Recovery and Purification of Light Gases by Pressure Swing

Jun 16, 1983 - The model is used to determine the light gas enrichment and recovery performance of a single-column recovery process and a two-column ...
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Recovery and Purification of Light Gases by Pressure Swing Adsorption HSING C. CHENG and FRANK B. HILL Brookhaven National Laboratory, Upton, NY 11973

A c e l l model is presented for the description of the separation of two-component gas mixtures by pressure swing adsorption processes. Local equi­ librium is assumed with linear, independent iso­ therms. The model is used to determine the light gas enrichment and recovery performance of a single-column recovery process and a two-column recovery and purification process. The results are discussed in general terms and with reference to the separation of helium and methane. Pressure swing a d s o r p t i o n (PSA) p r o c e s s e s are widely applied i n d u s t r i a l l y f o r gas s e p a r a t i o n s . Applications are numerous and i n c l u d e h y d r o g e n and h e l i u m r e c o v e r y and p u r i f i c a ­ t i o n , a i r d r y i n g , t h e p r o d u c t i o n o f o x y g e n from a i r , and the s e p a r a t i o n o f n o r m a l p a r a f f i n s from i s o p a r a f f i n s . I n s p i t e o f i t s w i d e s p r e a d u s e , d e s i g n i n f o r m a t i o n on PSA p r o c e s s e s h a s b e e n r a t h e r s p a r s e i n t h e open l i t e r a t u r e . In r e c e n t y e a r s , h o w e v e r , a b e g i n n i n g has been made i n terms o f t h e d e v e l o p m e n t o f m a t h e m a t i c a l m o d e l s o f PSA p r o c e s s e s . T h i s paper i s concerned w i t h the f u r t h e r development o f such m o d e l s . Modeling efforts to date have been confined to two processes: a s i n g l e c o l u m n r e c o v e r y p r o c e s s and a t w o - c o l u m n r e c o v e r y and p u r i f i c a t i o n p r o c e s s . The s i n g l e - c o l u m n p r o c e s s ( F i g u r e 1) i s s i m i l a r t o t h a t o f Jones et a l . ( 1 ) . This process i s useful for bulk separations. It produces a h i g h pressure p r o d u c t e n r i c h e d i n l i g h t com­ ponents. L o c a l e q u i l i b r i u m m o d e l s o f t h i s p r o c e s s have b e e n d e s c r i b e d by T u r n o c k and K a d l e c (2_), F l o r e s F e r n a n d e z and K e n n e y ( 3 ) , and H i l l ( 4 ) . V a r i o u s approaches were u s e d including d i r e c t n u m e r i c a l s o l u t i o n o f p a r t i a l d i f f e r e n t i a l e q u a t i o n s , use o f a c e l l m o d e l , and u s e o f t h e method o f c h a r a c t e r i s t i c s . F l o r e s F e r n a n d e z and K e n n e y ' s work was r e p o r t e d t o employ a c e l l m o d e l b u t no d e t a i l s were g i v e n . E q u i l i b r i u m models p r e d i c t 0097-6156/83/0223-0195$06.00/0 © 1983 American Chemical Society In Industrial Gas Separations; Whyte, Thaddeus E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

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196

INDUSTRIAL

GAS S E P A R A T I O N S

HIGH PRESSURIZATION WITH

FEED

PRESSURE FEED

BLOWDOWN

HIGH PRESSURE PRODUCT

F i g u r e 1.

S t e p s i n s i n g l e - c o l u m n PSA p r o c e s s .

In Industrial Gas Separations; Whyte, Thaddeus E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

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10.

CHENG AND HILL

Pressure Swing

197

Adsorption

t h a t t h i s p r o c e s s i s n o t c a p a b l e o f p r o d u c i n g t h e l i g h t com­ ponent i n pure form. Because o f t h i s f a c t the process is r e f e r r e d t o h e r e as a r e c o v e r y p r o c e s s . The t w o - c o l u m n p r o c e s s ( F i g u r e 2) i s t h e h e a t l e s s a d s o r p ­ t i o n p r o c e s s o f S k a r s t r o m (5^). T h i s p r o c e s s can p e r f o r m b o t h r e c o v e r y and p u r i f i c a t i o n o f a l i g h t component. Local e q u i l i ­ b r i u m m o d e l s o f t h i s p r o c e s s h a v e been p r e s e n t e d by Shendalman and M i t c h e l l ( 6 ) , Chan e t a l . (7), and K n a e b e l and H i l l ( 8 ) . In e a c h c a s e t h e method o f c h a r a c t e r i s t i c s was u s e d . Models with f i n i t e mass t r a n s f e r r a t e s h a v e b e e n p u b l i s h e d by Kawazoe and K a w a i ( 9 ) , M i t c h e l l and Shendalman ( 1 0 ) , C h i h a r a and Suzuki (11), and R i c h t e r e t a l . ( 1 2 ) . I n t h e s e m o d e l s t h e method o f c h a r a c t e r i s t i c s and d i r e c t i n t e g r a t i o n o f p a r t i a l d i f f e r e n t i a l e q u a t i o n s were e m p l o y e d . Much o f t h e m o d e l i n g work t o d a t e has d e a l t w i t h the separation of binary mixtures composed o f a c a r r i e r and an impurity. S u c h s e p a r a t i o n c a n be r e a d i l y t r e a t e d u s i n g the method o f c h a r a c t e r i s t i c s . W h i l e I n some s i t u a t i o n s ( K n a e b e l and H i l l , (8), f o r i n s t a n c e ) t h e same method can be u s e d f o r binary mixtures of a r b i t r a r y composition, the c e l l model i s r e a d i l y and g e n e r a l l y u s e f u l f o r t h i s s i t u a t i o n . I t was this f e a t u r e w h i c h p r o m p t e d t h e use o f t h e c e l l m o d e l i n t h e p r e s e n t work. I n the p r e s e n t p a p e r , a c e l l model i s employed to s i m u l a t e e q u i l i b r i u m i s o t h e r m a l PSA w i t h a b i n a r y f e e d o f a r b i t r a r y com­ position. L i n e a r I s o t h e r m s a r e assumed. The m o d e l e q u a t i o n s d e r i v e d a r e a p p l i e d t o the one- and two-column p r o c e s s e s men­ t i o n e d e a r l i e r t o g i v e a g e n e r a l d e s c r i p t i o n o f t h e i r l i g h t com­ p o n e n t e n r i c h m e n t and r e c o v e r y p e r f o r m a n c e . A l s o some d i s c u s ­ s i o n i s g i v e n o f t h e e f f e c t s o f v a r i o u s o p e r a t i n g p a r a m e t e r s on t h e s e p a r a t i o n o f methane and h e l i u m . C e l l Model A gas m i x t u r e c o n s i s t i n g o f two components i s s e p a r a t e d u s i n g one o r more a d s o r p t i o n b e d s . The b e d s a r e u s e d i n a c y c l i c p r o c e s s composed o f s t e p s i n v o l v i n g c o l u m n p r e s s u r i z a t i o n , d e p r e s s u r i z a t i o n (blowdown) and f l o w t h r o u g h t h e c o l u m n s at constant pressure. A n a l y s i s of such s e p a r a t i o n processes i n t e r m s o f a c e l l m o d e l p r o c e e d s as f o l l o w s . E a c h a d s o r p t i o n bed i s c o n s i d e r e d t o c o n s i s t o f Ν w e l l m i x e d c e l l s , e a c h c e l l b e i n g o f l e n g t h ΔΖ, as shown i n F i g u r e 3. T h i s f i g u r e d e p i c t s the n o t a t i o n used f o r p r o c e s s s t e p s w i t h f l o w from l e f t to r i g h t . The same n o t a t i o n c a n be u s e d f o r s t e p s w i t h f l o w i n the o p p o s i t e d i r e c t i o n i f the c e l l s are renumbered s t a r t i n g from the r i g h t , i . e . , i f i'

- Ν - i +

1

In Industrial Gas Separations; Whyte, Thaddeus E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

(1)

198

INDUSTRIAL

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SEPARATIONS

STEP 2

STEP 3

STEP 4

SLOWDOWN

LOW PRESSURE PURGE

PRESSURIZATION WITH F E E D

STEP I HIGH PRESSURE FEEO

GAS

PRODUCT

PRODUCT

±

LOW PRESSURE PURGE

F i g u r e 2.

S t e p s i n two-column PSA p r o c e s s .

Hi

UF_

uT

u

BLOWDOWN

HIGH PRESSURE FEED

PRESSURIZATION WITH FEED

2

F i g u r e 3.

Hid,

us ' ' uT"

UN

U^|

Flow diagram f o r c e l l

"u " N

model.

In Industrial Gas Separations; Whyte, Thaddeus E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

e—

upg

10.

CHENG

AND

HILL

Pressure Swing

Adsorption

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B e c a u s e o f i n t e r c h a n g e b e t w e e n t h e g a s and t h e a d s o r b e n t , t h e v e l o c i t y and c o m p o s i t i o n o f t h e g a s phase w i t h i n t h e bed c h a n g e w i t h p o s i t i o n and t i m e d u r i n g b o t h c o n s t a n t p r e s s u r e s t e p s and s t e p s w i t h c h a n g i n g p r e s s u r e . P r e s s u r e i s assumed t o v a r y w i t h time d u r i n g p r e s s u r e changes but n o t s p a t i a l l y . Also, p r e s s u r e d r o p due t o f l o w i s n e g l i g i b l e . F i n a l l y , heat e f f e c t s a r e n e g l e c t e d and l o c a l e q u i l i b r i u m w i t h l i n e a r i s o t h e r m s i s assumed t h r o u g h o u t t h e b e d . These i s o t h e r m s a r e r e p r e s e n t e d b y

where y i s t h e m o l e f r a c t i o n o f t h e l e s s s t r o n g l y a d s o r b e d o r l i g h t component. With the foregoing assumptions, the process steps o f i n t e r e s t may be d e s c r i b e d s t a r t i n g w i t h two m a t e r i a l b a l a n c e s , a b a l a n c e f o r t h e l i g h t component and a t o t a l b a l a n c e . The b a l a n c e s a r e t a k e n on t h e f i r s t and i - t h c e l l s and a r e w r i t t e n f o r a d i f f e r e n t i a l time d t . The b a l a n c e s on t h e l i g h t component c a n be e x p r e s s e d a s ϋ y Ρ - U y Ρ

d(Py,) - T ^ - - h d(P —

y i

ΔΖ

)

V

3

dt

*

-

a

P



ν

ι

ν

ι

(

ΔΖ

5

;

i = 2,3,...,N and

the t o t a l balance

yields d

(

p

V

dP

d

dp

(

P

y

i

)

u

p

i

u

"

V H

i "

u

i - i

i = 2,3,...,N where β

6

*

=

ε ε + (1-ε)ρ ^

(

8

)

8

h " ε + (1-ε)ρ k, s "h

In Industrial Gas Separations; Whyte, Thaddeus E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

(9)

200

INDUSTRIAL GAS SEPARATIONS

(10) P r e s s u r i z a t i o n a n d Blowdown. For these s t e p s , Eqs. ( 4 ) , ( 5 ) , ( 6 ) and ( 7 ) a r e c o m b i n e d by e l i m i n a t i n g d ( P y ) / d t b e t w e e n them, r e s p e c t i v e l y , o b t a i n i n g 1

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dF~

h

V P - V Ρ i F Η ΔΖ

i-1 (11)

ΔΖ

where (12) and [β + (1-Î5) ] U yi

(13)

£

1,2,.·.,Ν For a p r e s s u r i z a t i o n s t e p feed gas e n t e r s the f i r s t c e l l a t velocity U a n d t h e r e i s no f l o w f r o m t h e N - t h c e l l , i . e . 0. T h e r e f o r e , when E q . ( 1 1 ) i s w r i t t e n f o r c e l l Ν and N F

U

again f o r c e l l solution i s

i , a difference

V

i

=

equation i n

i s obtained

(N-i)P, Η —

rtiose

(14)

A d i m e n s i o n l e s s t i m e i s d e f i n e d as άτ

dt

LP

(15)

U s i n g t h i s d e f i n i t i o n and E q s . ( 1 1 ) , ( 1 2 ) and ( 1 5 ) i n E q s . ( 4 ) and ( 6 ) , r e s p e c t i v e l y , one o b t a i n s

2i

N-i

A

. Λ

N-i+1

(16)

v

i = 1,2,...,N with y = y . One c a n f i n d t h e d i m e n s i o n l e s s t i m e r e q u i r e d t o a c c o m p l i s h t h e f u l l p r e s s u r e change from P to P by s u b s t i t u t i n g Eqs. ( 1 4 ) and ( 1 5 ) i n t o E q . ( 1 1 ) and i n t e g r a t i n g . The r e s u l t i s 0

F

L

τ

ρ

H

- i n P /P R

(17)

L

Thus t h e mole f r a c t i o n p r o f i l e a f t e r t h e p r e s s u r e i n c r e a s e i s c a l c u l a t e d by i n t e g r a t i n g t h e Ν s i m u l t a n e o u s d i f f e r e n t i a l e q u a ­ t i o n s r e p r e s e n t e d by E q . ( 1 6 ) f r o m τ = 0 t o τ = τ . ρ

In Industrial Gas Separations; Whyte, Thaddeus E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

10.

CHENG

AND

HILL

Pressure

Swing

201

Adsorption

F o r a blowdown s t e p , g a s l e a v e s t h e b e d t h r o u g h t h e N - t h c e l l and t h e r e i s no f l o w i n t o t h e f i r s t c e l l , i . e . , Up • 0, and E q . ( 1 1 ) w r i t t e n f o r c e l l s Ν a n d i y i e l d s a d i f f e r e n c e equation i n whose s o l u t i o n i s (18)

V

ÏÏ N

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The a p p r o p r i a t e d i m e n s i o n l e s s

time i s 3*V

dx Using finds dy JL dT

this

Ν

dt

(19)

and E q s . ( 1 1 ) a n d ( 1 8 ) i n E q . (6)

definition

[3 + (1-3) y±

one

(20) " *]

7

1

3 +

(ί-β)7

1 β 1

i = 1,2,...,N As b e f o r e , one c a n show t h a t t h e l e n g t h o f d i m e n s i o n l e s s time r e q u i r e d f o r t h e p r e s s u r e d e c r e a s e d u r i n g blowdown i s t h a t g i v e n by E q . ( 1 7 ) . The d i m e n s i o n l e s s t i m e d e f i n i t i o n i n t h i s c a s e i s g i v e n b y E q . ( 1 9 ) . Hence t h e m o l e f r a c t i o n p r o f i l e a f t e r t h e p r e s s u r e decrease i s found by i n t e g r a t i n g E q . (20) from τ » 0 t o τ = τ„.

(4),

Constant Pressure Step. For treatment o f t h i s step Eqs. ( 5 ) , ( 6 ) and ( 7 ) c a n be c o m b i n e d , r e s p e c t i v e l y , t o y i e l d V

N =

(21)

i-1

W i t h t h i s r e s u l t , E q s . ( 6 ) and ( 7 ) c a n be w r i t t e n d

y

άτ

i _

Β 1-β

where d i m e n s i o n l e s s

N

H

[

1 [β + (1-β)

1 y

i

ι

(22)

β + (1-B)y _ j i - 1,2 Ν i

1

time i s d e f i n e d a s dT = —i——- d t

(23)

E q u a t i o n s (22) a r e i n t e g r a t e d over the i n t e r v a l τ = 0 t o τ = τ ρ where τ ρ i s a n y d e s i r e d v a l u e . E q u a t i o n s ( 1 6 ) , ( 2 0 ) and ( 2 2 ) e a c h a r e a s e t o f Ν s i m u l ­ t a n e o u s f i r s t o r d e r d i f f e r e n t i a l e q u a t i o n s w h i c h c a n be i n t e ­ g r a t e d t o g i v e t h e mole f r a c t i o n p r o f i l e w i t h i n the a d s o r p t i o n bed a s a f u n c t i o n o f t h e d i m e n s i o n l e s s t i m e τ d u r i n g t h e s t e p

In Industrial Gas Separations; Whyte, Thaddeus E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

I N D U S T R I A L GAS

202

SEPARATIONS

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under c o n s i d e r a t i o n . The t r a n s i e n t p r o f i l e s f o r a g i v e n PSA c y c l e a r e c a l c u l a t e d by i n t e g r a t i n g these sets o f equations c y c l i c a l l y i n the proper order. S i n g l e Column B u l k S e p a r a t i o n P r o c e s s . A t h r e e - s t e p s i n g l e c o l u m n p r o c e s s was d e s c r i b e d by H i l l ( 4 ) ( F i g u r e 1 ) . The p r o ­ c e s s i s s i m i l a r t o t h e r a p i d PSA p r o c e s s o f J o n e s e t a l . ( J L ) . The c y c l e f o r t h i s p r o c e s s c o n s i s t s o f p r e s s u r i z a t i o n w i t h f e e d i n t r o d u c e d t h r o u g h one end o f a c o l u m n f o l l o w e d by i n t r o d u c t i o n o f a d d i t i o n a l f e e d t h r o u g h t h e same end a t h i g h p r e s s u r e w i t h w i t h d r a w a l o f a p r o d u c t f r o m t h e o p p o s i t e e n d , and e n d i n g w i t h blowdown w i t h t h e e x h a u s t e d g a s l e a v i n g v i a t h e f e e d end o n l y . M o l e f r a c t i o n p r o f i l e s w i t h i n t h e bed a r e c a l c u l a t e d b y i n t e ­ g r a t i n g E q . ( 1 6 ) from τ = 0 t o τ = τ f o r t h e p r e s s u r i z a t i o n step. An e x p e r i m e n t a l l y s i g n i f i c a n t i n i t i a l c o n d i t i o n i s t h a t of y ^ ( 0 ) = y « The p r o f i l e r e s u l t i n g from t h e i n t e g r a t i o n o f E q . ( 1 6 ) t o t i m e τ ρ t h e n becomes t h e i n i t i a l c o n d i t i o n f o r t h e i n t e g r a t i o n o f E q . ( 2 2 ) from τ = 0 t o τ = Tp f o r t h e f e e d step. The p r o f i l e f o r τ = τ ρ t h e n becomes t h e i n i t i a l c o n d i ­ t i o n f o r t h e i n t e g r a t i o n o f E q . ( 2 0 ) from τ = 0 t o τ = τ f o r t h e blowdown s t e p . Before performing the l a t t e r i n t e g r a t i o n , t h e c e l l s and t h e c o r r e s p o n d i n g mole f r a c t i o n s a r e renumbered i n accordance with Eq. (1) s i n c e the f l o w d i r e c t i o n i s reversed i n t h e blowdown s t e p . Then t h e n e x t c y c l e i s s t a r t e d b y r e n u m b e r ­ i n g t h e c e l l s and mole f r a c t i o n s and u s i n g t h e mole f r a c t i o n s a s the i n i t i a l c o n d i t i o n f o r the next p r e s s u r i z a t i o n step. The c y c l i c i n t e g r a t i o n o f E q s . ( 1 6 ) , ( 2 2 ) and ( 2 0 ) i s t h e n c o n t i n u e d u n t i l the c y c l i c steady state i s reached. Two i n d i c e s o f p r o c e s s p e r f o r m a n c e w h i c h a r e o f i n t e r e s t are t h e a v e r a g e s t e a d y s t a t e e n r i c h m e n t o f t h e l i g h t component i n the product stream d e f i n e d as ρ

F

Ε = y /y PRD yF and t h e s t e a d y product stream

state

recovery

(24)

of the light

component

in

ρ = ΕΘ

(25)

where t h e p r o d u c t c u t , Θ , i s g i v e n b y N

PRD

θ =

(26) Ν

Since a t the c y l i c

steady N

Eq.

F

+

N

F

+ Ν PRS

state PRS " V u

+

%

(

2

( 2 6 ) may be e x p r e s s e d a s

In Industrial Gas Separations; Whyte, Thaddeus E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

?

)

the

10.

CHENG AND HILL

Pressure Swing

N

p

203

Adsorption

R

D

(28)

+ N__ PRD BD

The p r o d u c t m o l e f r a c t i o n , yp^n> i n E q . ( 2 4 ) i s t h e a v e r a g e s t e a d y s t a t e mole f r a c t i o n l e a v i n g the a d s o r b e r d u r i n g the feed step, i . e . , y

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y

PRD ~

3

/(¥

( T )

CF N 0 3 + (l-3)y (*0

d

1 3 + (l-3)y (O

3

7 0

N

d

T

(

2

9

)

N

where y ( T ) i s t h e m o l e f r a c t i o n t r a n s i e n t f o r t h e N - t h c e l l d u r i n g t h e f e e d s t e p i n a s t e a d y s t a t e c y c l e and i s o b t a i n e d from t h e i n t e g r a t i o n o f Eq. ( 2 2 ) . I t c a n be shown t h a t N , t h e m o l e s o f gas t a k e n o f f a s product a t c y c l i c steady s t a t e d u r i n g the feed step i s N

p R n

= W

PRD

(

£AL^H β RT

F

0

£

dT 3 + (l-3)y (T)

A l s o N , t h e moles o f gas taken from the column blowdown s t e p a t t h e c y c l i c s t e a d y s t a t e , i s B D

Ν

s

BD

Ρ f A L J L 3β RT

Î

τ c Ρ 0

l J

;

N

e

3+

during the

-τ dx (l-3)y (O

K

U

X

J

N

where i n t h i s e q u a t i o n ν^ίτ ) i s t h e m o l e f r a c t i o n t r a n s i e n t f r o m t h e N - t h c e l l d u r i n g t h e blowdown s t e p o f a s t e a d y s t a t e c y c l e and i s o b t a i n e d b y i n t e g r a t i o n o f E q . ( 2 0 ) . Two-Column P r o c e s s . The h e a t l e s s adsorption process ( F i g u r e 2 ) h a s two c o l u m n s . Each column undergoes a f o u r - s t e p cycle. T h r e e s t e p s i n v o l v e t h e same s e q u e n c e a s t h e s i n g l e column p r o c e s s : p r e s s u r i z a t i o n with feed, feed at high pres­ s u r e , and blowdown t h r o u g h t h e f e e d e n d . T h i s i s f o l l o w e d b y a low p r e s s u r e purge s t e p w i t h t h e purge b e i n g a f r a c t i o n o f t h e p r o d u c t f r o m t h e o t h e r c o l u m n and f l o w i n g f r o m t h e p r o d u c t end t o t h e f e e d e n d . F o r one c o l u m n t o p r o v i d e p u r g e f o r t h e o t h e r , t h e c y c l e s i n t h e two c o l u m n s a r e 180° o u t o f p h a s e . M o d e l i n g o f t h i s p r o c e s s p r o c e e d s i n t h e same way a s f o r t h e s i n g l e - c o l u m n p r o c e s s d e s c r i b e d above e x c e p t f o r i n t r o d u c ­ t i o n o f a purge s t e p . The p r o c e s s i s s t a r t e d w i t h one c o l u m n e q u i l i b r a t e d w i t h f e e d a t h i g h p r e s s u r e and t h e o t h e r a t l o w pressure. E q s . ( 1 6 ) , ( 2 0 ) and ( 2 2 ) a r e u s e d a s b e f o r e w i t h r e n u m b e r i n g o f c e l l s and m o l e f r a c t i o n s a t a p p r o p r i a t e p o i n t s i n the c y c l e , b u t t h e purge s t e p i s i n s e r t e d i n t o the sequence a t the a p p r o p r i a t e p o i n t .

In Industrial Gas Separations; Whyte, Thaddeus E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

INDUSTRIAL

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204

GAS

SEPARATIONS

Three i n d i c e s o f performance f o r t h i s process a r e o f interest: Ε , Ρ and H, t h e p u r g e - t o - t o t a l p r o d u c t r a t i o . The l a t t e r q u a n t i t y takes the place o f the purge-to-feed r a t i o i n the heavy i m p u r i t y - l i g h t c a r r i e r s e p a r a t i o n . For that separa­ t i o n i t h a s been shown t h a t t h e i m p u r i t y i s c o m p l e t e l y removed when t h e p u r g e - t o - f e e d r a t i o e x c e e d s a c r i t i c a l v a l u e ( 7 ) . When t h e h e a v y component c o n t e n t o f t h e f e e d i s a b o v e t h e i m p u r i t y l e v e l , a r a t i o w h i c h i s o p e r a t i o n a l l y more u s e f u l i n d e t e r m i n i n g w h e t h e r a p u r e l i g h t g a s c a n be o b t a i n e d i s t h e p u r g e - t o - t o t a l product r a t i o ( 8 ) . A t o t a l m a t e r i a l b a l a n c e a r o u n d one c o l u m n o f t h e twocolumn p r o c e s s a t c y c l i c steady s t a t e i s Ν

+ Ν PRS

The e x t e n t product i s

F

o f recovery

+ N ^ = N _ + Ν + N „ PGF PRD BD PG

of the l i g h t

( N n

(32)

n

gas i n the h i g h

N

PRD " P G F N

PRS

+

N

pressure

) E

(

3

3

)

F

I t c a n be shown t h a t H i s g i v e n b y τ

M Η

Ρ J L

P ; y

=



Ρ Η

PGF β + (l-6)v Ρ τ * PGF _ L _PGF dx Ρ „ τ, Η F 3 + (l-3)y Cx)

ί

Ρ 0

(

3

4

) J

< *'

N

R e s u l t s and D i s c u s s i o n E q n s . ( 1 6 ) , ( 2 0 ) a n d ( 2 2 ) were i n t e g r a t e d n u m e r i c a l l y t o o b t a i n t h e s e p a r a t i o n p e r f o r m a n c e o f t h e o n e - and t w o - c o l u m n processes. The GEAR p a c k a g e ( 1 3 ) was u s e d f o r t h e i n t e g r a t i o n a f t e r d e t e r m i n i n g t h a t i t was f a s t e r t h a n , s a y , R u n g e - K u t t a methods. F o r a l l c a l c u l a t i o n s Ν - 50 a n d ε = 0.40. Dimension­ V less parameters varied were 3, H^PL» F» and, f o r the t w o - c o l u m n p r o c e s s , H. C o m b i n a t i o n s o f t h e p a r a m e t e r s o f 3 and PH/PL were chosen to correspond to the methane-helium s y s t e m on B P L c a r b o n . A d s o r p t i o n i s o t h e r m d a t a f o r methane a t 25°C ( 1 4 ) were r e p r e s e n t e d b y P

5.69 n

χ 10" P 4

T

1 + 8.11 χ 10 ' P h

L

where P ^ i s i n atm and i s i n gm mole/gm c a r b o n . H e l i u m was t a k e n t o be i n e r t . The a d s o r p t i o n c o e f f i c i e n t k^ u s e d t o c a l c u ­ l a t e 3 was e v a l u a t e d a s t h e s l o p e o f t h e s t r a i g h t l i n e c o n n e c t ­ i n g p o i n t s on the i s o t h e r m , Eqn. ( 3 5 ) , c o r r e s p o n d i n g t o the h i g h and l o w p r e s s u r e s P H a n d Ρ^· W i t h v a l u e s o f 3 and P H / L P

In Industrial Gas Separations; Whyte, Thaddeus E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

10.

CHENG AND

HILL

Pressure Swing

Adsorption

205

r e l a t e d i n t h i s way, t h e c a l c u l a t e d p r o c e s s p e r f o r m a n c e c a n be d e s c r i b e d i n t e r m s o f b o t h i t s g e n e r a l f e a t u r e s and i t s a p p l i c a b i l i t y to the methane-helium s e p a r a t i o n . Single-Column Process. T y p i c a l r e l a t i o n s showing e n r i c h ment and r e c o v e r y o f t h e l i g h t component i n t h e p r o d u c t a s a f u n c t i o n o f p r o d u c t c u t a r e shown i n F i g u r e 4 w i t h f e e d l i g h t component m o l e f r a c t i o n a s a p a r a m e t e r . F i g u r e s 4 ( a ) and 4 ( b ) a r e f o r h i g h and l o w p r e s s u r e s o f 60 and 30 p s i a , f o r w h i c h 3 0.083. F o r F i g u r e s 4 ( c ) and 4 ( d ) t h e h i g h p r e s s u r e i s i n c r e a s e d t o 300 p s i a . B e c a u s e o f t h e l e v e l i n g o f f o f t h e methane i s o t h e r m , 3 i n c r e a s e s t o 0.156. F o r any f e e d m o l e f r a c t i o n t h e enrichment i s greatest a t small c u t s . T h i s f o l l o w s from the f a c t that p r e s s u r i z a t i o n leads to a s p a t i a l f r a c t i o n a t i o n w i t h i n t h e c o l u m n w i t h h i g h m o l e f r a c t i o n s o f t h e l i g h t component n e a r the c l o s e d end. Small c u t s then d i s p l a c e gas e n r i c h e d i n t h e light component i n t o the product stream. Enrichment a l s o i n c r e a s e s a s t h e m o l e f r a c t i o n o f t h e l i g h t component i n t h e feed decreases. As a c o m p a r i s o n o f F i g u r e 4 ( a ) and 4 ( c ) shows, i n c r e a s i n g t h e h i g h p r e s s u r e p r o d u c e s an i n c r e a s e i n e n r i c h ment. However, b e c a u s e o f t h e l e v e l i n g o f f o f t h e methane i s o t h e r m t h e i n c r e a s e i s not as l a r g e as t h a t expected f o r a l i n e a r i s o t h e r m (4_). As s e e n i n F i g u r e s 4 ( b ) and 4 ( d ) , r e c o v e r y increases r a p i d l y w i t h c u t a t s m a l l c u t s and l e v e l s o f f a t l a r g e c u t s . S m a l l l i g h t component m o l e f r a c t i o n s i n t h e f e e d and l a r g e pressure r a t i o s favor high recoveries. An e x a m p l e o f t h e e f f e c t o f p r e s s u r e on t h e p e r f o r m a n c e o f the s i n g l e column process f o r the methane-helium s e p a r a t i o n i s shown i n T a b l e 1. U s i n g F i g u r e 4 ( b ) and 4 ( d ) , t h e c u t s c o r r e s p o n d i n g t o 80 p e r c e n t r e c o v e r y o f h e l i u m were d e t e r m i n e d as a function of y and P H ^ L * Th t h e e n r i c h m e n t s and i n t u r n t h e p r o d u c t m o l e f r a c t i o n s c o r r e s p o n d i n g t o t h e s e c u t s were f o u n d f r o m F i g u r e s 4 ( a ) and 4 ( c ) . Except f o r the leanest feed mole f r a c t i o n , y - 0.005, t h e u s e o f t h e h i g h e r t o p p r e s s u r e l e a d s t o a s i g n i f i c a n t l y h i g h e r p r o d u c t mole f r a c t i o n .

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s

e n

F

F

Two-Column P r o c e s s . T y p i c a l enrichment-cut and r e c o v e r y c u t r e l a t i o n s f o r t h i s p r o c e s s a r e shown i n F i g u r e 5. For t h i s figure P • 60 p s i a , P 30 p s i a , and 3 - 0.083. For F i g u r e s 5 ( a ) and 5 ( b ) , y * 0.005 and f o r F i g u r e s 5 ( c ) and 5(d), y » 0.1. The p a r a m e t e r i n F i g u r e 5 i s H, t h e p u r g e to-product r a t i o . The maximum e n r i c h m e n t p o s s i b l e f o r t h e 0.5 p e r c e n t helium f e e d i s 200. F o r 10 p e r c e n t h e l i u m i t i s 10. Pure helium i s o b t a i n e d w i t h t h e 10 p e r c e n t f e e d w i t h H • 0.8 a t c u t s s m a l l e r t h a n 0.018. A t s m a l l e r v a l u e s o f H, p u r e h e l i u m c a n n o t be produced. Very l a r g e enrichments are obtained at small cuts f o r 0.5 p e r c e n t h e l i u m b u t p u r e h e l i u m i s n o t o b t a i n e d . This findi n g i s c o n s i s t e n t w i t h t h e r e s u l t s o f K n a e b e l and H i l l ( 8 ) who s

H

L

F

F

In Industrial Gas Separations; Whyte, Thaddeus E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

I N D U S T R I A L GAS

SEPARATIONS

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206

In Industrial Gas Separations; Whyte, Thaddeus E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

CHENG

AND

HILL

Pressure Swing

Adsorption

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10.

In Industrial Gas Separations; Whyte, Thaddeus E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

207

208

I N D U S T R I A L GAS

SEPARATIONS

Table I E f f e c t o f P r e s s u r e on Single-Column P r o c e s s f o r Helium-Methane S e p a r a t i o n

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Ρ = 0.80 p

H

/ p

L

θ

Ε

V

PRD

0.005

2 10

0.057 0.063

14 13

0.070 0.065

0.05

2 10

0.128 0.063

8.2 13

0.41 0.65

0.1

2 10

0.238 0.107

3.4 7.5

0.34 0.75

0.2

2 10

0.364 0.203

2.13 3.95

0.43 0.79

f o u n d t h a t a c r i t i c a l p r e s s u r e r a t i o ( a s w e l l a s a c r i t i c a l H) had t o be e x c e e d e d t o o b t a i n p u r e l i g h t g a s and t h a t t h i s r a t i o was h i g h e r t h e s m a l l e r t h e l i g h t g a s c o n t e n t o f t h e f e e d . The c r i t i c a l r a t i o s f o r t h e c o n d i t i o n s o f F i g u r e 5 c a n n o t be c a l c u ­ l a t e d from t h e r e s u l t s o f K n a e b e l and H i l l s i n c e t h e i r r e s u l t s were o b t a i n e d f o r t h e " s h o r t e s t c l e a n c o l u m n " c o n d i t i o n . B u t e v i d e n t l y a p r e s s u r e r a t i o o f 2.0 i s h i g h enough f o r p e r f e c t c l e a n u p f o r a 10 p e r c e n t h e l i u m f e e d b u t n o t h i g h enough f o r a 0.5 p e r c e n t f e e d . The c u r v e s f o r Η - 0 r e p r e s e n t t h e p e r f o r m a n c e o f t h e single-column process. I t i s apparent that t h e single-column process i s s u p e r i o r a t l a r g e product c u t s i n terms o f both e n r i c h m e n t and r e c o v e r y . F o r s m a l l c u t s , t h e two-column p r o c e s s is superior. The e f f e c t o f f e e d c o m p o s i t i o n on e n r i c h m e n t a t maximum r e c o v e r y i s shown i n T a b l e 2. B o t h h i g h e n r i c h m e n t and good r e c o v e r y a r e o b t a i n a b l e w i t h t h e l e a n e r feed c o m p o s i t i o n , a r e s u l t which i s counter t o i n t u i t i o n . The e x p l a n a t i o n l i e s i n t h e f a c t t h a t l i g h t g a s l o s s e s i n t h e p u r g e and blowdown g a s d e c r e a s e a s t h e f e e d becomes l e a n e r i n t h e l i g h t g a s .

In Industrial Gas Separations; Whyte, Thaddeus E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

10.

CHENG AND HILL

Pressure Swing

209

Adsorption

Table I I E n r i c h m e n t a t Maximum R e c o v e r y Two-Column P r o c e s s 3 = 0.083

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P-Pmax F

1.0 0.863 0.905 0.800

T

- 2 Ε

Λ

K

0.0 0.2 0.4 0.6

W

ϋ

Ρ max y

P /P

P'Pmax

- 0.005 1.0 0.122 0.032 0.017

1.0 7.0 24.3 50.0

= 0.1 0.0 0.2 0.4 0.6 0.8

1.0 0.835 0.750 0.522 0.244

1.0 0.2 0.115 0.062 0.037

1.0 4.28 6.5 8.4 6.6

Conclusion The equations f o r a local equilibrium cell model o f p r e s s u r e s w i n g a d s o r p t i o n p r o c e s s e s w i t h l i n e a r i s o t h e r m s have been d e r i v e d . These e q u a t i o n s may be used t o d e s c r i b e a n y PSA c y c l e composed o f p r e s s u r i z a t i o n and blowdown s t e p s a n d s t e p s with flow a t constant pressure. The u s e o f t h e e q u a t i o n s was i l l u s t r a t e d by o b t a i n i n g s o l u t i o n s f o r a single-column recovery p r o c e s s a n d a t w o - c o l u m n r e c o v e r y and p u r i f i c a t i o n p r o c e s s . The s i n g l e - c o l u m n p r o c e s s was s u p e r i o r i n e n r i c h m e n t and r e c o v e r y o f t h e l i g h t component a t l a r g e p r o d u c t c u t s . The t w o - c o l u m n p r o c e s s was s u p e r i o r a t s m a l l c u t s . A c k n o w l e dgment s This work was s u p p o r t e d by t h e D i v i s i o n o f Chemical S c i e n c e s , U.S. D e p a r t m e n t o f E n e r g y , W a s h i n g t o n , D.C., u n d e r C o n t r a c t No. DE-AC02-76CH00016.

In Industrial Gas Separations; Whyte, Thaddeus E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

I N D U S T R I A L GAS

210

SEPARATIONS

Notation

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Ε Η i L η Ν Ρ R t Τ U V y ΔΖ

enrichment o f l i g h gas i n product stream molar p u r g e - t o - t o t a l product r a t i o c e l l number column l e n g t h c o n c e n t r a t i o n o f s o r b a t e i n s o l i d phase number o f m o l e s e n t e r i n g o r l e a v i n g a d s o r b e r t o t a l number o f c e l l s gas p r e s s u r e gas constant time temperature i n t e r s t i t i a l g a s v e l o c i t y i n bed c o n c e n t r a t i o n v e l o c i t y d e f i n e d i n Eq . ( 1 3 ) g a s phase mole f r a c t i o n o f l i g h t g a s c e l l length

per c y c l e o r

Greek symbols 3 3^ ε Ρ Ρ θ τ

s

s e p a r a t i o n f a c t o r 3^/3^ e q u i l i b r i u m r a t i o o f g a s c a p a c i t y o f component i t o t o t a l c a p a c i t y o f g a s and s o l i d p h a s e s f o r component i void fraction recovery o f l i g h t gas density of solid particles p r o d u c t c u t , m o l e s o f p r o d u c t p e r mole o f f e e d d i m e n s i o n l e s s time

Subscripts BD F h H ι L PG PRD PRS

refers refers refers refers refers refers refers refers refers

to to to to to to to to to

blowdown feed heavy gas high pressure l i g h t gas low pressure purge high pressure product pressurization

In Industrial Gas Separations; Whyte, Thaddeus E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

10. CHENG AND HILL

Pressure Swing Adsorption

211

Literature Cited

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on January 18, 2016 | http://pubs.acs.org Publication Date: June 16, 1983 | doi: 10.1021/bk-1983-0223.ch010

1.

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In Industrial Gas Separations; Whyte, Thaddeus E., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1983.