w05 chap 3 material balance - reactive system-as1

8/18/2019 W05 Chap 3 Material Balance - Reactive System-As1

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MATERIAL ANDENERGY BALANCE

1

Mass Balance –Balance on ReactiveProcesses


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Contents for Material Balance

•Process classifcation

• Balances• Material Balance Calculations on Single Unit

Process•

Balance on Multiple Unit Processes• Balances on Reactive Processes

and Systems• Combustion Reaction• Recycle and Bypass


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Chemical Reaction Stoichiometry

Stoichiometry

ChemicalEuilibriu

m

MultipleReaction! "ield andSelectivity

#imiting and E$cessReactant! %ractional

Conversion andE$tent o& Reaction

Balance on Reactive System

'tomicSpeciesBalance

E$tent o&Reaction

Molecular SpeciesBalance


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Stoichiometry•

Stoichiometry – theory o& proportions in (hichchemical species combine (ith one another)

• Stoichiometric euation o& chemical reaction• statement o& the relative number o& molecules or moles

o& reactants and products that participate in thereaction)

• must be B'#'*CE

+ S,+ - ,+ .../ + S,0• Stoichiometric ratio

• ratio o& species stoichiometry coecients in the

balanced reaction euation• can be used as a conversion &actor to calculate the

amount o& particular reactant 2or product3 that(as consumed 2produced3)

+ mol S,0

generated

+ mol S,+

+ mol S,+

consumed

1 mol ,+ consumed


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Test Yourself

C4! " # $% &&&&&&&&' 4 C$% " 4 %$

1) 4s the stochiometric euation balance5

• "es

+) 6hat is stochiometric coecient &or C,+•

70) 6hat is stochiometric ratio o& 8+, to ,+ including it unit

• 7 mol 8+, generated9 : mol ,+ consumed

7) 8o( many lb.moles o& ,+ reacted to &orm 7;;lb.moles

C,+•

:;; lb.moles ,+ reacted


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Limitin( an) E*cess Reactant

• ?he reactant that (ould run out i& a reactionproceeded to completion is called the limitingreactant! and the other reactants are termede$cess reactants)

• ' reactant is limiting i& it is present in less than itsstoichiometric proportion relative to every otherreactant)

• 4& all reactants are present in stoichiometric

proportion! then no reactant is limiting)

%100n

n-n

ExcessPercentage

n

n-nExcessFractional

stoich

stoichfeed

stoich

stoichfeed

×=

=


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E*am+le

C%% " %% &&&&&&' C%#

4nlet condition@ +; Amol9h C+8+ and


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,ractional Con-ersion

%ractionalconversion!

&

Moles Reacted

Moles %eed – Mole,ut

Moles %eed Moles %eed

Percentageconversion

moles reacted $1;;>moles &ed


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E*tent of Reaction

e$tent o& reaction

ni moles o& species i present in the system a&ter the reaction

occurred

nio moles o& species i in the system (hen the reaction starts

v i stoichiometry coecient &or species i in the particular

chemical reaction euation 2-ve &or product! .ve &or reactant3

ξ

ξ

iioi

iioi

vnn

vnn

+=

+=

or


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E*am+le

*+ - 08+ ............/ +*80Reactor inlet@ 1;; mol *+9sD 0;; mol 8+9sD 1 mol 'r9s

4& &ractional conversion o& 8+ ;):! calculate e$tent o&reaction and the outlet composition)

Unreacted 8+ or 8+ outlet 21.;):3 0;; 1+; mol 8+9s

Solve &or e$tent o& reaction @ :; mol9s

ξ

ξ

ξ

2

1

100

3300

3

2

2

=

=

−=

−=

NH

Ar

N

H

n

n

n

n


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E*ercise

+ C+

87

- ,+

......./+ C+

87

,

?he &eed to a reactors contains 1;;Amol C+87 and 1;;Amol ,+)

a3 (hich is limiting reactant5

C+87

b3 Percentage o& e$cess5

21;;.c3 ,+ out5 C+87, &ormed5 E$tent o& reaction5


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E*ercise

'crylonitrile is produced in the reaction o&propylene! ammonia! and o$ygen@

C08: - *80 - 09+ ,+ C080* - 08+,

?he &eed contains 1;); mole> propylene! 1+);>ammonia! and G=);> air) ' &ractionalconversion o& 0;);> o& the limiting reactant isachieved) ?aAing 1;; mol o& &eed as a basis!

determine (hich reactant is limiting! thepercentage by (hich each o& the otherreactants is in e$cess! and the molar amountso& all product gas constituents &or a 0;>conversion o& the limiting reactant)


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Membrane ?echnology H %IIS'! UMP 10


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.ro/lem 4041

'mmonia is burned to &orm nitric o$ide in the &ollo(ingreaction@

7*80 - e$cess ,+)

c3 i&


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Chemical E2uili/rium

' &ull discussion o& the relations that can be used to determineeuilibrium compositions o& reactive mi$tures is beyond thescope during this course) ?he euilibrium relationship are

normally given in this course

Irre-ersi/le reaction• reaction proceeds only in a single

direction 2&rom reactants to products3• the concentration o& the limiting

reactant eventually approaches Jero)

Re-ersi/le reaction• reactants &orm products &or &or(ard reaction and products

undergo the reverse reactions to re&orm the reactants)• Euilibrium point is a rate o& &or(ard reaction and reverse

reaction are eual


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E*ercise

4& the (ater.gas shi&t reaction!

C, 2g3 - 8+, 2g3 C,+2g3 - 8+2g3

proceeds to euilibrium at a temperature ? 2I3! the mole&raction o& the &our reactive species satis&y the relation

(here I2?3 is the reaction euilibrium constant) 't ?11;


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Multi+les Reaction•

Some o& the chemical reaction has a sidereaction (hich is &ormed undesired product.multiple reaction occurred)

• EKects o& this side reaction might be@1) Economic loss

+) #ess o& desired product is obtained &or a given uantity o& ra(materials

0) Lreater uantity o& ra( materials must be &ed to the reactor toobtain a specifed product yield)

• Concept o& e$tent o& reaction can also be

applied &or multiple reaction• only no( each independent reaction has its

o(n e$tent)

ij j

jiioi vnn ∑+= ξ


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Yiel) an) Selecti-ity

• "ield defnition is diKerent depending on theprocess specifcation

#$el

&oles o' es$re (roc* 'orme

&oles *+* wol +-e been 'orme $' *+ere were no s$erec*$on n *+e l$m$*$n" rec*n* + rec*e com(le*el

#$el &oles o' es$re (roc* 'orme

&oles o' rec*n* 'e

#$el &oles o' es$re (roc* 'orme

&oles o' rec*n* consme

selec*$-$* moles o' es$re (roc*

moles o' nes$re (roc*


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E*ercise

C+8: .../C+87 - 8+C+8: - 8+ ..../ + C87

?he reaction taAes place in a continuous reactor

at steady state) ?he &eed contains =< mole>ethane 2C+8:3 and the balance is inert 243) ?he

&ractional conversion o& ethane is ;)


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Three 35 Metho)s to Sol-eMaterial Balance of Reacti-e

.rocesses

•

iKerent methods have diKerent approach o&degree.o&.&reedom analysis

• 6e must understand the concept o&independent euations! independent speciesand independent chemical reactions


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In)e+en)ent E2uations

• 'lgebraic euations are independent i& youC'**,? obtain any one o& them by'4*L and SUB?R'C?4*L multiples o&any o& the others

$ - +y 7 N1O

0$ - :y 1+ N+Oonly one independent equation because [2] = 3 x [1]

$ - +y 7 N1O+$ – J + N+O

7y - J : N0Oonly 2 independent equation because [3]= 2 x [1] – [2]


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In)e+en)ent Molecular S+ecies

• 4& t(o M,#ECU#'R species are in theS'ME R'?4, to each other (herever theyappear in a process 2output and inputstreams3! balance on those species (ill

not be independent 2i)e) only oneindependent M,#ECU#'R species balanceis obtained3)


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In)e+en)ent Molecular S+ecies

• Since *+ and ,+ have a same ratio on the input and

output streams 20)G: mol *+ 9 mol ,+3! only $NE

independent molecular species balance &or these +species is considered) 4n this reaction! there (ill beT6$ in)e+en)ent molecular s+ecies /alance 2&orCCl7 and &or either ,+ or *+3)

n3 mol O2

3.76 n3 mol N2

n/ mol 00l/-)

rocess

n$*

n1 mol O2

3.76 n1 mol N2

n2 mol 00l/l) n5 mol 00l/l)


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In)e+en)ent Atomic S+ecies

4& t(o '?,M4C species are in the S'MER'?4, to each other (herever theyappear in a process 2output and input

streams3! balance on those species (illnot be independent 2i)e) only oneindependent '?,M4C species balance isconsidered3)


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In)e+en)ents Chemical Reactions

• Chemical reactions are independent i& thestoichiometric euation any one o& themC'**,? be obtained by '4*L andSUB?R'C?4*L multiples o& thestoichiometric euations o& others


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• 'tomic * and , are al(ays in same proportion toeach other on the input and output streams20)G:@13! similar &or atom C and Cl (hich al(ays

same ratio too 21@73 on the input and those +output streams)

• 'lthough ,$7R atomic s+ecies e$ist! only T6$in)e+en)ent atomic s+ecies /alance canobtain &or this case 2&or , or * and &or C or Cl3)

n3 mol O2

3.76 n3 mol N2

n/ mol 00l/-)

rocessn$*

n1 mol O2

3.76 n1 mol N2

n2 mol 00l/l) n5 mol 00l/l)

4ndependent 'tomic Species


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?hree 203 Methods &or Solving MaterialBalance &or Reactive Process

'tomicSpeciesBalance

E$tent o&Reaction

Molecular SpeciesBalance


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D$, Analysis for Reacti-eSystem8

Atomic S+ecies Balance

*o) o& unAno(ns variables

. *o) o& independent reactive atomic species

balance. *o) o& molecular balance on indep)nonreactive species

. *o) o& other euation relating the variable

*o) o& degree o& &reedom


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E*tent of Reaction


- *o) o& independent chemical reaction

. *o) o& independent reactive species

. *o) o& independent nonreactive species




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Molecular S+ecies Balancesame as e*tent of reaction


- *o) o& independent chemical reaction

. *o) o& independent molecular species balance



&or reactive and nonreactive molecular species


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Three 35 Metho)s for Sol-in(Material Balance for Reacti-e

.rocess

Atomic S+ecies Balance


. *o) o& independent reactive atomic species balance

. *o) o& molecular balance onindep) nonreactive species

. *o) o& other euation relating thevariable


6rite a balance on atomD

e)g) atom C! atom 8! atom ,

Balance al(ays eual to 2 4*,U?3

E*tent of Reaction


- *o) o& independent chemicalreaction

. *o) o& independent reactivespecies

. *o) o& independentnonreactive species

. *o) o& other euation relatingthe variable


6rite an e$tent o& reactioneuation

6e need to determine the EoR

Molecular S+ecies Balance


- *o) o& independent chemicalreaction

. *o) o& independent reactivespecies

. *o) o& independentnonreactive species

. *o) o& other euation relatingthe variable


6rite a balance on molecules@

e)g) balance o& (ater! balance on,+! balance on C87! etc))

Balance depend (hether is areactant or product 2need toconsider gen) or consm)3


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E*am+le 4090:

Consider the dehydrogenation o& ethane in asteady.sate continuous reactor)

C+8: C+87 - 8+

1;; Amol9min o& ethane is &ed to the reactor) ?he molar Qo( rate o& 8+ in the product streamis 7; Amol9min)

Solve &or unAno(n by using 0 diKerent methodsin solving balance &or reactive process)


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C%# &&&&&&&' C%4 " %

/! kmol H2 4m$n

n1 kmol 02H6 4m$n

n2 kmol 02H/ 4m$n

Rec*or1!! kmol 02H6 4m$n


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M:8 Atomic S+ecies Balance

• 'll atomic balance is IN.7T;$7T.7T• egree.o&.&reedom analysis

+ unAno(ns variables 2n1! n+3

. + independent atomic species balance 2C! 83

. ; molecular balance on indep) nonreactive species

. ; other euation relating the variable

; *o) o& degree o& &reedom


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• Balance on atomic C 2input output3

+;;+n1 - +n+

1;;n1 - n+ N1O• Balance on atomic 8 2input output3

1;;2:37;2+3 - :n1-7n+


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M%8 E*tent of Reaction

•egree.o&.&reedom analysis

+ unAno(ns variables 2n1!n+3

- 1 independent chemical reaction

. 0 independent reactive species 2C+8:! C+87! 8+3

. ; independent nonreactive species

. ; other euation relating the variable



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•

6rite e$tent o& reaction &or eachspecies

C+8: @ n1 1;;.ξ

C+87 @ n+ ξ 8+ @ 7; ξ

Solve &or n1 and n+ 2ξ 7;3

n1 :; Amol C+8:9minD n+ 7; Amol

C+879min


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M8 molecular S+ecies Balance

•

egree.o&.&reedom analysis

+ unAno(ns variables 2n1! n+3

-1 independent chemical reaction

.0 independent molecular species balance2C+8:! C+87! 8+3

.; other euation relating the variable



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8+ balance 2Len,utput3@

8+ Len 7; Amol 8+9min

C+8: Balance 2inputoutput - cons)3@

1;; Amol C+8:9min n1 Amol C+8:9min -

7; Amol 8+ gen $ 21 Amol C+87 gen91 Amol 8+ gen3

n1 :; Amol C+8:9min

C+87 balance 2Len),uput3@

7; Amol 8+ gen $ 21 Amol C+87 gen)9 1 Amol 8+ gen3 n+

n+ 7; Amol C+879min


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E*am+le 4090:

Methane is burned (ith air in a continuous steady.sate combustion reactor to yield a mi$ture o& C,!C,+ and (ater) ?he reactions taAing place are

C87 - 09+ ,+

C, - +8+,C87 - +,+ C,+ - +8+,

?he &eed to the reactor contains G)=;> mole C87!1)7> ,+ and G+)=> *+) ?he conversionpercentage o& methane is ;> and the gas leavingthe reactor contains = mol C,+9mol C,) Calculatethe molar composition o& the product stream)


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43/45

E*ercise 404<

Methane and o$ygen react in the presence o& a catalyst to &orm&ormaldehyde) 4n a parallel reaction! methane is o$idiJed to carbondio$ide and (ater@

C87- ,+ 8C8, - 8+,

C87- +O2 C,+ - +8+;

?he &eed to the reactor contains euimolar amounts o& methane ando$ygen) 'ssume a basis o& 1;; mol &eed9so

2a3 ra( and label a Qo(chart) Use a degree.o&.&reedom analysisbased on e$tents o& reaction to determine ho( many process variablevalues must be specifed &or the remaining variable values to becalculated)

2b3 Use Euation 7):.: to derive e$pressions &or the product streamcomponent &lo( rates in terms o& the t(o e$tents o& reaction! 1 and

+)

2c3 ?he &ractional conversion o& methane is ;);; and the &ractionalyield o& &ormaldehyde is ;)=


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45/45

E*ercise 40=:Ethanol is produced commercially by the hydration o& ethylene@

C+87 - 8+; C+8

w05 chap 3 material balance - reactive system-as1

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