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8/16/2019 L13 Equilibrium Conversion
1/21
L13-1
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois, "r%ana-Cham!aign
'e#ie() *onisothermal 'eactor esignSteady–state total energy balance (TEB):
+or a SS nonisotherm
flo( reactor)
Sim!lified .EB)
Constant /a#erage0
heat ca!acities )
Can rearrange this euation to sol#e for .
. 2 reaction tem! .i 2 initial /feed0 tem!erature .'2 reference tem!
( ) ( )= =
= = − + − Θ − ∆∑ ∑n nsys s 43 i3 i i '5 43 4i 1 i 1
6dE 3 7 8 + 9 9 9 . + 5dt
& &
( )=
= − − Θ − ∆∑ ∫ .n
s 43 i !,i '5 43 4i 1.i3
3 7 8 + C d. 9 . + 5& &
[ ]=
= − − Θ − −∑ ∆n
s 43 i !,i i3 '5 43 4i 1
3 7 8 + C . . /.0+9 5& &
[ ] ( )=
= − − Θ − −∑ ∆ −+∆ '5 'n
s 4 i !,i i P ' 4 4i 1
9 /. 03 7 8 + 6 .C . . 5. +Co& &
8/16/2019 L13 Equilibrium Conversion
2/21
L13-:
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois, "r%ana-Cham!aign
'e#ie() Sol#e .EB for Con#ersion
Sol#e for 5 4)
Plug in 7 for the s!ecific ty!e of reactor
. 2 reaction tem! .i
2 initial /feed0 tem!erature .'
2 reference tem!
+or an adia%atic reaction /720 and shaft (or; can %e neglected /ẆS20
[ ] ( )n
s 43 i !,i i3 '5 ' P ' 43 4
i 1
63 7 8 + C . . 9 /. 0 C . . + 5
=
= − − Θ − − ∆ + ∆ −∑
o& &
[ ]
( )
n
43 i !,i i3 si 1
4
'5 ' P ' 43
+ C . . 8 7
59 /. 0 C . . +
=Θ − + −∑
→ = − ∆ + ∆ −
o
&&
[ ]
( )
ni !,i i3
i 1 4
'5 ' P '
C . .
59 /. 0 C . .
=Θ −∑
= − ∆ + ∆ −
o
8/16/2019 L13 Equilibrium Conversion
3/21
L13-3
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois, "r%ana-Cham!aign
'e#ie() 4!!lication to CS.'
a0 Sol#e .EB for . at the e
a0 Sol#e .EB for . as a function of 5 4 /ma;e a ta%le of . #s 5 4 using EB0
%0 Sol#e CS.' design euation for 5 4 as a function of . /!lug in ; 2 4e-E='. 0
/use design e to ma;e a ta%le of 5 4 #s .0
c0 Plot 5 4,EB #s . & 5 4,MB #s . on the same gra!h .he intersection of these :
lines is the conditions /. and 5 40 that satisfies the energy & mass %alance
Case :) ?i#en + 4, C 4, 4, E, C!i, 9@$, and >, calculate . & 5 4
5 4,EB 2 con#ersion determined from the .EB euation
5 4,MB 2 con#ersion determined using the design euation
5 4
.
5 4,EB
5 4,MB
5 4,e
8/16/2019 L13 Equilibrium Conversion
4/21
L13-A
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois, "r%ana-Cham!aign
'e#ie() 4!!lication to a SS P+'
P+'
P+'+ 4 + 4
distance
.5 4
*egligi%le shaft (or; /ẆS20 and adia%atic /720
a0 "se .EB to construct a ta%le of . as a function of 5 4%0 "se ; 2 4e-E='. to o%tain ; as a function of 5 4c0 "se stoichiometry to o%tain r 4 as a function of 5 4d0 Calculate) May use numerical
methods( )
5 4 4
4 4 45 4
d5> +
r 5 ,.= ∫
−
8/16/2019 L13 Equilibrium Conversion
5/21
L13-
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois, "r%ana-Cham!aign
L13) Euili%rium Con#ersion in
*onisothermal 'eactor esign
D .he highest con#ersion that can %e achie#ed in re#ersi%le
reactions is the euili%rium con#ersion
+or re#ersi%le reactions, the euili%rium con#ersion is
usually calculated first
D .he equilibrium conversion increases (ith increasing
temperature for endothermic reactions
D .he equilibrium conversion decreases (ith increasing
temperature for exothermic reactions
8/16/2019 L13 Equilibrium Conversion
6/21
L13-
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois, "r%ana-Cham!aign
'e#ie( of Euili%rium Kinetics
KC) euili%rium
constant /ca!ital K0)
?as-!hase reaction)
$f KC is gi#en at a single
tem!erature .:, &
∆C
Pcan
%e neglected then)
KP) euili%rium constant in
terms of !artial !ressures Pi)
+or ideal gases, KP 2 K
C/'.0 Fn (here
.em! de!endence of KP is
gi#en %y #anGt 9offGs euation)
$f ∆CP can %e
neglected then)
c dC
C a % 4 B
C CK
C C=
; 4
; 4
a4 % B c C d
−
+ +ˆ ˆ ˆ ˆ †‡ ˆ ˆ ˆˆ
!roducts
reactants
C raised to stoichiometric coefficients
C raised to stoichiometric coefficients
( ) ( ) ( )'5 '
C C :
:
9 . 1 1K . K . e
' . .
∆ = − ÷
o
c dC
P a % 4 B
P PK
P P= i iP C'.=
n c d % a∆ = + − −
( ) ( ) ( )'< '< ' P 'P: :
9 . 9 . C . .dlnK
d. '. '.
∆ ∆ + ∆ −= =
o
( ) ( ) ( )'5 '
P P :
:
9 . 1 1K . K . e
' . .
∆ = − ÷
o
8/16/2019 L13 Equilibrium Conversion
7/21
L13-H
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois, "r%ana-Cham!aign
Euili%rium Con#ersion 5 4e
.
5 4,e
1
e
8/16/2019 L13 Equilibrium Conversion
8/21
L13-I
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois, "r%ana-Cham!aign
5 4e and .em!erature
Su%stitute
for KC)
i#ide numerator &
denominator %y KC
Changed sign
( )
C 4e
C
K5
1 K
=
+
( ) ( ) ( )'5 '
C C :
:
9 . 1 1K . K . e
' . .
∆ = − ÷
o
( ) ( )
( )
( )
'5 'C :
: 4e
'5 '
C : :
9 . 1 1K . e
' . .5
9 . 1 11 K . e
' . .
∆ − ÷
= ∆
+ − ÷
o
o
( )
( ) 4e
'5 '
C : :
15
9 .1 1 1e
K . ' . .
→ = ∆
− + ÷
o
55
1e
e
−=
( )'
'5 ' 4e
:5
9E' .hermic) 9
., (hen .
∆ − ↑ ↓ ÷
< ↑
∆
oo
( )'
'5 ' 4e
:
5
9 .Endo
1thermic) 9 , (hen .
1 e
' . .
∆ − ↓ ↑ ÷
∆ > ↑o
o
8/16/2019 L13 Equilibrium Conversion
9/21
L13-J
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois, "r%ana-Cham!aign
5 4e and .em!erature
Ma;es sense from Le ChatelierGs !rinci!le
E
oo
( ) ( ) ∆
∆
↑ − ↓ ↑ ÷ ≈ > ∆
! ' '5 ':
' 4e5
9 . 1 1, (hen .Endothermic & C 3) 9 . 3 e
8/16/2019 L13 Equilibrium Conversion
10/21
L13-1
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois, "r%ana-Cham!aign
+or the elementary solid-catalyed liuid-!hase reaction
1 Ma;e a !lot of euili%rium con#ersion as a function of tem!erature
: etermine the adia%atic euili%rium tem!erature and con#ersion (hen
!ure 4 is fed to the reactor at a tem!erature of :JI K
4dia%atic Euili%rium . E
8/16/2019 L13 Equilibrium Conversion
11/21
L13-11
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois, "r%ana-Cham!aign
'ate la()euili%rium
-r 4 2
.he >anGt 9off euation)
X e = f (T)5e only de!ends on thermodynamics
*othing to do (ith the energy %alance
CBr ; C
4 4 Ke
− = − ÷
÷
Be 4e
e
CC
K
=
( ) 4 e
e 4 e
C 5K /.0
C 1 5=
−( )
( )e
ee
K .5
1 K .=
+
e e 1'
1
o5 1 1K K /. 0e
' . .
9 = ÷
∆
( ) ( )'
.!.5 ''
o'59 . C d.9 . +∆∆ ∆= ∫
B 4! ! !C C - C 3∆ = =
o o o'5 B 49 9 - 9 -:3333∆ = =
( )e:
d lnK
d. .
9
'
∆=
1. 2:JIK
4 B ƒ 4 BP P e 4 B
9 /:JIK0 A3333 cal = mol 9 /:JIK0 3333 cal = mol
C 3 cal = mol K C 3 cal = mol K K 133333 at :JIK
= − = −
= × = × =
o o
8/16/2019 L13 Equilibrium Conversion
12/21
L13-1:
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois, "r%ana-Cham!aign
'eaction is carried out adia%atically (ith an inlet tem! of :JI K, CP4 2
cal=molK, & the heat of reaction 2 :, cal=mol .he energy %alance is)
+rom thermodynamics5
.
+rom energy %alance
9o( to increase the con#ersionN
[ ]
( )
=Θ − + −∑
→ = − ∆ + ∆ −
n 4 i !,i i s
i 1 4
4'5 ' P '
+ C . . 8 7
69 /. 0 C . +.5
o
&&
( )
( )
n
i !i
i 1EB'5
C . .
59 .
=
Θ −∑
→ = −∆
% 4
n
i !i !
i 1
C 1 C
=
Θ = ×∑ ( )
( )
4P EB
'5
C . .5
9 .
−=
−∆
( )EB
. :JI5
:
−→ =
( ) .'5 '5 ' P.'9 . 9 /. 0 C d.∆ ∆ + ∆∫ =
o
( )C
4eC
K5
1 K=
+
( )
( )
−=−∆
4P EB
'5
C . .5
9 .
4 B ƒ
n
s A i pi i A RX R p Ri
ˆQ W F C ( T T ) F X H ( T ) C ( T T ) Rearrang e =
− − Θ − − ∆ + ∆ − =∑ 3 3 313o& %&
13 13
8/16/2019 L13 Equilibrium Conversion
13/21
L13-13
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois, "r%ana-Cham!aign
oes increasing the entering tem!erature increase 5 4N
5 4e
5 4
. /K0 5 4, E B f o
r a d i a % a
t i c o ! e r
a t i o n
/ s l a n t s
u ! f o r e
8/16/2019 L13 Equilibrium Conversion
14/21
L13-1A
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois, "r%ana-Cham!aign
O!timum +eed .em!erature+or a re#ersi%le and e
8/16/2019 L13 Equilibrium Conversion
15/21
L13-1
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois, "r%ana-Cham!aign
9o( does one increase 5 4 for adia%atic o!eration
of an e
8/16/2019 L13 Equilibrium Conversion
16/21
L13-1
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois, "r%ana-Cham!aign
.he euili%rium con#ersion increases (ith increasing tem!erature, so
use interstage heating to increase the con#ersion
Endothermic 'eactions
5EB
.
heating !rocess
final con#ersion
'ed lines are from
the energy %alance,slant %ac;(ards
%ecause ∆9@'5 forendothermic reaction
L13 1H
8/16/2019 L13 Equilibrium Conversion
17/21
L13-1H
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois, "r%ana-Cham!aign
Su!!ose !ure 4 enters a reactor at :JIK 8hat is the maSol#e .EB for 5 4)
Plot 5EB #s . and 5 4,e #s . to com!ute the ma
= ∆
− + ÷
o
L13 1I
8/16/2019 L13 Equilibrium Conversion
18/21
L13-1I
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois, "r%ana-Cham!aign
Su!!ose !ure 4 enters a reactor at :JIK 8hat is the maT XA,EB
200 02!"2#0 0$""2! 02# '00$#0 '0$#()# '02$
"00 '00("2# '0$"#0 '0"#(#00 '0(0(##0 '0)#((00 '0!0(
T XAe
200 0000$"!2#0 000$("2! 000)($22# 00$")"(#0 002")22)# 00"$
"00 00#($"2# 00)2(2"#0 0$0"0)#00 0$(#20##0 02"$#(00 00##"
[ ]!,4 43 4,EB
'5 '
C . .5
9 /. 0
−= −∆ o
( )( ) 4e '5 '
C : :
15
9 .1 1 1e
K . ' . .
= ∆ − + ÷
o
L13 1JS 4 t t t :JIK 8h t i th i 5
8/16/2019 L13 Equilibrium Conversion
19/21
L13-1J
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois, "r%ana-Cham!aign
Energy %alance con#ersion
Euili%rium con#ersion
Su!!ose !ure 4 enters a reactor at :JIK 8hat is the ma5 4e
E B f o r a d i a % a t i c o ! e r a t i o n ,
/ s l a n t s d o ( n f o r e n d o t h e r m i c r
8/16/2019 L13 Equilibrium Conversion
20/21
L13-:
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr e!t, "ni#ersity of $llinois, "r%ana-Cham!aign
Energy %alancecon#ersion
oes increasing the inlet tem!erature to K im!ro#e the con#ersion of this
reactionN ẆS2, and ∆CP 2 , CP42 Q=molK, ∆9@'5/.'02 :, Q=mol/endothermic0, & KC21 e
5 4e
.adia%atic) Outlet . if reactor had an infinite #olume
E B f o r a d i a % a t i c o ! e r a t i o n / e n d o t h e r m i c 0 .
3 2 : J I K
.adia%atic
5 4,e at .adia%atic is ma< achie#a%le 5 4 in adia%atic reactor
*early
con#ersion
[ ]!,4 43 4,EB
'5 '
C . .
5 9 /. 0
−
= −∆ o( )
( ) 4e
'5 '
C : :
15
9 .1 1 1e
8/16/2019 L13 Equilibrium Conversion
21/21
L13-:1
Slides courtesy of Prof M L Kraft Chemical & Biomolecular Engr e!t "ni#ersity of $llinois "r%ana Cham!aign
oes increasing the inlet tem!erature to K im!ro#e the con#ersion of this
reactionN ẆS2, and ∆CP 2 , CP42 Q=molK, ∆9@'5/.'02 :, Q=mol/endothermic0, & KC21 e
5 4e T
at . 2 :JIK E B f o r a d i a % a t i c o ! e r a t i o n / e n d o t h e r m i c 0 . 3 2 : J I K
.adia%atic
E B f o r a d i a % a t i c o ! e r a t i o n .
3 2 3 3 K 5 4e T : (hen . 2 K
.adia%atic/.2K0
Ues, higher con#ersion is achie#ed
[ ]!,4 43 4,EB
'5 '
C . .
5 9 /. 0
−
= −∆ o( )
( ) 4e
'5 '
C : :
15
9 .1 1 1e