Packed Bed Reactors - American Chemical Society

14 Packed Bed Reactors An Overview ARVIND VARMA

Downloaded by UNIV OF SYDNEY on February 1, 2014 | http://pubs.acs.org Publication Date: September 21, 1981 | doi: 10.1021/bk-1981-0168.ch014

Department of Chemical Engineering, University of Notre Dame, Notre Dame, IN 46556

Packed-bed reactors are discussed qualitatively, particularly with respect to their models. Features of the two basic types of models, the pseudohomogeneous and the heterogeneous models, are outlined. Additional issues -- such as catalyst deactivation; steady state multiplicity, stability, and complex transients; and parametric sensitivity -- which assume importance in specific reaction systems are also briefly discussed. Packed-bed r e a c t o r s are commonly used in i n d u s t r i a l p r a c t i c e f o r conducting s o l i d - c a t a l y z e d r e a c t i o n s . Most o f t e n , they physi c a l l y c o n s i s t of tube-bundles, which are packed with p e l l e t s on which the a c t i v e c a t a l y s t is deposited. The reactants enter at one end of the tubes, and the r e a c t i o n products are withdrawn from the other end. The r e a c t i o n ( s ) proceed over the length of the tube, and so the species concentrations, as w e l l as the fluid and s o l i d temperatures, vary as a f u n c t i o n of p o s i t i o n w i t h i n the tube. The tube bundles are stacked in a s h e l l , and because most i n d u s t r i a l r e a c t i o n s are exothermic, c o o l i n g medium flows in the s h e l l to maintain a d e s i r e d temperature d i s t r i b u t i o n over the tube length. At a f i x e d concentration of r e a c t i n g species and temperature, the r a t e of s o l i d - c a t a l y z e d r e a c t i o n s is d i r e c t l y p r o p o r t i o n a l to the a c t i v e c a t a l y s t surface area. The p e l l e t s are normally a means to support the c a t a l y t i c a l l y a c t i v e metal or metal oxide, and maintain it in dispersed form — thus with a high surface area. C a t a l y s t preparation is f r e q u e n t l y described as an a r t , with doses of s e r e n d i p i t y ; there is, of course, more to it than that - as S a t t e r f i e l d (1) has r e c e n t l y described. Some prominent i n d u s t r i a l examples of packed-bed r e a c t o r s are in ammonia, methanol or v i n y l acetate s y n t h e s i s , and in ethylene, methanol, naphthalene, xylene or S O 2 o x i d a t i o n . In recent years (since the 1975 model y e a r ) , an important a p p l i c a t i o n of packed-bed r e a c t o r s has been as c a t a l y t i c converters f o r p o l l u t i o n c o n t r o l from automotive exhausts. 0097-6156/81/0168-0279$05.00/0 © 1981 American Chemical Society In Chemical Reactors; Fogler, H.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

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A v a r i e t y of gradients in species concentrations and temperature e x i s t w i t h i n a packed-bed r e a c t o r . Since r e a c t i o n ( s ) proceed along the tube length, there are obvious gradients in conc e n t r a t i o n , and fluid and s o l i d temperatures in the a x i a l d i r e c t i o n . Because of heat t r a n s f e r at the tube w a l l between the r e a c t i n g mixture and the c o o l i n g medium, radial gradients in temperature and species concentrations a l s o e x i s t . At any l o c a t i o n w i t h i n the tube, there are concentration and temperature gradients between the fluid and s o l i d phases. F i n a l l y , there are species concentration (but n e g l i g i b l e temperature) gradients w i t h i n each of the i n d i v i d u a l c a t a l y s t p e l l e t s , i f the a c t i v e c a t a l y s t is d i s t r i b u t e d throughout the p e l l e t . A v a r i e t y of transport processes t h e r e f o r e occur in a packedbed r e a c t o r , simultaneously with chemical r e a c t i o n ( s ) . Accurate modeling of these processes is e s s e n t i a l to p r e d i c t r e a c t o r performance. Packed-Bed Reactor Models A r e l a t i v e l y l a r g e number of models can be w r i t t e n down f o r a packed-bed r e a c t o r , depending on what is accounted f o r in the model. These models, however, b a s i c a l l y f a l l i n t o two c a t e g o r i e s : pseudohomogeneous models and heterogeneous models. The v a r i o u s models are described in standard r e a c t i o n engineering t e x t s — such as those of Carberry (2), Froment and B i s c h o f f (3), and Smith (4), to c i t e j u s t a few — and in review a r t i c l e s ( c f . , 5-8), and so d e t a i l s of t h e i r equations w i l l not be reported here. We w i l l , i n s t e a d , only make some q u a l i t a t i v e remarks about the models. Pseudohomogeneous Models. The b a s i c assumption that is made in a pseudohomogeneous model is that the r e a c t o r can be described as an e n t i t y c o n s i s t i n g only of a s i n g l e phase. Since, in r e a l i t y , two phases are present, the p r o p e r t i e s used in d e s c r i b i n g the r e a c t o r are s o - c a l l e d " e f f e c t i v e " p r o p e r t i e s which respect the presence of two phases. A comprehensive review of estimating these e f f e c t i v e p r o p e r t i e s has r e c e n t l y been published (9). The simplest pseudohomogeneous model is the "plug-flow" model, in which the fluid is taken to move as a plug through the r e a c t o r tube, and the r e a c t i o n r a t e - which depends on l o c a l spec i e s concentration and temperature - is described as r a t e of species generation or consumption per u n i t r e a c t o r volume. In the steady s t a t e , the model equations are a set of coupled f i r s t order ordinary d i f f e r e n t i a l equations - one each f o r every independent r e a c t i o n , and one f o r temperature - with p r e s c r i b e d i n i t i a l c o n d i t i o n s d e s c r i b i n g the fluid composition and temperature at the r e a c t o r i n l e t . These equations are, in general, n o n l i n e a r but can be r e a d i l y and e f f i c i e n t l y i n t e g r a t e d numerically with

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


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modern-day d i g i t a l computers to provide c o n c e n t r a t i o n and temperature p r o f i l e s as a f u n c t i o n of a x i a l d i s t a n c e from the r e a c t o r inlet. The plug-flow model can be augmented by i n c l u d i n g a x i a l and/ or radial d i s p e r s i o n s , f o r both mass and heat t r a n s p o r t . These d i s p e r s i o n s are c h a r a c t e r i z e d by s o - c a l l e d P e c l e t numbers. I t is g e n e r a l l y agreed that a x i a l d i s p e r s i o n of mass is not s i g n i f i cant i f the tube l e n g t h / p e l l e t diameter r a t i o is >^ 50, while that f o r heat is a l s o n e g l i g i b l e i f the same r a t i o is _> 300. R a d i a l d i s p e r s i o n , on the other hand, is g e n e r a l l y more important than a x i a l d i s p e r s i o n , s i n c e the r a t i o of t u b e / p e l l e t diameters is f r e q u e n t l y q u i t e modest — as compared with the tube l e n g t h / p e l l e t diameter r a t i o . The radial P e c l e t number f o r mass t r a n s p o r t (udp/Dmr) is approximately 10, while f o r heat transport (udp/Dhr) it l i e s between 5-10 (2). R a d i a l d i s p e r s i o n becomes n e g l i g i b l e i f the r e a c t o r is a d i a b a t i c , because there is then no d r i v i n g f o r c e f o r long-range gradients to e x i s t in the radial direction. For non-adiabatic r e a c t o r s , along with radial d i s p e r s i o n , heat t r a n s f e r c o e f f i c i e n t a t the w a l l between the r e a c t i o n mixture and the c o o l i n g medium needs to be s p e c i f i e d . C o r r e l a t i o n s f o r these are a v a i l a b l e ( c f . 9_, 10); however, it is p o s s i b l e to modify the e f f e c t i v e radial thermal c o n d u c t i v i t y ( k ) , by making it a f u n c t i o n of radial p o s i t i o n , so that heat t r a n s f e r at the w a l l is accounted f o r by a smaller k value near the tube-wall than at the tube center (11). I n c l u s i o n of a x i a l d i s p e r s i o n in the plug-flow model makes the model equations a boundary-value problem, so that c o n d i t i o n s at both the r e a c t o r i n l e t and o u t l e t need to be s p e c i f i e d . The commonly used boundary c o n d i t i o n s a r e the s o - c a l l e d Danckwerts type (12), although t h e i r o r i g i n goes back to Langmuir (13). When radial d i s p e r s i o n is i n c l u d e d , even the steady s t a t e equat i o n s are p a r t i a l d i f f e r e n t i a l equations — in the a x i a l and radial space v a r i a b l e s . The d i s p e r s i o n model equations can be numerically solved by f i n i t e - d i f f e r e n c e schemes, or more e f f i c i e n t l y , by orthogonal c o l l o c a t i o n methods (14, 1 5 ) The b a s i c plug-flow model, with or without d i s p e r s i o n s , is a "continuous" model because the concentrations and temperature are described by d i f f e r e n t i a l equations. An a l t e r n a t i v e representat i o n is by a d i s c r e t e model - the s o - c a l l e d " c e l l " model (16, 17), in which it is assumed that the r e a c t o r can be broken down i n t o s e v e r a l connected c e l l s . I t had long been assumed that the continuous and d i s c r e t e models are equivalent ways of representing a r e a c t o r ; however, this assumption has r e c e n t l y been questioned in two d i f f e r e n t contexts (18, 19). r

r

t

Heterogeneous Models. The two-phase character of a packed-bed is preserved in a heterogeneous model. Thus mass and energy cons e r v a t i o n equations are w r i t t e n s e p a r a t e l y f o r the fluid and s o l i d phases. These equations a r e l i n k e d together by mass and heat t r a n s p o r t between the phases.


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The simplest heterogeneous model is one with plug-flow in the fluid phase, mass and heat t r a n s f e r between the fluid and s o l i d phases, and surface c a t a l y t i c r e a c t i o n on the s o l i d — i f the c a t a l y s t is indeed deposited near the p e l l e t e x t e r n a l surface. More complex fluid phase behavior can be accommodated by a x i a l and radial d i s p e r s i o n f e a t u r e s , among which radial d i s p e r s i o n ones are again the more important — and those only f o r a nonadiabatic reactor. If the c a t a l y s t is dispersed throughout the p e l l e t , then int e r n a l d i f f u s i o n of the species w i t h i n the pores of the p e l l e t , along with simultaneous r e a c t i o n ( s ) must be accounted f o r i f the p r e v a i l i n g T h i e l e modulus > 1. This aspect gives r i s e to the " e f f e c t i v e n e s s f a c t o r " problem, to which a s i g n i f i c a n t amount of e f f o r t , summarized by A r i s (20), has been devoted in the l i t e r a ture. I t is important to r e a l i z e that i f the c a t a l y s t p e l l e t e f f e c t i v e n e s s f a c t o r is d i f f e r e n t from u n i t y , then the packed-bed r e a c t o r model must be a heterogeneous model; it cannot be a pseudohomogeneous model. There are t h e o r e t i c a l l y sound c o r r e l a t i o n s a v a i l a b l e f o r estimating e f f e c t i v e d i f f u s i o n c o e f f i c i e n t s in porous c a t a l y s t p e l l e t s ( c f . , _21, 22). I t has been shown that f o r most g a s - s o l i d c a t a l y t i c r e a c t i o n s , the p e l l e t s are v i r t u a l l y isothermal, so that temperature gradients w i t h i n them can s a f e l y be ignored (23, 24). There are c o r r e l a t i o n s a v a i l a b l e f o r estimating heat and mass t r a n s f e r c o e f f i c i e n t s between the phases (2, _3, ; they are g e n e r a l l y cast in form of j - f a c t o r s , as f u n c t i o n s of the fluid Reynolds number. Caution must, however, be exercised in using these s i n c e most of the c o r r e l a t i o n s were developed f o r nonr e a c t i v e systems — although s u c c e s s f u l attempts have been made f o r r e l a t i v e l y simple r e a c t i v e cases (25). In a s p e c i f i c e x p e r i mental study in a packed-bed r e a c t o r (26), it was r e c e n t l y shown that because of increased convection between the c a t a l y s t p e l l e t and the bulk gas, caused by r e l a t i v e l y l a r g e temperature d i f f e r ences between the two phases when a h i g h l y exothermic r e a c t i o n occurs, the transport c o e f f i c i e n t s increase considerably — a l though t h e i r power dependence on Reynolds number, which a r i s e s from boundary l a y e r arguments, remains the same as in cases without r e a c t i o n . Along with w a l l heat t r a n s f e r c o e f f i c i e n t in non-adiabatic r e a c t o r s , another e f f e c t frequently added in models is that of thermal conduction in the s o l i d phase (_2_7, ^8, _29). One should be p a r t i c u l a r l y c a r e f u l here, s i n c e most of the c o r r e l a t i o n s a v a i l a b l e in the l i t e r a t u r e (9, 30, _31, 32) are f o r e f f e c t i v e transport parameters to be used with pseudohomogeneous models, and not f o r the s o l i d phase alone. I n t r i n s i c Reaction

Kinetics

E i t h e r with pseudohomogeneous or with heterogeneous models,


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the r e a c t i o n r a t e term must always be included in the r e a c t o r model. T h i s takes the form of s p e c i f y i n g the r a t e of r e a c t i o n , as a f u n c t i o n of species c o n c e n t r a t i o n and c a t a l y s t temperature; this i n f o r m a t i o n is always obtained experimentally f o r each r e a c t i o n system in k i n e t i c s experiments. I t is c r u c i a l that when r e a c t i o n k i n e t i c s are measured, that there be no t r a n s p o r t e f f e c t s present; otherwise the k i n e t i c data would be i n f l u e n c e d by such e f f e c t s . For g a s - s o l i d r e a c t i o n s , the most commonly used r e a c t o r s are the spinning-basket and the r e c y c l e r e a c t o r s ( 2 ) . Weekman (33), and Doraiswamy and T a j b l (34) have provided recent reviews summarizing advantages and l i m i t a t i o n s of v a r i o u s r e a c t o r s used in the l a b o r a t o r y f o r procurement of i n t r i n s i c k i n e t i c data. Some Other Issues Under this heading, some i s s u e s which assume importance in s p e c i f i c r e a c t i o n systems, are b r i e f l y o u t l i n e d . C a t a l y s t D e a c t i v a t i o n . Most c a t a l y s t s s u f f e r from decay in t h e i r a c t i v i t y w i t h time, which a r i s e s as a consequence, in gene r a l , of one among three causes. In "thermal s i n t e r i n g " , p u r e l y as a r e s u l t of h i g h temperature, nature of the r e a c t i v e atmosphere and of the support, smaller c r y s t a l l i t e s of the a c t i v e c a t a l y s t grow i n t o l a r g e r ones with time v i a v a r i o u s agglomeration processes (35). Thus the a c t i v e s u r f a c e area decreases, r e s u l t i n g in a l o s s of c a t a l y t i c a c t i v i t y per u n i t weight of the c a t a l y s t . The second cause is "chemical p o i s o n i n g " , normally the r e s u l t of chemisorption of r e a c t a n t s , r e a c t i o n products, or i m p u r i t i e s in the feedstream, whereby such species permanently occupy s i t e s otherwise a v a i l a b l e f o r c a t a l y s i s . F i n a l l y , " f o u l i n g " is a term commonly used f o r p h y s i c a l a d s o r p t i o n of a species upon the c a t a l y t i c s u r f a c e , thereby covering or b l o c k i n g it from f u t u r e c a t a l y t i c a c t i o n — such as in overcracking of hydrocarbons to produce coke ("coking"), or in lead poisoning of noble metal c a t a l y s t s in c a t a l y t i c converters f o r automotive exhausts. A thorough review of c a t a l y s t d e a c t i v a t i o n is a v a i l a b l e (36). With d e a c t i v a t i o n , the r e a c t o r model must immediately become a t r a n s i e n t one, to account f o r change in c a t a l y s t a c t i v i t y w i t h time. Among others, two s u c c e s s f u l instances of packed-bed r e a c t o r modeling, in the presence of c a t a l y s t d e a c t i v a t i o n and inc l u d i n g comparisons with experiments, are found in the works of Weekman (37, 38) and Butt (39, 40). Steady State M u l t i p l i c i t y , S t a b i l i t y , and Complex T r a n s i e n t s . T h i s subject is too l a r g e to do any r e a l j u s t i c e here. Ever s i n c e the p i o n e e r i n g works of L i l j e n r o t h (41), van Heerden (42), and Amundson (43) w i t h continuous-flow s t i r r e d tank r e a c t o r s , showing that m u l t i p l e steady s t a t e s — among them, some s t a b l e to p e r t u r b a t i o n s , while others unstable — can a r i s e , this t o p i c has



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become one of the major ones in r e a c t i o n engineering. Over the years, v i r t u a l l y all types of r e a c t o r s have shown these f e a t u r e s , in both experimental and modeling s t u d i e s . These features a r i s e e i t h e r as a consequence of i n t e r a c t i o n s between r e a c t i o n and transport processes, or purely as a consequence of complex r e a c t i o n k i n e t i c s ; examples in the former category p r e s e n t l y f a r outnumber those in the l a t t e r . An a u t h o r i t a t i v e survey of the area was given in 1974 by Schmitz (44); more recent reviews are a l s o a v a i l a b l e (45, 46, 47). These aspects in the d i f f u s i o n r e a c t i o n context were treated comprehensively by A r i s (20), and by Luss (48). For s t i r r e d tanks and empty tubular r e a c t o r s , Varma and A r i s (49) may be consulted. Jensen and Ray (50) have r e c e n t l y tabulated some 25 e x p e r i mental studies which have demonstrated steady s t a t e m u l t i p l i c i t y and i n s t a b i l i t i e s in fixed-bed r e a c t o r s ; many of these ( c f . , 29, 51, 52) have noted the importance of using a heterogeneous model in matching experimental r e s u l t s with t h e o r e t i c a l p r e d i c t i o n s . Using a pseudohomogeneous model, Jensen and Ray (50) a l s o present a d e t a i l e d c l a s s i f i c a t i o n of steady s t a t e and dynamic behavior ( i n c l u d i n g b i f u r c a t i o n to p e r i o d i c s o l u t i o n s ) that is p o s s i b l e in tubular r e a c t o r s . A feature r e l a t e d to steady s t a t e m u l t i p l i c i t y and s t a b i l i t y is that of "pattern formation", which has i t s o r i g i n s in the b i o l o g i c a l l i t e r a t u r e . Considering an assemblage of c e l l s c o n t a i n ing one c a t a l y s t p e l l e t each, Schmitz (47, 53) has shown how non-uniform steady s t a t e s - g i v i n g r i s e to a p a t t e r n - can a r i s e , i f communication between the p e l l e t s is s u f f i c i e n t l y small. This p o s s i b i l i t y has obvious i m p l i c a t i o n s to packed-bed r e a c t o r s . Parametric S e n s i t i v i t y . One l a s t f e a t u r e of packed-bed r e a c t o r s that is perhaps worth mentioning is the s o - c a l l e d "parametric s e n s i t i v i t y " problem. For exothermic g a s - s o l i d r e a c t i o n s o c c u r r i n g in non-adiabatic packed-bed r e a c t o r s , the temperature p r o f i l e in some cases e x h i b i t s extreme s e n s i t i v i t y to the operat i o n a l c o n d i t i o n s . For example, a r e l a t i v e l y small increase in the feed temperature, reactant concentration in the feed, or the coolant temperature can cause the hot-spot temperature to increase enormously ( c f . 54). This s e n s i t i v i t y is a type of i n s t a b i l i t y , which is important to understand f o r r e a c t o r design and operation. The problem was f i r s t studied by B i l o u s and Amundson (55). Various authors ( c f . 56^, 57) have attempted to provide estimates of the heat of r e a c t i o n and heat t r a n s f e r parameters d e f i n i n g the p a r a m e t r i c a l l y s e n s i t i v e r e g i o n ; f o r the plug-flow pseudohomogeneous model, critical values of these parameters can now be obtained f o r any r e a c t i o n order r a t h e r e a s i l y (58). A r e l a t e d phenomenon is the "wrong-way behavior" of packedbed r e a c t o r s , where a sudden r e d u c t i o n in the feed temperature leads to a t r a n s i e n t temperature r i s e . This has been observed (52, 59) and s a t i s f a c t o r i l y analyzed using a plug-flow pseudohomogeneous model (60).


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Acknowledgements We are g r a t e f u l f o r f i n a n c i a l support by the N a t i o n a l Science Foundation under Grant No. INT-7920843, and by the Nalco Foundation.

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3, 1981.


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