37 Multiphase Kinetic Studies with a Spinning Basket Reactor E . C . M Y E R S and Κ. K. R O B I N S O N
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Amoco O i l Company, P . O . Box 400, Naperville, I L 60540
The study of multiphase catalytic process such as petroleum hydrotreating requires laboratory reactors that ensure good contact between gas, l i q u i d , and solid phases at high temperatures and pressures. Numerous reactors have been developed for process studies and fall mainly into two categories: fixed bed and agitated (gradientless). For multiphase catalytic systems, the experimental studies are normally performed in a trickling fixed bed reactor. This type reactor is subject to problems with catalyst contacting and flow maldistribution unless certain pre cautions are taken. External mass transport limitations are also possible, particularly with the more active catalysts that are currently available. Vigorous gas-liquid-catalyst contacting will often remedy this situation. Weekman (1) concluded that the gradientless reactors are far superior to the fixed bed in terms of sampling ease, temperature maintenance, mass transport, and other operating variables. Although several gradientless reactors are available for studies of gas-phase reactions (2-6), none of them are suitable
for studying multiphase systems, p a r t i c u l a r l y at the high pressure
required i n such petroleum processes as distillate hydrotreating. Russian workers (7) did report a gradientless multiphase reactor but it was only suitable for atmospheric pressure operation. Now we have developed a high-pressure version to study hydrotreating reactions. It comprises a spinning basket held i n a 500 cc s t i r r e d autoclave. Baffles around the basket ensure good mixing and contacting of the l i q u i d and also eliminate vortexing at the gas-liquid interface. The flow pattern of the oil approximates that obtained in a single perfectly mixed reactor because the vaporized hydrocarbons which exit in the off-gas stream are recycled. The spinning basket reactor was used to study the desulfuri z a t i o n kinetics of a model sulfur compound—dibenzothiophene i n white o i l . This study i s confirming data for an e a r l i e r study by Frye and Mosby (8) with a t r i c k l e bed type reactor and actual petroleum fractions. There i s good agreement between the two k i n e t i c studies. This current study has achieved a further © 0-8412-0401-2/78/47-065-447$05.00/0 American Chemical Society Library 1 1 55 16th St., N.W. Weekman, V., et al.; In Chemical Reaction Engineering—Houston; Washington, D.C. 20 036 Washington, DC, 1978. ACS Symposium Series; American Chemical Society:
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refinement i n the k i n e t i c model; c o m p e t i t i v e a d s o r p t i o n e f f e c t s by the r e a c t a n t s u l f u r compound are accounted f o r .
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Experimental M a t e r i a l s . The feedstock was white o i l s p i k e d w i t h dibenzothiophene. The white o i l was obtained from the W h i t i n g r e f i n e r y o f Amoco O i l Company. The dibenzothiophene (Eastman Chemicals) and the hydrogen ( L i q u i d Carbonic) were used as received. The h y d r o d e s u l f u r i z a t i o n c a t a l y s t s were 1/16" c y l i n d r i c a l extrudates of commercial cobalt-molybdenum on alumina. Spinning Basket Reactor D e s c r i p t i o n . The s p i n n i n g c a t a l y s t basket of the r e a c t o r i s shown i n F i g u r e 1. The c a t a l y s t i s h e l d i n p l a c e by w i r e mesh i n an annular space i n s i d e the basket, where i n t e r n a l b a f f l e s are between the c a t a l y s t space and t h e center support s h a f t . The basket i s a l s o surrounded by a b a f f l e system which d i r e c t s the f l u i d f l o w and prevents l i q u i d v o r t e x i n g . A 500 cc autoclave designed and b u i l t by Autoclave Engineers serves as the b a s i s f o r the r e a c t o r system and i s equipped w i t h a p a c k l e s s magnetic d r i v e t o r o t a t e the basket. Good c o n t a c t i n g i s provided by t h e l i q u i d and e n t r a i n e d gas bubbles f l o w i n g r a p i d l y past the c a t a l y s t . This h i g h l y t u r b u l e n t g a s - l i q u i d mass i s a l i q u i d continuous bubble swarm. Backmixed ( g r a d i e n t l e s s ) o p e r a t i o n i s assured by good mixing i n the r e a c t o r . The f l o w p a t t e r n , shown i n F i g u r e 2, i s as f o l l o w s : (1) F l u i d enters near the center of the basket through the cutouts a t the top and bottom; (2) the f l u i d i n s i d e the basket r o t a t e s a t the same r a t e as the basket and moves by c e n t r i f u g a l f o r c e i n t o the c a t a l y s t ; (3) f l u i d e x i t s the c a t a l y s t and moves up o r down between the basket and autoclave w a l l ; (4) t h e f l u i d moves i n t o the spaces above and below the basket where i t then r e - e n t e r s the basket. Process D e s c r i p t i o n . The o v e r a l l flow scheme i s shown i n Figure 3. Hydrogen i s metered t o the r e a c t o r from the p i l o t p l a n t feed system. L i q u i d feed i s pumped t o the r e a c t o r by a Whitey pump which r e g u l a t e s the f l o w r a t e . Hydrogen, hydrogen s u l f i d e , and v a p o r i z e d o i l are removed from the vapor space above the s p i n n i n g basket. I t i s heated to r e a c t i o n temperature t o prevent condensation and r e f l u x i n g , then cooled t o room temperature i n a condenser where i t enters a s e p a r a t o r . The l i q u i d hydrocarbon i s r e c y c l e d w i t h an a i r d r i v e n Haskel pump t o the r e a c t o r . The uncondensed gas, hydrogen and hydrogen s u l f i d e , passes through the u n i t pressure c o n t r o l v a l v e t o the wet t e s t meter, which measures the gas f l o w r a t e . The l i q u i d e x i t s the r e a c t o r t o a high-pressure separator w i t h an overflow pipe p o s i t i o n e d i n s i d e . L i q u i d l e v e l i n the r e a c t o r i s maintained a t the same l e v e l as the top o f the over-
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
MYERS AND ROBINSON
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37.
Multiphase Kinetic Studies
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Figure 1. Annular catalyst basket
Catalyst
Figure 2.
Multiphase spinning basket reactor
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
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flow p i p e i n the s e p a r a t o r . The l i q u i d overflows from the p i p e i n t o the body o f t h e s e p a r a t o r . The l i q u i d l e v e l i n the body of t h e separator i s maintained below t h e top o f the overflow pipe. R e s u l t s and D i s c u s s i o n
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The s t u d i e s which we w i l l examine can be s u b d i v i d e d i n t o two areas: (1) Development o f the r e a c t o r system, (2) a k i n e t i c study on the h y d r o d e s u l f u r i z a t i o n of dibenzothiophene. Reactor D e v e l o p m e n t — C a t a l y s t Basket. The r e a c t o r i n t e r n a l s and f l o w scheme were designed a t Amoco O i l Research and Develop ment. Two types o f s p i n n i n g baskets were designed and b u i l t , the i n i t i a l design used a cross-shaped paddle, w h i l e a l a t e r one adopted an annular shape. The l a t t e r improved design was used i n a l l t e s t work. The improved design was an annular-shaped basket ( F i g u r e 1 ) , w i t h a basket c a p a c i t y o f 35 cc (^25 gm c a t a l y s t ) . The b a f f l e was designed t o i n c l u d e a l a r g e r i n g above the basket t o prevent v o r t e x i n g and b a f f l e extensions added below the basket t o d e c e l e r a t e the l i q u i d and a l l o w i t t o enter the middle o f the basket. M i x i n g and c o n t a c t i n g performance o f the improved b a s k e t - b a f f l e design was t e s t e d w i t h a i r and water a t ambient pressure and temperature i n a p l e x i g l a s s mockup of the r e a c t o r . The p l e x i g l a s s mockup s t u d i e s showed the f l o w p a t t e r n s s a t i s f i e d the requirements f o r e f f e c t i v e m i x i n g and c o n t a c t i n g i n the s p i n n i n g basket r e a c t o r . A h i g h degree of gas entrainment was observed i n the l i q u i d phase and resembled a bubble swarm. Reactor D e v e l o p m e n t — O v e r a l l System. A second p o r t i o n o f the o v e r a l l development was t h e system design f o r f e e d i n g o i l and hydrogen and removing l i q u i d product and o f f - g a s . F o r a n a l y s i s of the d a t a , the residence time d i s t r i b u t i o n o f the l i q u i d must be c l e a r l y d e f i n e d ; the s p i n n i n g basket r e a c t o r should approximate a s i n g l e backmixed r e a c t o r . H i g h l y v a p o r i z e d feeds work a g a i n s t t h i s o b j e c t i v e , however. To m a i n t a i n the p a r t i a l pressure o f the r e a c t i o n s p e c i e s (e.g. hydrogen s u l f i d e ) a t the d e s i r e d l e v e l , hydrogen i s c o n s t a n t l y fed and withdrawn from the r e a c t o r . As hydrogen i s withdrawn, so i s the v a p o r i z e d l i q u i d . T h i s r e s u l t s i n the residence time of the l i g h t e r components b e i n g l e s s than the r e s t of the r e a c t i o n m i x t u r e . To prevent t h i s , v a p o r i z e d l i q u i d l e a v i n g the r e a c t o r w i t h the gas stream should be condensed and then r e c y c l e d back t o the r e a c t o r . T h i s c o n t r o l s and d e f i n e s the r e s i d e n c e time d i s t r i b u t i o n of t h e l i q u i d i n the r e a c t o r by r e q u i r i n g a l l o f i t which enters t o e x i t the r e a c t o r as l i q u i d assuming h y d r o c r a c k i n g r e a c t i o n s are n e g l i g i b l e . More s p e c i f i c a l l y , the o f f - g a s i s cooled t o ambient temperature t o condense the l i g h t hydrocarbons b e f o r e being vented. Then the l i g h t hydrocarbons a r e returned to t h e r e a c t o r w i t h an a i r - d r i v e n r e c y c l e pump.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
37.
MYERS AND
ROBINSON
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Kinetic
Studies
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L i q u i d l e v e l i n the r e a c t o r was c o n t r o l l e d w i t h an overflow pipe l o c a t e d i n an e x t e r n a l separator. A l l l i q u i d then e x i t s through the overflow pipe i n t o the separator; the l e v e l i s measured w i t h a d i f f e r e n t i a l pressure t r a n s m i t t e r and maintained s l i g h t l y below the overflow t i p . K i n e t i c Study—Dibenzothiophene D e s u l f u r i z a t i o n . E a r l i e r work a t Amoco by Frye and Mosby (8) s t u d i e d the r a t e o f r e a c t i o n of s i n g l e s u l f u r compounds i n l i g h t c a t a l y t i c c y c l e o i l . Conclusions from that study were (1) the r e a c t i o n k i n e t i c s a r e f i r s t order i n hydrogen and reactant s u l f u r ; (2) hydrogen s u l f i d e i n h i b i t s the r e a c t i o n ; (3) o v e r a l l energy o f a c t i v a t i o n i s around 28-30 k c a l . A r e a c t i o n k i n e t i c study w i t h a model s u l f u r compound, dibenzothiophehe, was performed i n the s p i n n i n g basket r e a c t o r . A mixture o f dibenzothiophene i n white o i l was h y d r o d e s u l f u r i z e d over a wide range o f r e a c t i o n c o n d i t i o n s , v a r y i n g temperature, pressure, space v e l o c i t y , and hydrogen s u l f i d e l e v e l . The s t o i c h i o m e t r y f o r h y d r o d e s u l f u r i z a t i o n o f d i b e n z o t h i o phene may be w r i t t e n as f o l l o w s :
ODD dibenzothiophene
two
biphenyl
The k i n e t i c study o f dibenzothiophene d e s u l f u r i z a t i o n had objectives: 1. Evaluate r e a c t o r performance t o determine the minimum a g i t a t i o n r a t e which leads t o k i n e t i c a l l y c o n t r o l l e d conditions. 2. Confirm e a r l i e r d e s u l f u r i z a t i o n k i n e t i c s developed by Frye and Mosby on s e l e c t e d s u l f u r compounds using a t r i c k l e bed r e a c t o r ; r e f i n e t h e i r k i n e t i c model i f necessary.
A g i t a t i o n Tests. The observed r e a c t i o n r a t e should represent the c a t a l y t i c k i n e t i c s unclouded by phenomena such as the t r a n s f e r o f hydrogen a t the g a s - l i q u i d i n t e r f a c e o r r e a c t i o n species through the stagnant f i l m surrounding the c a t a l y s t . The minimum s t i r r i n g r a t e i s u s u a l l y e s t a b l i s h e d from a simple d i a g n o s t i c t e s t i n which conversion i s measured f o r v a r i o u s l e v e l s o f a g i t a t i o n . A g i t a t i o n r a t e was v a r i e d between 500 t o 1000 rpm and d e s u l f u r i z a t i o n l e v e l measured. R e s u l t s o f the a g i t a t i o n t e s t s are l i s t e d i n Table I . R a i s i n g a g i t a t i o n .
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
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r a t e from 500 t o 700 rpm i n c r e a s e s t h e d e s u l f u r i z a t i o n conversion by 2.6%. By r a i s i n g the a g i t a t i o n r a t e f u r t h e r t o 1000 rpm, a s m a l l e r 1.4% i n c r e a s e i n conversion was observed. I t was concluded t h a t 750 rpm should be an adequate a g i t a t i o n r a t e s i n c e h i g h speeds put s t r e s s on the s t i r r e r mechanism and eventually lead to bearing f a i l u r e .
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TABLE I EFFECT OF AGITATION RATE ON PERFORMANCE
Press., psig
Feedstock Dibenzothiophene i n White O i l .5% S
300 300 300
Agitation WHSV Temp., rpm °F Wo/hr-Wc 540 540 540
2.10 2.06 2.06
500 750 1000
Desulfurization % 68.0 70.6 72.0
K i n e t i c Study. The experimental method c o n s i s t e d o f changing a s i n g l e process v a r i a b l e (such as temperature o r t o t a l pressure) and then o b s e r v i n g the e f f e c t on conversion. G e n e r a l l y , t h e e f f e c t o f each v a r i a b l e was observed by making two excursions from a s e t o f base c o n d i t i o n s . Table I I summarizes the experimental r e s u l t s . TABLE I I DIBENZOTHIOPHENE IN WHITE OIL Pressure, psig 300 (*) * * * * * * 100 500 * * * *
Temperature, °F 540(*) * * * 523 545 566 * * * * 523 566
WHSV Wo/hr-Wc
H 2 Rate ft /hr
2.0(*) 6.25 1.69 .62 *
0.42(*) .87 .37 .23 .37 .46 .36 .46 .40 .10 1.5 .31 .99
* * * * * 1.17 4.4
3
Desulfurization, % 74.6 40.0 76.5 94.5 63.0 76.0 89.0 52.0 82.0 62.5 85.5 80.4 84.5
*Base C o n d i t i o n s K i n e t i c M o d e l l i n g . I f t h e r e a c t i o n were s t r i c t l y f i r s t order i n dibenzothiophene, then a p l o t o f r e a c t i o n r a t e versus
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
37. MYERS AND ROBINSON
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Multiphase Kinetic Studies
s u l f u r c o n c e n t r a t i o n would y i e l d a s t r a i g h t l i n e . F i g u r e 4 shows t h a t t h i s r e l a t i o n s h i p does not h o l d . Frequently c a t a l y t i c k i n e t i c s can be described u s i n g a Hougan-Watson k i n e t i c model, an e x t e n s i o n o f the e a r l i e r Langmuir-Hinshelwood forms. The general form of the model p a r a l l e l s the e a r l i e r work by Frye and Mosby (8) on s i n g l e s u l f u r compounds i n petroleum f r a c t i o n s . The b a s i c d i f f e r e n c e i s that competitive a d s o r p t i o n of the reactant i s accounted f o r which helps t o d e s c r i b e the n o n - f i r s t order behavior. The k i n e t i c model i s Downloaded by UNIV OF PITTSBURGH on October 14, 2015 | http://pubs.acs.org Publication Date: June 1, 1978 | doi: 10.1021/bk-1978-0065.ch037
p
r
* DBPH2
=
" DB
(1 + K where
D B
P
n
p
D B
+ %S Hs)
m
- r ^ g = r a t e o f r e a c t i o n , g moles/sec-gm c a t a l y s t k = r a t e constant ~P± = p a r t i a l pressure o f species i , atm K± = a d s o r p t i o n constant o f species i , atm ^DB = dibenzothiophene hydrogen HS = hydrogen s u l f i d e n,m = i n t e g e r constants, 1 o r 2 -
=
The two i n t e g e r constants, η and m, f o r hydrogen p a r t i a l pressure and the a d s o r p t i o n term were assigned values o f 1 o r 2. This r e s u l t s i n four p o s s i b l e models t o d e s c r i b e the experimental data. The data were f i t t e d w i t h the f o u r models by n o n - l i n e a r r e g r e s s i o n techniques. The r e s u l t s are summarized i n Table III. TABLE I I I KINETIC MODEL SUMMARY Integer Powers η m
Model A Β C D
l
l 1 2 2
2 2 1
F i t t e d Constants S t d . Dev. o f Rate k χ Ι Ο Κρβ KHS σ χ ΙΟ 6
4.64 2.47 .147 .32
8
607.9 90.0 89.1 671.8
9.5 1.4 2.7 2.2
.64 .81 1.25 1.14
Models A and Β which were f i r s t order i n hydrogen p a r t i a l pressure gave the best f i t . F i g u r e s 5 and 6 show f i t t e d v s . observed r e a c t i o n r a t e s f o r these two models. Furthermore, t h e s t a t i s t i c a l s i g n i f i c a n c e of the three f i t t e d parameters, k, Kj)g, and Kjjg, was c o n s i d e r a b l y b e t t e r f o r models A and B. U n f o r t u n a t e l y the data do not a l l o w d i s c r i m i n a t i o n on the power f o r the adsorption term.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
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CHEMICAL REACTION ENGINEERING—HOUSTON
Pressure sensor
0~
Pressure regulator Hydrogen I Flow ι control _j valve Pressure drop sensor
1
Pressure control valve
Ί
To
vent n
Wet t e s t meter
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Condenser
Feed tank
Liquid level valve
Feed scale Metering pump Figure 3.
Process flow diagram
W t % S in product
Figure 4.
Reaction rate as a function of product sulfur
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
Sample receiver
Multiphase Kinetic Studies
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MYERS AND ROBINSON
Figure 6.
Calculated vs. observed rate—dual site model
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION
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ENGINEERING—HOUSTON
An u n s u c c e s s f u l attempt was made t o f i t the a c t i v a t i o n energies f o r the k i n e t i c and a d s o r p t i o n c o n s t a n t s . The para meters were a l l h i g h l y i n t e r c o r r e l a t e d s i n c e the experiments were not designed t o uncouple the temperature e f f e c t s . As an a l t e r n a t e approach the o v e r a l l temperature response was determined by p l o t t i n g r a t e versus r e c i p r o c a l temperature i n F i g u r e 7 and the s l o p e , -ΔΕ/R, c a l c u l a t e d . F i g u r e 7 shows t h e o v e r a l l temperature response by l e a s t squares f i t t o be 28.0 k c a l . The o v e r a l l energy o f a c t i v a t i o n i n c l u d e s the e f f e c t of temperature on the vapor pressure o f dibenzothiophene. As discussed by Frye and Mosby ( 8 ) , the apparent energy of a c t i v a t i o n f o r a l i q u i d - v a p o r system i s a combination of s e v e r a l f a c t o r s which i n c l u d e the a d s o r p t i o n e n t h a l p i e s o f dibenzo thiophene and hydrogen, the l a t e n t heat o f v a p o r i z a t i o n and the r e a c t i o n a c t i v a t i o n energy. I f we assume that the enthalpy of v a p o r i z a t i o n i s 13 kcal/mole, then the a c t i v a t i o n energy i s about 15 k c a l / m o l . This a l s o suggests that f i l m d i f f u s i o n e f f e c t s a r e not c o n t r o l l i n g the observed r e a c t i o n r a t e . With the e x c e p t i o n of the r e a c t i o n order f o r the dibenzothiophene, good q u a l i t a t i v e agreement e x i s t s w i t h the r e s u l t s o f both s t u d i e s . The discrepancy i n the apparent r e a c t i o n order c o u l d be e x p l a i n e d by the d i f f e r e n c e s i n the r e a c t i o n environment. In c o n t r a s t to white o i l , l i g h t c a t a l y t i c c y c l e o i l i s h i g h l y aromatic. These aromatics c o m p e t i t i v e l y adsorb and i n h i b i t the d e s u l f u r i z a t i o n r e a c t i o n . At h i g h aromatics c o n c e n t r a t i o n , the dibenzothiophene a d s o r p t i o n would be masked by aromatic a d s o r p t i o n . Apparent f i r s t order k i n e t i c s w i t h respect t o dibenzothiophene would then be observed. Conclusions The Amoco annular s p i n n i n g basket r e a c t o r system i s a u s e f u l t o o l f o r s t u d y i n g the fundamental k i n e t i c s o f l i q u i d - v a p o r - s o l i d c a t a l y z e d r e a c t i o n systems. We b e l i e v e i t i s g e n e r a l l y s u p e r i o r to t r i c k l e bed systems f o r the study of pure compound k i n e t i c s i n l i q u i d - v a p o r - s o l i d c a t a l y z e d systems. A d e s u l f u r i z a t i o n k i n e t i c study w i t h dibenzothiophene i n white o i l was s u c c e s s f u l l y completed. The r e s u l t s of the study compare f a v o r a b l y w i t h an e a r l i e r study performed i n a t r i c k l e bed r e a c t o r by Frye and Mosby ( 8 ) . Abstract A s p i n n i n g basket r e a c t o r has been developed f o r s t u d y i n g multiphase r e a c t i o n s a t h i g h pressure. Studies have been performed on the h y d r o d e s u l f u r i z a t i o n of v a r i o u s petroleum f r a c t i o n s and a model s u l f u r compound. Hydrogen and l i q u i d feed are c o n t i n u o u s l y f e d t o t h e r e a c t o r and contacted w i t h the c a t a l y s t which i s h e l d i n a r o t a t i n g annular basket. The
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
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MYERS AND ROBINSON
Figure 7.
Multiphase Kinetic Studies
Reaction rate vs. reciprocal temperature
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING-HOUSTON
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residence time d i s t r i b u t i o n of the o i l approximates a s i n g l e backmixed r e a c t o r by r e c y c l i n g the l i g h t hydrocarbons which e x i t i n the o f f - g a s stream. A c a t a l y s t b a s k e t - b a f f l e design was developed which assures good m i x i n g and c o n t a c t i n g and e l i m i n a t e s v o r t e x i n g a t the g a s - l i q u i d i n t e r f a c e . P l e x i g l a s s mock-up s t u d i e s provided guidance i n the design of the r e a c t o r internals. D e s u l f u r i z a t i o n k i n e t i c s were s t u d i e d w i t h a model s u l f u r compound system, a dibenzothiophene i n white o i l . Tests on basket a g i t a t i o n r a t e i n d i c a t e that mass t r a n s f e r and c o n t a c t i n g e f f e c t s are s m a l l above 750 rpm. The r e a c t i o n k i n e t i c s agreed w e l l w i t h e a r l i e r work. The Langmuir-Hinshelwood k i n e t i c model was f u r t h e r r e f i n e d to account f o r competitive a d s o r p t i o n e f f e c t s due to dibenzothiophene as w e l l as hydrogen s u l f i d e . Literature Cited 1. 2. 3. 4. 5. 6. 7.
8.
Weekman, V. W., AIChE J., 20, 833 (1974). Carberry, J. J., Ind. Eng. Chem., 56, 39 (1964). Tajbl, D. J.; Simons, J. B.; and Carberry, J. J.; Ind. Eng. Chem. Fundam., 5, 171 (1966). Bennett, C. O.; C u t l i p , M. B.; and Yang, C. C . ; Chem. Eng. Sci., 27, 2255 (1972). Berty, J., Chem. Eng. Prog., 70, V o l . 6, 78 (1974). Mahoney, J. Α., J. of Cat., 32, 247 (1974). Tikhonov, G. F.; Shestov, G. K.; Temkin, O. N.; and Flid, R. M . ; "Gradientless Reactor Suitable for Studying the Kinetics of Liquid Phase Reactions in Gas-Liquid Systems," Kinetika, K a t a l i z , 7, No. 5, 914, Sept-0ct (1966). Frye, C. G . , and Mosby, J. F . , "Kinetics of Hydrodesulfur i z a t i o n , " Chem. Eng. Prog., 63, No. 9, 66 (1967).
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.