Catalyst Effectiveness Factor in Trickle-Bed Reactors

32 Catalyst Effectiveness Factor in Trickle-Bed Reactors

Downloaded by UNIV OF MASSACHUSETTS AMHERST on June 3, 2018 | https://pubs.acs.org Publication Date: June 1, 1978 | doi: 10.1021/bk-1978-0065.ch032

M . P.

DUDUKOVIĆ

and P. L . M I L L S

Chemical Reaction Engineering Laboratory, Department of Chemical Engineering, Washington University, St. Louis, MO 63130

Observed rates in a number of trickle-bed reactors employed in hydrodesulfurization and hydrotreating of heavy residuals indi cate that they operate in the regime free of major gas-liquid mass transfer limitations (1,2,3,4,5). Due to the fact that often the liquid reactants are nonvolatile or dilute at the operating condi tions used the reaction is frequently liquid reactant limited and confined to the catalyst effectively wetted by liquid. Since po rous packing, typically 1/32" to 1/8" (0.08 cm to 0.318 cm) extru dates is most often employed it is clear that reaction rates may be affected both by internal pore fill-up with liquid and by inter nal diffusional limitations. Catalyst effectiveness factors from 0.5 to 0.85 have been generally reported (1,3,5,6,7,8,). In order to interpret or predict trickle-bed performance at tempts have been made to account for liquid maldistribution, devia tion from plug flow and for incomplete wetting of catalyst parti cles (4,9,10,11,12). It has been shown that liquid phase d e v i a t i o n from plug flow does not have significant e f f e c t s on conver s i o n in commercial and pilot s c a l e t r i c k l e - b e d r e a c t o r s (13). A p p l i c a t i o n of Mears' (14) criterion confirms the i n s i g n i f i c a n c e of d i s p e r s i o n e f f e c t s . Incomplete c a t a l y s t w e t t i n g ( i . e . con t a c t i n g e f f i c i e n c y , c a t a l y s t u t i l i z a t i o n ) as a f f e c t e d by the hydrodynamic regime i n the bed was s i n g l e d out as the most important parameter which determines r e a c t o r performance (12). One may d i s t i n g u i s h between r e a c t o r s c a l e incomplete contacting caused p r i m a r i l y by flow m a l d i s t r i b u t i o n and g l o b a l hydrodynamic e f f e c t s , and p a r t i c l e s c a l e incomplete c o n t a c t i n g which i s determined by l o c a l v i s c o u s , i n e r t i a and surface f o r c e s . When transport e f f e c t s c o n t r o l the o v e r a l l r e a c t i o n r a t e r e a c t o r hydrodynamics has a dom inant e f f e c t on r e a c t o r performance. When k i n e t i c s masked by i n t e r n a l d i f f u s i o n c o n t r o l s the r a t e s i n g l e p a r t i c l e phenomena deter mine r e a c t o r performance to a great degree. The purpose of t h i s paper i s t o summarize previous i n t e r p r e t a t i o n s of the e f f e c t of incomplete c a t a l y s t w e t t i n g on t r i c k l e - b e d performance and to develop a model f o r the e f f e c t i v e n e s s f a c t o r f o r p a r t i a l l y wetted c a t a l y s t p e l l e t s . I n the case of a r e a c t i o n ©

0-8412-0401-2/78/47-065-387$05.00/0

Weekman and Luss; Chemical Reaction Engineering—Houston ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL


388

REACTION

ENGINEERING-HOUSTON

confined to the wetted p o r t i o n of the c a t a l y s t only the wetted volume of the p e l l e t c o n t r i b u t e s to r e a c t i o n and the supply of l i q u i d r e a c t a n t occurs only across the wetted, e x t e r n a l surface of the p e l l e t . Under these c o n d i t i o n s the 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 i s a f u n c t i o n of the r a t i o of the maximal k i n e t i c r a t e and maximal r a t e of i n t e r n a l d i f f u s i o n , of the 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 and of i n t e r n a l pore f i l l - u p . An approximate equation d e s c r i b i n g t h i s r e l a t i o n s h i p and based on the work of A r i s (15) can be incorporated i n the t r i c k l e - b e d r e a c t o r performance equa t i o n . S o l u t i o n s to more r i g o r o u s models r e p r e s e n t i n g the e f f e c t i v e n e s s of p a r t i a l l y wetted p e l l e t s were sought a l s o i n order to assess the v a l i d i t y of the approximate models. Review of Previous Models Most of the p r e v i o u s l y used expressions to account f o r incom p l e t e c a t a l y s t w e t t i n g i n t r i c k l e - b e d s are summarized i n Table I . A l l of these, w i t h the exception of the l a s t one, are based on the assumptions of a) plug flow of l i q u i d , b) no e x t e r n a l mass t r a n s f e r l i m i t a t i o n s , c) i s o t h e r m a l c o n d i t i o n s , d) f i r s t order i r r e v e r s i b l e r e a c t i o n w i t h respect to the l i q u i d r e a c t a n t , e) n o n v o l a t i l e l i q u i d r e a c t a n t , f ) no n o n c a t a l y t i c homogeneous l i q u i d phase reac tion. S a t t e r f i e l d (5) suggested comparing the apparent r a t e constant. k , obtained from t r i c k l e bed data to the r a t e constant, k , de termined i n p e r f e c t l y mixed s l u r r y r e a c t o r s , as a measure of t r i c k l e bed e f f e c t i v e n e s s . The r a t i o k / k t c l e s s than u n i t y was i n t e r preted on the b a s i s of l i q u i d d e v i a t i o n s from p l u g flow (10) and of incomplete c a t a l y s t w e t t i n g (8,16). Ross (12) i n t r e a t i n g the data from commercial and p i l o t p l a n t 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 o r s assumed that l i q u i d space time i s the b a s i c parameter i n r e a c t o r performance. This a s s e r t s that performance and the apparent r a t e constant are p r o p o r t i o n a l to l i q u i d holdup as shown i n equation (1). Bondi (17) developed an e m p i r i c a l expression (2a) i n i n t e r p r e t i n g data f o r the h y d r o d e s u l f u r i z a t i o n of heavy gas o i l . This expres s i o n r e l a t e s the space time r e q u i r e d to achieve 50% conversion, τ^, to the analogous space time at complete w e t t i n g , τ^°, and to 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 L « This can a l s o be w r i t t e n as equation (2b) i n terms of p r e v i o u s l y defined constants. Henry and G i l b e r t (11) extended Ross (12) formula by i n c o r p o r a t i n g i n t o i t an a v a i l able c o r r e l a t i o n f o r l i q u i d holdup which r e s u l t e d i n expression (3). F i n a l l y , Mears (4) hypothesized that the apparent r a t e constant, k , i s p r o p o r t i o n a l to the true r a t e constant on completely wetted c a t a l y s t , k^ to the 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 , η^, and to the c o n t a c t i n g e f f i c i e n c y , riçE> i . e . to the f r a c t i o n of the e x t e r n a l c a t a l y s t area contacted by l i q u i d . By i n c o r p o r a t i n g the c o r r e l a t i o n of Puranik and Vogelpohl (18), which was developed f o r i n complete c o n t a c t i n g i n absorbers packed w i t h d i f f e r e n t packing s i z e and shape, Mears (4) a r r i v e d to expression (4). S y l v e s t e r and P i t a y a g u l s a r n (19) reproduced the model of Suzuki and Smith v

t c

v

1

v

C9


32.

DUDUKovic A N D

Catalyst Effectiveness in Trickle-Bed Reactors 389

MILLS

Table I Suggested Performance Equations f o r T r i c k l e - B e d Reactors


-

k

1

H

tc TL

-

7"^ν

= T-^-

(2a)

5

+

ν

^

+

; 0.5 < b < 0.7

tc

,

n

(2b)

U L

1 in

krs.. L 1/3 tt cc m m /o (LHSV)2/3 _ 0.32, -0.68, 0.18 -0.05. ,.0.21 L (LHSV) d ν ( τ m ρ c AJ

Œ

:-

1-X 1 In -r-rr 1-X

œ

—

TtlotrN

σ

/o\

η

w

in J L = Λ ω

(5)

3

where

m

Τ

χτ

Λ

Β = -f-

3

[1 + 4 Λ / Ν 2

- 1]

β

(5a)

Ο Λ

( 5 b )

2 = 1/Α + 1/Ν , 1 st Ί

Λ

ι

=

Ί

[

V

o

t

h

φ

τ ~

1 1

( 5 c )

(20) f o r gas s o l i d c a t a l y t i c r e a c t i o n s and a p p l i e d i t t o three phase systems i n t r i c k l e beds. Incomplete w e t t i n g was accounted f o r by assuming only a p o r t i o n of the r e a c t o r , i . e . an e f f e c t i v e l y smaller volume, to be c o n t r i b u t i n g t o r e a c t a n t conversion. This i s again e q u i v a l e n t t o assuming t h a t a primary parameter i s l i q u i d space time. When the e x t e r n a l mass t r a n s f e r l i m i t a t i o n s and a x i a l d i s p e r s i o n e f f e c t s are neglected the model expressed by equations (5) i s reduced to Ross (12) expression (1) m u l t i p l i e d w i t h c a t a l y s t effectiveness factor. Recently (21) another approximate model f o r the c a t a l y s t s e f f e c t i v e n e s s f a c t o r i n t r i c k l e bed r e a c t o r has been proposed. I n t h i s model the e f f e c t i v e n e s s f a c t o r f o r a p a r t i a l l y wetted c a t a l y s t p e l l e t i n a t r i c k l e - b e d r e a c t o r f o r a r e a c t i o n o c c u r r i n g only i n the l i q u i d f i l l e d pore r e g i o n of the p e l l e t i s defined by: 1

η TB

= ( a c t u a l r a t e on a p a r t i a l l y wetted p e l l e t ) / i d e a l maximum r a t e a t bulk c o n d i t i o n s \ Ion a completely wetted p e l l e t J

=


CHEMICAL REACTION ENGINEERING-HOUSTON

390

= ( a c t u a l r a t e per u n i t volume of p a r t i a l l y wetted p e l l e t ) i d e a l maximum r a t e per u n i t volume of completely \ wetted p e l l e t )

χ

(

( f r a c t i o n of p e l l e t a c t u a l l y i n t e r n a l l y wetted) f


Using A r i s (15) d e f i n i t i o n f o r the modulus of i r r e g u l a r the f o l l o w i n g modified modulus was obtained: n Φ

particles

i

=

ΤΒ

(6)

( 7 )

*T

which r e s u l t s i n the expression f o r the e f f e c t i v e n e s s f a c t o r given below: . , , 1 . tanh ( — φ ) CE (8) \B CE η

N

=

n

Expression (8) reduces t o the product of η^ η , as used by Mears (4) under two c o n d i t i o n s . Ε

n Φ

Τ

>

>

1 ;

η

ΤΒ

~

CE 0Ε Τ

=

η

η

τ

( 9 a )

In t h i s case the i n t e r n a l pore d i f f u s i o n a l l i m i t a t i o n s a r e severe and thus r e a c t i o n occurs only i n a narrow zone ( s h e l l ) c l o s e t o the e x t e r i o r s u r f a c e . The u t i l i z a t i o n of the p e l l e t i s d i r e c t l y p r o p o r t i o n a l t o the s i z e of t h i s zone which i n t u r n i s d i r e c t l y r e l a t e d t o the f r a c t i o n of e x t e r n a l area wetted.

n./n

CE

= l;

= n

(9b)

CE

The second case i m p l i e s t h a t the pores i n the c a t a l y s t p e l l e t s a r e not interconnected and that the f r a c t i o n of i n t e r n a l w e t t i n g c o r responds d i r e c t l y t o e x t e r n a l w e t t i n g . This i n general i s not the case when d e a l i n g w i t h r e a l c a t a l y s i s and hydrocarbon feeds which r e a d i l y wet i n t e r n a l pore s t r u c t u r e s (22). For s m a l l m o d u l i i i . e . very slow r e a c t i o n s such as t y p i c a l of h y d r o d e s u l f u r i z e r s expression (12) reduces t o : ^TB

*\

t

1

" i

Catalyst Effectiveness Factor in Trickle-Bed Reactors

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