l13 equilibrium conversion

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& &


2/21

L13-:


'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


3/21

L13-3


'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


4/21

L13-A


'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 ,.= ∫

−


5/21

L13-


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


6/21

L13-


'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


7/21

L13-H


Euili%rium Con#ersion 5 4e

.

5 4,e

1

e


8/21

L13-I


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


9/21

L13-J


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


10/21

L13-1


+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


11/21

L13-11


'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


12/21

L13-1:


'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


13/21

L13-13


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


14/21

L13-1A


O!timum +eed .em!erature+or a re#ersi%le and e


15/21

L13-1


9o( does one increase 5 4 for adia%atic o!eration

of an e


16/21

L13-1


.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


17/21

L13-1H


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


18/21

L13-1I


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


19/21

L13-1J


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


20/21

L13-:


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


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

l13 equilibrium conversion

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