Chemical Reactors - American Chemical Society

18 Fixed Bed Reactors with Deactivating Catalysts JAMES M . POMMERSHEIM and RAVINDRA S. DIXIT

Downloaded by CORNELL UNIV on October 15, 2016 | http://pubs.acs.org Publication Date: September 21, 1981 | doi: 10.1021/bk-1981-0168.ch018

Bucknell University, Lewisburg, PA 17837

Models are formulated and solved for the deactivation of catalysts by feed stream poisons. Catalyst deactivation effects are scaled from single pores, to pellets to catalyst beds. Design equations were presented for fixed bed reactors with catalyst pellets which deactivate by both pore-mouth (shell-progressive) and uniform (homogeneous) poisoning mechanisms. Conversion and production levels are predicted as a function of time and reactant Thiele modulus (h). Levels increased with increases in pellet deactivation times (or time constants). Levels were found to increase with Thiele moduli h for pore-mouth poisoning and decrease for uniform poisoning. An upper limit on bed production exists for pore-mouth and uniform irreversible poisoning, but not for uniform reversible poisoning, where at long times the production rate becomes constant. For uniform poisoning the interior of the catalyst acts as an internal guard-bed removing poison which could otherwise inhibit reaction near the pellet surface. This effect is most pronounced at higher h. Spherical and flat plate pellets gave substantially equivalent results. In order to be able to p r e d i c t the chemical production from a c a t a l y t i c r e a c t o r , the k i n e t i c s of r e a c t i o n must f i r s t be known. By applying the conservation equations to a s i n g l e pore, the r e a c t i o n r a t e f o r a c a t a l y s t p e l l e t can be found. With a knowledge of this r a t e , the r e a c t o r design equations f o r a f i x e d bed of such p e l l e t s can be solved to p r e d i c t conversion l e v e l s and chemical production. For s o l i d c a t a l y t i c r e a c t o r s undergoing c a t a l y s t d e a c t i v a t i o n , the bed design equations must a l s o i n c o r porate the k i n e t i c s of d e a c t i v a t i o n and i t s e f f e c t on pore, p e l l e t and bed transport r a t e s . The o v e r a l l models are often complex and unwieldy, although s i m p l i f y i n g assumptions can be made f o r p a r t i c u l a r cases based on the degree of uncoupling which e x i s t s between

0097-6156/81/0168-0367$05.00/0 © 1981 American Chemical Society Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.


368

CHEMICAL REACTORS

the d e a c t i v a t i o n and r e a c t i o n processes. This type of approach can lead to i n s i g h t s about the o v e r a l l d e a c t i v a t i o n process which may l i e hidden in a more complicated a n a l y s i s . In pioneering work, Wheeler (1) showed the e f f e c t that two l i m i t i n g but important modes of c a t a l y s t d e a c t i v a t i o n , pore-mouth and uniform (or homogeneous) poisoning, can have on the o v e r a l l a c t i v i t y of a c a t a l y s t pore. In pore-mouth poisoning the c a t a l y s t has a strong chemical a f f i n i t y f o r the poison precursor and poison w i l l be s t r o n g l y adsorbed on the c a t a l y s t surface. The outer part of the c a t a l y s t is poisoned f i r s t and a moving band of t o t a l l y poisoned c a t a l y s t slowly moves i n t o the unpoisoned c a t a l y s t interior. C a t a l y s t f o u l i n g as a r e s u l t of coke d e p o s i t i o n can a l s o r e s u l t in a moving band or s h e l l of deactivated c a t a l y s t . Pore mouth d e a c t i v a t i o n by poisoning or f o u l i n g is more l i k e l y when precursor molecules are l a r g e and the pores are narrow and long. These f a c t o r s make the T h i e l e modulus f o r poison d e p o s i t i o n , h , l a r g e . In such instances the poison precursor molecules w i l l r e s i d e in the v i c i n i t y of the pore mouth longer and be more l i k e l y to l i e down there. On the other hand, uniform or homogeneous c a t a l y s t poisoning presumes that the poison precursor species has f u l l access to the c a t a l y s t i n t e r i o r before d e a c t i v a t i o n begins. There is no d i f f u s i o n a l r e s i s t a n c e f o r this species. This w i l l be more l i k e l y to occur when the pores are l a r g e , the c a t a l y s t p e l l e t s small, and the i n t r i n s i c d e a c t i v a t i o n r a t e is low. In a d d i t i o n smaller poison precursor molecules w i l l be able to d i f f u s e more r a p i d l y i n t o the c a t a l y s t i n t e r i o r . Here the T h i e l e modulus f o r poison laydown h w i l l be small, and in the l i m i t , zero. Masamune and Smith (2) examined the problem of f i n d i n g conv e r s i o n s in a f i x e d bed r e a c t o r c o n t a i n i n g a d e a c t i v a t i n g c a t a l y s t . Having obtained in d e t a i l the shape of the poisoning f r o n t in a s i n g l e c a t a l y s t p e l l e t , they i n d i c a t e d how these r e s u l t s can be used with the r e a c t o r design equations to numerically p r e d i c t o v e r a l l conversions. Olson (3) studied the time dependence of a c t i v i t y in a fixed-bed r e a c t o r . Wheeler and Robell (4) combined and condensed much of the previous theory. Their r e s u l t s pred i c t e d the d e c l i n e in a c t i v i t y of a f i x e d bed r e a c t o r . They were s u c c e s s f u l in o b t a i n i n g an a n a l y t i c a l s o l u t i o n which had some degree of g e n e r a l i t y . Haynes (_5) extended the work of Wheeler and R o b e l l to include a f a c t o r to account f o r strong i n t r a p a r t i c l e d i f f u s i o n r e s i s t a n c e to the poison precursor. The general equat i o n s were s i m p l i f i e d by making the assumption of s h e l l - p r o g r e s s i v e poisoning, and dimensionless p l o t s were obtained which showed the e f f e c t of the T h i e l e modulus, a dimensionless time, and the number of r e a c t i o n t r a n s f e r u n i t s on the a c t i v i t y and conversion in a f i x e d bed r e a c t o r . In a comprehensive review on c a t a l y s t d e a c t i v a t i o n , Butt (6) has summarized a number of experimental and theor e t i c a l s t u d i e s d e a l i n g with d e a c t i v a t i o n in f i x e d bed r e a c t o r s . Pommersheim and D i x i t (7) have developed models f o r poisoning o c c u r r i n g in the pores of f l a t p l a t e and s p h e r i c a l c a t a l y s t p e l l e t s .

Fogler; Chemical Reactors ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

18.

POMMERSHEIM AND

DIXIT

Deactivating Catalysts

369

They considered d e a c t i v a t i o n to occur by e i t h e r pore-mouth ( s h e l l p r o g r e s s i v e ) or uniform (homogeneous) poisoning and examined the e f f e c t these types of d e a c t i v a t i o n had on o v e r a l l a c t i v i t y and production r a t e s f o r a s i n g l e c a t a l y s t p e l l e t . A n a l y t i c a l s o l u t i o n s were obtained f o r the production per pore by c o n s i d e r i n g the time dependence of a c t i v i t y . T h e i r r e s u l t s w i l l be used here as the b a s i s f o r the development of models f o r d e a c t i v a t i o n in f i x e d bed r e a c t o r s . In the present work, s o l u t i o n s are presented f o r fixed-bed r e a c t o r s subject to the f o l l o w i n g kinds of p e l l e t poisoning:


(i) (ii) (iii)

The 1) 2) 3) 4) 5) 6) 7) 8) 9)

pore mouth poisoning f o r f l a t p l a t e type p e l l e t s homogeneous (uniform) r e v e r s i b l e poisoning f o r f l a t plate pellets homogeneous (uniform) r e v e r s i b l e poisoning f o r s p h e r i cal pellets f o l l o w i n g assumptions are made: the bed is isothermal throughout c o n c e n t r a t i o n gradients and a c t i v i t y v a r i a t i o n s in the radial d i r e c t i o n are n e g l i g i b l e no change in moles upon r e a c t i o n concentrations of poison species are much l e s s than concentrations of reactant species the r e a c t i o n is f i r s t order and i r r e v e r s i b l e r e a c t o r pressure drop does not e f f e c t r e a c t i o n k i n e t i c s or flow no mass t r a n s f e r f i l m e x t e r n a l to the p e l l e t s plug flow the change in a c t i v i t y with bed length is much slower than the changes in c o n c e n t r a t i o n with bed length.

The l a s t assumption is r e f e r r e d to as the quasi-steady-state assumption. The f r a c t i o n of the bed which is poisoned is a funct i o n of time only and not of bed length, r e a c t o r space time, or the c o n c e n t r a t i o n of the reactant A e x t e r n a l to the p e l l e t s . At any given time the bed a c t i v i t y w i l l be constant, and only one c o n c e n t r a t i o n of the poison precursor species S w i l l e x i s t in the bed. Such a s i t u a t i o n w i l l be more l i k e l y to occur when d e a c t i v a t i o n r a t e s are low compared to r e a c t i o n r a t e s . Under this c o n d i t i o n S w i l l spread evenly throughout the bed. Within p a r t i c l e s , however, c o n c e n t r a t i o n gradients of S may s t i l l e x i s t depending on the poisoning mechanism and the pore and p e l l e t p r o p e r t i e s . Bed

Concentration

Profiles

Feed gas or liquid enters the bottom of the packed bed c o n c e n t r a t i o n (C ) . Contained w i t h i n the feed is a small r Ao o„ . . , , of poison precursor S m c o n c e n t r a t i o n ( C ) , such as lead A

Q


with amount . in

CHEMICAL REACTORS

370

automotive exhaust gas or s u l f u r or metals (e.g., n i c k e l and vanadium) contained in a petroleum feed-stock. Consider a d i f f e r e n t i a l s e c t i o n of a f i x e d bed r e a c t o r which is packed with uniform sized c a t a l y s t p a r t i c l e s . The plug flow design equation f o r this s e c t i o n is (8) d X

dW F

Ao

"

A

(1)

^


where F is the molar flow r a t e of A at the bed i n l e t , X is the ( g l o b a l ; conversion of A, W is the weight of c a t a l y s t , and - r ^ is the moles of A reacted per second per gram of c a t a l y s t . Pore Mouth Poisoning: F l a t P l a t e P e l l e t s . For f l a t p l a t e type p e l l e t s undergoing pore mouth poisoning, the moles of A r e a c t i n g per pore is given by (7) 2 — irr C D h tanh h ( l -a) -r = (2) A L ( l + ah tanh h ( l -α)) ' A

A

o

K

where C ^ is the i n t r a p a r t i c l e c o n c e n t r a t i o n of A, r is the average pore r a d i u s , L is the p e l l e t h a l f width, is the e f f e c t i v e d i f f u s i v i t y of reactant in the p e l l e t and h is the T h i e l e modulus f o r the reactant A and is given by L/k/D^. k is the r e a c t i o n v e l o c i t y constant, based on pore volume, f o r the f i r s t order r e a c t i o n A •> R. C v a r i e s along the bed l e n g t h , but the other model parameters w i l l be constant. The r a t e of r e a c t i o n of A per u n i t weight of c a t a l y s t can be r e l a t e d to the r a t e of r e a c t i o n of A per pore. Thus ε . moles of A moles Α p (3) q

•£

'

= —

. sec. g c a t . A sec. pore p V A ° Ρ Ρ where ε and p are the p e l l e t p o r o s i t y and d e n s i t y , r e s p e c t i v e l y , and V ;s the Volume of one pore. The design equation then becomls _

dC d

Z

V (1 - ε ) ε

A

Ao

=

HL

2

Ρ

C Ao A

D A A

h tanh h ( l

ν (1 + a h tanh h ( l ο

-a) ( 4 )

-a))

where ν is the volumetric flow r a t e , Η and V are the height and volume of the r e a c t o r , r e s p e c t i v e l y , and ε is the p o r o s i t y of the f i x e d bed. Because of assumptions number 1), 3) and 6), V remains constant. Introducing dimensionless v a r i a b l e s f o r con c e n t r a t i o n and d i s t a n c e : Q


18.

POMMERSHEIM

equation

(4)

d0

AND


DIXIT

371

becomes

- V (1 - ε) ε

dA

ν

T

ο

D

ρ

A

h

2 L

t

a

n

h

h

(

i

- g)

1 + ah tanh h ( l - α)

φ

K

J

The boundary c o n d i t i o n is 0

=

1

at

λ = 0


Because of assumption 9), α w i l l be independent of λ, and (5) can be d i r e c t l y i n t e g r a t e d to give -N^Ah 0

where

is

=

e x p

tanh h ( l - a)

1 + ah tanh h ( l -a)

a dimensionless

( 6 )

number defined as

V (1 - ε) ε H.

equation

=

D E _ A

ν

L

(

7

)

2

Ο

V/v is the ( s u p e r f i c i a l ) r e a c t o r space time. Ν represents r a t i o of r e a c t o r space time to p e l l e t d i f f u s i o n time. The v a r i a t i o n of α with time f o l l o w s a p a r a b o l i c curve

a

2

= — 1

= Θ

the (7)

(8)

τ

where τ^, the timg f o r complete d e a c t i v a t i o n of the p e l l e t , is equal to = a^L / r D ( C ) . J i n t r i n s i c poison laydown per u n i t of pore surface ^moles/cm ), and D is the d i f f u s i v i t y of S. Because of the p a r a b o l i c nature of equation (8), over t h i r t y percent of the c a t a l y s t a c t i v i t y is already gone when Θ = O.1. Figure 1 shows a p l o t of dimensionless concentration of r e a c t a n t 0 versus dimensionless time Θ, with Ν-λ f i x e d at u n i t y . The T h i e l e modulus h is shown as a parameter. When both and λ are u n i t y , the t r a c e on the f i g u r e at any given modulus represents the way the output concentration from the f i x e d bed r e a c t o r v a r i e s with time. As time proceeds it increases towards the incoming c o n c e n t r a t i o n in the c h a r a c t e r i s t i c "S" shape shown. From this f i g u r e , it can be seen that f o r small values of h ( l e s s than about O.1) there is l i t t l e or no r e a c t i o n and the concentration of A at the bed e x i t remains the same as the feed concentration. At t = (0 = 1 in f i g u r e 1) each pore (and p e l l e t ) becomes completely d e a c t i v a t e d . Since the bed d e a c t i v a t e s uniformly, it w i l l a l s o completely l o s e i t s a c t i v i t y at this time. This is ω

g

s

s

t n e

0


372

CHEMICAL

REACTORS

shown in f i g u r e 1 by the f a c t that the c o n c e n t r a t i o n of reactant coming from the bed becomes the incoming c o n c e n t r a t i o n 0=1. The i n t e r c e p t of the curves ( i n d i c a t e d by black circîes at time zero) corresponds to the initial c o n c e n t r a t i o n of reactant in the bed, before d e a c t i v a t i o n begins. The t o t a l production from such a d e a c t i v a t i n g f i x e d bed corresponds g r a p h i c a l l y to the area l o c a t e d above each curve and below the l i n e 0 = 1 . The area out to θ = 1 would represent the t o t a l u l t i m a t e production. In f i g u r e 1 the parameter Ν is f i x e d . This i m p l i e s that the diffusivity is a l s o f i x e d . Thus, increases in the T h i e l e modulus h, shown as a parameter in f i g u r e 1, are a s s o c i a t e d with increases in the r e a c t i o n r a t e constant k. Higher r e a c t i o n r a t e s lead to greater conversions at any given time as evidenced by the lower values of the o r d i n a t e . Increases in temperature r a i s e the r a t e constant k and r a i s e the production. T h i s e f f e c t becomes l e s s and l e s s important as the temperature i n c r e a s e s . Figure 1 shows that there is a l i m i t curve at very high moduli (h -> and 0 -> exp [Ν^λ/ν^δ~~] ), above which no f u r t h e r increase in production appears p o s s i b l e . However, some f u r t h e r increase can occur with increases in (N^ i n c r e a s e s ) , although this may be o f f s e t i f a l s o increases (τ^ drops). The i n t r i n s i c r a t e of poison laydown ω may a l s o change with tempera ture, but whether it r i s e s or f a l l s w i l l depend on the s p e c i f i c system under c o n s i d e r a t i o n .


a t

00

Uniform (homogeneous) R e v e r s i b l e Poisoning: F l a t P l a t e Pellets. The r a t e of r e a c t i o n f o r uniform or homogeneous r e v e r s i b l e poisoning in f l a t p l a t e p e l l e t s is given by (1) 2ïïr L k

C

/l

A

- α tanh h / l

- α

where k is the surface (pore) r e a c t i o n r a t e constant. c e n t r a t i o n p r o f i l e s are given by

0 where Ν

Ν. = 2

-Ν λ / l —

= exp

is

5

con

- α (10)

a dimensionless number defined as

2irrLk ε Ρ V v p ο T7

- α tanh h / l -

The

(1-ε)

V = 1

r

k

s

ε

(1-ε) p v

1

= ke ο

r

p

(1-ε) ^ -

ν ο

(11)

represents the r a t i o of r e a c t o r space time to r e a c t i o n time. Comparison of equations (7) and (11) shows ~ h N^. a, the f r a c t i o n of the pore (or p e l l e t ) poisoned, is given by (7)


18.

POMMERSHEiM A N D DIXIT


373

(12)

1

^ - = 1 - exp (-t/τ) = l-expC-Θ )

τ is the time constant f o r poison laydown f o r homogeneous r e v e r s i b l e poisoning and is given by: τ = ^ [ k ^ + ^ ^ g ^ l » where ω is the maximum value of ω when all the adsorption s i t e s are f u l l y occupied, k^ is the desorption r a t e constant and k^ the adsorption r a t e constant f o r poison laydown, Θ is the dimension l e s s time t/τ, and α is the e q u i l i b r i u m f r a c t i o n of a c t i v e s i t e s on the c a t a l y s t surface which are poisoned. When α = 1 the poisoning is i r r e v e r s i b l e , and all c a t a l y t i c s i t e s e v e n t u a l l y become d e a c t i v a t e d . U n l i k e pore mouth poisoning τ is not a pore burn-out time but a true f i r s t order time constant f o r poisoning. Thus Θ ( u n l i k e Θ) can assume values greater than u n i t y s i n c e some c a t a l y s t a c t i v i t y is always present. At 0' = 1 only 63.2% of the poisonable c a t a l y t i c s i t e s on the surface have been deactivated* while at 0' = 3 it has r i s e n to 95%. a

0

0

Μ


1

1

Equations (10) and (11) were solved f o r d i f f e r e n t values of Θ , α , h and Ν . Figure 2 shows the v a r i a t i o n of the dimension l e s s c o n c e n t r a t i o n 0 as a f u n c t i o n of the dimensionless time Θ with h as a parameter. The product Ν λ is f i x e d at u n i t y , and the poisoning is i r r e v e r s i b l e (a = 1). Unlike the pore mouth poison ing case, concentrations were found to increase with i n c r e a s i n g h. Thus the conversion decreased with increases in the T h i e l e modulus With Ν f i x e d , the r e a c t i o n r a t e k w i l l be f i x e d . Increases in h are then a s s o c i a t e d with decreases in reactant d i f f u s i v i t y , D^, or increases in p e l l e t dimension, L. Reaction is then confined more to the periphery of the c a t a l y s t . Since poisoning is uniform, the i n s i d e of the c a t a l y s t w i l l be able to sponge up poison which otherwise would i n h i b i t r e a c t i o n . The i n s i d e of the c a t a l y s t acts as an i n t e r n a l guard bed. The lower slope of the curves in f i g u r e 2 at higher values of h is a t t r i b u t a b l e to this guard-bed action. 1

;

Uniform R e v e r s i b l e Poisoning: Spherical Pellets. The r a t e of r e a c t i o n f o r uniform r e v e r s i b l e poisoning in s p h e r i c a l p e l l e t s is given by (7_)

-r

(-1 +• h

A

1

/ l - α coth h

f

/ l - a)

(13)

where h

f

- R Α Τ Ο " A

h' is the T h i e l e modulus f o r s p h e r i c a l p e l l e t s of r a d i u s R.


(14)


374

CHEMICAL REACTORS

Figure 1. Dimensionless reactant con centration Φ vs. dimensionless time Θ for pore mouth poisoning: Ν,λ = 7; parame ter, h

θ

O.2 Figure 2. Dimensionless reactant con centration Φ vs. dimensionless time Θ ' for uniform poisoning: Ν*λ == 1; a —= 1; parameter, h e

0 | 0

ι 1

ι 2 ^


ι 3

4

18.


POMMERSHEiM AND DIXIT

375

The dimensionless c o n c e n t r a t i o n p r o f i l e s are -Ν λ 2


0

-

(-1 + h

f

/ l - α coth h

T

/ l - a) (15)

exp

a, the f r a c t i o n poisoned, is given by equation (12). For s p h e r i c a l p e l l e t s as with uniform poisoning of f l a t p l a t e p e l l e t s , i n c r e a s i n g h i n c r e a s e s the reduced c o n c e n t r a t i o n r e s u l t i n g in lower conver sions at a f i x e d time. As h i n c r e a s e s , the d i f f u s i o n a l r e s i s t a n c e f o r A i n c r e a s e s , decreasing the conversion and i n c r e a s i n g the reduced c o n c e n t r a t i o n . Equation (15) can be d i r e c t l y compared to equation (10) i f the concept of an equivalent sphere ( 8 ) is used. For f l a t p l a t e p e l l e t s of width 2L, the equivalent r a d i u s is 3L. Thus, equations (10) and (15) can be made analogous to one another by r e p l a c i n g h by 3h. C a l c u l a t i o n s made on this b a s i s i n d i c a t e d that 0 v a l u e s were s l i g h t l y l e s s (within 3%) f o r the s p h e r i c a l case compared to the f l a t p l a t e case. When h = 0 both equations (10) and (15) reduce to 0 = exp[Ν λ(α-1)]. For both cases a decrease in the e q u i l i b r i u m surface coverage of poison α as w e l l as an i n c r e a s e in the space time to r e a c t i o n time r a t i o results in increased conversions (lower 0 ' s ) . Higher values of give higher initial conversions and lower v a l u e s of α give lower d e a c t i v a t i o n r a t e s . For these c o n d i t i o n s the analogous curves in f i g u r e 2 would begin lower and be f l a t t e r . f

2

Production From A Fixed Bed Reactor. The production from a f i x e d bed r e a c t o r can be found by i n t e g r a t i n g the instantaneous molar flow r a t e of product over the time of r e a c t o r o p e r a t i o n . The production w i l l be equal to the t o t a l consumption of r e a c t a n t when the r e a c t i o n has the same number of moles of product as r e a c t a n t . The t o t a l production of product R f o r the r e a c t i o n A -> R is given by

φ In the absence of d e a c t i v a t i o n N = F d u c t i o n v a r y i n g l i n e a r l y with time. R

a

[1 - 0(α = 0 ) ] t ; the pro

Pore Mouth Poisoning: F l a t P l a t e P e l l e t s . For pore mouth poisoning of f l a t p l a t e p e l l e t s , s u b s t i t u t i o n of equation (6) i n t o equation (16) y i e l d s -N

h tanh h (1 -α)

Γ da] 1 + ah tanh h ( l -a)


(17)

376

CHEMICAL

REACTORS

f o r the production coming from a f i x e d bed r e a c t o r . The u l t i m a t e or f i n a l t o t a l production (at t = τ , and α = 1) is given by 1 N

R

( 1 )

-

2

F

Ao

T

1

l t

/

2

"

{

a

-N

h tanh h ( l -a)

1 I ah tanh h ( l -a)

« P

d

a

]

(

1

8

)

F i g u r e 3 shows the dimensionless production ( d i v i d e d by the s c a l e f a c t o r 2 F ^ T ^ ) c a l c u l a t e d using equation (17) and expres sed as a f u n c t i o n of dimensionless time Θ with h as a parameter. The value of Ν λ is f i x e d at u n i t y . The production r i s e s with time towards i t s f i n a l value a t complete d e a c t i v a t i o n (Θ = 1 ) , p r e d i c t e d by equation (18). Low values of h give low production, while high values give high production. T h i s is in agreement with the increased r e a c t i v i t y at l a r g e r moduli. At very high values of h f u r t h e r increase in production is not gained by higher h s . The initial slope of the curves in f i g u r e 3 represents the r a t e of increase of production in the absence of d e a c t i v a t i o n . The s t r a i g h t e r curves a t the higher values of h i n d i c a t e that d e a c t i v a t i o n is not as important at high moduli, and that during d e a c t i v a t i o n there is not as much l o s t production. R a i s i n g the d e a c t i v a t i o n time τ^, w i l l p r o p o r t i o n a l l y r a i s e the production at any time. F i g u r e 4 shows a p l o t of the f r a c t i o n of the f i n a l production N /N (1) vs time Θ with h as a parameter. Lower values of h r e s u l t in higher values of this f r a c t i o n at any f i x e d time, i n d i c a t i n g that d e a c t i v a t i o n has a more pronounced e f f e c t on produc t i o n a t lower T h i e l e moduli. At high h values the curves are r e l a t i v e l y s t r a i g h t and appear to approach a common asymptote at very high moduli. T h i s is c o n s i s t e n t with equations (17) and (18).


Q

f

R

Uniform or Homogeneous R e v e r s i b l e Poisoning: F l a t P l a t e Pellets. S u b s t i t u t i n g equation (10) i n t o equation (16), the t o t a l production f o r uniform r e v e r s i b l e poisoning in f l a t p l a t e p e l l e t s becomes 1

οι \

(

T

>

=

2 F

AO

τ

if

-

N

" o y

Λ7

'

« p

1

y*

-τ —

y -1+α

-

2

t

a

n

h

h

y

— s

d

y

]

(

1

9

)

(

2

0

)

e

where the lower l i m i t on the i n t e g r a l is given by y* = / l

- a

1

e

[1 - exp (-Θ )]

With a = 1, equations (19) and (20) reduce to the case of uniform i r r e v e r s i b l e poisoning. For uniform poisoning in f l a t p l a t e p e l l e t s , f i g u r e 5 presents a p l o t of the production r a t i o / ( 1 ) f u n c t i o n of the dimensionless time 0 with h as a parameter. The dimensionless group was set a t u n i t y , while the poisoning was i r r e v e r s i b l e e

N

N

R

a

s

a

R

T


POMMERSHEiM

A N D DIXIT


377


18.

Figure 4. Fraction of final production N /N (1) vs. dimensionless time Θ for pore mouth poisoning: N j A = 7; parameter, h R

R


378

CHEMICAL REACTORS

N

(α = 1 ) . ( 1 ) represents the production at t = τ, the f i r s t or§er time constant f o r d e a c t i v a t i o n . At this point 63.2% of the c a t a l y s t has become d e a c t i v a t e d . As shown in f i g u r e 5 all curves pass through the common point Θ =1. Both the production and the production r a t i o f i r s t r i s e r a p i d l y with time and then l e v e l o f f at long times, g e n e r a l l y only a f t e r the c a t a l y s t is almost completely d e a c t i v a t e d . Thus the production is f i n i t e even though, u n l i k e the pore mouth case, the d e a c t i v a t i o n , does not have a f i n i t e e x t i n c t i o n time. For times l e s s than τ, all curves are more or l e s s common, r e g a r d l e s s of the value of h. For times greater than τ, the production r a t i o l e v e l s o f f most r a p i d l y f o r small moduli. At s u i t a b l y small h, the production r a t i o becomes independent of h. This r e s u l t can a l s o be obtained t h e o r e t i c a l l y by examining equation (17). As the value of the T h i e l e modulus is r a i s e d , the a c t u a l production Ν f a l l s , as is i n d i c a t e d by equation (17) or by examining the r e l a t i v e areas above the curves in f i g u r e 2. Higher values of h are a s s o c i a t e d with severe d i f f u s i o n a l l i m i t a t i o n s . The higher slope of the curve in f i g u r e 5 at the higher values of h is a t t r i b u t a b l e to the guard bed a c t i o n of the p e l l e t i n t e r i o r . Because the i n t e r i o r of the c a t a l y s t sponges up poison, it is r e l a t i v e l y more e f f e c t i v e at higher moduli in r a i s i n g the production r a t i o . Equation (19) p r e d i c t s that increases in α , the f i n a l f r a c t i o n of the surface poisoned (as Θ ->· °°), w i l l decrease the production of R. This e f f e c t is shown in f i g u r e 6 which presents a p l o t of the production r a t i o as a f u n c t i o n of Θ' with the e q u i l i b r i u m f r a c t i o n poisoned (a ) shown as a parameter. Ν^λ and h were both set at u n i t y . A l l curves cross at Θ = 1. Comparing the curves f o r α = O.1, O.5-and 1.0, i r r e v e r s i b l e poisoning, = 1.0, gives Ë i g h e r production r a t i o s for times l e s s than τ, but s i g n i f i c a n t l y lower r a t i o s at greater times. At a low degree of poisoning, as i n d i c a t e d by α = O.1, the production r a t i o curve is s u b s t a n t i a l l y l i n e a r . A c a t a l y s t which would not d e a c t i v a t e would have α = O. On f i g u r e 6 this appears as a l i n e of u n i t slope. The v e r t i c a l d i s t a n c e between this l i n e and any of the curves in f i g u r e 6 gives a measure of the production l o s s due to d e a c t i v a t i o n . U n l i k e the case of i r r e v e r s i b l e poisoning (a = 1), for r e v e r s i b l e poisoning (a < 1) there is no upper l i m i t on production. Note in f i g u r e 6 that only the curve f o r α = 1 becomes h o r i z o n t a l at longer times. With r e v e r s i b l e poisoning at longer times Θ , α < α and the production r a t e becomes constant. The c a t a l y s t is e f f e c t i v e l y f u n c t i o n i n g then with a reduced but constant a c t i v i t y , p r o p o r t i o n a l to (1 a^). R


1

1

1

1

Uniform R e v e r s i b l e Poisoning: S p h e r i c a l P e l l e t s . For u n i form r e v e r s i b l e poisoning in s p h e r i c a l p e l l e t s an expression f o r the instantaneous t o t a l production is obtained by s u b s t i t u t i n g equation (15) i n t o equation (16)


379



POMMERSHEiM AND DIXIT

Figure 6. Production ratio Ν / Ν ( 7 ) vs. dimensionless time Θ' for uniform poi soning: Ν λ = 1; h = 1; parameter, a β

2

Λ

e


380

CHEMICAL REACTORS

1 N

R

( t )

=

2 F

Ao

τ

II "

f

-Ν (-1 + h'y coth h y) exp

f

y* y

dy]

(21)

-1+α

where the lower l i m i t on the i n t e g r a l is again given by equation (20). C a l c u l a t i o n s performed with this equation gave s u b s t a n t i a l l y i d e n t i c a l r e s u l t s with those found using equation (19) with h replaced by h /3. f


Conclusions With e i t h e r pore-mouth or uniform poisoning, f i x e d bed con v e r s i o n s and production l e v e l s are a strong f u n c t i o n of the reactant T h i e l e modulus h, i n c r e a s i n g with h f o r pore mouth poisoning and decreasing with h f o r uniform poisoning. These trends depend on the constancy of the dimensionless groups and N^. Conversions and production l e v e l s both increased with i n c r e a s e s in the p e l l e t d e a c t i v a t i o n time (pore-mouth) or time constant f o r poison d e p o s i t i o n (uniform). For pore-mouth poisoning, d e a c t i v a t i o n has a more pronounced e f f e c t on production at lower moduli. At high values of h, f u r t h e r increases in h do not gain s i g n i f i c a n t i n c r e a s e s in production. Since p e l l e t d e a c t i v a t i o n times decrease with increases in temperature, a best temperature may e x i s t f o r maximum production. For both pore mouth and i r r e v e r s i b l e uniform poisoning, an upper l i m i t was found f o r the bed production of R, while with uniform r e v e r s i b l e poisoning no such l i m i t e x i s t e d . For uniform r e v e r s i b l e poisoning, the production increased with a decrease in the e q u i l i b r i u m surface of the c a t a l y s t p o i soned. At long times the production r a t e became constant. For uniform poisoning, the i n t e r i o r of the c a t a l y s t a c t s as an i n t e r n a l guard-bed, removing poison which might otherwise i n h i b i t r e a c t i o n near the p e l l e t s u r f a c e . This e f f e c t is most pronounced at high values of h, where r e a c t i o n is confined to the periphery of the c a t a l y s t . S p h e r i c a l and f l a t p l a t e p e l l e t s give s u b s t a n t i a l l y equiva l e n t conversions and production l e v e l s f o r uniform r e v e r s i b l e poisoning when the T h i e l e moduli are put on an equivalent b a s i s .


18.

POMMERSHEiM A N D DIXIT


381

Legend o f Symbols. A

reactant

species

i n t r a p e ^ l e t c o n c e n t r a t i o n of A e x t e r n a l to the p e l l e t s , moles/m (C^ ) q

(C

3 o

c o n c e n t r a t i o n o f A in the feed stream, moles/m

3 ) so ο

c o n c e n t r a t i o n of S in feed, moles/m

2 D

A

e f f e c t i v e d i f f u s i v i t y of A, m /s

D

g

e f f e c t i v e d i f f u s i v i t y of S, m /s


2 F. Ao

molar flow r a t e of A at r e a c t o r i n l e t , moles/s

H

height o f f i x e d bed, cm

h,h

h

f

g

k

T h i e l e modulus f o r reactant A, L /k/D^, or R A / D , r e s p e c t i v e l y , dimensionless A

T h i e l e modulus f o r poison r e a c t i o n r a t e constant,

precursor

s^

4

k

a

2

a d s o r p t i o n r a t e constant, m /mole , s

2 k^

d e s o r p t i o n r a t e constant, m / mole, s

k

r e a c t i o n r a t e constant

g

L

of A based on surface area, m/s

l e n g t h of c a t a l y s t pore, h a l f width of f l a t p l a t e pellets, m

N

R

N (1) R

production of product

R, moles 1

production of R at Θ (or Θ ) = 1 dimensionless

group f o r pore mouth poisoning

(equation 7)

dimensionless group f o r uniform r e v e r s i b l e poisoning (equation 11) r

average or mean pore r a d i u s , m

3 r^

r a t e o f r e a c t i o n of A, mole / m , s

r^

r a t e o f r e a c t i o n , moles/g c a t a l y s t , s


CHEMICAL REACTORS r a d i u s of s p h e r i c a l p e l l e t s , m; product of r e a c t i o n time, s

3 volume of f i x e d bed, m

3 volume of s i n g l e pore, m

3 (input) v o l u m e t r i c flow r a t e , m /s weight of c a t a l y s t , g


τ

l i m i t in i n t e g r a t i o n , / l - α (-exp - Θ ) , equation (20), d imen s i o n l e s s d i s t a n c e along f i x e d bed, m Greek L e t t e r s . f r a c t i o n of c a t a l y s t surface poisoned e q u i l i b r i u m f r a c t i o n of surface poisoned f i x e d bed p o r o s i t y ( i n t e r p a r t i c l e ) pellet porosity (intraparticle) Θ

1

a n

Chemical Reactors - American Chemical Society

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