flow rate (k molsdotsminus1) of species ldquoxrdquo

which is representative of species A B RS C and D

NB119905NA119905 Ratio of total moles of B to total moles ofA taken for the reaction

119873119909119865 Final kg moles of the species ldquoxrdquo k mol

WR Weight kg of total intermediate (desired)product formed at the end of reaction inFed Batch Reactor and at the end of agiven space time in the Plug Flow Reactor

Acknowledgment

The author would like to thank Chandra Kanth Terupally ofPlanck Technical Hyderabad India for providing adequatesupport in MATLAB Programming

References

[1] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1998

[2] J F Richardson and D G Peacock Coulson and RichardsonrsquosChemical Engineering Chemical and Biochemical Reactors andProcess Control Butterworth-Heinemann Boston Mass USA3rd edition 1994

[3] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart I model developmentrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 750162 16pages 2012

[4] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart II design protocolsrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 65432113 pages 2012

[5] J R Bourne ldquoMixing and the selectivity of chemical reactionsrdquoOrganic Process Research andDevelopment vol 7 no 4 pp 471ndash508 2003

[6] J Bałdyga J R Bourne and S J Hearn ldquoInteraction betweenchemical reactions and mixing on various scalesrdquo ChemicalEngineering Science vol 52 no 4 pp 457ndash466 1997

[7] N G Anderson ldquoPractical use of continuous processing indeveloping and scaling up laboratory processesrdquo Organic Pro-cess Research and Development vol 5 no 6 pp 613ndash621 2001

[8] C Brechtelsbauer and F Ricard ldquoReaction engineering evalua-tion and utilization of static mixer technology for the synthesisof pharmaceuticalsrdquoOrganic Process Research andDevelopmentvol 5 no 6 pp 646ndash651 2001

[9] Z Anxionnaz M Cabassud C Gourdon and P Tochon ldquoHeatexchangerreactors (HEX reactors) concepts technologiesstate-of-the-artrdquo Chemical Engineering and Processing vol 47no 12 pp 2029ndash2050 2008

[10] P Barthe C Guermeur O Lobet et al ldquoContinuous multi-injection reactor for multipurpose productionmdashpart Irdquo Chem-ical Engineering and Technology vol 31 no 8 pp 1146ndash11542008

[11] M Patel and G Gasparini ldquoReactor technology flow reactorsand dynamic mixingrdquo Specialty Chemicals Magazine 2009

[12] X W Ni ldquoContinuous oscilatory baffled reactor technologyrdquoin Innovations in Pharmaceutical TechnologymdashManufacturingpp 90ndash96 2006 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=392

[13] L Proctor ldquoContinuous chemical processingrdquo in Innovationsin Pharmaceutical Technology pp 84ndash88 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=290

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ISRN Chemical Engineering 9

Table 4 (a) Reactor-1 (Fed-Batch Scheme 3 Part 1) (b) Reactor-2 (Plug Flow Scheme 3 Part 1) (c) Reactor-1 (Fed-Batch Scheme 3 Part2) (d) Reactor-2 (Plug Flow Scheme 3 Part 2) (e) Reactor-1 (Fed-Batch Scheme 3 Part 3) (f) Reactor-2 (Plug Flow Scheme 3 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1909 2148 0027 000 019 245 9600 195 2149 0027 000 0079 2561 4

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1448 2136 0027 3119864 minus 08 1419 12 665260 1447 2136 0027 3119864 minus 05 142 12 6657

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1598 214 0027 5119864 minus 13 1019 1621 4776900 1661 2142 0027 3119864 minus 13 0851 1789 39891800 1722 2143 0027 7119864 minus 13 0687 1953 3222900 1655 2141 0027 1119864 minus 12 0868 1772 4067900 1668 2142 0027 1119864 minus 12 0833 1807 3905

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1448 2136 0027 4119864 minus 12 1419 1221 6652360 1448 2136 0027 4119864 minus 12 1419 1221 6652720 1448 2136 0027 4119864 minus 12 1419 1221 6652240 1448 2136 0027 4E minus 12 1419 1221 6652240 1448 2136 0027 4E minus 12 1419 1221 6652

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1214 213 0027 0000 2043 0597 9575900 1251 2131 0027 0000 1943 0697 9107

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1172 2129 0027 0071 2227 0413 1044360 1163 2129 0027 0003 2182 0458 1023

1012 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 The data lines (rows) 4 and 5 in Tables 5(c) and 5(d)correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 9

1013 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 and 119870

2=

0002 (See Tables 5(e) and 5(f)) Tables 5(a)ndash5(f) and Figure 9show that this non elementary reaction yields higher desiredproduct in Plug Flow Reactor than in Fed-Batch Reactor

As in Scheme 3 the reduced addition time in Fed BatchReactor results in increased product yield However in actualpractice heat transfer and other limitations of the reactorvessel could possibly determine the minimum addition timebeyond which addition time cannot be reduced So the FedBatch reactor yield is limited

Themarginal change in the yield in FedBatch reactorwithrelative concentration of reacting streams (Table 5(c) rows 24 and 5) may be noted However this variation is too low tocatch up with Plug Flow Reactor yield

102 (Scheme 5 119886 = 15 119887 = 05 119888 = 05 119889 = 15Nonelementary)

1021 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 6(a) and 6(b)

1022 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 119870

2=

001 In Table 6(c) and 6(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1023 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50 119870

2=

0002 (See Tables 6(e) and 6(f)) Tables 6(a)ndash6(f) show that

10 ISRN Chemical Engineering

0

05

1

15

2

25

3

0 100 200 300 400 500 600 700

Con

cent

ratio

n (m

olL

)

Time (s)minus05

(a)

002040608

112141618

2

0 05 1 15 2 25 3 35

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(b)

0

05

1

15

2

25

3

0 500 1000 1500 2000 2500Time (s)minus05

Con

cent

ratio

n (m

olL

)

AB

RS

(c)

002040608

112141618

2

0 100

AB

RS

200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(d)

Figure 7 (a) Concentration as a function of time Fed-Batch Reactor (Scheme 3 Part 1 119905119886= 60 s 119905

119898= 600 s) (b) Concentration as a function

of time Plug Flow Reactor (Scheme 3 Part 1 119905end = 6 s for brevity graph is plotted for 3 s only) (c) Concentration as a function of timeFed-Batch Reactor (Scheme 3 Part 2 119905

119886= 900 s 119905

119898= 1200 s) (d) Concentration as a function of time Plug Flow Reactor (Scheme 3 Part 2

119905end = 360 s)

this type of nonelementary reaction yields the same amountof desired product in fed batch reactor and in Plug FlowReactor Moreover the yield values in Part 2 remain the sameas those in Part 1 That is because 119870

11198702values remain the

same in both Part 1 and Part 2 even though the individual1198701and119870

2values are different It is to be noted that in Part 3

yield values are different from that in Part 1 and Part 2That isbecause 119870

11198702value in Part 3 is different from those in Part

1 and Part 2The change in the relative concentration of both the

reacting streams (as shown in Table 6(c) rows 2 4 and 5 andTable 6(d) rows 1 4 and 5) does not have any effect on theyield

103 (Scheme 6 119886 = 05 119887 = 15 119888 = 15 119889 = 05Nonelementary)

1031 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 7(a) and 7(b)

1032 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 7(c) and 7(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1033 Part 3 (Cases 1 and 2)1198701= 01119870

11198702= 50 and119870

2=

0002 (See Tables 7(e) and 7(f)) Tables 7(a)ndash7(f) show thatthis type of nonelementary reaction also behaves similar toelementary reaction and nonelementary reaction Scheme 5with respect to product selectivity that is the yield is the samein both the reactors The change in the relative concentrationof both the reacting streams (as shown in Table 7(c) rows 24 and 5 and Table 7(d) rows 1 4 and 5) does not have anyeffect on the yield

104 (Scheme 7 119886 = 15 119887 = 05 119888 = 15 119889 = 05Nonelementary)

1041 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 8(a) and 8(b)

ISRN Chemical Engineering 11

Table 5 (a) Reactor-1 (Fed-Batch Scheme 4 Part 1) (b) Reactor-2 (Plug Flow Scheme 4 Part 1) (c) Reactor-1 (Fed-Batch Scheme 4 Part2) (d) Reactor-2 (Plug Flow Scheme 4 Part 2) (e) Reactor-1 (Fed-Batch Scheme 4 Part 3) (f) Reactor-2 (Plug Flow Scheme 4 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1927 2148 0027 000 0141 2499 7600 1961 2149 0027 000 005 259 2

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1313 2133 0027 6119864 minus 08 1778 09 833460 1313 2667 0027 6119864 minus 08 1778 09 8334

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1562 2139 0027 000 1113 1527 5219900 1654 2141 0027 1119864 minus 10 0869 1771 40751800 1733 2143 0027 6119864 minus 13 0658 1982 3085900 1646 2141 0027 1E minus 12 0868 175 4171900 1662 2142 0027 1E minus 10 0848 1792 3974

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1313 2133 0027 000 1778 0862 8334360 1313 2133 0027 000 1778 0862 8334720 1313 2133 0027 8119864 minus 12 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1203 213 0027 7119864 minus 11 2071 0569 971900 1265 2132 0027 6119864 minus 11 1907 0733 894

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 2997 2128 0027 0021 2304 0336 108360 1124 2128 0027 000 2284 0356 107

609

477

6

398

9

322

2

746

266

52

665

2

665

2

0 500 1000 1500 2000ta or tend (s)

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 8 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 3 Part 2)

ta or tend (s)

741

521

9

407

5

308

5

857

1

8334

833

4

833

4

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 9 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 4 Part 2)

12 ISRN Chemical Engineering

Table 6 (a) Reactor-1 (Fed-Batch Scheme 5 Part 1) (b) Reactor-2 (Plug Flow Scheme 5 Part 2) (c) Reactor-1 (Fed-Batch Scheme 5 Part2) (d) Reactor-2 (Plug Flow Scheme 5 Part 2) (e) Reactor-1 (Fed-Batch Scheme 5 Part 2) (f) Reactor-2 (Plug Flow Scheme 5 Part 2)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1664 2142 0027 000 0843 1797 3954600 1664 2149 0027 000 0843 1797 3954

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1664 2142 0027 6119864 minus 09 0843 18 395460 1664 2142 0027 6119864 minus 09 0843 18 3954

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1664 2142 0027 1119864 minus 10 0844 1796 3956900 1664 2142 0027 1119864 minus 10 0843 1797 39541800 1664 2142 0027 1119864 minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1794 2145 0027 0348 0843 1797 3954360 1672 2142 0027 0022 0844 1796 3954720 1664 2142 0027 000 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 124 2131 0027 7119864 minus 11 1973 0667 9249900 124 2131 0027 7119864 minus 11 1973 0667 9248

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1442 2136 0027 0537 1973 0667 9247360 1277 2132 0027 0099 1973 0667 9248

116

211

79

119

5

120

7

121

2

121

8

122

500

280

6 101

5

104

9

105

1

105

1

105

1

105

1

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 10 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 7 Part 2)

1042 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 8(c) and 8(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 10

1043 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 8(c) and 8(d)) Tables 7(a)ndash

7(d) and Figure 10 show that this non elementary reactionyields higher desired product in Fed-Batch Reactor than inContinuous Plug Flow Reactor

As in Scheme 2 the Plug Flow Reactor yield initiallyincreases with the increase in reaction time (ie lengthierreactor pipe) consequently 119873B119905119873A119905 value decreases asshown in Table 8(d) (ie reduced consumption of ReactantB) However the Plug Flow Reactor yield saturates out below

ISRN Chemical Engineering 13

Table 7 (a) Reactor-1 (Fed-Batch Scheme 6 Part 1) (b) Reactor-2 (Plug Flow Scheme 6 Part 1) (c) Reactor-1 (Fed-Batch Scheme 6 Part2) (d) Reactor-2 (Plug Flow Scheme 6 Part 2) (e) Reactor-1 (Fed-Batch Scheme 6 Part 3) (f) Reactor-2 (Plug Flow Scheme 6 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1121 2128 0027 000 229 035 1073600 1121 2128 0027 000 229 035 1073

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1121 2128 0027 4119864 minus 04 229 04 107360 1121 2128 0027 5119864 minus 06 229 04 1073

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7119864 minus 03 229 035 10731800 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1152 2129 0027 0083 229 035 1073360 1139 2128 0027 0048 229 035 1073720 1128 2128 0027 0017 229 035 1073240 1152 2129 0027 0083 229 035 1073240 1152 2129 0027 0083 229 035 1073

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1022 2126 0027 0012 2568 0073 1204900 1022 2126 0027 0012 2567 0072 1203

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1058 2126 0027 0108 2567 0072 1204360 1042 2126 0027 0066 2568 0073 1204

Fed-Batch Reactor yield (Figure 10) Overall the Fed BatchReactor yields higher product R than Plug Flow Reactor eventhough there is a verymarginal change in yield for the changein the relative concentration of reacting streams (Table 8(c)rows 2 4 and 5)

105 (Scheme 8 a = 05 b = 15 c = 1 d = 1 Nonelementary)

1051 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 9(a) and 9(b)

1052 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 9(c) and 9(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 11

1053 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 9(e) and 9(f)) Tables 9(a)ndash9(f)

and Figure 11 show that this non elementary reaction yieldshigher desired product in Plug Flow Reactor than in Fed-Batch Reactor Also the yield in Fed batch reactor decreaseswith addition time

As in Scheme 3 and Scheme 4 the reduced additiontime in Fed Batch Reactor results in increased productyield However in actual practice heat transfer and otherlimitations of the reactor vessel could possibly determine theminimum addition time beyond which addition time cannotbe reduced So the Fed Batch reactor yield is limited

It is to be noted that there is amarginal change in the yieldin Fed Batch reactor with relative concentration of reacting

14 ISRN Chemical Engineering

Table 8 (a) Reactor-1 (Fed-Batch Scheme 7 Part 1) (b) Reactor-2 (Plug Flow Scheme 7 Part 1) (c) Reactor-1 (Fed-Batch Scheme 7 Part2) (d) Reactor-2 (Plug Flow Scheme 7 Part 2) (e) Reactor-1 (Fed-Batch Scheme 7 Part 3) (f) Reactor-2 (Plug Flow Scheme 7 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 0992 2125 0026 000 2636 0004 1236600 099 2125 0027 000 264 8119864 minus 05 1237

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1139 2128 0027 2119864 minus 11 2242 04 105160 1139 2128 0027 2119864 minus 11 2242 04 1051

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1037 2126 0027 5119864 minus 04 2515 0125 1179900 1024 2126 0027 3119864 minus 04 2548 0092 11951800 1014 2125 0027 1119864 minus 04 2576 0064 1207900 1025 2126 0027 3E minus 04 2547 0093 1194900 1024 2126 0027 3E minus 04 255 009 1195

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1757 2144 0027 0472 1067 1573 5002360 1397 2135 0027 0165 172 092 806720 1176 2129 0027 0021 2166 0474 1015240 1757 2144 0027 0472 1067 1573 5002240 1757 2144 0027 0472 1067 1573 5002

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 0998 2125 0027 0001 2619 0021 1228900 0996 2125 0027 9119864 minus 04 2624 0016 1230

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1372 2134 0027 0687 2309 0331 1082360 115 2129 0027 0258 2472 0168 1159

913

3

827

768

696

999

1

965

595

8

955

1

955

0 500 1000 1500 2000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 11 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 8 Part 2)

80 847 91

2

985 101

4

105

3

107

2

452

5 586 694

9

701

701

701

701

701

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 12 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 9 Part 2)

ISRN Chemical Engineering 15

Table 9 (a) Reactor-1 (Fed-Batch Scheme 8 Part 1) (b) Reactor-2 (Plug Flow Scheme 8 Part 1) (c) Reactor-1 (Fed-Batch Scheme 8 Part2) (d) Reactor-2 (Plug Flow Scheme 8 Part 2) (e) Reactor-1 (Fed-Batch Scheme 8 Part 3) (f) Reactor-2 (Plug Flow Scheme 8 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 176 2144 0027 000 0588 2052 275600 1892 2147 0027 000 0234 2406 110

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1216 213 0027 3119864 minus 26 2037 06 95560 1216 213 0027 0000 2037 06 955

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1318 2133 0027 6119864 minus 06 1765 0875 827900 1366 2124 0027 9119864 minus 06 1638 1002 7681800 1423 2136 0027 2119864 minus 05 1485 1155 696900 1359 2134 0027 8E minus 06 1656 0984 776900 1374 2667 0027 1E minus 05 1615 1025 757

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1218 213 0027 0029 206 058 9655360 1216 213 0027 0008 2044 0596 958720 1216 213 0027 2119864 minus 04 2038 0602 9551240 1218 213 0027 0029 206 058 9655240 1218 213 0027 0029 206 058 9655

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1078 2127 0027 0003 2408 0232 1129900 109 2127 0027 0002 2376 0264 1114

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1076 2127 0027 0087 2498 0142 1171360 1065 2127 0027 0046 2486 0154 1166

streams (Table 9(c) rows 2 4 and 5) However this variationis too low to catch up with Plug Flow Reactor yield

106 (Scheme 9 119886 = 15 119887 = 05 119888 = 1 and 119889 = 1Nonelementary)

1061 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 10(a) and 10(b)

1062 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Theyield values for varying reaction times are capturedin Figure 12

In Tables 10(c) and 10(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1063 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 Tables 10(a)ndash10(f) and Figure 12 show that

this nonelementary reaction yields higher desired productin Fed-Batch Reactor than in Continuous Plug Flow Reac-tor

As in Scheme 2 and Scheme 7 the Plug Flow Reactoryield initially increases with the increase in reaction time(ie lengthier reactor pipe) consequently 119873B119905119873A119905 valuedecreases (ie reduced consumption of Reactant B) How-ever the Plug Flow Reactor yield saturates out below Fed-Batch Reactor yield (Figure 12)

Overall the Fed Batch Reactor yields higher product Rthan Plug Flow Reactor even though there is a very marginalchange in yield for the change in the relative concentration ofreacting streams (Table 10(c) rows 2 4 and 5) in Fed-BatchReactor

16 ISRN Chemical Engineering

Table 10 (a) Reactor-1 (Fed-Batch Scheme 9 Part 1) (b) Reactor-2 (Plug Flow Scheme 9 Part 1) (c) Reactor-1 (Fed-Batch Scheme 9 Part2) (d) Reactor-2 (Plug Flow Scheme 9 Part 2) (e) Reactor-1 (Fed-Batch Scheme 9 Part 3) (f) Reactor-2 (Plug Flow Scheme 9 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1019 2125 0027 000 2564 0077 1202600 0994 2125 0027 000 263 1119864 minus 02 1233

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1419 2135 0027 2119864 minus 11 1497 11 701560 1419 2135 0027 2119864 minus 11 1497 11 7015

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1302 2133 0027 4119864 minus 15 1807 0833 847900 125 2131 0027 4119864 minus 15 1946 0694 9121800 1192 213 0027 4119864 minus 15 2101 0539 985900 1254 2131 0027 4E minus 15 1936 0704 907900 1246 2131 0027 4E minus 15 1957 0683 917

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1771 2144 0027 0408 0965 1675 4525360 1544 2139 0027 0088 1251 1389 586720 1425 2136 0027 0001 1482 1158 6949240 1771 2144 0027 0408 0965 1675 4525240 1771 2144 0027 0408 0965 1675 4525

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 104 2667 0027 1119864 minus 06 2506 0134 1175900 1034 2126 0027 4119864 minus 15 2523 0117 1183

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 14 2135 0027 0624 217 047 1017360 1191 213 0027 0202 2307 0333 1081

Table 11 Summary of results

Schemenumber

119886 119887 119888 119889 Favored reactorRelationship

between 119886 119887 119888 and119889

1 1 1 1 1 Both equally 119886 + 119888 = 119887 + 119889

2 1 1 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

3 1 1 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

4 05 15 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

5 15 05 05 15 Both equally 119886 + 119888 = 119887 + 119889

6 05 15 15 05 Both equally 119886 + 119888 = 119887 + 119889

7 15 05 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

8 05 15 1 1 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

9 15 05 1 1 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

11 Conclusion

Under the simulated conditions elementary Second ordercompetitive consecutive reactions of the type mentioned in(1) yield the same amount of intermediate product R in bothideal fed batch and ideal Plug Flow Reactors for a constantconversion (99) of limiting reactant A Yield and selectivityof the product depends only on119870

11198702in both the reactors

However of the 8 nonelementary scenarios simulatedthree (Schemes 3 4 and 8) favor Plug Flow Reactor and threeother (Schemes 2 7 and 9) favor Fed Batch Reactor Twoothers (Schemes 5 and 6) like elementary reaction yield thesame in both Plug Flow Reactor and Fed batch reactor

Among the schemes simulated previously (Schemes 1 to9) the schemes giving increased yield R with reduced addi-tion time in Fed batch reactor favor Plug Flow Reactor andthe schemes giving increased yield with increased addition

ISRN Chemical Engineering 17

time in fed batch reactor favor Fed batch reactor This couldwell be a practical reckoner to screen the potential candidateamong the simulated schemes for Plug Flow Reactor eventhough this idea is only with respect to suitability of kineticparameters

The relationship between the exponents 119886 119887 119888 and 119889 andthe favourable reactor found in the simulation as shown inTable 11 is noteworthy

Nomenclature

1198701 Rate constant of reaction between A and

B in Litresdotmolminus1sdotsminus1K2 Rate constant of 2nd reaction between R

and B in Litresdotmolminus1sdotsminus1t Time s119905119886 Reactant B addition time in Fed Batch

Reactor s119905119898 Reaction mass maintenance time in Fed

Batch Reactor stlowast Space time in Plug Flow Reactor stend Space time for which each case of plug

flow rector simulation has been done s119903119909 Rate of change of species ldquoxrdquo

(molsdotLitreminus1sdotsminus1) ldquoxrdquo is representative ofspecies A B R S C and D

119862119909= 119873119909119881 Concentration molsdotLitreminus1 of any species

say ldquoxrdquoV Reaction volume m3119873119909 Number of Kg moles of species ldquoxrdquo k mol

NB119905 Total Kg moles of reactant B used inreaction k mol

NA119905 Total kg moles of reactant A used inreaction k mol

119881119886119905 Volume of stream containing reactant B

m3119881119905 Total volume of contents including

streams of reactant A and reactant B m3v Plug Flow Reactor volume m3v1015840 Volumetric flow rate m3s119865119909 Molar flow rate (k molsdotsminus1) of species ldquoxrdquo

which is representative of species A B RS C and D

NB119905NA119905 Ratio of total moles of B to total moles ofA taken for the reaction

119873119909119865 Final kg moles of the species ldquoxrdquo k mol

WR Weight kg of total intermediate (desired)product formed at the end of reaction inFed Batch Reactor and at the end of agiven space time in the Plug Flow Reactor

Acknowledgment

The author would like to thank Chandra Kanth Terupally ofPlanck Technical Hyderabad India for providing adequatesupport in MATLAB Programming

References

[1] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1998

[2] J F Richardson and D G Peacock Coulson and RichardsonrsquosChemical Engineering Chemical and Biochemical Reactors andProcess Control Butterworth-Heinemann Boston Mass USA3rd edition 1994

[3] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart I model developmentrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 750162 16pages 2012

[4] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart II design protocolsrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 65432113 pages 2012

[5] J R Bourne ldquoMixing and the selectivity of chemical reactionsrdquoOrganic Process Research andDevelopment vol 7 no 4 pp 471ndash508 2003

[6] J Bałdyga J R Bourne and S J Hearn ldquoInteraction betweenchemical reactions and mixing on various scalesrdquo ChemicalEngineering Science vol 52 no 4 pp 457ndash466 1997

[7] N G Anderson ldquoPractical use of continuous processing indeveloping and scaling up laboratory processesrdquo Organic Pro-cess Research and Development vol 5 no 6 pp 613ndash621 2001

[8] C Brechtelsbauer and F Ricard ldquoReaction engineering evalua-tion and utilization of static mixer technology for the synthesisof pharmaceuticalsrdquoOrganic Process Research andDevelopmentvol 5 no 6 pp 646ndash651 2001

[9] Z Anxionnaz M Cabassud C Gourdon and P Tochon ldquoHeatexchangerreactors (HEX reactors) concepts technologiesstate-of-the-artrdquo Chemical Engineering and Processing vol 47no 12 pp 2029ndash2050 2008

[10] P Barthe C Guermeur O Lobet et al ldquoContinuous multi-injection reactor for multipurpose productionmdashpart Irdquo Chem-ical Engineering and Technology vol 31 no 8 pp 1146ndash11542008

[11] M Patel and G Gasparini ldquoReactor technology flow reactorsand dynamic mixingrdquo Specialty Chemicals Magazine 2009

[12] X W Ni ldquoContinuous oscilatory baffled reactor technologyrdquoin Innovations in Pharmaceutical TechnologymdashManufacturingpp 90ndash96 2006 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=392

[13] L Proctor ldquoContinuous chemical processingrdquo in Innovationsin Pharmaceutical Technology pp 84ndash88 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=290

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10 ISRN Chemical Engineering

0

05

1

15

2

25

3

0 100 200 300 400 500 600 700

Con

cent

ratio

n (m

olL

)

Time (s)minus05

(a)

002040608

112141618

2

0 05 1 15 2 25 3 35

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(b)

0

05

1

15

2

25

3

0 500 1000 1500 2000 2500Time (s)minus05

Con

cent

ratio

n (m

olL

)

AB

RS

(c)

002040608

112141618

2

0 100

AB

RS

200 300 400

Con

cent

ratio

n (m

olL

)

Time (s)minus02

(d)

Figure 7 (a) Concentration as a function of time Fed-Batch Reactor (Scheme 3 Part 1 119905119886= 60 s 119905

119898= 600 s) (b) Concentration as a function

of time Plug Flow Reactor (Scheme 3 Part 1 119905end = 6 s for brevity graph is plotted for 3 s only) (c) Concentration as a function of timeFed-Batch Reactor (Scheme 3 Part 2 119905

119886= 900 s 119905

119898= 1200 s) (d) Concentration as a function of time Plug Flow Reactor (Scheme 3 Part 2

119905end = 360 s)

this type of nonelementary reaction yields the same amountof desired product in fed batch reactor and in Plug FlowReactor Moreover the yield values in Part 2 remain the sameas those in Part 1 That is because 119870

11198702values remain the

same in both Part 1 and Part 2 even though the individual1198701and119870

2values are different It is to be noted that in Part 3

yield values are different from that in Part 1 and Part 2That isbecause 119870

11198702value in Part 3 is different from those in Part

1 and Part 2The change in the relative concentration of both the

reacting streams (as shown in Table 6(c) rows 2 4 and 5 andTable 6(d) rows 1 4 and 5) does not have any effect on theyield

103 (Scheme 6 119886 = 05 119887 = 15 119888 = 15 119889 = 05Nonelementary)

1031 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 7(a) and 7(b)

1032 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 7(c) and 7(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1033 Part 3 (Cases 1 and 2)1198701= 01119870

11198702= 50 and119870

2=

0002 (See Tables 7(e) and 7(f)) Tables 7(a)ndash7(f) show thatthis type of nonelementary reaction also behaves similar toelementary reaction and nonelementary reaction Scheme 5with respect to product selectivity that is the yield is the samein both the reactors The change in the relative concentrationof both the reacting streams (as shown in Table 7(c) rows 24 and 5 and Table 7(d) rows 1 4 and 5) does not have anyeffect on the yield

104 (Scheme 7 119886 = 15 119887 = 05 119888 = 15 119889 = 05Nonelementary)

1041 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 8(a) and 8(b)

ISRN Chemical Engineering 11

Table 5 (a) Reactor-1 (Fed-Batch Scheme 4 Part 1) (b) Reactor-2 (Plug Flow Scheme 4 Part 1) (c) Reactor-1 (Fed-Batch Scheme 4 Part2) (d) Reactor-2 (Plug Flow Scheme 4 Part 2) (e) Reactor-1 (Fed-Batch Scheme 4 Part 3) (f) Reactor-2 (Plug Flow Scheme 4 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1927 2148 0027 000 0141 2499 7600 1961 2149 0027 000 005 259 2

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1313 2133 0027 6119864 minus 08 1778 09 833460 1313 2667 0027 6119864 minus 08 1778 09 8334

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1562 2139 0027 000 1113 1527 5219900 1654 2141 0027 1119864 minus 10 0869 1771 40751800 1733 2143 0027 6119864 minus 13 0658 1982 3085900 1646 2141 0027 1E minus 12 0868 175 4171900 1662 2142 0027 1E minus 10 0848 1792 3974

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1313 2133 0027 000 1778 0862 8334360 1313 2133 0027 000 1778 0862 8334720 1313 2133 0027 8119864 minus 12 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1203 213 0027 7119864 minus 11 2071 0569 971900 1265 2132 0027 6119864 minus 11 1907 0733 894

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 2997 2128 0027 0021 2304 0336 108360 1124 2128 0027 000 2284 0356 107

609

477

6

398

9

322

2

746

266

52

665

2

665

2

0 500 1000 1500 2000ta or tend (s)

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 8 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 3 Part 2)

ta or tend (s)

741

521

9

407

5

308

5

857

1

8334

833

4

833

4

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 9 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 4 Part 2)

12 ISRN Chemical Engineering

Table 6 (a) Reactor-1 (Fed-Batch Scheme 5 Part 1) (b) Reactor-2 (Plug Flow Scheme 5 Part 2) (c) Reactor-1 (Fed-Batch Scheme 5 Part2) (d) Reactor-2 (Plug Flow Scheme 5 Part 2) (e) Reactor-1 (Fed-Batch Scheme 5 Part 2) (f) Reactor-2 (Plug Flow Scheme 5 Part 2)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1664 2142 0027 000 0843 1797 3954600 1664 2149 0027 000 0843 1797 3954

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1664 2142 0027 6119864 minus 09 0843 18 395460 1664 2142 0027 6119864 minus 09 0843 18 3954

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1664 2142 0027 1119864 minus 10 0844 1796 3956900 1664 2142 0027 1119864 minus 10 0843 1797 39541800 1664 2142 0027 1119864 minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1794 2145 0027 0348 0843 1797 3954360 1672 2142 0027 0022 0844 1796 3954720 1664 2142 0027 000 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 124 2131 0027 7119864 minus 11 1973 0667 9249900 124 2131 0027 7119864 minus 11 1973 0667 9248

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1442 2136 0027 0537 1973 0667 9247360 1277 2132 0027 0099 1973 0667 9248

116

211

79

119

5

120

7

121

2

121

8

122

500

280

6 101

5

104

9

105

1

105

1

105

1

105

1

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 10 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 7 Part 2)

1042 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 8(c) and 8(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 10

1043 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 8(c) and 8(d)) Tables 7(a)ndash

7(d) and Figure 10 show that this non elementary reactionyields higher desired product in Fed-Batch Reactor than inContinuous Plug Flow Reactor

As in Scheme 2 the Plug Flow Reactor yield initiallyincreases with the increase in reaction time (ie lengthierreactor pipe) consequently 119873B119905119873A119905 value decreases asshown in Table 8(d) (ie reduced consumption of ReactantB) However the Plug Flow Reactor yield saturates out below

ISRN Chemical Engineering 13

Table 7 (a) Reactor-1 (Fed-Batch Scheme 6 Part 1) (b) Reactor-2 (Plug Flow Scheme 6 Part 1) (c) Reactor-1 (Fed-Batch Scheme 6 Part2) (d) Reactor-2 (Plug Flow Scheme 6 Part 2) (e) Reactor-1 (Fed-Batch Scheme 6 Part 3) (f) Reactor-2 (Plug Flow Scheme 6 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1121 2128 0027 000 229 035 1073600 1121 2128 0027 000 229 035 1073

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1121 2128 0027 4119864 minus 04 229 04 107360 1121 2128 0027 5119864 minus 06 229 04 1073

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7119864 minus 03 229 035 10731800 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1152 2129 0027 0083 229 035 1073360 1139 2128 0027 0048 229 035 1073720 1128 2128 0027 0017 229 035 1073240 1152 2129 0027 0083 229 035 1073240 1152 2129 0027 0083 229 035 1073

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1022 2126 0027 0012 2568 0073 1204900 1022 2126 0027 0012 2567 0072 1203

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1058 2126 0027 0108 2567 0072 1204360 1042 2126 0027 0066 2568 0073 1204

Fed-Batch Reactor yield (Figure 10) Overall the Fed BatchReactor yields higher product R than Plug Flow Reactor eventhough there is a verymarginal change in yield for the changein the relative concentration of reacting streams (Table 8(c)rows 2 4 and 5)

105 (Scheme 8 a = 05 b = 15 c = 1 d = 1 Nonelementary)

1051 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 9(a) and 9(b)

1052 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 9(c) and 9(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 11

1053 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 9(e) and 9(f)) Tables 9(a)ndash9(f)

and Figure 11 show that this non elementary reaction yieldshigher desired product in Plug Flow Reactor than in Fed-Batch Reactor Also the yield in Fed batch reactor decreaseswith addition time

As in Scheme 3 and Scheme 4 the reduced additiontime in Fed Batch Reactor results in increased productyield However in actual practice heat transfer and otherlimitations of the reactor vessel could possibly determine theminimum addition time beyond which addition time cannotbe reduced So the Fed Batch reactor yield is limited

It is to be noted that there is amarginal change in the yieldin Fed Batch reactor with relative concentration of reacting

14 ISRN Chemical Engineering

Table 8 (a) Reactor-1 (Fed-Batch Scheme 7 Part 1) (b) Reactor-2 (Plug Flow Scheme 7 Part 1) (c) Reactor-1 (Fed-Batch Scheme 7 Part2) (d) Reactor-2 (Plug Flow Scheme 7 Part 2) (e) Reactor-1 (Fed-Batch Scheme 7 Part 3) (f) Reactor-2 (Plug Flow Scheme 7 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 0992 2125 0026 000 2636 0004 1236600 099 2125 0027 000 264 8119864 minus 05 1237

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1139 2128 0027 2119864 minus 11 2242 04 105160 1139 2128 0027 2119864 minus 11 2242 04 1051

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1037 2126 0027 5119864 minus 04 2515 0125 1179900 1024 2126 0027 3119864 minus 04 2548 0092 11951800 1014 2125 0027 1119864 minus 04 2576 0064 1207900 1025 2126 0027 3E minus 04 2547 0093 1194900 1024 2126 0027 3E minus 04 255 009 1195

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1757 2144 0027 0472 1067 1573 5002360 1397 2135 0027 0165 172 092 806720 1176 2129 0027 0021 2166 0474 1015240 1757 2144 0027 0472 1067 1573 5002240 1757 2144 0027 0472 1067 1573 5002

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 0998 2125 0027 0001 2619 0021 1228900 0996 2125 0027 9119864 minus 04 2624 0016 1230

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1372 2134 0027 0687 2309 0331 1082360 115 2129 0027 0258 2472 0168 1159

913

3

827

768

696

999

1

965

595

8

955

1

955

0 500 1000 1500 2000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 11 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 8 Part 2)

80 847 91

2

985 101

4

105

3

107

2

452

5 586 694

9

701

701

701

701

701

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 12 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 9 Part 2)

ISRN Chemical Engineering 15

Table 9 (a) Reactor-1 (Fed-Batch Scheme 8 Part 1) (b) Reactor-2 (Plug Flow Scheme 8 Part 1) (c) Reactor-1 (Fed-Batch Scheme 8 Part2) (d) Reactor-2 (Plug Flow Scheme 8 Part 2) (e) Reactor-1 (Fed-Batch Scheme 8 Part 3) (f) Reactor-2 (Plug Flow Scheme 8 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 176 2144 0027 000 0588 2052 275600 1892 2147 0027 000 0234 2406 110

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1216 213 0027 3119864 minus 26 2037 06 95560 1216 213 0027 0000 2037 06 955

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1318 2133 0027 6119864 minus 06 1765 0875 827900 1366 2124 0027 9119864 minus 06 1638 1002 7681800 1423 2136 0027 2119864 minus 05 1485 1155 696900 1359 2134 0027 8E minus 06 1656 0984 776900 1374 2667 0027 1E minus 05 1615 1025 757

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1218 213 0027 0029 206 058 9655360 1216 213 0027 0008 2044 0596 958720 1216 213 0027 2119864 minus 04 2038 0602 9551240 1218 213 0027 0029 206 058 9655240 1218 213 0027 0029 206 058 9655

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1078 2127 0027 0003 2408 0232 1129900 109 2127 0027 0002 2376 0264 1114

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1076 2127 0027 0087 2498 0142 1171360 1065 2127 0027 0046 2486 0154 1166

streams (Table 9(c) rows 2 4 and 5) However this variationis too low to catch up with Plug Flow Reactor yield

106 (Scheme 9 119886 = 15 119887 = 05 119888 = 1 and 119889 = 1Nonelementary)

1061 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 10(a) and 10(b)

1062 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Theyield values for varying reaction times are capturedin Figure 12

In Tables 10(c) and 10(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1063 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 Tables 10(a)ndash10(f) and Figure 12 show that

this nonelementary reaction yields higher desired productin Fed-Batch Reactor than in Continuous Plug Flow Reac-tor

As in Scheme 2 and Scheme 7 the Plug Flow Reactoryield initially increases with the increase in reaction time(ie lengthier reactor pipe) consequently 119873B119905119873A119905 valuedecreases (ie reduced consumption of Reactant B) How-ever the Plug Flow Reactor yield saturates out below Fed-Batch Reactor yield (Figure 12)

Overall the Fed Batch Reactor yields higher product Rthan Plug Flow Reactor even though there is a very marginalchange in yield for the change in the relative concentration ofreacting streams (Table 10(c) rows 2 4 and 5) in Fed-BatchReactor

16 ISRN Chemical Engineering

Table 10 (a) Reactor-1 (Fed-Batch Scheme 9 Part 1) (b) Reactor-2 (Plug Flow Scheme 9 Part 1) (c) Reactor-1 (Fed-Batch Scheme 9 Part2) (d) Reactor-2 (Plug Flow Scheme 9 Part 2) (e) Reactor-1 (Fed-Batch Scheme 9 Part 3) (f) Reactor-2 (Plug Flow Scheme 9 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1019 2125 0027 000 2564 0077 1202600 0994 2125 0027 000 263 1119864 minus 02 1233

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1419 2135 0027 2119864 minus 11 1497 11 701560 1419 2135 0027 2119864 minus 11 1497 11 7015

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1302 2133 0027 4119864 minus 15 1807 0833 847900 125 2131 0027 4119864 minus 15 1946 0694 9121800 1192 213 0027 4119864 minus 15 2101 0539 985900 1254 2131 0027 4E minus 15 1936 0704 907900 1246 2131 0027 4E minus 15 1957 0683 917

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1771 2144 0027 0408 0965 1675 4525360 1544 2139 0027 0088 1251 1389 586720 1425 2136 0027 0001 1482 1158 6949240 1771 2144 0027 0408 0965 1675 4525240 1771 2144 0027 0408 0965 1675 4525

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 104 2667 0027 1119864 minus 06 2506 0134 1175900 1034 2126 0027 4119864 minus 15 2523 0117 1183

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 14 2135 0027 0624 217 047 1017360 1191 213 0027 0202 2307 0333 1081

Table 11 Summary of results

Schemenumber

119886 119887 119888 119889 Favored reactorRelationship

between 119886 119887 119888 and119889

1 1 1 1 1 Both equally 119886 + 119888 = 119887 + 119889

2 1 1 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

3 1 1 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

4 05 15 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

5 15 05 05 15 Both equally 119886 + 119888 = 119887 + 119889

6 05 15 15 05 Both equally 119886 + 119888 = 119887 + 119889

7 15 05 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

8 05 15 1 1 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

9 15 05 1 1 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

11 Conclusion

Under the simulated conditions elementary Second ordercompetitive consecutive reactions of the type mentioned in(1) yield the same amount of intermediate product R in bothideal fed batch and ideal Plug Flow Reactors for a constantconversion (99) of limiting reactant A Yield and selectivityof the product depends only on119870

11198702in both the reactors

However of the 8 nonelementary scenarios simulatedthree (Schemes 3 4 and 8) favor Plug Flow Reactor and threeother (Schemes 2 7 and 9) favor Fed Batch Reactor Twoothers (Schemes 5 and 6) like elementary reaction yield thesame in both Plug Flow Reactor and Fed batch reactor

Among the schemes simulated previously (Schemes 1 to9) the schemes giving increased yield R with reduced addi-tion time in Fed batch reactor favor Plug Flow Reactor andthe schemes giving increased yield with increased addition

ISRN Chemical Engineering 17

time in fed batch reactor favor Fed batch reactor This couldwell be a practical reckoner to screen the potential candidateamong the simulated schemes for Plug Flow Reactor eventhough this idea is only with respect to suitability of kineticparameters

The relationship between the exponents 119886 119887 119888 and 119889 andthe favourable reactor found in the simulation as shown inTable 11 is noteworthy

Nomenclature

1198701 Rate constant of reaction between A and

B in Litresdotmolminus1sdotsminus1K2 Rate constant of 2nd reaction between R

and B in Litresdotmolminus1sdotsminus1t Time s119905119886 Reactant B addition time in Fed Batch

Reactor s119905119898 Reaction mass maintenance time in Fed

Batch Reactor stlowast Space time in Plug Flow Reactor stend Space time for which each case of plug

flow rector simulation has been done s119903119909 Rate of change of species ldquoxrdquo

(molsdotLitreminus1sdotsminus1) ldquoxrdquo is representative ofspecies A B R S C and D

119862119909= 119873119909119881 Concentration molsdotLitreminus1 of any species

say ldquoxrdquoV Reaction volume m3119873119909 Number of Kg moles of species ldquoxrdquo k mol

NB119905 Total Kg moles of reactant B used inreaction k mol

NA119905 Total kg moles of reactant A used inreaction k mol

119881119886119905 Volume of stream containing reactant B

m3119881119905 Total volume of contents including

streams of reactant A and reactant B m3v Plug Flow Reactor volume m3v1015840 Volumetric flow rate m3s119865119909 Molar flow rate (k molsdotsminus1) of species ldquoxrdquo

which is representative of species A B RS C and D

NB119905NA119905 Ratio of total moles of B to total moles ofA taken for the reaction

119873119909119865 Final kg moles of the species ldquoxrdquo k mol

WR Weight kg of total intermediate (desired)product formed at the end of reaction inFed Batch Reactor and at the end of agiven space time in the Plug Flow Reactor

Acknowledgment

The author would like to thank Chandra Kanth Terupally ofPlanck Technical Hyderabad India for providing adequatesupport in MATLAB Programming

References

[1] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1998

[2] J F Richardson and D G Peacock Coulson and RichardsonrsquosChemical Engineering Chemical and Biochemical Reactors andProcess Control Butterworth-Heinemann Boston Mass USA3rd edition 1994

[3] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart I model developmentrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 750162 16pages 2012

[4] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart II design protocolsrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 65432113 pages 2012

[5] J R Bourne ldquoMixing and the selectivity of chemical reactionsrdquoOrganic Process Research andDevelopment vol 7 no 4 pp 471ndash508 2003

[6] J Bałdyga J R Bourne and S J Hearn ldquoInteraction betweenchemical reactions and mixing on various scalesrdquo ChemicalEngineering Science vol 52 no 4 pp 457ndash466 1997

[7] N G Anderson ldquoPractical use of continuous processing indeveloping and scaling up laboratory processesrdquo Organic Pro-cess Research and Development vol 5 no 6 pp 613ndash621 2001

[8] C Brechtelsbauer and F Ricard ldquoReaction engineering evalua-tion and utilization of static mixer technology for the synthesisof pharmaceuticalsrdquoOrganic Process Research andDevelopmentvol 5 no 6 pp 646ndash651 2001

[9] Z Anxionnaz M Cabassud C Gourdon and P Tochon ldquoHeatexchangerreactors (HEX reactors) concepts technologiesstate-of-the-artrdquo Chemical Engineering and Processing vol 47no 12 pp 2029ndash2050 2008

[10] P Barthe C Guermeur O Lobet et al ldquoContinuous multi-injection reactor for multipurpose productionmdashpart Irdquo Chem-ical Engineering and Technology vol 31 no 8 pp 1146ndash11542008

[11] M Patel and G Gasparini ldquoReactor technology flow reactorsand dynamic mixingrdquo Specialty Chemicals Magazine 2009

[12] X W Ni ldquoContinuous oscilatory baffled reactor technologyrdquoin Innovations in Pharmaceutical TechnologymdashManufacturingpp 90ndash96 2006 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=392

[13] L Proctor ldquoContinuous chemical processingrdquo in Innovationsin Pharmaceutical Technology pp 84ndash88 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=290

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ISRN Chemical Engineering 11

Table 5 (a) Reactor-1 (Fed-Batch Scheme 4 Part 1) (b) Reactor-2 (Plug Flow Scheme 4 Part 1) (c) Reactor-1 (Fed-Batch Scheme 4 Part2) (d) Reactor-2 (Plug Flow Scheme 4 Part 2) (e) Reactor-1 (Fed-Batch Scheme 4 Part 3) (f) Reactor-2 (Plug Flow Scheme 4 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1927 2148 0027 000 0141 2499 7600 1961 2149 0027 000 005 259 2

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1313 2133 0027 6119864 minus 08 1778 09 833460 1313 2667 0027 6119864 minus 08 1778 09 8334

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1562 2139 0027 000 1113 1527 5219900 1654 2141 0027 1119864 minus 10 0869 1771 40751800 1733 2143 0027 6119864 minus 13 0658 1982 3085900 1646 2141 0027 1E minus 12 0868 175 4171900 1662 2142 0027 1E minus 10 0848 1792 3974

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1313 2133 0027 000 1778 0862 8334360 1313 2133 0027 000 1778 0862 8334720 1313 2133 0027 8119864 minus 12 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334240 1313 2133 0027 000 1778 0862 8334

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1203 213 0027 7119864 minus 11 2071 0569 971900 1265 2132 0027 6119864 minus 11 1907 0733 894

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 2997 2128 0027 0021 2304 0336 108360 1124 2128 0027 000 2284 0356 107

609

477

6

398

9

322

2

746

266

52

665

2

665

2

0 500 1000 1500 2000ta or tend (s)

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 8 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 3 Part 2)

ta or tend (s)

741

521

9

407

5

308

5

857

1

8334

833

4

833

4

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Prod

uct R

yie

ld (k

g)

Fed-Batch ReactorPlug Flow Reactor

Figure 9 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 4 Part 2)

12 ISRN Chemical Engineering

Table 6 (a) Reactor-1 (Fed-Batch Scheme 5 Part 1) (b) Reactor-2 (Plug Flow Scheme 5 Part 2) (c) Reactor-1 (Fed-Batch Scheme 5 Part2) (d) Reactor-2 (Plug Flow Scheme 5 Part 2) (e) Reactor-1 (Fed-Batch Scheme 5 Part 2) (f) Reactor-2 (Plug Flow Scheme 5 Part 2)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1664 2142 0027 000 0843 1797 3954600 1664 2149 0027 000 0843 1797 3954

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1664 2142 0027 6119864 minus 09 0843 18 395460 1664 2142 0027 6119864 minus 09 0843 18 3954

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1664 2142 0027 1119864 minus 10 0844 1796 3956900 1664 2142 0027 1119864 minus 10 0843 1797 39541800 1664 2142 0027 1119864 minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1794 2145 0027 0348 0843 1797 3954360 1672 2142 0027 0022 0844 1796 3954720 1664 2142 0027 000 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 124 2131 0027 7119864 minus 11 1973 0667 9249900 124 2131 0027 7119864 minus 11 1973 0667 9248

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1442 2136 0027 0537 1973 0667 9247360 1277 2132 0027 0099 1973 0667 9248

116

211

79

119

5

120

7

121

2

121

8

122

500

280

6 101

5

104

9

105

1

105

1

105

1

105

1

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 10 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 7 Part 2)

1042 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 8(c) and 8(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 10

1043 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 8(c) and 8(d)) Tables 7(a)ndash

7(d) and Figure 10 show that this non elementary reactionyields higher desired product in Fed-Batch Reactor than inContinuous Plug Flow Reactor

As in Scheme 2 the Plug Flow Reactor yield initiallyincreases with the increase in reaction time (ie lengthierreactor pipe) consequently 119873B119905119873A119905 value decreases asshown in Table 8(d) (ie reduced consumption of ReactantB) However the Plug Flow Reactor yield saturates out below

ISRN Chemical Engineering 13

Table 7 (a) Reactor-1 (Fed-Batch Scheme 6 Part 1) (b) Reactor-2 (Plug Flow Scheme 6 Part 1) (c) Reactor-1 (Fed-Batch Scheme 6 Part2) (d) Reactor-2 (Plug Flow Scheme 6 Part 2) (e) Reactor-1 (Fed-Batch Scheme 6 Part 3) (f) Reactor-2 (Plug Flow Scheme 6 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1121 2128 0027 000 229 035 1073600 1121 2128 0027 000 229 035 1073

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1121 2128 0027 4119864 minus 04 229 04 107360 1121 2128 0027 5119864 minus 06 229 04 1073

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7119864 minus 03 229 035 10731800 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1152 2129 0027 0083 229 035 1073360 1139 2128 0027 0048 229 035 1073720 1128 2128 0027 0017 229 035 1073240 1152 2129 0027 0083 229 035 1073240 1152 2129 0027 0083 229 035 1073

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1022 2126 0027 0012 2568 0073 1204900 1022 2126 0027 0012 2567 0072 1203

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1058 2126 0027 0108 2567 0072 1204360 1042 2126 0027 0066 2568 0073 1204

Fed-Batch Reactor yield (Figure 10) Overall the Fed BatchReactor yields higher product R than Plug Flow Reactor eventhough there is a verymarginal change in yield for the changein the relative concentration of reacting streams (Table 8(c)rows 2 4 and 5)

105 (Scheme 8 a = 05 b = 15 c = 1 d = 1 Nonelementary)

1051 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 9(a) and 9(b)

1052 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 9(c) and 9(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 11

1053 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 9(e) and 9(f)) Tables 9(a)ndash9(f)

and Figure 11 show that this non elementary reaction yieldshigher desired product in Plug Flow Reactor than in Fed-Batch Reactor Also the yield in Fed batch reactor decreaseswith addition time

As in Scheme 3 and Scheme 4 the reduced additiontime in Fed Batch Reactor results in increased productyield However in actual practice heat transfer and otherlimitations of the reactor vessel could possibly determine theminimum addition time beyond which addition time cannotbe reduced So the Fed Batch reactor yield is limited

It is to be noted that there is amarginal change in the yieldin Fed Batch reactor with relative concentration of reacting

14 ISRN Chemical Engineering

Table 8 (a) Reactor-1 (Fed-Batch Scheme 7 Part 1) (b) Reactor-2 (Plug Flow Scheme 7 Part 1) (c) Reactor-1 (Fed-Batch Scheme 7 Part2) (d) Reactor-2 (Plug Flow Scheme 7 Part 2) (e) Reactor-1 (Fed-Batch Scheme 7 Part 3) (f) Reactor-2 (Plug Flow Scheme 7 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 0992 2125 0026 000 2636 0004 1236600 099 2125 0027 000 264 8119864 minus 05 1237

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1139 2128 0027 2119864 minus 11 2242 04 105160 1139 2128 0027 2119864 minus 11 2242 04 1051

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1037 2126 0027 5119864 minus 04 2515 0125 1179900 1024 2126 0027 3119864 minus 04 2548 0092 11951800 1014 2125 0027 1119864 minus 04 2576 0064 1207900 1025 2126 0027 3E minus 04 2547 0093 1194900 1024 2126 0027 3E minus 04 255 009 1195

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1757 2144 0027 0472 1067 1573 5002360 1397 2135 0027 0165 172 092 806720 1176 2129 0027 0021 2166 0474 1015240 1757 2144 0027 0472 1067 1573 5002240 1757 2144 0027 0472 1067 1573 5002

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 0998 2125 0027 0001 2619 0021 1228900 0996 2125 0027 9119864 minus 04 2624 0016 1230

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1372 2134 0027 0687 2309 0331 1082360 115 2129 0027 0258 2472 0168 1159

913

3

827

768

696

999

1

965

595

8

955

1

955

0 500 1000 1500 2000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 11 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 8 Part 2)

80 847 91

2

985 101

4

105

3

107

2

452

5 586 694

9

701

701

701

701

701

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 12 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 9 Part 2)

ISRN Chemical Engineering 15

Table 9 (a) Reactor-1 (Fed-Batch Scheme 8 Part 1) (b) Reactor-2 (Plug Flow Scheme 8 Part 1) (c) Reactor-1 (Fed-Batch Scheme 8 Part2) (d) Reactor-2 (Plug Flow Scheme 8 Part 2) (e) Reactor-1 (Fed-Batch Scheme 8 Part 3) (f) Reactor-2 (Plug Flow Scheme 8 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 176 2144 0027 000 0588 2052 275600 1892 2147 0027 000 0234 2406 110

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1216 213 0027 3119864 minus 26 2037 06 95560 1216 213 0027 0000 2037 06 955

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1318 2133 0027 6119864 minus 06 1765 0875 827900 1366 2124 0027 9119864 minus 06 1638 1002 7681800 1423 2136 0027 2119864 minus 05 1485 1155 696900 1359 2134 0027 8E minus 06 1656 0984 776900 1374 2667 0027 1E minus 05 1615 1025 757

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1218 213 0027 0029 206 058 9655360 1216 213 0027 0008 2044 0596 958720 1216 213 0027 2119864 minus 04 2038 0602 9551240 1218 213 0027 0029 206 058 9655240 1218 213 0027 0029 206 058 9655

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1078 2127 0027 0003 2408 0232 1129900 109 2127 0027 0002 2376 0264 1114

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1076 2127 0027 0087 2498 0142 1171360 1065 2127 0027 0046 2486 0154 1166

streams (Table 9(c) rows 2 4 and 5) However this variationis too low to catch up with Plug Flow Reactor yield

106 (Scheme 9 119886 = 15 119887 = 05 119888 = 1 and 119889 = 1Nonelementary)

1061 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 10(a) and 10(b)

1062 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Theyield values for varying reaction times are capturedin Figure 12

In Tables 10(c) and 10(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1063 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 Tables 10(a)ndash10(f) and Figure 12 show that

this nonelementary reaction yields higher desired productin Fed-Batch Reactor than in Continuous Plug Flow Reac-tor

As in Scheme 2 and Scheme 7 the Plug Flow Reactoryield initially increases with the increase in reaction time(ie lengthier reactor pipe) consequently 119873B119905119873A119905 valuedecreases (ie reduced consumption of Reactant B) How-ever the Plug Flow Reactor yield saturates out below Fed-Batch Reactor yield (Figure 12)

Overall the Fed Batch Reactor yields higher product Rthan Plug Flow Reactor even though there is a very marginalchange in yield for the change in the relative concentration ofreacting streams (Table 10(c) rows 2 4 and 5) in Fed-BatchReactor

16 ISRN Chemical Engineering

Table 10 (a) Reactor-1 (Fed-Batch Scheme 9 Part 1) (b) Reactor-2 (Plug Flow Scheme 9 Part 1) (c) Reactor-1 (Fed-Batch Scheme 9 Part2) (d) Reactor-2 (Plug Flow Scheme 9 Part 2) (e) Reactor-1 (Fed-Batch Scheme 9 Part 3) (f) Reactor-2 (Plug Flow Scheme 9 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1019 2125 0027 000 2564 0077 1202600 0994 2125 0027 000 263 1119864 minus 02 1233

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1419 2135 0027 2119864 minus 11 1497 11 701560 1419 2135 0027 2119864 minus 11 1497 11 7015

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1302 2133 0027 4119864 minus 15 1807 0833 847900 125 2131 0027 4119864 minus 15 1946 0694 9121800 1192 213 0027 4119864 minus 15 2101 0539 985900 1254 2131 0027 4E minus 15 1936 0704 907900 1246 2131 0027 4E minus 15 1957 0683 917

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1771 2144 0027 0408 0965 1675 4525360 1544 2139 0027 0088 1251 1389 586720 1425 2136 0027 0001 1482 1158 6949240 1771 2144 0027 0408 0965 1675 4525240 1771 2144 0027 0408 0965 1675 4525

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 104 2667 0027 1119864 minus 06 2506 0134 1175900 1034 2126 0027 4119864 minus 15 2523 0117 1183

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 14 2135 0027 0624 217 047 1017360 1191 213 0027 0202 2307 0333 1081

Table 11 Summary of results

Schemenumber

119886 119887 119888 119889 Favored reactorRelationship

between 119886 119887 119888 and119889

1 1 1 1 1 Both equally 119886 + 119888 = 119887 + 119889

2 1 1 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

3 1 1 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

4 05 15 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

5 15 05 05 15 Both equally 119886 + 119888 = 119887 + 119889

6 05 15 15 05 Both equally 119886 + 119888 = 119887 + 119889

7 15 05 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

8 05 15 1 1 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

9 15 05 1 1 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

11 Conclusion

Under the simulated conditions elementary Second ordercompetitive consecutive reactions of the type mentioned in(1) yield the same amount of intermediate product R in bothideal fed batch and ideal Plug Flow Reactors for a constantconversion (99) of limiting reactant A Yield and selectivityof the product depends only on119870

11198702in both the reactors

However of the 8 nonelementary scenarios simulatedthree (Schemes 3 4 and 8) favor Plug Flow Reactor and threeother (Schemes 2 7 and 9) favor Fed Batch Reactor Twoothers (Schemes 5 and 6) like elementary reaction yield thesame in both Plug Flow Reactor and Fed batch reactor

Among the schemes simulated previously (Schemes 1 to9) the schemes giving increased yield R with reduced addi-tion time in Fed batch reactor favor Plug Flow Reactor andthe schemes giving increased yield with increased addition

ISRN Chemical Engineering 17

time in fed batch reactor favor Fed batch reactor This couldwell be a practical reckoner to screen the potential candidateamong the simulated schemes for Plug Flow Reactor eventhough this idea is only with respect to suitability of kineticparameters

The relationship between the exponents 119886 119887 119888 and 119889 andthe favourable reactor found in the simulation as shown inTable 11 is noteworthy

Nomenclature

1198701 Rate constant of reaction between A and

B in Litresdotmolminus1sdotsminus1K2 Rate constant of 2nd reaction between R

and B in Litresdotmolminus1sdotsminus1t Time s119905119886 Reactant B addition time in Fed Batch

Reactor s119905119898 Reaction mass maintenance time in Fed

Batch Reactor stlowast Space time in Plug Flow Reactor stend Space time for which each case of plug

flow rector simulation has been done s119903119909 Rate of change of species ldquoxrdquo

(molsdotLitreminus1sdotsminus1) ldquoxrdquo is representative ofspecies A B R S C and D

119862119909= 119873119909119881 Concentration molsdotLitreminus1 of any species

say ldquoxrdquoV Reaction volume m3119873119909 Number of Kg moles of species ldquoxrdquo k mol

NB119905 Total Kg moles of reactant B used inreaction k mol

NA119905 Total kg moles of reactant A used inreaction k mol

119881119886119905 Volume of stream containing reactant B

m3119881119905 Total volume of contents including

streams of reactant A and reactant B m3v Plug Flow Reactor volume m3v1015840 Volumetric flow rate m3s119865119909 Molar flow rate (k molsdotsminus1) of species ldquoxrdquo

which is representative of species A B RS C and D

NB119905NA119905 Ratio of total moles of B to total moles ofA taken for the reaction

119873119909119865 Final kg moles of the species ldquoxrdquo k mol

WR Weight kg of total intermediate (desired)product formed at the end of reaction inFed Batch Reactor and at the end of agiven space time in the Plug Flow Reactor

Acknowledgment

The author would like to thank Chandra Kanth Terupally ofPlanck Technical Hyderabad India for providing adequatesupport in MATLAB Programming

References

[1] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1998

[2] J F Richardson and D G Peacock Coulson and RichardsonrsquosChemical Engineering Chemical and Biochemical Reactors andProcess Control Butterworth-Heinemann Boston Mass USA3rd edition 1994

[3] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart I model developmentrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 750162 16pages 2012

[4] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart II design protocolsrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 65432113 pages 2012

[5] J R Bourne ldquoMixing and the selectivity of chemical reactionsrdquoOrganic Process Research andDevelopment vol 7 no 4 pp 471ndash508 2003

[6] J Bałdyga J R Bourne and S J Hearn ldquoInteraction betweenchemical reactions and mixing on various scalesrdquo ChemicalEngineering Science vol 52 no 4 pp 457ndash466 1997

[7] N G Anderson ldquoPractical use of continuous processing indeveloping and scaling up laboratory processesrdquo Organic Pro-cess Research and Development vol 5 no 6 pp 613ndash621 2001

[8] C Brechtelsbauer and F Ricard ldquoReaction engineering evalua-tion and utilization of static mixer technology for the synthesisof pharmaceuticalsrdquoOrganic Process Research andDevelopmentvol 5 no 6 pp 646ndash651 2001

[9] Z Anxionnaz M Cabassud C Gourdon and P Tochon ldquoHeatexchangerreactors (HEX reactors) concepts technologiesstate-of-the-artrdquo Chemical Engineering and Processing vol 47no 12 pp 2029ndash2050 2008

[10] P Barthe C Guermeur O Lobet et al ldquoContinuous multi-injection reactor for multipurpose productionmdashpart Irdquo Chem-ical Engineering and Technology vol 31 no 8 pp 1146ndash11542008

[11] M Patel and G Gasparini ldquoReactor technology flow reactorsand dynamic mixingrdquo Specialty Chemicals Magazine 2009

[12] X W Ni ldquoContinuous oscilatory baffled reactor technologyrdquoin Innovations in Pharmaceutical TechnologymdashManufacturingpp 90ndash96 2006 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=392

[13] L Proctor ldquoContinuous chemical processingrdquo in Innovationsin Pharmaceutical Technology pp 84ndash88 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=290

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12 ISRN Chemical Engineering

Table 6 (a) Reactor-1 (Fed-Batch Scheme 5 Part 1) (b) Reactor-2 (Plug Flow Scheme 5 Part 2) (c) Reactor-1 (Fed-Batch Scheme 5 Part2) (d) Reactor-2 (Plug Flow Scheme 5 Part 2) (e) Reactor-1 (Fed-Batch Scheme 5 Part 2) (f) Reactor-2 (Plug Flow Scheme 5 Part 2)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1664 2142 0027 000 0843 1797 3954600 1664 2149 0027 000 0843 1797 3954

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1664 2142 0027 6119864 minus 09 0843 18 395460 1664 2142 0027 6119864 minus 09 0843 18 3954

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1664 2142 0027 1119864 minus 10 0844 1796 3956900 1664 2142 0027 1119864 minus 10 0843 1797 39541800 1664 2142 0027 1119864 minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954900 1664 2142 0027 1E minus 10 0843 1797 3954

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1794 2145 0027 0348 0843 1797 3954360 1672 2142 0027 0022 0844 1796 3954720 1664 2142 0027 000 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954240 1794 2145 0027 0348 0843 1797 3954

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 124 2131 0027 7119864 minus 11 1973 0667 9249900 124 2131 0027 7119864 minus 11 1973 0667 9248

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1442 2136 0027 0537 1973 0667 9247360 1277 2132 0027 0099 1973 0667 9248

116

211

79

119

5

120

7

121

2

121

8

122

500

280

6 101

5

104

9

105

1

105

1

105

1

105

1

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 10 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 7 Part 2)

1042 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 8(c) and 8(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 10

1043 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 8(c) and 8(d)) Tables 7(a)ndash

7(d) and Figure 10 show that this non elementary reactionyields higher desired product in Fed-Batch Reactor than inContinuous Plug Flow Reactor

As in Scheme 2 the Plug Flow Reactor yield initiallyincreases with the increase in reaction time (ie lengthierreactor pipe) consequently 119873B119905119873A119905 value decreases asshown in Table 8(d) (ie reduced consumption of ReactantB) However the Plug Flow Reactor yield saturates out below

ISRN Chemical Engineering 13

Table 7 (a) Reactor-1 (Fed-Batch Scheme 6 Part 1) (b) Reactor-2 (Plug Flow Scheme 6 Part 1) (c) Reactor-1 (Fed-Batch Scheme 6 Part2) (d) Reactor-2 (Plug Flow Scheme 6 Part 2) (e) Reactor-1 (Fed-Batch Scheme 6 Part 3) (f) Reactor-2 (Plug Flow Scheme 6 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1121 2128 0027 000 229 035 1073600 1121 2128 0027 000 229 035 1073

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1121 2128 0027 4119864 minus 04 229 04 107360 1121 2128 0027 5119864 minus 06 229 04 1073

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7119864 minus 03 229 035 10731800 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1152 2129 0027 0083 229 035 1073360 1139 2128 0027 0048 229 035 1073720 1128 2128 0027 0017 229 035 1073240 1152 2129 0027 0083 229 035 1073240 1152 2129 0027 0083 229 035 1073

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1022 2126 0027 0012 2568 0073 1204900 1022 2126 0027 0012 2567 0072 1203

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1058 2126 0027 0108 2567 0072 1204360 1042 2126 0027 0066 2568 0073 1204

Fed-Batch Reactor yield (Figure 10) Overall the Fed BatchReactor yields higher product R than Plug Flow Reactor eventhough there is a verymarginal change in yield for the changein the relative concentration of reacting streams (Table 8(c)rows 2 4 and 5)

105 (Scheme 8 a = 05 b = 15 c = 1 d = 1 Nonelementary)

1051 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 9(a) and 9(b)

1052 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 9(c) and 9(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 11

1053 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 9(e) and 9(f)) Tables 9(a)ndash9(f)

and Figure 11 show that this non elementary reaction yieldshigher desired product in Plug Flow Reactor than in Fed-Batch Reactor Also the yield in Fed batch reactor decreaseswith addition time

As in Scheme 3 and Scheme 4 the reduced additiontime in Fed Batch Reactor results in increased productyield However in actual practice heat transfer and otherlimitations of the reactor vessel could possibly determine theminimum addition time beyond which addition time cannotbe reduced So the Fed Batch reactor yield is limited

It is to be noted that there is amarginal change in the yieldin Fed Batch reactor with relative concentration of reacting

14 ISRN Chemical Engineering

Table 8 (a) Reactor-1 (Fed-Batch Scheme 7 Part 1) (b) Reactor-2 (Plug Flow Scheme 7 Part 1) (c) Reactor-1 (Fed-Batch Scheme 7 Part2) (d) Reactor-2 (Plug Flow Scheme 7 Part 2) (e) Reactor-1 (Fed-Batch Scheme 7 Part 3) (f) Reactor-2 (Plug Flow Scheme 7 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 0992 2125 0026 000 2636 0004 1236600 099 2125 0027 000 264 8119864 minus 05 1237

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1139 2128 0027 2119864 minus 11 2242 04 105160 1139 2128 0027 2119864 minus 11 2242 04 1051

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1037 2126 0027 5119864 minus 04 2515 0125 1179900 1024 2126 0027 3119864 minus 04 2548 0092 11951800 1014 2125 0027 1119864 minus 04 2576 0064 1207900 1025 2126 0027 3E minus 04 2547 0093 1194900 1024 2126 0027 3E minus 04 255 009 1195

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1757 2144 0027 0472 1067 1573 5002360 1397 2135 0027 0165 172 092 806720 1176 2129 0027 0021 2166 0474 1015240 1757 2144 0027 0472 1067 1573 5002240 1757 2144 0027 0472 1067 1573 5002

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 0998 2125 0027 0001 2619 0021 1228900 0996 2125 0027 9119864 minus 04 2624 0016 1230

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1372 2134 0027 0687 2309 0331 1082360 115 2129 0027 0258 2472 0168 1159

913

3

827

768

696

999

1

965

595

8

955

1

955

0 500 1000 1500 2000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 11 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 8 Part 2)

80 847 91

2

985 101

4

105

3

107

2

452

5 586 694

9

701

701

701

701

701

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 12 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 9 Part 2)

ISRN Chemical Engineering 15

Table 9 (a) Reactor-1 (Fed-Batch Scheme 8 Part 1) (b) Reactor-2 (Plug Flow Scheme 8 Part 1) (c) Reactor-1 (Fed-Batch Scheme 8 Part2) (d) Reactor-2 (Plug Flow Scheme 8 Part 2) (e) Reactor-1 (Fed-Batch Scheme 8 Part 3) (f) Reactor-2 (Plug Flow Scheme 8 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 176 2144 0027 000 0588 2052 275600 1892 2147 0027 000 0234 2406 110

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1216 213 0027 3119864 minus 26 2037 06 95560 1216 213 0027 0000 2037 06 955

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1318 2133 0027 6119864 minus 06 1765 0875 827900 1366 2124 0027 9119864 minus 06 1638 1002 7681800 1423 2136 0027 2119864 minus 05 1485 1155 696900 1359 2134 0027 8E minus 06 1656 0984 776900 1374 2667 0027 1E minus 05 1615 1025 757

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1218 213 0027 0029 206 058 9655360 1216 213 0027 0008 2044 0596 958720 1216 213 0027 2119864 minus 04 2038 0602 9551240 1218 213 0027 0029 206 058 9655240 1218 213 0027 0029 206 058 9655

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1078 2127 0027 0003 2408 0232 1129900 109 2127 0027 0002 2376 0264 1114

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1076 2127 0027 0087 2498 0142 1171360 1065 2127 0027 0046 2486 0154 1166

streams (Table 9(c) rows 2 4 and 5) However this variationis too low to catch up with Plug Flow Reactor yield

106 (Scheme 9 119886 = 15 119887 = 05 119888 = 1 and 119889 = 1Nonelementary)

1061 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 10(a) and 10(b)

1062 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Theyield values for varying reaction times are capturedin Figure 12

In Tables 10(c) and 10(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1063 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 Tables 10(a)ndash10(f) and Figure 12 show that

this nonelementary reaction yields higher desired productin Fed-Batch Reactor than in Continuous Plug Flow Reac-tor

As in Scheme 2 and Scheme 7 the Plug Flow Reactoryield initially increases with the increase in reaction time(ie lengthier reactor pipe) consequently 119873B119905119873A119905 valuedecreases (ie reduced consumption of Reactant B) How-ever the Plug Flow Reactor yield saturates out below Fed-Batch Reactor yield (Figure 12)

Overall the Fed Batch Reactor yields higher product Rthan Plug Flow Reactor even though there is a very marginalchange in yield for the change in the relative concentration ofreacting streams (Table 10(c) rows 2 4 and 5) in Fed-BatchReactor

16 ISRN Chemical Engineering

Table 10 (a) Reactor-1 (Fed-Batch Scheme 9 Part 1) (b) Reactor-2 (Plug Flow Scheme 9 Part 1) (c) Reactor-1 (Fed-Batch Scheme 9 Part2) (d) Reactor-2 (Plug Flow Scheme 9 Part 2) (e) Reactor-1 (Fed-Batch Scheme 9 Part 3) (f) Reactor-2 (Plug Flow Scheme 9 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1019 2125 0027 000 2564 0077 1202600 0994 2125 0027 000 263 1119864 minus 02 1233

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1419 2135 0027 2119864 minus 11 1497 11 701560 1419 2135 0027 2119864 minus 11 1497 11 7015

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1302 2133 0027 4119864 minus 15 1807 0833 847900 125 2131 0027 4119864 minus 15 1946 0694 9121800 1192 213 0027 4119864 minus 15 2101 0539 985900 1254 2131 0027 4E minus 15 1936 0704 907900 1246 2131 0027 4E minus 15 1957 0683 917

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1771 2144 0027 0408 0965 1675 4525360 1544 2139 0027 0088 1251 1389 586720 1425 2136 0027 0001 1482 1158 6949240 1771 2144 0027 0408 0965 1675 4525240 1771 2144 0027 0408 0965 1675 4525

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 104 2667 0027 1119864 minus 06 2506 0134 1175900 1034 2126 0027 4119864 minus 15 2523 0117 1183

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 14 2135 0027 0624 217 047 1017360 1191 213 0027 0202 2307 0333 1081

Table 11 Summary of results

Schemenumber

119886 119887 119888 119889 Favored reactorRelationship

between 119886 119887 119888 and119889

1 1 1 1 1 Both equally 119886 + 119888 = 119887 + 119889

2 1 1 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

3 1 1 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

4 05 15 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

5 15 05 05 15 Both equally 119886 + 119888 = 119887 + 119889

6 05 15 15 05 Both equally 119886 + 119888 = 119887 + 119889

7 15 05 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

8 05 15 1 1 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

9 15 05 1 1 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

11 Conclusion

Under the simulated conditions elementary Second ordercompetitive consecutive reactions of the type mentioned in(1) yield the same amount of intermediate product R in bothideal fed batch and ideal Plug Flow Reactors for a constantconversion (99) of limiting reactant A Yield and selectivityof the product depends only on119870

11198702in both the reactors

However of the 8 nonelementary scenarios simulatedthree (Schemes 3 4 and 8) favor Plug Flow Reactor and threeother (Schemes 2 7 and 9) favor Fed Batch Reactor Twoothers (Schemes 5 and 6) like elementary reaction yield thesame in both Plug Flow Reactor and Fed batch reactor

Among the schemes simulated previously (Schemes 1 to9) the schemes giving increased yield R with reduced addi-tion time in Fed batch reactor favor Plug Flow Reactor andthe schemes giving increased yield with increased addition

ISRN Chemical Engineering 17

time in fed batch reactor favor Fed batch reactor This couldwell be a practical reckoner to screen the potential candidateamong the simulated schemes for Plug Flow Reactor eventhough this idea is only with respect to suitability of kineticparameters

The relationship between the exponents 119886 119887 119888 and 119889 andthe favourable reactor found in the simulation as shown inTable 11 is noteworthy

Nomenclature

1198701 Rate constant of reaction between A and

B in Litresdotmolminus1sdotsminus1K2 Rate constant of 2nd reaction between R

and B in Litresdotmolminus1sdotsminus1t Time s119905119886 Reactant B addition time in Fed Batch

Reactor s119905119898 Reaction mass maintenance time in Fed

Batch Reactor stlowast Space time in Plug Flow Reactor stend Space time for which each case of plug

flow rector simulation has been done s119903119909 Rate of change of species ldquoxrdquo

(molsdotLitreminus1sdotsminus1) ldquoxrdquo is representative ofspecies A B R S C and D

119862119909= 119873119909119881 Concentration molsdotLitreminus1 of any species

say ldquoxrdquoV Reaction volume m3119873119909 Number of Kg moles of species ldquoxrdquo k mol

NB119905 Total Kg moles of reactant B used inreaction k mol

NA119905 Total kg moles of reactant A used inreaction k mol

119881119886119905 Volume of stream containing reactant B

m3119881119905 Total volume of contents including

streams of reactant A and reactant B m3v Plug Flow Reactor volume m3v1015840 Volumetric flow rate m3s119865119909 Molar flow rate (k molsdotsminus1) of species ldquoxrdquo

which is representative of species A B RS C and D

NB119905NA119905 Ratio of total moles of B to total moles ofA taken for the reaction

119873119909119865 Final kg moles of the species ldquoxrdquo k mol

WR Weight kg of total intermediate (desired)product formed at the end of reaction inFed Batch Reactor and at the end of agiven space time in the Plug Flow Reactor

Acknowledgment

The author would like to thank Chandra Kanth Terupally ofPlanck Technical Hyderabad India for providing adequatesupport in MATLAB Programming

References

[1] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1998

[2] J F Richardson and D G Peacock Coulson and RichardsonrsquosChemical Engineering Chemical and Biochemical Reactors andProcess Control Butterworth-Heinemann Boston Mass USA3rd edition 1994

[3] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart I model developmentrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 750162 16pages 2012

[4] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart II design protocolsrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 65432113 pages 2012

[5] J R Bourne ldquoMixing and the selectivity of chemical reactionsrdquoOrganic Process Research andDevelopment vol 7 no 4 pp 471ndash508 2003

[6] J Bałdyga J R Bourne and S J Hearn ldquoInteraction betweenchemical reactions and mixing on various scalesrdquo ChemicalEngineering Science vol 52 no 4 pp 457ndash466 1997

[7] N G Anderson ldquoPractical use of continuous processing indeveloping and scaling up laboratory processesrdquo Organic Pro-cess Research and Development vol 5 no 6 pp 613ndash621 2001

[8] C Brechtelsbauer and F Ricard ldquoReaction engineering evalua-tion and utilization of static mixer technology for the synthesisof pharmaceuticalsrdquoOrganic Process Research andDevelopmentvol 5 no 6 pp 646ndash651 2001

[9] Z Anxionnaz M Cabassud C Gourdon and P Tochon ldquoHeatexchangerreactors (HEX reactors) concepts technologiesstate-of-the-artrdquo Chemical Engineering and Processing vol 47no 12 pp 2029ndash2050 2008

[10] P Barthe C Guermeur O Lobet et al ldquoContinuous multi-injection reactor for multipurpose productionmdashpart Irdquo Chem-ical Engineering and Technology vol 31 no 8 pp 1146ndash11542008

[11] M Patel and G Gasparini ldquoReactor technology flow reactorsand dynamic mixingrdquo Specialty Chemicals Magazine 2009

[12] X W Ni ldquoContinuous oscilatory baffled reactor technologyrdquoin Innovations in Pharmaceutical TechnologymdashManufacturingpp 90ndash96 2006 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=392

[13] L Proctor ldquoContinuous chemical processingrdquo in Innovationsin Pharmaceutical Technology pp 84ndash88 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=290

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ISRN Chemical Engineering 13

Table 7 (a) Reactor-1 (Fed-Batch Scheme 6 Part 1) (b) Reactor-2 (Plug Flow Scheme 6 Part 1) (c) Reactor-1 (Fed-Batch Scheme 6 Part2) (d) Reactor-2 (Plug Flow Scheme 6 Part 2) (e) Reactor-1 (Fed-Batch Scheme 6 Part 3) (f) Reactor-2 (Plug Flow Scheme 6 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1121 2128 0027 000 229 035 1073600 1121 2128 0027 000 229 035 1073

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1121 2128 0027 4119864 minus 04 229 04 107360 1121 2128 0027 5119864 minus 06 229 04 1073

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7119864 minus 03 229 035 10731800 1124 2128 0027 7119864 minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073900 1124 2128 0027 7E minus 03 229 035 1073

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1152 2129 0027 0083 229 035 1073360 1139 2128 0027 0048 229 035 1073720 1128 2128 0027 0017 229 035 1073240 1152 2129 0027 0083 229 035 1073240 1152 2129 0027 0083 229 035 1073

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1022 2126 0027 0012 2568 0073 1204900 1022 2126 0027 0012 2567 0072 1203

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1058 2126 0027 0108 2567 0072 1204360 1042 2126 0027 0066 2568 0073 1204

Fed-Batch Reactor yield (Figure 10) Overall the Fed BatchReactor yields higher product R than Plug Flow Reactor eventhough there is a verymarginal change in yield for the changein the relative concentration of reacting streams (Table 8(c)rows 2 4 and 5)

105 (Scheme 8 a = 05 b = 15 c = 1 d = 1 Nonelementary)

1051 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 9(a) and 9(b)

1052 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 In Tables 9(c) and 9(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

The yield values for varying reaction times are capturedin Figure 11

1053 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 (See Tables 9(e) and 9(f)) Tables 9(a)ndash9(f)

and Figure 11 show that this non elementary reaction yieldshigher desired product in Plug Flow Reactor than in Fed-Batch Reactor Also the yield in Fed batch reactor decreaseswith addition time

As in Scheme 3 and Scheme 4 the reduced additiontime in Fed Batch Reactor results in increased productyield However in actual practice heat transfer and otherlimitations of the reactor vessel could possibly determine theminimum addition time beyond which addition time cannotbe reduced So the Fed Batch reactor yield is limited

It is to be noted that there is amarginal change in the yieldin Fed Batch reactor with relative concentration of reacting

14 ISRN Chemical Engineering

Table 8 (a) Reactor-1 (Fed-Batch Scheme 7 Part 1) (b) Reactor-2 (Plug Flow Scheme 7 Part 1) (c) Reactor-1 (Fed-Batch Scheme 7 Part2) (d) Reactor-2 (Plug Flow Scheme 7 Part 2) (e) Reactor-1 (Fed-Batch Scheme 7 Part 3) (f) Reactor-2 (Plug Flow Scheme 7 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 0992 2125 0026 000 2636 0004 1236600 099 2125 0027 000 264 8119864 minus 05 1237

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1139 2128 0027 2119864 minus 11 2242 04 105160 1139 2128 0027 2119864 minus 11 2242 04 1051

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1037 2126 0027 5119864 minus 04 2515 0125 1179900 1024 2126 0027 3119864 minus 04 2548 0092 11951800 1014 2125 0027 1119864 minus 04 2576 0064 1207900 1025 2126 0027 3E minus 04 2547 0093 1194900 1024 2126 0027 3E minus 04 255 009 1195

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1757 2144 0027 0472 1067 1573 5002360 1397 2135 0027 0165 172 092 806720 1176 2129 0027 0021 2166 0474 1015240 1757 2144 0027 0472 1067 1573 5002240 1757 2144 0027 0472 1067 1573 5002

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 0998 2125 0027 0001 2619 0021 1228900 0996 2125 0027 9119864 minus 04 2624 0016 1230

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1372 2134 0027 0687 2309 0331 1082360 115 2129 0027 0258 2472 0168 1159

913

3

827

768

696

999

1

965

595

8

955

1

955

0 500 1000 1500 2000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 11 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 8 Part 2)

80 847 91

2

985 101

4

105

3

107

2

452

5 586 694

9

701

701

701

701

701

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 12 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 9 Part 2)

ISRN Chemical Engineering 15

Table 9 (a) Reactor-1 (Fed-Batch Scheme 8 Part 1) (b) Reactor-2 (Plug Flow Scheme 8 Part 1) (c) Reactor-1 (Fed-Batch Scheme 8 Part2) (d) Reactor-2 (Plug Flow Scheme 8 Part 2) (e) Reactor-1 (Fed-Batch Scheme 8 Part 3) (f) Reactor-2 (Plug Flow Scheme 8 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 176 2144 0027 000 0588 2052 275600 1892 2147 0027 000 0234 2406 110

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1216 213 0027 3119864 minus 26 2037 06 95560 1216 213 0027 0000 2037 06 955

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1318 2133 0027 6119864 minus 06 1765 0875 827900 1366 2124 0027 9119864 minus 06 1638 1002 7681800 1423 2136 0027 2119864 minus 05 1485 1155 696900 1359 2134 0027 8E minus 06 1656 0984 776900 1374 2667 0027 1E minus 05 1615 1025 757

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1218 213 0027 0029 206 058 9655360 1216 213 0027 0008 2044 0596 958720 1216 213 0027 2119864 minus 04 2038 0602 9551240 1218 213 0027 0029 206 058 9655240 1218 213 0027 0029 206 058 9655

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1078 2127 0027 0003 2408 0232 1129900 109 2127 0027 0002 2376 0264 1114

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1076 2127 0027 0087 2498 0142 1171360 1065 2127 0027 0046 2486 0154 1166

streams (Table 9(c) rows 2 4 and 5) However this variationis too low to catch up with Plug Flow Reactor yield

106 (Scheme 9 119886 = 15 119887 = 05 119888 = 1 and 119889 = 1Nonelementary)

1061 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 10(a) and 10(b)

1062 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Theyield values for varying reaction times are capturedin Figure 12

In Tables 10(c) and 10(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1063 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 Tables 10(a)ndash10(f) and Figure 12 show that

this nonelementary reaction yields higher desired productin Fed-Batch Reactor than in Continuous Plug Flow Reac-tor

As in Scheme 2 and Scheme 7 the Plug Flow Reactoryield initially increases with the increase in reaction time(ie lengthier reactor pipe) consequently 119873B119905119873A119905 valuedecreases (ie reduced consumption of Reactant B) How-ever the Plug Flow Reactor yield saturates out below Fed-Batch Reactor yield (Figure 12)

Overall the Fed Batch Reactor yields higher product Rthan Plug Flow Reactor even though there is a very marginalchange in yield for the change in the relative concentration ofreacting streams (Table 10(c) rows 2 4 and 5) in Fed-BatchReactor

16 ISRN Chemical Engineering

Table 10 (a) Reactor-1 (Fed-Batch Scheme 9 Part 1) (b) Reactor-2 (Plug Flow Scheme 9 Part 1) (c) Reactor-1 (Fed-Batch Scheme 9 Part2) (d) Reactor-2 (Plug Flow Scheme 9 Part 2) (e) Reactor-1 (Fed-Batch Scheme 9 Part 3) (f) Reactor-2 (Plug Flow Scheme 9 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1019 2125 0027 000 2564 0077 1202600 0994 2125 0027 000 263 1119864 minus 02 1233

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1419 2135 0027 2119864 minus 11 1497 11 701560 1419 2135 0027 2119864 minus 11 1497 11 7015

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1302 2133 0027 4119864 minus 15 1807 0833 847900 125 2131 0027 4119864 minus 15 1946 0694 9121800 1192 213 0027 4119864 minus 15 2101 0539 985900 1254 2131 0027 4E minus 15 1936 0704 907900 1246 2131 0027 4E minus 15 1957 0683 917

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1771 2144 0027 0408 0965 1675 4525360 1544 2139 0027 0088 1251 1389 586720 1425 2136 0027 0001 1482 1158 6949240 1771 2144 0027 0408 0965 1675 4525240 1771 2144 0027 0408 0965 1675 4525

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 104 2667 0027 1119864 minus 06 2506 0134 1175900 1034 2126 0027 4119864 minus 15 2523 0117 1183

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 14 2135 0027 0624 217 047 1017360 1191 213 0027 0202 2307 0333 1081

Table 11 Summary of results

Schemenumber

119886 119887 119888 119889 Favored reactorRelationship

between 119886 119887 119888 and119889

1 1 1 1 1 Both equally 119886 + 119888 = 119887 + 119889

2 1 1 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

3 1 1 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

4 05 15 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

5 15 05 05 15 Both equally 119886 + 119888 = 119887 + 119889

6 05 15 15 05 Both equally 119886 + 119888 = 119887 + 119889

7 15 05 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

8 05 15 1 1 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

9 15 05 1 1 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

11 Conclusion

Under the simulated conditions elementary Second ordercompetitive consecutive reactions of the type mentioned in(1) yield the same amount of intermediate product R in bothideal fed batch and ideal Plug Flow Reactors for a constantconversion (99) of limiting reactant A Yield and selectivityof the product depends only on119870

11198702in both the reactors

However of the 8 nonelementary scenarios simulatedthree (Schemes 3 4 and 8) favor Plug Flow Reactor and threeother (Schemes 2 7 and 9) favor Fed Batch Reactor Twoothers (Schemes 5 and 6) like elementary reaction yield thesame in both Plug Flow Reactor and Fed batch reactor

Among the schemes simulated previously (Schemes 1 to9) the schemes giving increased yield R with reduced addi-tion time in Fed batch reactor favor Plug Flow Reactor andthe schemes giving increased yield with increased addition

ISRN Chemical Engineering 17

time in fed batch reactor favor Fed batch reactor This couldwell be a practical reckoner to screen the potential candidateamong the simulated schemes for Plug Flow Reactor eventhough this idea is only with respect to suitability of kineticparameters

The relationship between the exponents 119886 119887 119888 and 119889 andthe favourable reactor found in the simulation as shown inTable 11 is noteworthy

Nomenclature

1198701 Rate constant of reaction between A and

B in Litresdotmolminus1sdotsminus1K2 Rate constant of 2nd reaction between R

and B in Litresdotmolminus1sdotsminus1t Time s119905119886 Reactant B addition time in Fed Batch

Reactor s119905119898 Reaction mass maintenance time in Fed

Batch Reactor stlowast Space time in Plug Flow Reactor stend Space time for which each case of plug

flow rector simulation has been done s119903119909 Rate of change of species ldquoxrdquo

(molsdotLitreminus1sdotsminus1) ldquoxrdquo is representative ofspecies A B R S C and D

119862119909= 119873119909119881 Concentration molsdotLitreminus1 of any species

say ldquoxrdquoV Reaction volume m3119873119909 Number of Kg moles of species ldquoxrdquo k mol

NB119905 Total Kg moles of reactant B used inreaction k mol

NA119905 Total kg moles of reactant A used inreaction k mol

119881119886119905 Volume of stream containing reactant B

m3119881119905 Total volume of contents including

streams of reactant A and reactant B m3v Plug Flow Reactor volume m3v1015840 Volumetric flow rate m3s119865119909 Molar flow rate (k molsdotsminus1) of species ldquoxrdquo

which is representative of species A B RS C and D

NB119905NA119905 Ratio of total moles of B to total moles ofA taken for the reaction

119873119909119865 Final kg moles of the species ldquoxrdquo k mol

WR Weight kg of total intermediate (desired)product formed at the end of reaction inFed Batch Reactor and at the end of agiven space time in the Plug Flow Reactor

Acknowledgment

The author would like to thank Chandra Kanth Terupally ofPlanck Technical Hyderabad India for providing adequatesupport in MATLAB Programming

References

[1] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1998

[2] J F Richardson and D G Peacock Coulson and RichardsonrsquosChemical Engineering Chemical and Biochemical Reactors andProcess Control Butterworth-Heinemann Boston Mass USA3rd edition 1994

[3] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart I model developmentrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 750162 16pages 2012

[4] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart II design protocolsrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 65432113 pages 2012

[5] J R Bourne ldquoMixing and the selectivity of chemical reactionsrdquoOrganic Process Research andDevelopment vol 7 no 4 pp 471ndash508 2003

[6] J Bałdyga J R Bourne and S J Hearn ldquoInteraction betweenchemical reactions and mixing on various scalesrdquo ChemicalEngineering Science vol 52 no 4 pp 457ndash466 1997

[7] N G Anderson ldquoPractical use of continuous processing indeveloping and scaling up laboratory processesrdquo Organic Pro-cess Research and Development vol 5 no 6 pp 613ndash621 2001

[8] C Brechtelsbauer and F Ricard ldquoReaction engineering evalua-tion and utilization of static mixer technology for the synthesisof pharmaceuticalsrdquoOrganic Process Research andDevelopmentvol 5 no 6 pp 646ndash651 2001

[9] Z Anxionnaz M Cabassud C Gourdon and P Tochon ldquoHeatexchangerreactors (HEX reactors) concepts technologiesstate-of-the-artrdquo Chemical Engineering and Processing vol 47no 12 pp 2029ndash2050 2008

[10] P Barthe C Guermeur O Lobet et al ldquoContinuous multi-injection reactor for multipurpose productionmdashpart Irdquo Chem-ical Engineering and Technology vol 31 no 8 pp 1146ndash11542008

[11] M Patel and G Gasparini ldquoReactor technology flow reactorsand dynamic mixingrdquo Specialty Chemicals Magazine 2009

[12] X W Ni ldquoContinuous oscilatory baffled reactor technologyrdquoin Innovations in Pharmaceutical TechnologymdashManufacturingpp 90ndash96 2006 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=392

[13] L Proctor ldquoContinuous chemical processingrdquo in Innovationsin Pharmaceutical Technology pp 84ndash88 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=290

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

14 ISRN Chemical Engineering

Table 8 (a) Reactor-1 (Fed-Batch Scheme 7 Part 1) (b) Reactor-2 (Plug Flow Scheme 7 Part 1) (c) Reactor-1 (Fed-Batch Scheme 7 Part2) (d) Reactor-2 (Plug Flow Scheme 7 Part 2) (e) Reactor-1 (Fed-Batch Scheme 7 Part 3) (f) Reactor-2 (Plug Flow Scheme 7 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 0992 2125 0026 000 2636 0004 1236600 099 2125 0027 000 264 8119864 minus 05 1237

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1139 2128 0027 2119864 minus 11 2242 04 105160 1139 2128 0027 2119864 minus 11 2242 04 1051

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1037 2126 0027 5119864 minus 04 2515 0125 1179900 1024 2126 0027 3119864 minus 04 2548 0092 11951800 1014 2125 0027 1119864 minus 04 2576 0064 1207900 1025 2126 0027 3E minus 04 2547 0093 1194900 1024 2126 0027 3E minus 04 255 009 1195

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1757 2144 0027 0472 1067 1573 5002360 1397 2135 0027 0165 172 092 806720 1176 2129 0027 0021 2166 0474 1015240 1757 2144 0027 0472 1067 1573 5002240 1757 2144 0027 0472 1067 1573 5002

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 0998 2125 0027 0001 2619 0021 1228900 0996 2125 0027 9119864 minus 04 2624 0016 1230

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1372 2134 0027 0687 2309 0331 1082360 115 2129 0027 0258 2472 0168 1159

913

3

827

768

696

999

1

965

595

8

955

1

955

0 500 1000 1500 2000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 11 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 8 Part 2)

80 847 91

2

985 101

4

105

3

107

2

452

5 586 694

9

701

701

701

701

701

0 1000 2000 3000 4000 5000

Prod

uct R

yie

ld (k

g)

ta or tend (s)

Fed-Batch ReactorPlug Flow Reactor

Figure 12 Product yield as a function of addition time and reactionend time in Fed Batch Reactor and Plug Flow Reactor respectively(Scheme 9 Part 2)

ISRN Chemical Engineering 15

Table 9 (a) Reactor-1 (Fed-Batch Scheme 8 Part 1) (b) Reactor-2 (Plug Flow Scheme 8 Part 1) (c) Reactor-1 (Fed-Batch Scheme 8 Part2) (d) Reactor-2 (Plug Flow Scheme 8 Part 2) (e) Reactor-1 (Fed-Batch Scheme 8 Part 3) (f) Reactor-2 (Plug Flow Scheme 8 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 176 2144 0027 000 0588 2052 275600 1892 2147 0027 000 0234 2406 110

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1216 213 0027 3119864 minus 26 2037 06 95560 1216 213 0027 0000 2037 06 955

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1318 2133 0027 6119864 minus 06 1765 0875 827900 1366 2124 0027 9119864 minus 06 1638 1002 7681800 1423 2136 0027 2119864 minus 05 1485 1155 696900 1359 2134 0027 8E minus 06 1656 0984 776900 1374 2667 0027 1E minus 05 1615 1025 757

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1218 213 0027 0029 206 058 9655360 1216 213 0027 0008 2044 0596 958720 1216 213 0027 2119864 minus 04 2038 0602 9551240 1218 213 0027 0029 206 058 9655240 1218 213 0027 0029 206 058 9655

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1078 2127 0027 0003 2408 0232 1129900 109 2127 0027 0002 2376 0264 1114

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1076 2127 0027 0087 2498 0142 1171360 1065 2127 0027 0046 2486 0154 1166

streams (Table 9(c) rows 2 4 and 5) However this variationis too low to catch up with Plug Flow Reactor yield

106 (Scheme 9 119886 = 15 119887 = 05 119888 = 1 and 119889 = 1Nonelementary)

1061 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 10(a) and 10(b)

1062 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Theyield values for varying reaction times are capturedin Figure 12

In Tables 10(c) and 10(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1063 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 Tables 10(a)ndash10(f) and Figure 12 show that

this nonelementary reaction yields higher desired productin Fed-Batch Reactor than in Continuous Plug Flow Reac-tor

As in Scheme 2 and Scheme 7 the Plug Flow Reactoryield initially increases with the increase in reaction time(ie lengthier reactor pipe) consequently 119873B119905119873A119905 valuedecreases (ie reduced consumption of Reactant B) How-ever the Plug Flow Reactor yield saturates out below Fed-Batch Reactor yield (Figure 12)

Overall the Fed Batch Reactor yields higher product Rthan Plug Flow Reactor even though there is a very marginalchange in yield for the change in the relative concentration ofreacting streams (Table 10(c) rows 2 4 and 5) in Fed-BatchReactor

16 ISRN Chemical Engineering

Table 10 (a) Reactor-1 (Fed-Batch Scheme 9 Part 1) (b) Reactor-2 (Plug Flow Scheme 9 Part 1) (c) Reactor-1 (Fed-Batch Scheme 9 Part2) (d) Reactor-2 (Plug Flow Scheme 9 Part 2) (e) Reactor-1 (Fed-Batch Scheme 9 Part 3) (f) Reactor-2 (Plug Flow Scheme 9 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1019 2125 0027 000 2564 0077 1202600 0994 2125 0027 000 263 1119864 minus 02 1233

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1419 2135 0027 2119864 minus 11 1497 11 701560 1419 2135 0027 2119864 minus 11 1497 11 7015

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1302 2133 0027 4119864 minus 15 1807 0833 847900 125 2131 0027 4119864 minus 15 1946 0694 9121800 1192 213 0027 4119864 minus 15 2101 0539 985900 1254 2131 0027 4E minus 15 1936 0704 907900 1246 2131 0027 4E minus 15 1957 0683 917

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1771 2144 0027 0408 0965 1675 4525360 1544 2139 0027 0088 1251 1389 586720 1425 2136 0027 0001 1482 1158 6949240 1771 2144 0027 0408 0965 1675 4525240 1771 2144 0027 0408 0965 1675 4525

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 104 2667 0027 1119864 minus 06 2506 0134 1175900 1034 2126 0027 4119864 minus 15 2523 0117 1183

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 14 2135 0027 0624 217 047 1017360 1191 213 0027 0202 2307 0333 1081

Table 11 Summary of results

Schemenumber

119886 119887 119888 119889 Favored reactorRelationship

between 119886 119887 119888 and119889

1 1 1 1 1 Both equally 119886 + 119888 = 119887 + 119889

2 1 1 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

3 1 1 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

4 05 15 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

5 15 05 05 15 Both equally 119886 + 119888 = 119887 + 119889

6 05 15 15 05 Both equally 119886 + 119888 = 119887 + 119889

7 15 05 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

8 05 15 1 1 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

9 15 05 1 1 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

11 Conclusion

Under the simulated conditions elementary Second ordercompetitive consecutive reactions of the type mentioned in(1) yield the same amount of intermediate product R in bothideal fed batch and ideal Plug Flow Reactors for a constantconversion (99) of limiting reactant A Yield and selectivityof the product depends only on119870

11198702in both the reactors

However of the 8 nonelementary scenarios simulatedthree (Schemes 3 4 and 8) favor Plug Flow Reactor and threeother (Schemes 2 7 and 9) favor Fed Batch Reactor Twoothers (Schemes 5 and 6) like elementary reaction yield thesame in both Plug Flow Reactor and Fed batch reactor

Among the schemes simulated previously (Schemes 1 to9) the schemes giving increased yield R with reduced addi-tion time in Fed batch reactor favor Plug Flow Reactor andthe schemes giving increased yield with increased addition

ISRN Chemical Engineering 17

time in fed batch reactor favor Fed batch reactor This couldwell be a practical reckoner to screen the potential candidateamong the simulated schemes for Plug Flow Reactor eventhough this idea is only with respect to suitability of kineticparameters

The relationship between the exponents 119886 119887 119888 and 119889 andthe favourable reactor found in the simulation as shown inTable 11 is noteworthy

Nomenclature

1198701 Rate constant of reaction between A and

B in Litresdotmolminus1sdotsminus1K2 Rate constant of 2nd reaction between R

and B in Litresdotmolminus1sdotsminus1t Time s119905119886 Reactant B addition time in Fed Batch

Reactor s119905119898 Reaction mass maintenance time in Fed

Batch Reactor stlowast Space time in Plug Flow Reactor stend Space time for which each case of plug

flow rector simulation has been done s119903119909 Rate of change of species ldquoxrdquo

(molsdotLitreminus1sdotsminus1) ldquoxrdquo is representative ofspecies A B R S C and D

119862119909= 119873119909119881 Concentration molsdotLitreminus1 of any species

say ldquoxrdquoV Reaction volume m3119873119909 Number of Kg moles of species ldquoxrdquo k mol

NB119905 Total Kg moles of reactant B used inreaction k mol

NA119905 Total kg moles of reactant A used inreaction k mol

119881119886119905 Volume of stream containing reactant B

m3119881119905 Total volume of contents including

streams of reactant A and reactant B m3v Plug Flow Reactor volume m3v1015840 Volumetric flow rate m3s119865119909 Molar flow rate (k molsdotsminus1) of species ldquoxrdquo

which is representative of species A B RS C and D

NB119905NA119905 Ratio of total moles of B to total moles ofA taken for the reaction

119873119909119865 Final kg moles of the species ldquoxrdquo k mol

WR Weight kg of total intermediate (desired)product formed at the end of reaction inFed Batch Reactor and at the end of agiven space time in the Plug Flow Reactor

Acknowledgment

The author would like to thank Chandra Kanth Terupally ofPlanck Technical Hyderabad India for providing adequatesupport in MATLAB Programming

References

[1] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1998

[2] J F Richardson and D G Peacock Coulson and RichardsonrsquosChemical Engineering Chemical and Biochemical Reactors andProcess Control Butterworth-Heinemann Boston Mass USA3rd edition 1994

[3] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart I model developmentrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 750162 16pages 2012

[4] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart II design protocolsrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 65432113 pages 2012

[5] J R Bourne ldquoMixing and the selectivity of chemical reactionsrdquoOrganic Process Research andDevelopment vol 7 no 4 pp 471ndash508 2003

[6] J Bałdyga J R Bourne and S J Hearn ldquoInteraction betweenchemical reactions and mixing on various scalesrdquo ChemicalEngineering Science vol 52 no 4 pp 457ndash466 1997

[7] N G Anderson ldquoPractical use of continuous processing indeveloping and scaling up laboratory processesrdquo Organic Pro-cess Research and Development vol 5 no 6 pp 613ndash621 2001

[8] C Brechtelsbauer and F Ricard ldquoReaction engineering evalua-tion and utilization of static mixer technology for the synthesisof pharmaceuticalsrdquoOrganic Process Research andDevelopmentvol 5 no 6 pp 646ndash651 2001

[9] Z Anxionnaz M Cabassud C Gourdon and P Tochon ldquoHeatexchangerreactors (HEX reactors) concepts technologiesstate-of-the-artrdquo Chemical Engineering and Processing vol 47no 12 pp 2029ndash2050 2008

[10] P Barthe C Guermeur O Lobet et al ldquoContinuous multi-injection reactor for multipurpose productionmdashpart Irdquo Chem-ical Engineering and Technology vol 31 no 8 pp 1146ndash11542008

[11] M Patel and G Gasparini ldquoReactor technology flow reactorsand dynamic mixingrdquo Specialty Chemicals Magazine 2009

[12] X W Ni ldquoContinuous oscilatory baffled reactor technologyrdquoin Innovations in Pharmaceutical TechnologymdashManufacturingpp 90ndash96 2006 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=392

[13] L Proctor ldquoContinuous chemical processingrdquo in Innovationsin Pharmaceutical Technology pp 84ndash88 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=290

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

ISRN Chemical Engineering 15

Table 9 (a) Reactor-1 (Fed-Batch Scheme 8 Part 1) (b) Reactor-2 (Plug Flow Scheme 8 Part 1) (c) Reactor-1 (Fed-Batch Scheme 8 Part2) (d) Reactor-2 (Plug Flow Scheme 8 Part 2) (e) Reactor-1 (Fed-Batch Scheme 8 Part 3) (f) Reactor-2 (Plug Flow Scheme 8 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 176 2144 0027 000 0588 2052 275600 1892 2147 0027 000 0234 2406 110

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1216 213 0027 3119864 minus 26 2037 06 95560 1216 213 0027 0000 2037 06 955

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1318 2133 0027 6119864 minus 06 1765 0875 827900 1366 2124 0027 9119864 minus 06 1638 1002 7681800 1423 2136 0027 2119864 minus 05 1485 1155 696900 1359 2134 0027 8E minus 06 1656 0984 776900 1374 2667 0027 1E minus 05 1615 1025 757

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1218 213 0027 0029 206 058 9655360 1216 213 0027 0008 2044 0596 958720 1216 213 0027 2119864 minus 04 2038 0602 9551240 1218 213 0027 0029 206 058 9655240 1218 213 0027 0029 206 058 9655

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1078 2127 0027 0003 2408 0232 1129900 109 2127 0027 0002 2376 0264 1114

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1076 2127 0027 0087 2498 0142 1171360 1065 2127 0027 0046 2486 0154 1166

streams (Table 9(c) rows 2 4 and 5) However this variationis too low to catch up with Plug Flow Reactor yield

106 (Scheme 9 119886 = 15 119887 = 05 119888 = 1 and 119889 = 1Nonelementary)

1061 Part 1 (Cases 1 and 2) 1198701= 100 119870

11198702= 10 and

1198702= 10 See Tables 10(a) and 10(b)

1062 Part 2 (Cases 1 to 5) 1198701= 01 119870

11198702= 10 and 119870

2=

001 Theyield values for varying reaction times are capturedin Figure 12

In Tables 10(c) and 10(d) the data lines (rows) 4 and 5correspond to the fraction Sol A(Sol A + Sol R) = 025 and075 respectively

1063 Part 3 (Cases 1 and 2) 1198701= 01 119870

11198702= 50

and 1198702= 0002 Tables 10(a)ndash10(f) and Figure 12 show that

this nonelementary reaction yields higher desired productin Fed-Batch Reactor than in Continuous Plug Flow Reac-tor

As in Scheme 2 and Scheme 7 the Plug Flow Reactoryield initially increases with the increase in reaction time(ie lengthier reactor pipe) consequently 119873B119905119873A119905 valuedecreases (ie reduced consumption of Reactant B) How-ever the Plug Flow Reactor yield saturates out below Fed-Batch Reactor yield (Figure 12)

Overall the Fed Batch Reactor yields higher product Rthan Plug Flow Reactor even though there is a very marginalchange in yield for the change in the relative concentration ofreacting streams (Table 10(c) rows 2 4 and 5) in Fed-BatchReactor

16 ISRN Chemical Engineering

Table 10 (a) Reactor-1 (Fed-Batch Scheme 9 Part 1) (b) Reactor-2 (Plug Flow Scheme 9 Part 1) (c) Reactor-1 (Fed-Batch Scheme 9 Part2) (d) Reactor-2 (Plug Flow Scheme 9 Part 2) (e) Reactor-1 (Fed-Batch Scheme 9 Part 3) (f) Reactor-2 (Plug Flow Scheme 9 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1019 2125 0027 000 2564 0077 1202600 0994 2125 0027 000 263 1119864 minus 02 1233

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1419 2135 0027 2119864 minus 11 1497 11 701560 1419 2135 0027 2119864 minus 11 1497 11 7015

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1302 2133 0027 4119864 minus 15 1807 0833 847900 125 2131 0027 4119864 minus 15 1946 0694 9121800 1192 213 0027 4119864 minus 15 2101 0539 985900 1254 2131 0027 4E minus 15 1936 0704 907900 1246 2131 0027 4E minus 15 1957 0683 917

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1771 2144 0027 0408 0965 1675 4525360 1544 2139 0027 0088 1251 1389 586720 1425 2136 0027 0001 1482 1158 6949240 1771 2144 0027 0408 0965 1675 4525240 1771 2144 0027 0408 0965 1675 4525

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 104 2667 0027 1119864 minus 06 2506 0134 1175900 1034 2126 0027 4119864 minus 15 2523 0117 1183

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 14 2135 0027 0624 217 047 1017360 1191 213 0027 0202 2307 0333 1081

Table 11 Summary of results

Schemenumber

119886 119887 119888 119889 Favored reactorRelationship

between 119886 119887 119888 and119889

1 1 1 1 1 Both equally 119886 + 119888 = 119887 + 119889

2 1 1 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

3 1 1 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

4 05 15 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

5 15 05 05 15 Both equally 119886 + 119888 = 119887 + 119889

6 05 15 15 05 Both equally 119886 + 119888 = 119887 + 119889

7 15 05 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

8 05 15 1 1 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

9 15 05 1 1 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

11 Conclusion

Under the simulated conditions elementary Second ordercompetitive consecutive reactions of the type mentioned in(1) yield the same amount of intermediate product R in bothideal fed batch and ideal Plug Flow Reactors for a constantconversion (99) of limiting reactant A Yield and selectivityof the product depends only on119870

11198702in both the reactors

However of the 8 nonelementary scenarios simulatedthree (Schemes 3 4 and 8) favor Plug Flow Reactor and threeother (Schemes 2 7 and 9) favor Fed Batch Reactor Twoothers (Schemes 5 and 6) like elementary reaction yield thesame in both Plug Flow Reactor and Fed batch reactor

Among the schemes simulated previously (Schemes 1 to9) the schemes giving increased yield R with reduced addi-tion time in Fed batch reactor favor Plug Flow Reactor andthe schemes giving increased yield with increased addition

ISRN Chemical Engineering 17

time in fed batch reactor favor Fed batch reactor This couldwell be a practical reckoner to screen the potential candidateamong the simulated schemes for Plug Flow Reactor eventhough this idea is only with respect to suitability of kineticparameters

The relationship between the exponents 119886 119887 119888 and 119889 andthe favourable reactor found in the simulation as shown inTable 11 is noteworthy

Nomenclature

1198701 Rate constant of reaction between A and

B in Litresdotmolminus1sdotsminus1K2 Rate constant of 2nd reaction between R

and B in Litresdotmolminus1sdotsminus1t Time s119905119886 Reactant B addition time in Fed Batch

Reactor s119905119898 Reaction mass maintenance time in Fed

Batch Reactor stlowast Space time in Plug Flow Reactor stend Space time for which each case of plug

flow rector simulation has been done s119903119909 Rate of change of species ldquoxrdquo

(molsdotLitreminus1sdotsminus1) ldquoxrdquo is representative ofspecies A B R S C and D

119862119909= 119873119909119881 Concentration molsdotLitreminus1 of any species

say ldquoxrdquoV Reaction volume m3119873119909 Number of Kg moles of species ldquoxrdquo k mol

NB119905 Total Kg moles of reactant B used inreaction k mol

NA119905 Total kg moles of reactant A used inreaction k mol

119881119886119905 Volume of stream containing reactant B

m3119881119905 Total volume of contents including

streams of reactant A and reactant B m3v Plug Flow Reactor volume m3v1015840 Volumetric flow rate m3s119865119909 Molar flow rate (k molsdotsminus1) of species ldquoxrdquo

which is representative of species A B RS C and D

NB119905NA119905 Ratio of total moles of B to total moles ofA taken for the reaction

119873119909119865 Final kg moles of the species ldquoxrdquo k mol

WR Weight kg of total intermediate (desired)product formed at the end of reaction inFed Batch Reactor and at the end of agiven space time in the Plug Flow Reactor

Acknowledgment

The author would like to thank Chandra Kanth Terupally ofPlanck Technical Hyderabad India for providing adequatesupport in MATLAB Programming

References

[1] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1998

[2] J F Richardson and D G Peacock Coulson and RichardsonrsquosChemical Engineering Chemical and Biochemical Reactors andProcess Control Butterworth-Heinemann Boston Mass USA3rd edition 1994

[3] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart I model developmentrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 750162 16pages 2012

[4] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart II design protocolsrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 65432113 pages 2012

[5] J R Bourne ldquoMixing and the selectivity of chemical reactionsrdquoOrganic Process Research andDevelopment vol 7 no 4 pp 471ndash508 2003

[6] J Bałdyga J R Bourne and S J Hearn ldquoInteraction betweenchemical reactions and mixing on various scalesrdquo ChemicalEngineering Science vol 52 no 4 pp 457ndash466 1997

[7] N G Anderson ldquoPractical use of continuous processing indeveloping and scaling up laboratory processesrdquo Organic Pro-cess Research and Development vol 5 no 6 pp 613ndash621 2001

[8] C Brechtelsbauer and F Ricard ldquoReaction engineering evalua-tion and utilization of static mixer technology for the synthesisof pharmaceuticalsrdquoOrganic Process Research andDevelopmentvol 5 no 6 pp 646ndash651 2001

[9] Z Anxionnaz M Cabassud C Gourdon and P Tochon ldquoHeatexchangerreactors (HEX reactors) concepts technologiesstate-of-the-artrdquo Chemical Engineering and Processing vol 47no 12 pp 2029ndash2050 2008

[10] P Barthe C Guermeur O Lobet et al ldquoContinuous multi-injection reactor for multipurpose productionmdashpart Irdquo Chem-ical Engineering and Technology vol 31 no 8 pp 1146ndash11542008

[11] M Patel and G Gasparini ldquoReactor technology flow reactorsand dynamic mixingrdquo Specialty Chemicals Magazine 2009

[12] X W Ni ldquoContinuous oscilatory baffled reactor technologyrdquoin Innovations in Pharmaceutical TechnologymdashManufacturingpp 90ndash96 2006 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=392

[13] L Proctor ldquoContinuous chemical processingrdquo in Innovationsin Pharmaceutical Technology pp 84ndash88 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=290

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

16 ISRN Chemical Engineering

Table 10 (a) Reactor-1 (Fed-Batch Scheme 9 Part 1) (b) Reactor-2 (Plug Flow Scheme 9 Part 1) (c) Reactor-1 (Fed-Batch Scheme 9 Part2) (d) Reactor-2 (Plug Flow Scheme 9 Part 2) (e) Reactor-1 (Fed-Batch Scheme 9 Part 3) (f) Reactor-2 (Plug Flow Scheme 9 Part 3)

(a)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

60 1019 2125 0027 000 2564 0077 1202600 0994 2125 0027 000 263 1119864 minus 02 1233

(b)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

6 1419 2135 0027 2119864 minus 11 1497 11 701560 1419 2135 0027 2119864 minus 11 1497 11 7015

(c)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 1302 2133 0027 4119864 minus 15 1807 0833 847900 125 2131 0027 4119864 minus 15 1946 0694 9121800 1192 213 0027 4119864 minus 15 2101 0539 985900 1254 2131 0027 4E minus 15 1936 0704 907900 1246 2131 0027 4E minus 15 1957 0683 917

(d)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 1771 2144 0027 0408 0965 1675 4525360 1544 2139 0027 0088 1251 1389 586720 1425 2136 0027 0001 1482 1158 6949240 1771 2144 0027 0408 0965 1675 4525240 1771 2144 0027 0408 0965 1675 4525

(e)

119905119886(s) 119873B119905119873A119905 119881

119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

450 104 2667 0027 1119864 minus 06 2506 0134 1175900 1034 2126 0027 4119864 minus 15 2523 0117 1183

(f)

119905end (s) 119873B119905119873A119905 119881119905(m3) 119873AF (kmol) 119873BF (kmol) 119873RF (kmol) 119873SF (kmol) 119882R (kg)

240 14 2135 0027 0624 217 047 1017360 1191 213 0027 0202 2307 0333 1081

Table 11 Summary of results

Schemenumber

119886 119887 119888 119889 Favored reactorRelationship

between 119886 119887 119888 and119889

1 1 1 1 1 Both equally 119886 + 119888 = 119887 + 119889

2 1 1 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

3 1 1 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

4 05 15 05 15 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

5 15 05 05 15 Both equally 119886 + 119888 = 119887 + 119889

6 05 15 15 05 Both equally 119886 + 119888 = 119887 + 119889

7 15 05 15 05 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

8 05 15 1 1 Plug Flow Reactor 119886 + 119888 lt 119887 + 119889

9 15 05 1 1 Fed-Batch Reactor 119886 + 119888 gt 119887 + 119889

11 Conclusion

Under the simulated conditions elementary Second ordercompetitive consecutive reactions of the type mentioned in(1) yield the same amount of intermediate product R in bothideal fed batch and ideal Plug Flow Reactors for a constantconversion (99) of limiting reactant A Yield and selectivityof the product depends only on119870

11198702in both the reactors

However of the 8 nonelementary scenarios simulatedthree (Schemes 3 4 and 8) favor Plug Flow Reactor and threeother (Schemes 2 7 and 9) favor Fed Batch Reactor Twoothers (Schemes 5 and 6) like elementary reaction yield thesame in both Plug Flow Reactor and Fed batch reactor

Among the schemes simulated previously (Schemes 1 to9) the schemes giving increased yield R with reduced addi-tion time in Fed batch reactor favor Plug Flow Reactor andthe schemes giving increased yield with increased addition

ISRN Chemical Engineering 17

time in fed batch reactor favor Fed batch reactor This couldwell be a practical reckoner to screen the potential candidateamong the simulated schemes for Plug Flow Reactor eventhough this idea is only with respect to suitability of kineticparameters

The relationship between the exponents 119886 119887 119888 and 119889 andthe favourable reactor found in the simulation as shown inTable 11 is noteworthy

Nomenclature

1198701 Rate constant of reaction between A and

B in Litresdotmolminus1sdotsminus1K2 Rate constant of 2nd reaction between R

and B in Litresdotmolminus1sdotsminus1t Time s119905119886 Reactant B addition time in Fed Batch

Reactor s119905119898 Reaction mass maintenance time in Fed

Batch Reactor stlowast Space time in Plug Flow Reactor stend Space time for which each case of plug

flow rector simulation has been done s119903119909 Rate of change of species ldquoxrdquo

(molsdotLitreminus1sdotsminus1) ldquoxrdquo is representative ofspecies A B R S C and D

119862119909= 119873119909119881 Concentration molsdotLitreminus1 of any species

say ldquoxrdquoV Reaction volume m3119873119909 Number of Kg moles of species ldquoxrdquo k mol

NB119905 Total Kg moles of reactant B used inreaction k mol

NA119905 Total kg moles of reactant A used inreaction k mol

119881119886119905 Volume of stream containing reactant B

m3119881119905 Total volume of contents including

streams of reactant A and reactant B m3v Plug Flow Reactor volume m3v1015840 Volumetric flow rate m3s119865119909 Molar flow rate (k molsdotsminus1) of species ldquoxrdquo

which is representative of species A B RS C and D

NB119905NA119905 Ratio of total moles of B to total moles ofA taken for the reaction

119873119909119865 Final kg moles of the species ldquoxrdquo k mol

WR Weight kg of total intermediate (desired)product formed at the end of reaction inFed Batch Reactor and at the end of agiven space time in the Plug Flow Reactor

Acknowledgment

The author would like to thank Chandra Kanth Terupally ofPlanck Technical Hyderabad India for providing adequatesupport in MATLAB Programming

References

[1] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1998

[2] J F Richardson and D G Peacock Coulson and RichardsonrsquosChemical Engineering Chemical and Biochemical Reactors andProcess Control Butterworth-Heinemann Boston Mass USA3rd edition 1994

[3] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart I model developmentrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 750162 16pages 2012

[4] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart II design protocolsrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 65432113 pages 2012

[5] J R Bourne ldquoMixing and the selectivity of chemical reactionsrdquoOrganic Process Research andDevelopment vol 7 no 4 pp 471ndash508 2003

[6] J Bałdyga J R Bourne and S J Hearn ldquoInteraction betweenchemical reactions and mixing on various scalesrdquo ChemicalEngineering Science vol 52 no 4 pp 457ndash466 1997

[7] N G Anderson ldquoPractical use of continuous processing indeveloping and scaling up laboratory processesrdquo Organic Pro-cess Research and Development vol 5 no 6 pp 613ndash621 2001

[8] C Brechtelsbauer and F Ricard ldquoReaction engineering evalua-tion and utilization of static mixer technology for the synthesisof pharmaceuticalsrdquoOrganic Process Research andDevelopmentvol 5 no 6 pp 646ndash651 2001

[9] Z Anxionnaz M Cabassud C Gourdon and P Tochon ldquoHeatexchangerreactors (HEX reactors) concepts technologiesstate-of-the-artrdquo Chemical Engineering and Processing vol 47no 12 pp 2029ndash2050 2008

[10] P Barthe C Guermeur O Lobet et al ldquoContinuous multi-injection reactor for multipurpose productionmdashpart Irdquo Chem-ical Engineering and Technology vol 31 no 8 pp 1146ndash11542008

[11] M Patel and G Gasparini ldquoReactor technology flow reactorsand dynamic mixingrdquo Specialty Chemicals Magazine 2009

[12] X W Ni ldquoContinuous oscilatory baffled reactor technologyrdquoin Innovations in Pharmaceutical TechnologymdashManufacturingpp 90ndash96 2006 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=392

[13] L Proctor ldquoContinuous chemical processingrdquo in Innovationsin Pharmaceutical Technology pp 84ndash88 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=290

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

ISRN Chemical Engineering 17

time in fed batch reactor favor Fed batch reactor This couldwell be a practical reckoner to screen the potential candidateamong the simulated schemes for Plug Flow Reactor eventhough this idea is only with respect to suitability of kineticparameters

The relationship between the exponents 119886 119887 119888 and 119889 andthe favourable reactor found in the simulation as shown inTable 11 is noteworthy

Nomenclature

1198701 Rate constant of reaction between A and

B in Litresdotmolminus1sdotsminus1K2 Rate constant of 2nd reaction between R

and B in Litresdotmolminus1sdotsminus1t Time s119905119886 Reactant B addition time in Fed Batch

Reactor s119905119898 Reaction mass maintenance time in Fed

Batch Reactor stlowast Space time in Plug Flow Reactor stend Space time for which each case of plug

flow rector simulation has been done s119903119909 Rate of change of species ldquoxrdquo

(molsdotLitreminus1sdotsminus1) ldquoxrdquo is representative ofspecies A B R S C and D

119862119909= 119873119909119881 Concentration molsdotLitreminus1 of any species

say ldquoxrdquoV Reaction volume m3119873119909 Number of Kg moles of species ldquoxrdquo k mol

NB119905 Total Kg moles of reactant B used inreaction k mol

NA119905 Total kg moles of reactant A used inreaction k mol

119881119886119905 Volume of stream containing reactant B

m3119881119905 Total volume of contents including

streams of reactant A and reactant B m3v Plug Flow Reactor volume m3v1015840 Volumetric flow rate m3s119865119909 Molar flow rate (k molsdotsminus1) of species ldquoxrdquo

which is representative of species A B RS C and D

NB119905NA119905 Ratio of total moles of B to total moles ofA taken for the reaction

119873119909119865 Final kg moles of the species ldquoxrdquo k mol

WR Weight kg of total intermediate (desired)product formed at the end of reaction inFed Batch Reactor and at the end of agiven space time in the Plug Flow Reactor

Acknowledgment

The author would like to thank Chandra Kanth Terupally ofPlanck Technical Hyderabad India for providing adequatesupport in MATLAB Programming

References

[1] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1998

[2] J F Richardson and D G Peacock Coulson and RichardsonrsquosChemical Engineering Chemical and Biochemical Reactors andProcess Control Butterworth-Heinemann Boston Mass USA3rd edition 1994

[3] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart I model developmentrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 750162 16pages 2012

[4] S I A Shah L W Kostiuk and S M Kresta ldquoThe effects ofmixing reaction rates and stoichiometry on yield for mixingsensitive reactionsmdashpart II design protocolsrdquo InternationalJournal of Chemical Engineering vol 2012 Article ID 65432113 pages 2012

[5] J R Bourne ldquoMixing and the selectivity of chemical reactionsrdquoOrganic Process Research andDevelopment vol 7 no 4 pp 471ndash508 2003

[6] J Bałdyga J R Bourne and S J Hearn ldquoInteraction betweenchemical reactions and mixing on various scalesrdquo ChemicalEngineering Science vol 52 no 4 pp 457ndash466 1997

[7] N G Anderson ldquoPractical use of continuous processing indeveloping and scaling up laboratory processesrdquo Organic Pro-cess Research and Development vol 5 no 6 pp 613ndash621 2001

[8] C Brechtelsbauer and F Ricard ldquoReaction engineering evalua-tion and utilization of static mixer technology for the synthesisof pharmaceuticalsrdquoOrganic Process Research andDevelopmentvol 5 no 6 pp 646ndash651 2001

[9] Z Anxionnaz M Cabassud C Gourdon and P Tochon ldquoHeatexchangerreactors (HEX reactors) concepts technologiesstate-of-the-artrdquo Chemical Engineering and Processing vol 47no 12 pp 2029ndash2050 2008

[10] P Barthe C Guermeur O Lobet et al ldquoContinuous multi-injection reactor for multipurpose productionmdashpart Irdquo Chem-ical Engineering and Technology vol 31 no 8 pp 1146ndash11542008

[11] M Patel and G Gasparini ldquoReactor technology flow reactorsand dynamic mixingrdquo Specialty Chemicals Magazine 2009

[12] X W Ni ldquoContinuous oscilatory baffled reactor technologyrdquoin Innovations in Pharmaceutical TechnologymdashManufacturingpp 90ndash96 2006 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=392

[13] L Proctor ldquoContinuous chemical processingrdquo in Innovationsin Pharmaceutical Technology pp 84ndash88 httpwwwiptonlinecompdf viewarticleaspcat=5amparticle=290

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International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

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