Multiplicity and Propagating Fronts in Adiabatic and Nonadiabatic

8 Multiplicity and Propagating Fronts in Adiabatic and Nonadiabatic Fixed-Bed Reactors 1

V. H L A V A C E K , J. PUSZYNSKI , and P. V A N ROMPAY*

Downloaded by CORNELL UNIV on October 9, 2016 | http://pubs.acs.org Publication Date: September 16, 1982 | doi: 10.1021/bk-1982-0196.ch008

State University of New York at Buffalo, Department of Chemical Engineering, Buffalo, N Y 14260

A t h e o r e t i c a l and experimental study o f multiplicity and t r a n s i e n t a x i a l profiles in a d i a b a t i c and non-adiabatic f i x e d bed t u b u l a r e a c t o r s has been performed. A classification of possible adiabatic o p e r a t i o n is presented and is extended t o the nona d i a b a t i c case. The c a t a l y t i c o x i d a t i o n of CO o c c u r r i n g on a Pt/alumina c a t a l y s t has been used as a model r e a c t i o n . U n l i k e t h e a d i a b a t i c o p e r a t i o n the speed o f the propagating temperature wave in a nonadiabatic bed depends on its axial p o s i t i o n . For c e r t a i n inlet CO c o n c e n t r a t i o n multiplicity of temperature f r o n t s have been observed. For a downstream moving wave l a r g e f l u c t u a t i o n o f the wave v e l o c i t y , h o t spot temperature and e x i t convers i o n have been measured. For c e r t a i n o p e r a t i n g condit i o n s e r r a t i c behavior o f temperature p r o f i l e s in the r e a c t o r has been observed. For a numerical s i m u l a t i o n the one-phase onedimensional model has been used. The model f a i l e d to p r e d i c t in nonadiabatic case multiplicity of propagating f r o n t s and e r r a t i c behavior as w e l l . The phenomenon o f m u l t i p l i c i t y and propagating f r o n t s i n a d i a b a t i c f i x e d bed r e a c t o r s has r e c e i v e d much a t t e n t i o n i n the l i t e r a t u r e and i s the s u b j e c t o f a r a t h e r exhaustive treatment [1-6]. U n l i k e the a d i a b a t i c o p e r a t i o n , the nonadiabatic case enjoyed f a r l e s s a t t e n t i o n and many questions a r e s t i l l t o be answered. Hence, the p r i n c i p a l i n t e r e s t i n t h i s work was t o i n v e s t i g a t e e x p e r i m e n t a l l y the t h e o r e t i c a l l y the c h a r a c t e r i s t i c f e a t u r e s o f m u l t i p l i c i t y and propagating f r o n t s created under d i f f e r e n t c o n d i t i o n s i n a n o n a d i a b a t i c a l l y operated packed bed r e a c t o r s and t o make a comparison w i t h the a d i a b a t i c o p e r a t i o n . 1

Current address: University of Wroclaw, Chemical Engineering Department, Wroclaw, Poland. Current address: Catholic University of Leuven, Chemical Engineering Department, Leuven, Belgium. 2

0097-6156/82/0196-0089$06.00/0 © 1982 American Chemical Society Wei and Georgakis; Chemical Reaction Engineering—Boston ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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Experimental The c a t a l y t i c CO o x i d a t i o n by pure oxygen was s e l e c t e d as a model r e a c t i o n . The Pt/alumina c a t a l y s t i n the form of 3.4 mm s p h e r i c a l p e l l e t s was used. The CO used i n t h i s study was obtained by a thermal decomposition of formic a c i d i n a hot s u l p h u r i c a c i d . The r e a c t o r was constructed by three c o a x i a l g l a s s tubes. Through the outer j a c k e t s i l i c o n o i l was pumped, w h i l e a i r was blown through the inner j a c k e t as a c o o l i n g medium. The c a t a l y s t was placed i n the c e n t r a l p a r t of the tube. The a x i a l temperature p r o f i l e s were measured by a thermocouple moving a x i a l l y i n a thermowell. Gas a n a l y s i s was performed by an i n f r a red a n a l y z e r or by a thermal c o n d u c t i v i t y c e l l . [ 7 ] . Model Equations

and Numerical

Solution

A one-dimensional one-phase d i s p e r s i o n model s u b j e c t to the Danckwerts boundary c o n d i t i o n s has been used f o r a d e s c r i p t i o n of the dynamics of a nonisothermal nonadiabatic packed bed r e a c t o r . The dimensionless governing equations a r e :

y

*T !τ • PeJJ !f ~ H ξ = 0:

« -

1

8

If

- Pe

y

y

+

f| =

D a B e x p

Pe

T

f

(y)

-^-V

θ

I f - Ί Ι - °·

2)

ν ) . T y p i c a l f o r low v a l u e s o f Pe. The k i n e t i c (quasiisothermal) regime i s a s s o c i a t e d with low e x i t conversion and temperature. The upper steady s t a t e i s near the r e a c t o r i n l e t ; here the i n l e t c o n c e n t r a t i o n and tem perature d i f f e r e s s e n t i a l l y from the i n l e t values f o r the q u a s i i sothermal o p e r a t i o n . Strong p e r t u r b a t i o n may r e s u l t i n propagat i n g f r o n t s between steady s t a t e s . I n a packed bed experimentally observed by Wicke [2, 3] and Hlavacek and Votruba [13]. (2) m u l t i p l e steady s t a t e s (τ > τ, ω < ν ) . T y p i c a l f o r higher v a l u e s o f Pe (Pe > 50) and s t r o n g l y exothermic systems. The com b u s t i o n f r o n t i s i n s i d e the bed, and does not s t r o n g l y a f f e c t the i n l e t c o n d i t i o n s . The quasiisothermal case i s analogous t o that s p e c i f i e d i n (1).' Experimentally observed by Wicke [1, 2] and Votruba [14]. (3) unique steady s t a t e (τ ν ) . Operation t y p i c a l f o r h i g h v a l u e s of Da (Da > O . l f and low or moderate values o f Pe. The r e a c t i o n mixture i s able t o r e a c t , i g n i t i o n occurs a t the r e a c t o r e x i t and a r e a c t i o n f r o n t moves toward r e a c t o r i n l e t . The r e s u l t i n g steady s t a t e i s a t the r e a c t o r i n l e t and a strong pre h e a t i n g o f the i n l e t gas occurs. The t r a n s i e n t o p e r a t i o n i s r e f e r r e d t o as "creeping p r o f i l e s " and was e x t e n s i v e l y s t u d i e d by Amundson [4-6]. Experimentally observed i n [1, 1 5 ] . (4) unique steady s t a t e (τ < τ, ω « ν ) . C h a r a c t e r i s t i c f o r high v a l u e s o f Da (Da > O . l f and high values o f Pe. Similar to (3) however, the steady s t a t e stays i n the middle o f the bed. Common i n o p e r a t i o n o f i n d u s t r i a l packed a d i a b a t i c r e a c t o r s .

Wei and Georgakis; Chemical Reaction Engineering—Boston ACS Symposium Series; American Chemical Society: Washington, DC, 1982.


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ENGINEERING

(5) unique steady s t a t e (τ > τ, ω < ν ) . Q u a s i i so thermal opera t i o n . A l l the above mentioned operations of the bed were e x p e r i mentally observed and the experiments are i n q u a l i t a t i v e agreement w i t h theory 114]. The "creeping p r o f i l e s " are represented by a propagating f r o n t moving w i t h constant v e l o c i t y and without a change of i t s geome t r i c a l form [4-6]. Frank-Kameneckii [16] i n d i c a t e d that i n an i n f i n i t e r e a c t o r the propagating r e a c t i o n zone can be stopped a t an a r b i t r a r y p o s i t i o n f o r c e r t a i n v a l u e s of i n l e t c o n d i t i o n s . However, s i n c e the bed i s of i n f i n i t e l e n g t h a simple t r a n s l a t i o n of the coordinate i n d i c a t e s that a l l these p r o f i l e s are identical. For an a d i a b a t i c bed having a f i n i t e l e n g t h t h i s phenomenon does not e x i s t , i . e . , f o r a given v a l u e of i n l e t c o n d i t i o n s only one s i n g l e p r o f i l e occurs. P u s z y n s k i [15] obser ved experimentally that f o r a long a d i a b a t i c bed and f o r c e r t a i n v a l u e s of i n l e t c o n d i t i o n s the propagating f r o n t can be " f r o z e n " and i t behaves almost l i k e a "standing wave". However, a f t e r a long time, the r e a c t i o n zone s t a r t s moving. Nonadiabatic case The c l a s s i f i c a t i o n of a d i a b a t i c o p e r a t i o n presented above may be a l s o used f o r nonadiabatic r e a c t o r s , however, new pheno mena were observed. Numerical c a l c u l a t i o n and experimental observations r e v e a l e d t h a t the "constant p a t t e r n p r o f i l e s " do not e x i s t , the shape of a propagating f r o n t changes. In problems a s s o c i a t e d w i t h a steep temperature f r o n t , r e g a r d l e s s of the r e a c t o r l e n g t h , the a x i a l d i s p e r s i o n e f f e c t s must not be n e g l e c t e d . Experiments as w e l l as numerical s i m u l a t i o n pointed out t h a t m u l t i p l i c i t y can e x i s t f o r v e r y long bed (Pe > 1000) [11]. For c e r t a i n o p e r a t i o n a l c o n d i t i o n s and p h y s i c a l p r o p e r t i e s of the r e a c t i n g system ( a c t i v a t i o n energy and heat of r e a c t i o n ) a number of d i f f e r e n t m u l t i p l i c i t y regimes may e x i s t . Three s t a b l e steady s t a t e s i n the bed were t h e o r e t i c a l l y p r e d i c t e d [18] and experimentally observed [13]. For a h i g h l y a c t i v e c a t a l y s t , the t h e o r e t i c a l l y p r e d i c t e d t h i r d steady s t a t e occurs near the r e a c t o r e x i t . A systematic experimental search d i d not f i n d i t [20]. A c a l c u l a t i o n w i t h more r e a l i s t i c boundary c o n d i t i o n s [19] r e s u l t e d i n i t s e l i m i n a t i o n . However, f o r a c a t a l y s t of lower a c t i v i t y the t h i r d steady s t a t e was experimentally l o c a t e d [13]. For a s h o r t nonadiabatic bed ( e q u i v a l e n t to case (1)) m u l t i p l i c i t y was experimentally found and t r a n s i e n t o p e r a t i o n i n v e s t i g a t e d [20]. T r a n s i t i o n from the q u a s i i s o t h e r m a l to the d i f f u s i o n regime r e s u l t e d i n an i g n i t i o n process at the r e a c t o r o u t l e t . The r e a c t i o n f r o n t was i g n i t e d at the r e a c t o r o u t l e t and moved upstream. The hot spot temperature increased toward the r e a c t o r inlet. Decreasing the i n l e t temperature the r e a c t i o n f r o n t moves downstream and disappears i n the middle p a r t of the r e a c t o r . Experiments and numerical s i m u l a t i o n i n d i c a t e d that i n long non a d i a b a t i c r e a c t o r the i g n i t i o n process does not s t a r t a t the r e a c t o r o u t l e t but i n s i d e the bed [21].



8.

HLAVACEK E T A L .

Adiabatic & Nonadiabatic Fixed-Bed Reactors

93

I n v e s t i g a t i o n o f the propagating f r o n t s f o r nonadiabatic c o n d i t i o n s shown that the f r o n t v e l o c i t y i s not constant and depends on the p o s i t i o n of the f r o n t i n the r e a c t o r 115]. For a downstream propagating f r o n t , the v e l o c i t y , hot spot temperature and e x i t conversion e x h i b i t e d an o s c i l l a t o r y character 17]· For a nonadiabatic operation of a packed bed m u l t i p l i c i t y of propagating f r o n t s has been observed [ 7 ] . F i g s . 1 and 2 d i s p l a y m u l t i p l e f r o n t s . The s t r a t e g y of a d j u s t i n g a p a r t i c u l a r f r o n t i s reported i n these f i g u r e s i n the upper right-hand p o r t i o n o f the drawings. Obviously, f o r the i d e n t i c a l i n l e t c o n d i t i o n s a downstream or an upstream propagating f r o n t may e x i s t . A d e t a i l e d experimental study of o p e r a t i n g c o n d i t i o n s i n a nonadiabatic f i x e d bed r e a c t o r revealed that f o r c e r t a i n i n l e t cond i t i o n s o s c i l l a t o r y or e r r a t i c behavior o f temperature p r o f i l e s can be observed [23]. To f o l l o w t h i s phenomenon l o c a l thermocouple temperature reading and a x i a l temperature p r o f i l e s were monitored. The r e s u l t s o f measurements are reported i n F i g . 3. From the r e s u l t s measured, i t i s obvious that a temperature f r o n t a r i s e s i n the i n l e t p a r t o f the r e a c t o r , moves downstream and disappears i n the middle p a r t of the r e a c t o r . The l o c a l temperat u r e readings i n d i c a t e t h a t a very complicated dynamic process occurs. For a case that one s t a b l e steady s t a t e e x i s t s t r a n s i e n t temperature p r o f i l e s c a l c u l a t e d agree s a t i s f a c t o r i l y with the measurements. For a case o f three steady s t a t e s the s i t u a t i o n i s q u i t e complicated. The model used d e s c r i b e s propagation o f the f r o n t s however, apparently cannot d e s c r i b e f r o n t m u l t i p l i c i t y . A d e t a i l e d c a l c u l a t i o n o f the two-dimensional steady s t a t e equations i n c l u d i n g a l s o the r a d i a l d i s p e r s i o n terms i n d i c a t e s that the onedimensional model i s a very rough approximation f o r the " d i f f u s i o n " regime. We expect that dynamic c a l c u l a t i o n s w i t h the one-phase two-dimensional model could e x p l a i n m u l t i p l i c i t y of the f r o n t s . The s i t u a t i o n e x h i b i t i n g f i v e steady s t a t e s i s s i m i l a r t o t h a t f o r three steady s t a t e s . R e s u l t s of the steady s t a t e s i m u l a t i o n revealed that the t h i r d s t a b l e steady s t a t e i s l o c a t e d a t the r e a c t o r o u t l e t [22]. C a l c u l a t i o n o f the r e a c t o r with an a f t e r s e c t i o n packed by i n e r t m a t e r i a l i n d i c a t e d that f i v e steady s t a t e s are e l i m i n a t e d . [15]. For the same type o f c a t a l y s t we have observed i n a r e c i r c u l a t i o n l a b o r a t o r y r e a c t o r m u l t i p l i c i t y , p e r i o d i c and c h a o t i c behavior. Unfortunately, so f a r we are not able t o suggest such a r e a c t i o n r a t e expression which would be capable o f p r e d i c t i n g a l l three regimes [ 8 ] . However, there i s a number o f complex k i n e t i c expressions which can d e s c r i b e p e r i o d i c a c t i v i t y . One can expect that such k i n e t i c expressions combined with heat and mass balances of a tubular nonadiabatic r e a c t o r may g i v e r i s e t o o s c i l l a t o r y behavior. D e t a i l e d c a l c u l a t i o n s o f o s c i l l a t o r y behavior of s i n g u l a r l y perturbed p a r a b o l i c systems d e s c r i b i n g heat and mass t r a n s f e r and exothermic r e a c t i o n are apparently beyond, the c a p a b i l i t y o f both standard current computers and mathematical sof tware·



94

CHEMICAL REACTION ENGINEERING

x(mH0 Figure 1.

2

Temperature profiles for an upstream moving wave. Conditions: G 9.26 χ 10*kg/m s;T = 90°C;and Y° = 3.15% CO.

0

=

2

0

Li

1 0

1

1 iO

1

co

1

.

20

I

I

ι

30

40

,

\ 50

•

x(mH0 Figure 2.

I »

60 2

Temperature profiles for a downstream moving wave. Conditions: G 9.26 χ W* kg/mh; T = 90°C; and Y° = 3.15%.

0

0

co


=

Wei and Georgakis; Chemical Reaction Engineering—Boston ACS Symposium Series; American Chemical Society: Washington, DC, 1982. 1

2

10

J

.

I u

12

14

16

0

18

20

_L

0

22 T(h)

Figure 3. Recording of oscillations of local temperature. Conditions: T = 145°C; 1 % CO; G = 1.852 X 1Ô kg/m S; and position of the thermocouple at I — 0.2 m.

140

160 -

180 -

200-

220 -

240

T(°C)


vo

δ.

I

I

I.

δ"

w Η

w

I

00

96

CHEMICAL REACTION

ENGINEERING

Literature Cited 1. 2. 3. 4. 5.


6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.

Padberg G., Wicke Ε., Chem. Engng. S c i . 1967, 22, 1035. F i e g u t h P., Wicke Ε., Chem. Engng. Techn. 1971, 43, 604. Vortmeyer D., J a h n e l W., Chem. Engng. S c i . 1972, 27, 1485. Chem. Engng. Techn. 1971, 43, 461. Rhee H. K., Amundson N. R., Ind. Engng. Chem. Fund,1974, 13,1. Rhee Η. Κ., Lewis R. P. Amundson, N. R. Ind. Engng. Chem. Fund. 1973, 28, 607. Rhee H. K., Foley D., Amundson N. R., Chem. Engng. S c i . 1973, 28, 607. Puszynski J . , Hlavacek V., Chem. Engng. Sci. 1980, 35, 1769. Rathousky J . , Hlavacek V., Jour. Chem. Phys. 1981, 75, 749. Hlavacek V., Rathousky J . , Chem. Engng. Sci. 1982, 37, 375. Eigenberger G. and Butt J . B., Chem. Eng. Sci. 1976, 31, 681. Lubeck B., Chem. Eng. Sci. 1974, 29, 1320. Carey G. F. and F i n l a y s o n Β. Α., Chem. Eng. Sci., 1975, 30, 587. Hlavacek V. and Votruba J . , Adv. Chem. Ser. No. 133, 1974, pg. 545. Votruba J . , Ph.D. T h e s i s (Prague, 1973). P u s z y n s k i , J., Ph.D. Thesis (Prague, 1981). Franck-Kameneckij D. Α., D i f f u s i o n and Heat T r a n s f e r in Chemi cal K i n e t i c s , 2nd Ed. Plenum P r e s s , New York, 1969. Puszynski J . , S n i t a D., Hlavacek V. and Hofmann Η., Chem. Eng. S c i . 1981, 36, 1605. Hlavacek F., Hofman Η., Chem. Eng. Sci., 1971, 26, 1629. Hlavacek V., Holodniok Μ., Sinkule J . and Kubicek Μ., Chem. Eng. Commun., 1979, 3, 451. Puszynski J . , Hlavacek F., Chem. Eng. Sci., in p r e s s . Puszynski J . , S n i t a D., Hlavacek V., Chem. Eng. Sci., i n p r e s s . K a l t h o f f O., Vortmeyer D., Chem. Eng. Sci. 1980, 35, 1637. Rathousky J . , Puszynski J., Hlavacek J . , Z e i t . N a t u r f o r s c h . 1980, 35a, 1238.

R E C E I V E D April 27, 1982.


Multiplicity and Propagating Fronts in Adiabatic and Nonadiabatic

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