chapter 4 reactor design

8/16/2019 Chapter 4 Reactor Design

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4. A LGORITHM FOR I SOTHERMAL R EACTOR D ESIGN *

Topics

Part 1: Mole Balances in Terms of Conversion1. Algorithm for Isothermal Reactor Design

2. Applications/ !amples of CR Algorithm

". Reversi#le Reactions

$. %D &Pol'math( )ol*tions to CR Pro#lems

+. ,eneral ,*i-elines for California Pro#lems

. PBR ith Press*re Drop

0. ngineering Anal'sis

Part 2: Meas*res %ther Than Conversion1. Meas*res %ther Than Conversion

2. Mem#rane Reactors

". )emi#atch Reactors

Part 1: Mol !ala"c s i" T r#s o$ Co"% rsio"

1. Algorithm for Isothermal Reactor Design top

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rench Men*Analog'

4.1 T& r actio" '(A)! +C,carri - o t i" a CSTR/ PFR a"- a !atc&R actor.

4.( La0rator E2p ri# "t 4.3 S #ilo plot to $i"- r actio"

rat co"sta"t to a clos - "- - PFR5CSTR

2a#pl . CHEM6IN R actor Mo- ls

E2a#pl : T& l # "tar li7 i- p&asr actio"

is carrie- o*t isothermall' in a C)TR. P*re Aenters at a vol*metric flo rate of 2+ -m " /s

an- at a concentration of .2 mol/-m"

.3hat C)TR vol*me is necessar' to achieve a4 5 conversion hen 6 7 1 -m " /&mol8s(9

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Mol !ala"c

Rat La8

Stoic&io# tr li *i- phase &v 7 v o(

Co#0i"

E%al at at ; 7 .4<

= 7 112+ -m "


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)pace Time

>ere are some lin6s to e!ample pro#lems.?o* co*l- also *se these pro#lems as selftests.

CSTR T p 1 Ho# Pro0l # CSTR T p ( Ho# Pro0l # CSTR T p 3 Ho# Pro0l # Critical T&i"9i" stio"s $or

CSTR

The follo ing movies ere ma-e #' thest*-ents of Professor Alan @ane s chemicalreaction engineering class at the niversit' of Ala#ama T*scaloosa

2. Applications/ !amples of the CR Algorithm top

Gas P&asEl # "tar R actio"

A--itio"alI"$or#atio"

onl' A fe- P 7 .2 atm

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T 7 + CA 7 .2mol/-m "

6 7 .+-m " /molEs

v o 7 2.+-m " /s

)olve for ; 7 .4Appl'ing the algorithm to the a#ove reactionocc*rring in a Batch< C)TR< an- P R.

!atc& CSTR PFR Mol!ala"c :

Rat La8:

Stoic&io# tr:

,as: = 7 =&e.g.< constant vol*me

steel container(

,as: T 7T < P 7P ,as: T 7 T < P 7 P

Per Mole of A: Per Mole of A:


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Co#0i" :

I"t rat

E%al at

For ; < =.>: = 7 . -m " = 7 4 .0 -m "

?is al E"c clop -ia o$ R actio"

E" i" ri" E7 ip# "t 4.4 Gas P&as R actio" E2a#pl CSTR a"- PFR E2a#pl 4.1 Calc lat ? $or a @ ro Or- r

R actio"


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". Reversi#le Reactions top

To -etermine the conversion or reactorvol*me for reversi#le reactions< onem*st $irst calc*late the ma!im*m conversionthat can #e achieve- at the isothermalreaction temperat*re< hich is the e *ili#ri*m

conversion. &)ee !ample "E in the te!t fora--itional coverage of e *ili#ri*m conversionin isothermal reactor -esign.(

*ili#ri*m Conversion< ; e

rom Appen-i! C:

4. Calc lat E7 ili0ri #Co"% rsio" '; , $or a Co"sta"t ?ol #S st #

E2a#pl : Determine ; e for a P R ith nopress*re -rop< P 7 P



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,iven that the s'stem is gas phase an-isothermal< -etermine the reactor vol*me

hen ; 7 . ; e .

R actio" A--itio"al I"$or#atio"

CA 7 .2 mol/-m "

C 7 1 -m " /mol6 7 2 -m " /molEmin

A 7 + mol/min

irst calc*late ; e :

; e 7 . 4

; 7 . ; e 7 .011

%ne co*l- then *se Pol'math to-etermine the vol*me of the P R. Thecorrespon-ing Pol'math program is sho n#elo .

$. %D &Pol'math( )ol*tions to CR Pro#lems top

Al orit St ps Pol #at& E7 atio"s



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Mole Balance -&;(/-&=( 7 ErA/ A

Rate @a rA 7 E68&&CA882(E&CB/ C((

)toichiometr' CA 7 &CA 8&1E;((/&1Feps8;(

CB 7 &CA 8;(/&28&1Feps8;((

Parameter val*ation eps 7 E .+ CA 7 .2 6 7 2

A 7 + C 7 1

Initial an- inal =al*es ; 7 = 7 = f 7 +

Pol #at& Scr " S&ots*ations

Plot of ; vs. =

Res*lts in Ta#*lar orm

A vol*me of 4$ -m " &ro*n-ing *p fromslightl' more than 4" -m " ( appears to #e o*r

ans er.

4.B !atc& R actor it& aR % rsi0l R actio"+. ,eneral ,*i-elines for California Pro#lems top

ver' state has an e!amination engineersm*st pass to #ecome a registere-professional engineer. In the past there have

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t'picall' #een si! pro#lems in a three ho*rsegment of the California Professional

ngineers !am. Conse *entl' one sho*l- #ea#le to or6 each pro#lem in " min*tes orless. Man' of these pro#lems involve aninterme-iate calc*lation to -etermine the finalans er.

So# Hi"ts:

1. gro*p *n6no n parameters/val*es on the same si-e of the e *ation e!ample:

G*n6no nsH 7 G6no nsH

2. loo6 for a Case 1 an- a Case 2 &*s*all' t o -ata points( to ma6e interme-iatecalc*lations

". ta6e ratios of Case 1 an- Case 2 to cancel as man' *n6no ns as possi#le

$. carr' all s'm#ols to the en- of the manip*lation #efore eval*ating< @ )) T> ?AR J R%

Cali$or"ia Pro$ ssio"al E" i" rs

R istratio" Pro0l #

4. !atc& R actor Opti#i atio". PBR ith Press*re Drop top

ote: Press*re -rop -oes %T affect li *i-phase reactions



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Sample Question:

Anal'Ke the follo ing secon- or-er gas phase

reaction that occ*rs isothermall' in a PBR:

Mol !ala"c

M*st *se the -ifferential form of the mole#alance to separate varia#les

Rat La8

)econ- or-er in A an- irreversi#le:

Stoic&io# tr

Isothermal< T 7 T

Co#0i"


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ee- to fin- &P/P ( as a f*nction of 3 &or = if

'o* have a P R(.

Press*re Drop in Pac6e- Be- Reactors

Er " E7 atio"

=aria#le ,as Densit'

let

Catal'st 3eight

here


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let

then

nglishE

spanolE

)vens6aE

3e ill *se this form for m*ltiple reactions:

3e ill *se this form for single reactions:


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Isothermal%peration

recall that

notice that

The t o e!pressions are co*ple- or-inar' -ifferential e *ations. 3e cansolve them sim*ltaneo*sl' *sing an %D solver s*ch as Pol'math. or the

special case of isothermal operation an- epsilon 7 < e can o#tain ananal'tical sol*tion.

Pol'math ill com#ine the mole #alance< rate la an- stoichiometr'.

Anal'tical )ol*tion < GeH< P R ith

CA TI% : ever *se this form if


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Com#ine

)olve

Co*l- no solve for ; given 3< or for 3 given;.

or gas phase reactions< as the press*re -ropincreases< the concentration -ecreases<res*lting in a -ecrease- rate of reaction<hence a lo er conversion hen compare- to

a reactor itho*t a press*re -rop.


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4.( Pr ss r Drop i" a Pac9 -! - R actor

4.3 Pr ss r a"- R actio" Or- rs 4. For#atio" o$ Et& l Ac tat

>ere are some lin6s to e!ample pro#lems-ealing ith pac6e- #e- reactors. ?o* co*l-also *se these pro#lems as self tests.

P!R T p 1 Ho# Pro0l # P!R T p ( Ho# Pro0l # P!R T p 3 Ho# Pro0l #

P%@?MAT>


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Consi-er the follo ing gas phase reactioncarrie- o*t isothermall' in a pac6e- #e-reactor. P*re A is fe- at a rate of 2.+ moles/san- ith < an- α 7 . 2 6g E1.

2A B

Mol !ala"c

Rat La8

lementar'

Stoic&io# tr

,as ith T 7 T

A B/2

P%@?MAT> ill com#ine ever'thing E ?o* -onot nee- the com#ine step. Than6 'o*P%@?MAT>


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Profiles 4.4 &at Fo r T&i" s ar ro"

8it& t&is Sol tio"

Opti# # Paritcl Dia# t r


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@aminar lo < i! P < L <

L 7 P &M3(/RT

L P ∼P 2


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Increasing the particle -iameter -escreasesthe press*re -rop an- increases the rate an-conversion.

>o ever< there is a competing effect. Thespecific reaction rate -ecreases as the particlesiKe increases< therefore so -eos theconversion.

6 ∼ 1/D p


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DP1 D P26 1 6 2

>igher 6< higher conversion

The larger the particle< the more time it ta6esthe reactant to get in an- o*t of the catal'stparticle. or a given catal'st eight< there isa greater e!ternal s*rgace area for smaller

particles than larger particles. Therefore<there are more entr' a's into the catal'stparticle.


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In CDER%M chapter 12< e ill learn thateffectiveness factor -ecreases as the particlesiKe increases

0. ngineering Anal'sis E Critical Thin6ing an- Creative Thin6ing top

3e ant to learn ho the vario*s parameters&particle -iameter< porosit'< etc.( affect thepress*re -rop an- hence conversion. 3e nee-to 6no ho to respon- to N3hat ifN

*estions< s*ch as:NIf e -o*#le the particle siKe< -ecrease theporosit' #' a factor of "< an- -o*#le the pipesiKe< hat ill happen to D P an- ;9N

&)ee Critical Thin6ing in Preface page !!.

e.g.< O*estions the pro#e consen *ences(To ans er these *estions e nee- to seeho a varies ith these parameters.

T*r#*lent lo



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Compare Case 1 an- Case 2:

or e!ample< Case 1 might #e o*r c*rrentsit*ation an- Case 2 might #e the parameters

e ant to change to.

or constant mass flo thro*gh the s'stem 7constant

@aminar lo

4. E$$ ct o$ R - ci" Particl

Si o" Co"% rsio" i" a P!R


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>ere are more lin6s to e!ample pro#lems-ealing ith pac6e- #e- reactors. Again< 'o*co*l- also *se these pro#lems as self tests.

P!R T p Ho# Pro0l # P!R T p Ho# Pro0l # P!R T p Ho# Pro0l #

Part (: M as r s Ot& r T&a" Co"% rsio"

1. Meas*res %ther Than Conversion top

ses:

A. Mem#rane reactorsB. M*ltiple reaction

@i *i-s: se concentrations< I. . C A

1. or the elementar' li *i- phasereaction carrie- o*t in a C)TR< here =<v o< CAo< 6< an- c are given an- the fee- is



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p*re A< the com#ine- mole #alance< ratela s< an- stoichiometr' are:

There are t o e *ations< t o *n6no ns<CA an- C B

,ases: se Molar lo Rates< I. . I

2. If the a#ove reaction<


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stoichiometr' 'iel-< for isothermal operation&T7To( an- no press*re -rop & ∆ P7 ( are:

se Pol'math to plot A an- B -o n thelength of the reactor.

4.> Stoic&io# tr $or M as r sOt& r t&a" Co"% rsio"

4.B Gas P&as PFR 4. Li7 i- P&as CSTR s Cr ati% a"- t& " Critical

T&i"9i" 4. &at Fo r T&i" s ar ro"

it& t&is sol tio"Micror actors

or isothermal microreactors< e *se thesame e *ations as a P R as long as the flo


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is not laminar. If the flo is laminar< e m*st*se the techni *es -isc*sse- in chapter 1".)ee e!ample $. of the te!t.

niversit' of 3ashington Transportffects in Microreactors site

Instit*t f r Mi6rotechni6 MainK�


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Com#ine Pol'math ill com#ine for 'o*EE Than6s Pol'math...'o* roc6Q

Parameters

)olve Pol'math

4.> &at $o r t&i" s ar 8ro"8it& t&is # #0ra" r actor sol tio"

>ere are lin6s to e!ample pro#lems -ealingith mem#rane reactors. ?o* co*l- also *se

these pro#lems as self tests.

M #0ra" T p 4 Ho# Pro0l #'H t ro " o s,

M #0ra" T p 4 Ho# Pro0l #'Ho#o " o s,

M #0ra" T p Ho# Pro0l #

M #0ra" T p Ho# Pro0l #". )emi#atch Reactors p. 14 top

)emi#atch reactors can #e ver' effective inma!imiKing selectivit' in li *i- phasereactions.



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to )electivit'

The reactant that starts in the reactor isal a's the limiting reactant.

T&r For#s o$ t& Mol !ala"c Appli - to S #i0atc& R actors:

1. Molar !asis

(. Co"c "tratio" !asis

3. Co"% rsio"

For co"sta"t #olar $ -:

For co"sta"t - "sit :


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se the algorithm to solve the remain-er ofthe pro#lem.

E2a#pl : lementar' Irreversi#le Reaction

Consi-er the follo ing irreversi#le elementar'reaction:

ErA 7 6C ACB

The com#ine- mole #alance< rate la < an-stoichiometr' ma' #e ritten in terms ofn*m#er of moles< conversion< an-/orconcentration:

Co"% rsio" Co"c "tratio" N #0 r o$ Mol s

Pol #at& E7 atio"s:Co"% rsio" Co"c "tratio" Mol s

-&;(/-&t( 7 Era8=/ ao -&Ca(/-&t( 7 ra E &Ca8vo(/= -& a(/-&t( 7 ra8=


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ra 7 E68Ca8C# -&C#(/-&t( 7 r# F &&C#oEC#(8vo(/=-& #(/-&t( 7 r#8= F

#o

Ca 7 ao8&1 E ;(/= ra 7 E68Ca8C# ra 7 E68Ca8C#

C# 7 & #i F #o8t Eao8;(/= r# 7 ra r# 7 ra

= 7 =o F vo8t = 7 =o F vo8t = 7 =o F vo8t

=o 7 1 =o 7 1 =o 7 1

vo 7 2 vo 7 2 vo 7 2

ao 7 1 #o 7 + #o 7 +

#o 7 + ao 7 1 Ca 7 a/=

#i 7 C#o 7 #o/vo C# 7 #/=

6 7 .1 6 7 . 1 6 7 . 1

a 7 Ca8=

; 7 & aoE a(/ ao


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Pol #at& Scr "s&ots:

Co"% rsio" Co"c "tratio"

Pol'math *ations Pol'math *ations

)*mmar'Ta#le )*mmar' Ta#le

Conversion vs.Time Conversion vs.Time

Concentration vs.Time Concentration vs.Time

=ol*me vs.Time =ol*me vs.Time

Critical T&i"9i" stio"sE7 ili0ri # Co"% rsio" i" S #i0atc& R actors 8it& R % rsi0lR actio"s

Consi-er the follo ing reversi#le reaction:

ver'thing is the same as for the irreversi#lecase< e!cept for the rate la :

3here:

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* All chapter references are for the $th -itionof the te!t Elements of Chemical ReactionEngineering .

top

ogler ,*rmenS 2 0 niversit' of Michigan

CHAPTER 4 E ;AMPLElementar' gas phase reaction in -ifferent reactor t'pes.

CSTR

The elementar' gas phase reaction

ta6es place in a C)TR at constanttemperat*re &+ ( an- constant press*re&1 .$ atm(. The fee- is e *al molar in A an-B.

Mole Balance

Rate @a

)toichiometr' gas phase< isothermal &T 7 T (< no press*re -rop &P 7 P (



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3h' -o 'o* s*ppose C B is a constant< hen B is #eing cons*me-9

Com#ine

val*ate

PFR and Batch Reactors

lementar' ,as Phase Reaction:

P RMole Balance


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Rate @a

)toichiometr' gas phase< isothermal &T 7 T (< no press*re -rop &P 7 P (<CAo7C Bo &Θ 71(< v7v o&1F ε ;(

Com#ine

Parameterval*ation

CAo7 .2< v7v o72+ -m " /s< 671 -m /mol 2 s< ε 7E .+< ;7 .4


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=7220 -m "

Batch Reactor Constant =ol*me< =7= oan- thepress*re changes.Mole Balance

Rate @a

)toichiometr'

Com#ine

Parameter val*ation C Ao7 .2< 671 -m /mol 2 s


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Bac6 to Chapter $

Example Algorithm for Steps in Solving Closed-Ended Problems

1. Statement

The elementary, liquid-phase, irreversible reaction

is to be carried out in a flow reactor. Two reactors are available, an 800dm 3 !" that can only be operated at 300 # and a $00 dm 3 %&T" that can beoperated at 3'0 #. The two feed streams to the reactor mi( to form a sin)le feed stream that is equal molar in * and +, with a total volumetric flowrate of 10dm 3 min. hich of the two reactors will )ive us the hi)hest conversion

*dditional /nformation at 300 #, k 0.02 dm 3 mol-min 8'000 4 mol-#

%*0+ %+0+ $ mol dm 3 v *0 v +0 0.'5 v 0 ' dm 3 min

$. Real Problem

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e have two choices, a !" operated at 300 # and a %&T" operated at 3'0 #.hich one do we choose

3. Sketch

6. Identify and Name

*. Relevant Theories and Equations

*rrhenius quation

The hi)her the temperature, the faster the reaction rate.

+.

"ate 7aw

ole +alances


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9. Systems

:olume of %&T" :olume of !"

. Dependent and Independent Variables

/ndependent :, ! *0 , T 9ependent ;

!. Knowns and Unknowns

#nowns k 0, , :, ν 0, %*0+ , %+0+ . Inputs and Outputs

/n ! *0 ! +0 , so Θ + 1 ?ut ! * ! *0 @1-;A, !+ ! *0 @1-;A, !% ! *0 ;

B. hat !olor should we paint the rea!tor"

Cot an issue.

'.

D. Assumptions

/sothermal, no pressure drop. The %&T" is well mi(ed. There are no radialvariations in the !".

2. Specifications

There is neither too much redundant information, nor is there too littleinformation )iven. Therefore, the problem is neither over-specified, nor under-specified.

8. Similar or Related Example Problems


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This problem has a solution procedure in common with (amples 6-$ and 6-6in the te(t.

E. Algorithm

CSTR PFR

10.

*. #ole $alan!e

+. Rate %aw

%. Stoi!hiometry - liquid, v v oF equal molar ∴ Θ + 1

%* %*0 @1-;A

%+ %*0 @1-;A

9. &ombine

@eqn 1A

@eqn $A

. Evaluate v *0 ' dm 3 min

+efore mi(in)


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%*0+ $ mol dm 3 ! *0 %*0+ 5 v *0 ! *0 @' dm3 minA@$ mol dm3A 10 mol min

*fter mi(in) v 0 v *0 G v +0 ' dm 3 min G ' dm 3 min 10 dm 3 min %*0 1 mol dm 3

at 3'0 #,

k 8.662 dm 3 mol-min

11. Manipulate

*. &STR ' ()* K

the combined %&T" equation @eqn 1A can be arran)ed as

+. +,R ' (** K


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1$.%hoose the %&T", because it )ives the hi)hest conversion.

13.

16. nits !heck

; is dimensionless

1'. Is it reasonable"

This is a reasonable conversion.

This the end of the !" %&T" e(ample. * sample re)istration e(am problem is alsoavailable.

CHAPTER 4 E ;AMPLEDeriving The *ili#ri*m Constant & C( an- *ili#ri*mConversion&; e( for a Constant =ol*me )'stem:

?o* are given the reversi#le reaction:

hich ta6es place in a constant vol*me #atch reactor. The e *ili#ri*m constant< C< forthis reaction is:

http://www.umich.edu/~elements/fogler&gurmen/html/probsolv/closed/alg/cre-exam/srp/index.htmhttp://www.umich.edu/~elements/fogler&gurmen/html/probsolv/closed/alg/cre-exam/srp/index.htm


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here C Ae an- C Be are:

)*#stit*ting for C Ae an- C Be gives *s:

)*#stit*ting 6no n val*es &C A 7 .2 mol/-m " an- C 7 1 -m " /mol(:

)olving for the e *ili#ri*m conversion< ; e< 'iel-s:

; e 7 . "

chapter 4 reactor design

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