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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°ree.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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D$, Analysis for Reacti-eSystem8
E*tent of Reaction
*o) o& unAno(ns variables
- *o) o& independent chemical reaction
. *o) o& independent reactive species
. *o) o& independent nonreactive species
. *o) o& other euation relating the variable
*o) o& degree o& &reedom
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D$, Analysis for Reacti-eSystem8
Molecular S+ecies Balancesame as e*tent of reaction
*o) o& unAno(ns variables
- *o) o& independent chemical reaction
. *o) o& independent molecular species balance
. *o) o& other euation relating the variable
*o) o& degree o& &reedom
&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& unAno(ns variables
. *o) o& independent reactive atomic species balance
. *o) o& molecular balance onindep) nonreactive species
. *o) o& other euation relating thevariable
*o) o& degree o& &reedom
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& unAno(ns variables
- *o) o& independent chemicalreaction
. *o) o& independent reactivespecies
. *o) o& independentnonreactive species
. *o) o& other euation relatingthe variable
*o) o& degree o& &reedom
6rite an e$tent o& reactioneuation
6e need to determine the EoR
Molecular S+ecies Balance
*o) o& unAno(ns variables
- *o) o& independent chemicalreaction
. *o) o& independent reactivespecies
. *o) o& independentnonreactive species
. *o) o& other euation relatingthe variable
*o) o& degree o& &reedom
6rite a balance on molecules@
e)g) balance o& (ater! balance on,+! balance on C87! etc))
Balance depend (hether is areactant or product 2need toconsider gen) or consm)3
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E*am+le 4090:
Consider the dehydrogenation o& ethane in asteady.sate continuous reactor)
C+8: C+87 - 8+
1;; Amol9min o& ethane is &ed to the reactor) ?he molar Qo( rate o& 8+ in the product streamis 7; Amol9min)
Solve &or unAno(n by using 0 diKerent methodsin solving balance &or reactive process)
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C%# &&&&&&&' C%4 " %
/! kmol H2 4m$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;$7T.7T• egree.o&.&reedom analysis
+ unAno(ns variables 2n1! n+3
. + independent atomic species balance 2C! 83
. ; molecular balance on indep) nonreactive species
. ; other euation relating the variable
; *o) o& degree o& &reedom
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• Balance on atomic C 2input output3
+;;+n1 - +n+
1;;n1 - n+ N1O• Balance on atomic 8 2input output3
1;;2:37;2+3 - :n1-7n+
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M%8 E*tent of Reaction
•egree.o&.&reedom analysis
+ unAno(ns variables 2n1!n+3
- 1 independent chemical reaction
. 0 independent reactive species 2C+8:! C+87! 8+3
. ; independent nonreactive species
. ; other euation relating the variable
; *o) o& degree o& &reedom
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•
6rite e$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
; *o) o& degree o& &reedom
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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$ture o& C,!C,+ and (ater) ?he reactions taAing place are
C87 - 09+ ,+
C, - +8+,C87 - +,+ C,+ - +8+,
?he &eed to the reactor contains G)=;> mole C87!1)7> ,+ and G+)=> *+) ?he conversionpercentage o& methane is ;> and the gas leavingthe reactor contains = mol C,+9mol C,) Calculatethe molar composition o& the product stream)
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E*ercise 404<
Methane and o$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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E*ercise 40=:Ethanol is produced commercially by the hydration o& ethylene@
C+87 - 8+; C+8