Chemical and Catalytic Reactor Modeling - American Chemical Society

3 A Comparison of Current Models for Isothermal Trickle-Bed Reactors Application to a Model Reaction System P. L. MILLS Corporate Research Laboratory, Monsanto Company, St. Louis, MO 63167

Downloaded by UNIV OF BATH on June 27, 2016 | http://pubs.acs.org Publication Date: December 9, 1984 | doi: 10.1021/bk-1984-0237.ch003

M. P. DUDUKOVIĆ Chemical Reaction Engineering Laboratory, Washington University, St. Louis, MO 63130 Trickle-bed reactors are packed-beds of catalyst which utilize cocurrent downflow of gas and liquid reactants. This paper summarizes the various reaction studies which have been performed to support development of appropriate reactor models for this reactor type, and gives a critical review of these models. Prediction of the integral trickle-bed reactor performance for a first-order, gaseous reactant limiting reaction is attempted. Conversion predicted by various models are compared to experimental results obtained in a laboratory-scale trickle-bed reactor using the hydrogenation of α-methylstyrene in organic sol vents as a test reaction. It is shown that cer tain key items, such as i) extent of liquid-solid wetting, ii) presence or absence of stagnant versus actively flowing liquid films on the catalyst surface, and iii) magnitude of mass transport resistances, can a l l have a significant effect on the predicted reactor behavior. The in ability of current correlations to predict mass transfer coefficients is demonstrated. Reactions between gases and liquids that are catalyzed by either homogeneous organometallic complexes or heterogeneous catalysts provide the basis for a significant portion of the products manufactured in both chemical and petroleum processing. Reactor types used to carry out these reactions include mechanically agitated autoclaves, bubble columns, gas-lift reactors, packedbed reactors, or three-phase fluidized-bed reactors (1-3). Heterogeneous catalyzed reactions are carried out using the catalyst in a powdered form for slurry operation or a tableted form for packed-bed operation (l). The problems associated with filtration, regeneration, and recycle of spent powdered catalysts, including the higher installed costs of slurry-type reactor systems, to name a few (2), suggests that packed-bed 0097-6156/84/0237-0037$06.25/0 © 1984 American Chemical Society Dudukovi and Mills; Chemical and Catalytic Reactor Modeling ACS Symposium Series; American Chemical Society: Washington, DC, 1984.


38

CHEMICAL AND CATALYTIC REACTOR MODELING

t r i c k l e - f l o w r e a c t o r s o f f e r s e v e r a l advantages over s l u r r y operation. However, the design and scale-up of t r i c k l e - b e d r e a c t o r s i s more d i f f i c u l t than s l u r r y r e a c t o r s which seems to be a disadvantage ( 2 ) . Accurate p r e d i c t i o n of t r i c k l e - b e d r e actor performance r e q u i r e s r e l i a b l e methods f o r estimation of such items as i n t r i n s i c r e a c t i o n k i n e t i c s , l i q u i d - g a s flow d i s t r i b u t i o n , l i q u i d - s o l i d contacting e f f e c t i v e n e s s , i n t e r phase and intraphase heat and mass t r a n s f e r , texture of l i q u i d f i l m s , and thermodynamic parameters. While methods f o r measurement and i n t e r p r e t a t i o n of i n t r i n s i c r e a c t i o n k i n e t i c s f o r heterogeneous g a s - l i q u i d systems i s f a i r l y w e l l understood CL>A) > l i t t l e progress has been made toward s o l u t i o n of fundamental problems r e l a t e d to t r i c k l e - b e d design and scale-up. A consensus of o p i n i o n from recent symposia on multiphase r e a c t o r s (5) supports t h i s conclusion. Summary of Previous

Reaction

Studies and Models

The above issues a s s o c i a t e d with p r e d i c t i o n of t r i c k l e - b e d r e a c t o r performance has motivated a number of researchers over the past two decades to perform l a b o r a t o r y - s c a l e studies using a p a r t i c u l a r model-reaction system. These are l i s t e d i n Table I. Although a more d e t a i l e d summary i s given elsewhere (29) , a general conclusion seems to be that both incomplete c a t a l y s t wetting and mass t r a n s f e r l i m i t a t i o n s are s i g n i f i c a n t f a c t o r s which a f f e c t t r i c k l e - b e d r e a c t o r performance. Several forms of incomplete c a t a l y s t wetting were v i s u a l l y observed and reported i n previous s t u d i e s . These observations i n c l u d e : i ) dry areas on a p o r t i o n of the c a t a l y s t surface with e i t h e r stagnant l i q u i d or a c t i v e l y flowing l i q u i d present on the remaining surface (7-10), i i ) no dry area i s present on the c a t a l y s t surface, i n s t e a d , the c a t a l y s t surface i s covered by a combination of stagnant l i q u i d f i l m s and a c t i v e l y flowing l i q u i d (7,11-13), and i i i ) the e n t i r e c a t a l y s t surface and i n t e r n a l c a t a l y s t pores may be completely dry as a r e s u l t of l i q u i d reactant evaporation at r e a c t o r conditions (9,14-15) Some of the remaining studies d i d not n e c e s s a r i l y observe i n complete c a t a l y s t wetting, but included t h i s concept e i t h e r d i r e c t l y as an adjustable parameter i n the model to f i t the observed conversion versus l i q u i d mass v e l o c i t y data,(7,9,13, 16-18), or i n d i r e c t l y v i a use of a c o r r e l a t i o n f o r l i q u i d - s o l i d contacting e s t a b l i s h e d f o r non-porous absorber column packings (11,19-20). Observed transport l i m i t a t i o n s i n the studies given i n Table I depend upon the magnitude of the i n t r i n s i c r e a c t i o n r a t e . Petroleum h y d r o d e s u l f u r i z a t i o n (19-21), c e r t a i n types of petroleum hydrogénations (22),' or chemical decomposition r e a c t i o n s (11) are l i q u i d - l i m i t i n g and proceed slowly enough that only i n t e r n a l p a r t i c l e d i f f u s i o n or combined pore d i f f u s i o n and l i q u i d - t o - s o l i d r e s i s t a n c e s are c o n t r o l l i n g . Chemical

Dudukovi and Mills; Chemical and Catalytic Reactor Modeling ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

3.

MILLS AND DUDUKOVIC

Table I .

Previous Reaction Studies i n T r i c k l e - B e d Reactors

Investigator Hartman and Coughlin (7_) S a t t e r f i e l d and Way (39_) Germain, Le febvre and L Homme (10) Henry and G i l b e r t (21) f


Isothermal Trickle-Bed Reactors: Current Models

Sedriks and Kenney (9) S a t t e r f i e l d and Ozel (8) Montagna and Shah (19) Goto and Smith (27) Koros (11) Levee and Smith (28J Jawad (26) Hanika e t a l

(25) Enright and Chuang (40) Hanika et a l (15) Mo r i t a and Smith (16) Germain et a l

(12) Mejstrikovâ

Reaction System Oxidation of s u l f u r d i o x i d e on a c t i v a t e d carbon Isomerization of cyclopropane t o propylene on s i l i c a - a l u m i n a Hydrogénation of α-methylstyrene to cumene i n 0.5% and 1% Pd-on-alumina Petroleum hydrocracking, hydrodenitrogenation, h y d r o d e s u l f u r i z a t i o n , and hydrogénation Hydrogénation of crotonaldehyde on 0.5% Pd-on-alumina Hydrogénation o f benzene to cyclohexane on 2% Pt H y d r o d e s u l f u r i z a t i o n of 36% and 53% reduced Kuwait crude Oxidation of formic a c i d on CuO - ZnO Hydrogen p e r i o x i d e decomposition on a c t i v a t e d carbon Oxidation of a c e t i c a c i d on f e r r i c oxide Hydrogénation of α-methylstyrene to cumene on Pd c a t a l y s t Hydrogénation of cyclohexene to cyclohexane using 3% Pd and 5% Pt-on-carbon catalysts Deuterium exchange between hydrogen and water using 0.2% Pd-on-carbon Hydrogénation of 1,5 cyclo-octadiene i n cyclooctane using 38% Ni-on-kieselguhr Hydrogénation of α-methylstyrene to cumene using 0.5% and 2.5% Pd-on-alumina Hydrogénation of 2-butanone using Ru-on alumina Hydrogénation of nitrobenzene on 1% Pd

(24) Hanika et a l

(14) Somers, Shah, and Paraskos (22) B i s k i s and Smith (23) Mata and Smith (13) Herskowitz, Carbone11 and Smith (JL7) Turek and Lange (JL8 ) Mont agna, Shah, and Paraskos (20)

Hydrogénation of cyclohexene to c y c l o hexene on 5% Pd-on-carbon Hydrogénation of d i o l e f i n s Hydrogénation of α-methylstyrene to cumene on 0.5% Pd-on-alumina Oxidation of s u l f u r d i o x i d e on a c t i v a t e d carbon Hydrogénation of α-methylstyrene t o cumene using Pd-on-alumina Hydrogénation of α-methylstyrene to cumene using Pd-on-alumina H y d r o d e s u l f u r i z a t i o n o f 22% and 36% reduced Kuwait crude


39



40

hydrogénations at low to moderate pressures (8-10»14-18, 23-26) or oxidations (7_,_13,_27 28) are u s u a l l y gaseous r e actant l i m i t i n g and i n v o l v e more a c t i v e c a t a l y s t s so that both i n t e r n a l and e x t e r n a l transport processes or the l a t t e r ones only are c o n t r o l l i n g . A summary of r e a c t o r models used by various authors t o i n t e r p r e t t r i c k l e - b e d r e a c t o r data mainly from l i q u i d - l i m i t i n g petroleum h y d r o d e s u l f u r i z a t i o n r e a c t i o n s (19-21) i s given i n Table I o f reference (37). These models are based upon: i ) plug-flow of the l i q u i d - p h a s e , i i ) the apparent r a t e of r e a c t i o n i s c o n t r o l l e d by e i t h e r i n t e r n a l d i f f u s i o n o r i n t r i n s i c k i n e t i c s , i i i ) the r e a c t o r operates i s o t h e r m a l l y , and i v ) the i n t r i n s i c r e a c t i o n r a t e i s f i r s t - o r d e r with respect to the nonv o l a t i l e l i q u i d - l i m i t i n g r e a c t a n t . Model 4 i n t h i s t a b l e accounts f o r both incomplete e x t e r n a l and i n t e r n a l c a t a l y s t wetting by i n t r o d u c t i o n o f the e f f e c t i v e n e s s f a c t o r η β developed e s p e c i a l l y f o r t h i s s i t u a t i o n (37 ). A few r e a c t o r models have r e c e n t l y been proposed (30-31) f o r p r e d i c t i o n of i n t e g r a l t r i c k l e - b e d r e a c t o r performance when the gaseous reactant i s l i m i t i n g . Common features or assumptions i n c l u d e : i ) g a s - t o - l i q u i d and l i q u i d - t o - s o l i d e x t e r n a l mass t r a n s f e r r e s i s t a n c e s are present, i i ) i n t e r n a l 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 i s present, i i i ) c a t a l y s t par t i c l e s are completely e x t e r n a l l y and i n t e r n a l l y wetted, i v ) gas s o l u b i l i t y can be described by Henry's law, v) isothermal operation, v i ) the a x i a l - d i s p e r s i o n model can be used t o describe d e v i a t i o n s from plug-flow, and v i i ) the i n t r i n s i c r e a c t i o n k i n e t i c s e x h i b i t f i r s t - o r d e r behavior. A few others have used s i m i l a r assumptions except were developed f o r non l i n e a r k i n e t i c s (2 7—28). Only i n a couple of instances (7,13, 29) was incomplete e x t e r n a l c a t a l y s t wetting accounted f o r . Crine and co-workers (32—33) have developed a t r i c k l e - b e d r e a c t o r model based upon p e r c o l a t i o n theory which more c l o s e l y approximates the physiochemical processes on a p a r t i c l e and r e a c t o r - s c a l e than previous models. D e t a i l s which e x p l a i n the model development have not been given by these authors so i t has not gained wide a p p l i c a b i l i t y . Τ

Objectives The above d i s c u s s i o n on previous experimental s t u d i e s i n t r i c k l e - b e d r e a c t o r s suggests that both l i q u i d - s o l i d contacting and mass t r a n s f e r l i m i t a t i o n s play a r o l e i n a f f e c t i n g t r i c k l e - b e d r e a c t o r performance. Except f o r a few i s o l a t e d cases, the r e a c t o r models proposed i n the l i t e r a t u r e f o r gaseous reactant l i m i t i n g r e a c t i o n s have not incorporated p a r t i c l e - s c a l e incomplete c o n t a c t i n g as paît o f t h e i r development. For cases where i t was used, t h i s parameter served as an adjustable constant t o match the observed conversion versus l i q u i d mass v e l o c i t y data so that the true p r e d i c t i v e a b i l i t y o f the model



3. MILLS AND DUDUKOVIC

isothermal Trickle-Bed Reactors: Current Models

41

was not r e a l l y t e s t e d . A d d i t i o n a l l y , i t has not been c l e a r l y e s t a b l i s h e d whether or not mass t r a n s f e r c o e f f i c i e n t s d e t e r mined from d i s s o l u t i o n or gas absorption experiments under non-reacting c o n d i t i o n s give r e l i a b l e values f o r porous c a t a l y s t s under r e a c t i o n c o n d i t i o n s . Some r e l a t e d questions such as whether i n a c t i v e l y wetted p e l l e t surfaces under i s o thermal c o n d i t i o n s are covered by a t h i n , s t a g n a n t , l i q u i d f i l m versus being completely dry i n d i r e c t contact with the gas (17) a l s o have not been answered. The present i n v e s t i g a t i o n has the o v e r a l l o b j e c t i v e o f t e s t i n g the p r e d i c t i v e a b i l i t y f o r a t r i c k l e - b e d r e a c t o r model i n which t h e gaseous reactant i s l i m i t i n g . F i r s t , a model i s presented which contains p a r t i c l e - s c a l e incomplete c o n t a c t i n g as one of the key parameters. Second, model p r e d i c t i o n s f o r v a r i o u s l i m i t i n g cases are compared t o experimental r e s u l t s obtained i n a l a b o r a t o r y s c a l e t r i c k l e - b e d r e a c t o r using independently measured model parameters and a v a i l a b l e l i t e r a t u r e mass t r a n s f e r c o r r e l a t i o n s . T r i c k l e - B e d Reactor Model f o r Gas L i m i t i n g Reactions For purposes of developing a model f o r t r i c k l e - b e d s that correspond t o the t e s t r e a c t i o n given l a t e r , a s i n g l e , i r r e v e r s i b l e heterogeneous c a t a l y z e d r e a c t i o n o f the f o l l o w i n g form i s assumed to occur:

A(g) + bB(£)

(1)

xXU)

The mass balances which are given below assume that i ) l i q u i d r e a c t a n t s are n o n v o l a t i l e , i i ) gas and l i q u i d are i n cocurrent flow, i i i ) d e v i a t i o n s of the gas and l i q u i d flow p a t t e r n from plug-flow are n e g l i g i b l e , i v ) s o l u b i l i t y of the gaseous reactant i n the l i q u i d can be d e s c r i b e d by Henry's law, v) e x t e r n a l mass t r a n s p o r t and i n t r a p a r t i c l e d i f f u s i o n e f f e c t s may be present, v i ) the c a t a l y s t surface contains a f r a c t i o n ηςΕ which i s contacted by a c t i v e l y flowing l i q u i d , while the remaining f r a c t i o n 1 - η ^ i s covered e i t h e r by a stagnant l i q u i d or i s i n d i r e c t contact with the gas, v i i ) e x t e r n a l con t a c t i n g e f f i c i e n c y η ^ , gas and l i q u i d holdups, and gas and l i q u i d flow r a t e s are constant over the a c t i v e c a t a l y s t bed. A key point to be emphasized here i s that the c a t a l y s t surface i s assumed t o contain both a c t i v e l y wetted and i n a c t i v e l y wetted (or dry) regions which are subject to f i n i t e mass t r a n s f e r r e s i s t a n c e s having unequal v a l u e s . Besides t h i s , a constant gas-phase concentration of the gaseous ( l i m i t i n g ) reactant i s assumed s i n c e t h i s was implemented experimentally. Based upon these assumptions, the f o l l o w i n g dimensionless mass balance equations are obtained: Ε

Ε


42


d u

A£

" ~dT

+

S

V , A

(

u

~ *-aws,A St

Ag"V

( u

U

M" A£,aws

)

=

0

(

2

)

d u

B£ " " d T " CE n

S

St Downloaded by UNIV OF BATH on June 27, 2016 | http://pubs.acs.org Publication Date: December 9, 1984 | doi: 10.1021/bk-1984-0237.ch003

(u

Vaws,A

η

Γ

D a

η

Γ

U

( 1

o A*,iws " o A£,iws °

D a

U

=

U

Ail- A£,aws

)

=

n

CE

η

Da

(

U

(

o M,aws

. (u. - u . ) = (1 - η_„) η Da u . g-iws,A Ag A£,iws' 'CE o Ax,,iws A

A 0

v

)

)

(5)

A 0

1

4

3

The boundary c o n d i t i o n s at the r e a c t o r i n l e t ξ = 0 are: u

( A*

=

u

(

Ail,i

6

a

)

(

6

B

ς=0

ΚΑ

•

" B M -

1

)

S e t t i n g u^£ i = 0 corresponds t o a l i q u i d feed which i s innocent of d i s s o l v e d gaseous r e a c t a n t , while s e t t i n g u^X i 1 corresponds to a l i q u i d feed which e x i s t s i n e q u i l i b r i u m with the gas at the feed temperature, pressure, and composition. D e f i n i t i o n s f o r the dimensionless v a r i a b l e s which appear i n Equations 2 - 6 are given i n the nomenclature. The s o l u t i o n o f Equations 2 - 6 gives the f o l l o w i n g expressions f o r the dimensionless d i s s o l v e d gas c o n c e n t r a t i o n u^& snd l i q u i d reactant conversion Xg as a f u n c t i o n of the dimensionless a x i a l coordinate ξ and model parameters: =

1

α (ξ) =

"

( 1

"

λ

"Α*,!*

β

Χ

Ρ

(

-

S t

Α λ

£,A S> Β_ί λ

g

(7)

b C*

n

CE

Γ»Α&,1 ~ \ X

(1-e

Stg£

'

A λ

S +ξΙ

(8)

λ (η

Bi W

The parameter λ contains the Damkoehler number, Da , the Stanton number f o r g a s - t o - l i q u i d t r a n s f e r , S t £ A , external contactt n e

g


3. MILLS AND DUDUKOVIC


43

ing e f f i c i e n c y , ΐΊς^, the e f f e c t i v e n e s s f a c t o r f o r a t o t a l l y wetted p e l l e t , η, A r i s ' modified modulus, Λ, and B i o t number f o r a c t i v e l y flowing l i q u i d - t o - s o l i d mass t r a n s f e r , B i . I t i s given by w

(

λ - 1 + ^ g£,A 1

+


η

9

)

£ _ i i

An a d d i t i o n a l parameter which appears i n the above expression f o r Χβ(ξ) i s the B i o t number f o r stagnant l i q u i d - t o - s o l i d mass transfer, B i ^ . Since d i s s o l v e d gas concentrations i n the l i q u i d phase are more d i f f i c u l t to measure experimentally than the l i q u i d r e actant c o n c e n t r a t i o n , Equation 8 evaluated at the r e a c t o r e x i t ξ = 1 represents the key equation f o r p r a c t i c a l a p p l i c a t i o n s i n v o l v i n g t h i s model. Nevertheless, the r e s u l t i n g expression s t i l l contains a s i g n i f i c a n t number of parameters, most of which cannot be c a l c u l a t e d from f i r s t p r i n c i p l e s . This gives the model a complex form and makes i t d i f f i c u l t t o use with c e r t a i n t y f o r p r e d i c t i v e purposes. Reaction r a t e para meters can be determined i n a s l u r r y and basket-type r e a c t o r with completely wetted c a t a l y s t p a r t i c l e s of t h e same k i n d that are used i n t r i c k l e flow operation so that Da , η , and Λ2 can be c a l c u l a t e d f o r t r i c k l e - b e d o p e r a t i o n . This leaves four para meters (TICE> g £ > S i , Bid) to be determined from the a v a i l a b l e c o n t a c t i n g e f f i c i e n c y and mass t r a n s f e r c o r r e l a t i o n s . I t was shown that the model i n t h i s form does not have good p r e d i c t i v e a b i l i t y (29_, 34) . A simpler model form can be obtained i f the d i s s o l v e d gaseous reactant c o n c e n t r a t i o n i n the bulk l i q u i d i s assumed to be constant. Setting = 0 i n Equation 2 leads to the f o l l o w i n g expression f o r the conversion of l i q u i d reactant Β at the r e a c t o r e x i t , where ξ = 1: Q

S t

w

D

*»·· •

'o

("CK - v

• « - w wo

\

mass t r a n s f e r c o e f f i c i e n t s k and kg£s> l i q u i d s u p e r f i c i a l v e l o c i t y , u £ , and v a r i o u s c a t a l y s t and r e a c t o r bed c h a r a c t e r i s t i c s . Previous t r i c k l e - b e d r e a c t o r s t u d i e s quoted e a r l i e r i n Table I cannot provide a r i g o r o u s t e s t of the model s i n c e some key model parameters such as e x t e r n a l c o n t a c t i n g e f f i c i e n c y riCE or the i n t r i n s i c r a t e constant k were not determined i n independent experiments,but used as parameters to match the experimental conversion versus l i q u i d flow-rate data. In the recent study of El-Hisnawi (29), however, most of the key para meters l i s t e d above which are needed to t e s t the model pre d i c t i o n s were measured v i a independent experiments. These have been described (34) so that the d e t a i l s have been omitted here for brevity. AH&rief d e s c r i p t i o n i s given below. v

s

S

v

1

The f i r s t p o r t i o n of E l - H i s n a w i s study (29) c o n s i s t e d of determining both the i n t r i n s i c and apparent r e a c t i o n k i n e t i c s f o r the hydrogénation of α-methylstyrene to cumene using cyclohexane, hexane, toluene, and 2-propanol as r e a c t i o n s o l v e n t s i n s l u r r y and basket r e a c t o r runs. Measurements were performed using both 0.5% and 2.5% Pd-on-alumina c a t a l y s t s s p e c i a l l y prepared by Engelhard as 0.13 cm χ 0.56 cm extrudates. Both the i n t r i n s i c and apparent k i n e t i c s e x h i b i t e d zero-order dependence with respect to α-methylstyrene and f i r s t - o r d e r dependence with respect to hydrogen over the temperature range from 15°C t o 30°C. E f f e c t i v e n e s s f a c t o r s f o r 0.5% Pd c a t a l y s t were between 0.05 - 0.083 when cyclohexane was used as the s o l v e n t , while values between 0.172 - 0.212 were obtained when hexane was used as the s o l v e n t . The second p o r t i o n of E l - H i s n a w i s study c o n s i s t e d of e v a l u a t i n g l i q u i d - s o l i d c o n t a c t i n g e f f i c i e n c y and l i q u i d holdup using impulse response t r a c e r experiments. Experiments were performed using the same c a t a l y s t packing and s o l v e n t s employed T


3.

MILLS AND DUDUKOVIC


47

i n the k i n e t i c study to examine the e f f e c t of l i q u i d p h y s i c a l p r o p e r t i e s . The c o n t a c t i n g e f f i c i e n c y was evaluated from the square-root of the r a t i o s of e f f e c t i v e d i f f u s i v i t i e s i n twophase flow to those obtained i n single-phase l i q u i d flow using the v a r i a n c e of t h e i r impulse responses f o l l o w i n g the work of B a l d i (38): (D e


η

o

a

=

) PP

(19)

A more d e t a i l e d explanation about the use of t r a c e r methods to evaluate c o n t a c t i n g e f f i c i e n c y , the r e l a t i o n s h i p s needed to i n t e r p r e t t r a c e r response data, the experimental methodology, and v a r i o u s r e s u l t s are given by M i l l s and Dudukovic (41). I t s u f f i c e s to say here that the f o l l o w i n g c o r r e l a t i o n s based upon Reynolds and G a l i l e o numbers were determined by El-Hisnawi to represent the a v a i l a b l e data on small porous packings i n the t r i c k l e - f l o w regime: n

τ , = 1.617

1 7

C E

U3

D

= 2.021

D

0.146

n

-0.0711

Re

£

Ga

Re

£

Ga^

,

£

9 r n

(20)

(21)

Equations (20) and (21) match the a v a i l a b l e data with an average e r r o r b e t t e r than 7% and are v a l i d w i t h i n the f o l l o w i n g ranges of parameters: 0.161 £ Re^ < 31.9, 18.5 dimensionless. = s u p e r f i c i a l l i q u i d v e l o c i t y , cm s ~ l . dimensionless gas concentration, C^/C^ ±. = dimensionless c o n c e n t r a t i o n o f d i s s o l v e ! gaseous reactant A i n the l i q u i d , C ^ / C ^ ^ = C^/(C^g,ί/Η^) . k

St _ ^ ^

Isothermal Trickle-Bed Reactors: Current Models 57

DUDUKOVIĆ

a

L

=

w s

i w s

a

u £ Ag u^ s


u

w s

S

u

=

u

=

u

=

U

=

A&,aws A&,iws B& Vp Χ β

c

c

A£,aws/ A£,iA&,iws/ M,,i« dimensionless l i q u i d c o n c e n t r a t i o n , Cg^/Cg£ ±. = c a t a l y s t p e l l e t volume, cm3. = conversion of reactant Β a t p o s i t i o n ξ, c

c

c

c

/ c

( B£,i - B ) B £ , i = conversion of reactant Β at the r e a c t o r e x i t .

Χβ,β

Greek Symbols εβ η riCE Λ

λ U£ ξ P£ OJj)

=

= bed p o r o s i t y . = c a t a l y s t e f f e c t i v e n e s s f a c t o r f o r a t o t a l l y wetted pellet. external contacting e f f i c i e n c y . = modified modulus based on p a r t i c l e volume,

= = = = =

parameter defined by Equation 9. l i q u i d v i s c o s i t y , gm cm""! s~-*-. a x i a l coordinate, z/L, dimensionless. l i q u i d d e n s i t y , gm cm~^. dynamic s a t u r a t i o n , Η^/ε^.

Acknowle dgment s This research was p a r t i a l l y supported by grants from Monsanto Company, Amoco O i l and S h e l l Development, which i s g r e a t l y appreciated.

Literature Cited 1. 2.

Ramachandran, P. Α.; Chaudhari, R. V. "Three-Phase Catalytic Reactors", Gordon and Breach Science Publishers, Ltd.: London,1983; Chapter 12. Germain, A. H.; L'Homme, G. A. "Chemical Engineering of Gas-Liquid-Solid Catalyzed Reactions, L'Homme, G. Α., Ed.; CEBEDOC: Liege, 1978.


58 3. 4.

5. 6. 7. 8.


9. 10. 11.

12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.

CHEMICAL AND CATALYTIC REACTOR MODELING Van Landeghem, H . Chem. Eng. Sci., 1980, 35, 1912-1949. Roberts, G. W . , " C a t a l y s i s in Organic S y n t h e s i s " , Rylander, P. Ν . , and G r e e n f i e l d , H., E d s . , Academic P r e s s , New York, 1976; pgs. 1-47. "NATO Advanced Study I n s t i t u t e on Multiphase R e a c t o r s " , V i m e i r o , P o r t u g a l , August 18-30, 1980. Turek, F.; C h a k r a b a r t i c , R. K . ; Lange, R.; Geike, R.; F l o c k , W. Chem. Eng. Sci., 1983, 3 8 ( 2 ) , 275-283. Hartman, M . ; C o u g h l i n , R. W. Chem. Eng. Sci., 1972, 27, 867-881. S a t t e r f i e l d , C. N.; O z e l , F. AIChE J,, 1973, 19(6), 1259-1261. S e d r i c k s , W . ; Kenney, C. N. Chem. Eng. Sci., 1973, 28, 559-569. Germain, A . H.; Lefebvre, A . G . ; L'Homme, G. Α., Adv. Chem. S e r i e s , 1974, 133, 164-179. Koros, R. Μ . , paper presented at the 4th I n t e r n a t i o n a l Symposium on Chemical Reaction E n g i n e e r i n g , H e i d e l b e r g , West Germany, 1976. Germain, Α . ; C r i n e , M . ; Marchot, P . ; L'Homme, G. A . Adv. Chem. Ser. Symp. S e r . , 1978, 65, 411-424. Mata, A . R . ; Smith, J . M. Chem. Eng. J., 1981, 22, 229-235. Hanika, J.; Sporka, K.; U l b r i c h o v á , Z.; Novák, J.; P y z i c k a , V. C o l l . Czechoslov. Chem. Commun., 1974, 39, 210-215. Hanika, J.; Vosecký, V.; R u z i c k a , V . Chem. Eng. J., 1981, 21, 108-114. M o r i t a , S.; Smith, J . M. Ind. Eng. Chem. Fundam., 1978, 17(2), 113-119. Herskowitz, M . ; C a r b o n e l l , R. G . ; Smith, J . M. AIChE J . 1979, 25(2), 272-283. Turek, F.; Lange, R. Chem. Eng. Sci., 1981, 36, 569-579. Montagna, Α. Α . ; Shah, Y . T . Ind. Eng. Chem. Process D e s . D e v . , 1975, 14(4), 479-483. Montagna, Α. Α.; Shah, Y . T.; Paraskos, J . A . Ind. Eng. Chem. P r o c . Des. D e v . , 1977, 16(1), 152-155. Henry, H. C . ; G i l b e r t , J . Β . Ind. Eng. Chem. P r o c . Des. D e v e l o p . , 1973, 12(3), 328-334. Somers, Α . ; Shah, Y . T.; Paraskos, J . Chem. Eng. Sci., 1976, 31, 759-765. B i s k i s , E . G . ; Smith, J . M. AIChE J., 1963,9(5), 677-680. M e j s t r i k o v a , M. C o l l . Czechoslov. Chem. Commun., 1974, 39, 210-215. Hanika, J.; Sporka, K . ; Ruzicka, V . ; Krausova, J . Chem. Eng. Commun., 1975, 2, 19-25. Jawad, Α . , P h . D . T h e s i s , U n i v e r s i t y of Birmingham, England, 1974. Goto, S.; Smith, J . M. AIChE J., 1975, 21, 714-718.


3.

28. 29. 30. 31. 32. 33.


34. 35. 36. 37. 38. 39. 40. 41.

MILLS AND

DUDUKOVIĆ

Isothermal Trickle-Bed Reactors: Current Models 59

Levec, J.; Smith, J. M. AIChE J., 1976, 22, 159-168. El-Hisnawi, A. A. D.Sc. Thesis, Washington University, St. Louis, Missouri, 1981. Goto, S.; Smith, J. M. AIChE J., 1978, 24(2), 286-293. Goto, S.; Smith, J. M. AIChE J., 1978, 24(2), 294-302. Crine, M.; Marchot, P.; L'Homme, G. A. Chem. Eng. Sci., 1980, 35, 51-57. Crine, M.; Marchot, P.; L'Homme, G. A. American Institute of Chemical Engineers Meeting, San Francisco, California, 1979. El-Hisnawi, Α. Α.; Duduković, M. P.; Mills, P. L. ACS Symposium Series, 1982, 196, 421-440. Goto, S.; Smith, J. M. AIChE J., 1975, 21(4), 706-713. Dwivedi, P. N.; Upadhyay, S. N. Ind. Eng. Chem. Proc. Des. Dev., 1977, 16, 157. Duduković, M. P.; Mills, P. L. ACS Symposium Series, 1978, 65, 387-399. Baldi, G., "NATO Advanced Study Institute on Multiphase Chemical Reactors", Vimeiro, Portugal, August 18-30, 1980. Satterfield, C. N.; Way, P. N. AIChE J., 1972, 18(2), 305-311. Enright, J. J.; Chuang, T. T. Can. J. Chem. Eng., 1978, 56, 236-250. Mills, P. L.; Duduković, M. P. AIChE J., 1981,27(6), 843-904.

RECEIVED August 22, 1983


Chemical and Catalytic Reactor Modeling - American Chemical Society

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