Modeling of Tubular Nonisothermal Nonadiabatic Packed-Bed

21 Modeling of Tubular Nonisothermal Nonadiabatic Packed-Bed Reactors with Catalyst Poisoning Downloaded by UNIV OF SOUTHERN CALIFORNIA on August 10, 2013 | http://pubs.acs.org Publication Date: December 9, 1984 | doi: 10.1021/bk-1984-0237.ch021

QAMARDEEP S. BHATIA and VLADIMIR HLAVACÈK Department of Chemical Engineering, State University of New York at Buffalo, Amherst, NY 14260

One-and two dimensional models are used to describe deactivation of nonadiabatic packed bed reactors. The models are based on the quasistationary assumptions. Numerical methods of integration of both models are described. It is shown that the deactivation process can be reasonably described by the one-dimensional model. The two-dimensional model must be used only for a deactivation process having high activation energy which is carried out in tubes of large diameter. Two major regimes of deactivation are described: (a) standing wave deactivation and (b) travelling wave deactivation. The former corresponds to low rates of deactivation,while for high deactivation rates, travelling wave deactivation occurs. For the standing wave deactivation,the hot spot temperature decreases during deactivation, while for the travelling wave deactivation, constant pattern profiles exist and the hot spot temperature increases. C a t a l y s t d e a c t i v a t i o n i s of major concern i n c a t a l y s t development and design of packed bed r e a c t o r s . Decay of c a t a l y t i c a c t i v i t y with time can be caused by s e v e r a l mechanisms such as f o u l i n g , s i n t e r i n g and p o i s o n i n g . Although much fundamental experimental work has been done on d e a c t i v a t i o n , v e r y l i t t l e a t t e n t i o n has been focused on modelling and systematic a n a l y s i s of nona d i a b a t i c f i x e d bed r e a c t o r s where a d e a c t i v a t i o n process occurs. T h e o r e t i c a l and experimental r e s u l t s on d e a c t i v a t i o n have been summarized i n two reviews by Butt (1,2). Previous work of p a r t i c u l a r i n t e r e s t to the present study has been done by Blaum (3) who used a one-dimensional two-phase model to explore the dynamic behavior of a d e a c t i v a t i n g c a t a l y s t bed. Butt arid coworkers (4,5,6)have performed d e a c t i v a t i o n s t u d i e s i n a short t u b u l a r r e a c t o r f o r benzene hydrogénation f o r both a d i a b a t i c and nonadiab a t i c arrangements. They experimentally observed both the standing (6) and t r a v e l l i n g (4) d e a c t i v a t i o n wave. Hlavacek 0097-6156/84/0237-0393$06.25/0 © 1984 American Chemical Society In Chemical and Catalytic Reactor Modeling; Dudukovi, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

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394

CHEMICAL AND CATALYTIC REACTOR MODELING

et. a l . (7, 8) have shown that the d e a c t i v a t i o n process give r i s e to t r a n s i e n t hot spots which move downstream and may grow beyond the a d i a b a t i c temperature l i m i t . T h i s growing t r a n s i e n t hot spot i s a c e r t a i n type of the "wrong-way" behavior of a packed bed. The growing t r a n s i e n t hot spot may damage the c a t a l y s t and r e s u l t i n complications i n r e a c t o r operation (9). At present there i s no systematic work on s i m u l a t i o n and design of packed bed nonadiabatic r e a c t o r s of i n d u s t r i a l s i z e where a d e a c t i v a t i o n process occurs. The purpose of t h i s work i s to analyze the operation of a nonadiabatic d e a c t i v a t i n g c a t a l y s t bed and to develop simple techniques f o r s i m u l a t i o n . Based on hydrogénation of b e n z e n e , f u l l - s c a l e r e a c t o r behavior i s c a l c u " l a t e d f o r a number of d i f f e r e n t o p e r a t i o n a l c o n d i t i o n s . R a d i a l transport processes are i n c o r p o r a t e d i n the model, and i t i s shown that the two-dimensional model i s necessary i n some cases. Mathematical

Models

Both one-and two-dimensional quasi-homogeneous models have been used to simulate the r e a c t o r . The f o l l o w i n g major assumptions have been made: (a) the heterogeneous s y s t e m , c o n s i s t i n g of the s o l i d p a r t i c l e s and r e a c t i n g g a s , i s treated as though i t were homogeneous and a h y p o t h e t i c a l a n i s o t r o p i c continuum i s considered, (b) a x i a l d i s p e r s i o n processes are n e g l e c t e d . Since systematic a n a l y s i s by Puszynski et a l . ( 1 0 ) r e v e a l s that f o r r e a c t i o n s with a lower a c t i v a t i o n energy (e.g.,hydrogénation r e a c t i o n s ) the a x i a l d i s p e r s i o n term does not p l a y an important r o l e i n modelling of a f u l l s i z e r e a c t o r and may be omitted, and (c) the d e a c t i v a t i o n process i s very slow and hence a quasi-steady s t a t e assumption can be made. dC One-dimensional model. Reactant balance: u -r- = -θρr (1) — dz c dC Poison balance: u -r-^- = -θρ r (2) dz ρ HT 2TT Energy balance: u < pC > ψ=- = Θ ( - Δ Η ) Ρ + ^ ( T -Τ) (3) pf dz ' c R c o κ

ν

Γ

r x

A c t i v i t y balance:

=

I n i t i a l conditions:

t=0,

(4) z=0:

Two-Dimensional Model. ε

ν4

Poison balance:

, C =C , T=T , θ=1.0 ο ρ po o Reactant balance:

- £ - B p r - 0 2 3 C - 3C ac cD ( — + - -r-^) -u -θρτ = 0 pr\ 2 r 8r ' 8 z p 3r

+ 7 ΐ > 9 r

C=C

c

r

r

In Chemical and Catalytic Reactor Modeling; Dudukovi, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

(5)

p

p


>

r

c

BHATIA AND HLAVACÈK

Nonadiabatic

Packed-Bed Reactors


480

one-dimensional model

two- dimensional model.


401




Nonadiabatic

Packed-Bed

Reactors


21. BHATIA AND HLAVACÈK


403



χ

Ο

m r

α

Ο

η

Η

|

σ η

> >

η

m

η

21.

BHATIA AND

Nonadiabatic

HLAVACÈK

Packed-Bed

Reactors

405

heated up to the temperature of the c o o l i n g medium, d the r e a c t i o n can s t a r t a f t e r the r e a c t i n g gas leaves the completely d e a c t i v a ted p a r t of the c a t a l y s t . an

We can e a s i l y show that there e x i s t s a s i m i l a r i t y between temperature and concentration f i e l d s i n a d e a c t i v a t i n g bed i f r » r . D i f f e r e n t i a t i n g Eq. 1 w i t h respect to t g i v e s : c

2


u 3C ρ 3z3t

=

_ _8Θ 3t

r

c

ac

c _9C at

c

σΤ

3T

(17)

at

3θ S u b s t i t u t i o n of Eq, 4 £gr — and p u t t i n g zero f o r q u a n t i t i e s i n the bracket (because — and we get at-K)) Λ

9 t

^ = _ p 3z3t D c r

D i f f e r e n t i a t i o n of Eq-

3

gives

A f t e r comparing

we have

Eq. 18 and

2

Ώ

« 19 and

>r ) are s i m i l a r , c.f,, Figures 1 and 4. For the case r = r or r Τ ,the feed i s cooled down to Τ . As a r e s u l t ? f o r t h i s type of Seact i v a t i o n , the unreacted îeed enters the f r e s h p a r t of the c a t a l y s t bed t the same temperature. For a standing wave type of deact i v a t i o n s the s i t u a t i o n i s completely d i f f e r e n t . The i n l e t temper a t u r e d i c t a t e s the depth of p e n e t r a t i o n of the poison ( c f . F i g ures 12 and 13). For i n c r e a s i n g time of d e a c t i v a t i o n the hot spot temperature moves slowly toward the r e a c t o r i n l e t , see F i g ure 12. a

E f f e c t of Poison Concentration. The e f f e c t of poison conc e n t r a t i o n can be a n t i c i p a t e d according to the type of d e a c t i v a t i o n . For the t r a v e l l i n g wave d e a c t i v a t i o n , the higher concentrat i o n of the poison i n the feed w i l l increase the speed of the f r o n t . E v i d e n t l y , the v e l o c i t y of the t r a v e l l i n g wave i s given by the r a t e of d e a c t i v a t i o n . For the case of low E^ and r >>r , the speed of the wave i s p r o p o r t i o n a l to the poison concenlratîon i n the feed, as shown i n Figure 14. For the standing wave d e a c t i v a t i o n , the higher poison concent r a t i o n w i l l r e s u l t i n a higher amplitude of the standing wave, c f . , F i g u r e 15. E f f e c t of Tube Diameter. For 1" tubes,the r a d i a l p r o f i l e s of a c t i v i t y are parabola - l i k e functions with minimum value at the center of the tube. For tubes w i t h higher values of the d i a meter, e.g., 2" tubes, the p i c t u r e can be rather d i f f e r e n t . High r a d i a l temperature gradients r e s u l t a l s o i n l a r g e gradients of benzene and poison. For a d e a c t i v a t i o n process with high E^,a minimum on the a c t i v i t y p r o f i l e can occur between the r e a c t o r a x i s and w a l l , see Figure 8. Blaum (3) observed r a d i a l hot spots of temperature between the r e a c t o r a x i s and w a l l f o r a very r a p i d deactivation. For slow d e a c t i v a t i o n , t h e s e hot spots are not likely. E f f e c t of K i n e t i c Parameters. The d e a c t i v a t i o n process i s a f f e c t e d by two important k i n e t i c parameters: (a) A c t i v a t i o n energy of the d e a c t i v a t i o n step, E ; (b) Value of the p r e exponential f a c t o r of the d e a c t i v a t i o n , k£. The e f f e c t of Εβ was e x t e n s i v e l y discussed above. Here, only the e f f e c t of k| w i l l be i n v e s t i g a t e d . D



470

—

=

Figure 10. A x i a l temperature p r o f i l e s , one-dimensional model. Constant p a t t e r n f r o n t s . E f f e c t of i n l e t tempera 298°K E. Τ = 373°K ture. ο D 545[K],k° = α R 1.0.


1

S

3

rry 7!

î

χ

α

> >

X

DO


408


Figure 11. A x i a l a c t i v i t y p r o f i l e s , one-dimensional model. Constant p a t t e r n f r o n t s . E f f e c t of i n l e t temperature Ε ^ = 545[K],k°=1.0 Τ =373 Τ =298°K κ αο υ


Nonadiabatic

Packed-Bed

Reactors



Figure 14. A x i a l temperature p r o f i l e s . Constant p a t t e r n E f f e c t of the i n l e t poison f r o n t . One-dimensional model 0.00958 concentration Ε /R = 545[K],k° =J-« 0. po C =0.0196[mor/m ], [mol/m ]. P° J


409


410


F i g u r e 15. A x i a l temperature p r o f i l e s . Standing wave s i t u a t i o n . One-dimensional model. E f f e c t of the i n l e t poison conc e n t r a t i o n . E /R=15,00Q[K] ,k.°=10 . C =0.00958[mol/m ] C = 0.0196[mol/in ] . ^ n


21.


Nonadiabatic

Packed-Bed Reactors

411


E f f e c t of k j . For a very low value of k^ and E ^ J the a x i a l p r o f i l e of a c t i v i t y θ does not depend s t r o n g l y on the a x i a l c o ordinate z. The loweris k£ the more uniform i s Θ. E v i d e n t l y , f o r low values of k j , a standing wave type of d e a c t i v a t i o n occurs. Here, during the slow d e a c t i v a t i o n process, the temperature i n the hot spot decreases. For k^=20.0 ( f a s t d e a c t i v a t i o n ) J a con stant p a t t e r n p r o f i l e e x i s t and the temperature i n c r e a s e s during the d e a c t i v a t i o n process. D i s c u s s i o n and Conclusions The models of c a t a l y s t d e a c t i v a t i o n i n tubular nonadiabatic r e a c t o r s proposed here i n c l u d e convection i n a x i a l d i r e c t i o n and e f f e c t i v e d i f f u s i o n and conduction i n the r a d i a l d i r e c t i o n . For a m a j o r i t y of i n d u s t r i a l l y operated nonadiabatic r e a c t o r s , the a x i a l temperature gradients are not extremely steep and the a x i a l d i s p e r s i o n process can be neglected. T h i s c o n c l u s i o n i s true f o r a l l types of f u l l - s i z e nonadiabatic hydrogénation r e a c t o r s . F r e quently, the a c t i v a t i o n energy of the d e a c t i v a t i o n process i s very low and the r e a c t o r may be simulated u s i n g a one-dimensional desc r i p t i o n . Depending on the r a t e of d e a c t i v a t i o n ( i . e . on the value k p , t w o d i f f e r e n t d e a c t i v a t i o n processes can occur. For a low value of standing wave d e a c t i v a t i o n process occurs. The temperature i n the hot spot w i l l decrease during d e a c t i v a t i o n . For a f a s t d e a c t i v a t i o n , ( i . e . higher values of k p , a porpagating wave d e a c t i v a t i o n occurs. For t h i s type of d e a c t i v a t i o n the hot spot temperature w i l l i n c r e a s e and constant p a t t e r n p r o f i l e s of temperature and c o n c e n t r a t i o n can be observed. For high values of E^,the poison w i l l penetrate i n the c a t a l y s t bed and a standing wave of d e a c t i v a t i o n occurs i n s i d e the r e a c t o r . For t h i s type of d e a c t i v a t i o n , the r a d i a l p r o f i l e s of a c t i v i t y can e x h i b i t a complicated shape and a two-dimensional model i s necessary f o r c a l c u l a t i o n . The q u a s i s t a t i o n a r y model without d i s p e r s i o n can s a t i s f a c t o r i l y d e s c r i b e the m a j o r i t y of d e a c t i v a t i o n processes t a k i n g p l a c e i n i n d u s t r i a l packed bed r e a c t o r s and can be used s a f e l y f o r calculations. Legend of Symbols C, C

Concentration of benzene and poison, r e s p e c t i v e l y . Heat c a p a c i t y of the gas

V D ,D r pr

R a d i a l d i s p e r s i o n c o e f f i c i e n t of benzene and poison respectively. A c t i v a t i o n energy f o r p o i s o n i n g .

h

w (-ΔΗ)

Wall heat t r a n s f e r

coefficient

Heat of r e a c t i o n .


412

CHEMICAL AND CATALYTIC REACTOR MODELING Pre-exponential f a c t o r f o r

L

Length of the r e a c t o r

M,^

C a t a l y s t adsorption

p^

P a r t i a l pressure

Ρ

T o t a l pressure

r Downloaded by UNIV OF SOUTHERN CALIFORNIA on August 10, 2013 | http://pubs.acs.org Publication Date: December 9, 1984 | doi: 10.1021/bk-1984-0237.ch021

c

,r ,r Ρ

tube

c a p a c i t y f o r poison,

Reaction r a t e , r a t e of poison chemisorption, r a t e of a c t i v i t y decay respective±y.

D

r R

poisoning.

radial Reactor

ο

t

coordinate radius

time

T,T

,T

Temperature, temperature of c o o l i n g medium and w a l l temperature, r e s p e c t i v e l y .

u

Interstitial velocity.

U O v e r a l l heat t r a n s f e r c o e f f i c i e n t . Xp Mole f r a c t i o n of poison ζ Length v a r i a b l e . Greek Symbols ε

Bed v o i d f r a c t i o n .

θ

er

Bed e f f e c t i v e thermal c o n d u c t i v i t y i n the r a d i a l » . . - , , direction. A c t i v i t y of the bed.

p,

C a t a l y s t and gas density

Subscript ο

Initial

c

conditions

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Butt, J . B . , Adv. Chem. 1972, 109, 259. Butt, J . B . ; B i l l i m o r i a , R. Μ., Am. Chem. Soc. Symp.1978, 72, 323. Blaum, E., Chem. Eng. S c i . 1974, 29, 2263. Weng, H. S.; Eigenberger, G.; Butt, J . B . , Chem. Eng. S c i . 1975. 30, 1341. Price, T. H . ; Butt, J . B . , Chem. Eng. S c i . 1977 ,32, 393. B i l l i m o r i a , R. M . ; Butt, J . B . , Chem. Eng. J.1981,22, 71. Mikus, O.; Pour, V . ; Hlavacek, V. ; J . C a t a l . 1977, 48, 98. Mikus, O.; Pour, V . ; Hlavacek, V. ; J. Catal. 1981, 69, 140. Franks, R. G. Ε . , paper presented at the 3rd Iranian Inter national Chemical Engineering Meeting (Shiraz, Iran 1977). Puszynski, J.; Snita, D . ; Hlavacek V . , Hofmann, Η . , Chem. Eng. S c i . 1981, 36, 1605.


21.

11.

12.


13.

B H A T I A AND H L A V A C É K

Nonadiabatic Packed-Bed Reactors

413

Pexider, V . ; Cerny, V.; Pasek, J., "A Contribution to Kinetic Studies Performed on a Nonisothermal Pilot-Plant Reactor," in Chem. React. Engng., (Brussel, Sept. 1968), p. 239 (Perganum Press, Oxford 1971). Hlavacek, V . ; Votruba, J., Chapter 6 in "Chemical Reaction Theory. A Review", L . Lapidus, and N. R. Amundson (Editors), Prentice H a l l , Englewood C l i f f s , N . J . 1977. Bhatia, Q.S., M.S. Thesis, State University of New York at Buffalo, 1983.

R E C E I V E D July 19, 1983


Modeling of Tubular Nonisothermal Nonadiabatic Packed-Bed

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