Operational Flexibility Consideration in the Design of Multitubular

18 Operational Flexibility Consideration in the Design of Multitubular Reactors C. M c G R E A V Y Department of Chemical Engineering, Leeds University, Leeds, LS2 9JT, England B. R. D U N B O B B I N

Downloaded by PURDUE UNIV on May 23, 2016 | http://pubs.acs.org Publication Date: June 1, 1978 | doi: 10.1021/bk-1978-0065.ch018

Union Carbide Corporation, Chemicals and Plastics, Bound Brook, N J 08805

Multitubular reactor design methods based on the assumption that the tube bundle can be represented by a single, t y p i c a l tube are adequate when the operating conditions are remote from regions of high performance, and where maldistribution of the feed to the tubes cannot occur. In other circumstances, s i g n i f i c a n t l y different conditions are found i n the tubes depending on t h e i r position i n the bundle. Moreover, when optimal performance i s being sought, it is often the case that the preferred operating state is i n a region where it is no longer possible to make simplifying assumptions, since it is essential to have r e l i a b l e information on the detailed behaviour of the system. This i s required not only to ensure that adequate flexibilty of operation is possible, but also to be able to evaluate what potential hazardous conditions might a r i s e . To do this, it i s essential to take account o f the multitubular characteristics explicitly and to examine the effects of the coolant flow because s i g n i f i c a n t l y different patterns of behaviour are possible both in respect to s t a b i l i t y as w e l l as having an important bearing on the economic attractiveness of using certain reactor configur ations. At the design stage, the decisions to be taken i n respect of the l a t t e r are obviously of some importance. These considerations will necessarily be influenced by the particular operations, reaction scheme and many other specific factors. Nevertheless, it would be useful to be able to suggest general guide-lines as to how to select initial configurations so as to realise particular operational characteristics. Despite i t s importance, very l i t t l e work has been done i n t h i s area, perhaps because of the considerable amount of inform ation on s h e l l and tube heat exchangers. Unfortunately, t h i s expertise i s not d i r e c t l y applicable. For example, for highly exothermic reactions of the type to be considered here, i t i s better to avoid counter-current flow between coolant and reactants because of operational d i f f i c u l t i e s which can a r i s e . For this reason, i t i s the intention of t h i s work to explore the general operating characteristics o f both co- and counter-current ©

0-8412-0401-2/78/47-065-214$05.00/0

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


18.

MCGREAVY

A N D DUNBOBBIN

Flexibility of Multitubular Reactors

215

u n i t s t o enable c r i t e r i a f o r design t o be e s t a b l i s h e d . The i n s i g h t gained from t h i s can be used t o d e v i s e a l t e r n a t i v e arrangements which i s a b l e t o take advantage o f each o f the above modes w h i l e a l l o w i n g adequate f l e x i b i l i t y o f o p e r a t i o n . I n a d d i t i o n , v a l u a b l e i n f o r m a t i o n can be o b t a i n e d as t o how t o deal w i t h c o n t r o l problems. As w i t h the simple heat exchanger systems, the counterc u r r e n t r e a c t o r w i l l g e n e r a l l y r e q u i r e a s m a l l e r heat t r a n s f e r area than a co-current system f o r the same thermal l o a d i n g . In t h i s sense, comparison o f the two systems i s not s t r a i g h t f o r w a r d . But f o r convenience, t h e f o l l o w i n g d i s c u s s i o n w i l l be based on the assumption t h a t a common s h e l l and tube arrangement i s being used and the d i f f e r e n t arrangements are obtained by changing connections a t the i n l e t and o u t l e t n o z z l e s , where a p p r o p r i a t e . As a l r e a d y i n d i c a t e d , the p r i n c i p a l concern i s w i t h f l e x i b i l i t y and o p e r a b i l i t y , which would o b v i o u s l y have t o be considered i n relation to capital cost. Although t h i s w i l l not be e x p l o r e d f u r t h e r , i t can be i n c o r p o r a t e d i n t o the procedure o u t l i n e d here, when more d e t a i l e d s t u d i e s are being c a r r i e d out ( O . Model o f the M u l t i t u b u l a r Reactor The f o r m u l a t i o n o f a mathematical d e s c r i p t i o n o f a m u l t i t u b u l a r r e a c t o r poses no s p e c i a l problems, although the comput a t i o n a l e f f o r t needed t o s o l v e the equations can be v e r y c o n s i d e r a b l e , p a r t i c u l a r l y where extreme o p e r a t i n g c o n d i t i o n s are being e x p l o r e d . I t i s under these circumstances t h a t s i g n i f i c a n t i n t e r a c t i o n occurs between the tubes a s a r e s u l t o f the d i s t r i b u t i o n o f the coolant i n the s h e l l . Dunbobbin (J_) and Adderley (2) have shown t h a t u n l e s s these e f f e c t s are accounted f o r i n the heat balances,the r e s u l t s are o f l i m i t e d v a l u e . C l e a r l y , i t would be d e s i r a b l e t o have a general a n a l y t i c a l framework which could be used t o i n d i c a t e when d i f f i c u l t c o n d i t i o n s might a r i s e and how they could be handled. A t the present time, t h i s i s not p o s s i b l e , so a technique must be developed which can demonstrate the broad c h a r a c t e r i s t i c s o f systems and enable the r e l e v a n t i n s i g h t t o be g a i n e d . As a s t e p i n t h i s d i r e c t i o n , a case study o f a r e p r e s e n t a t i v e o f a c l a s s o f important problems o f f e r s a s u i t a b l e compromise, and w i l l be the approach adopted here. The p a r t i c u l a r system to be considered belongs t o the important c l a s s o f c a t a l y t i c p a r t i a l o x i d a t i o n r e a c t i o n s , as represented by the p r o d u c t i o n o f m a l e i c anhydride from benzene. Although these are b a s i c a l l y complex r e a c t i o n schemes, i n t h e i r l i m i t i n g behaviour, where temperature runaway and o t h e r i n s t a b i l i t i e s develop, the k i n e t i c equations approximate a s i n g l e i r r e v e r s i b l e r e a c t i o n t o the complete o x i d a t i o n products. As f a r as heat e f f e c t s are concerned, i t i s then p o s s i b l e t o d i s p l a y a l l t h e important p a t h o l o g i c a l f e a t u r e s . The f o l l o w i n g a n a l y s i s assumes t h a t such an approximation i s acceptable f o r the purposes o f


CHEMICAL REACTION ENGINEERING—HOUSTON

216


i l l u s t r a t i o n , but i n no way r e s t r i c t s the v a l i d i t y o f the procedure. More complex schemes would merely r e q u i r e a much more d e t a i l e d analysis. An approximation which adequately represents a continuum v e r s i o n o f the system shown i n f i g u r e 1 can be obtained by r e p l a c i n g the equation f o r the heat balance on the coolant by a s e r i e s o f m i x i n g c e l l s ( j j , where a volume element o f the c o o l a n t , together w i t h a small group o f r e a c t o r tube s e c t i o n s , i s c o n s i d ered i n one o f the passes. The dimensionless heat balance f o r a t y p i c a l c e l l are g i v e n by the a p p r o p r i a t e equations (1) and (2) below: Co-current flow. Nu Τ

= Τ c

C

(i)

1

+ (i-D

Counter-current f l o w .

^ Nu

Τ

= Τ c

c

(i)

w

(i-t)

1

(T-T C

G — c J z

)dz (i-D

(2)

2

Figure 1 i n d i c a t e s the nomenclature used i n d e s c r i b i n g the r e a c t o r . The s u b s c r i p t i r e f e r s t o the i t h c e l l , numbered from the c o o l a n t i n l e t (co-current case), or o u t l e t (counter-current). The s o l u t i o n o f the model i s obtained by c o u p l i n g the tubeside r e a c t o r equations w i t h equation (!) o r (2) as a p p r o p r i a t e , and u s i n g a marching procedure to pass through the assembly from c e l l to c e l l , i t e r a t i o n around a guessed o u t l e t coolant temperature being necessary i n the counter-current case. For the r e a c t i o n i n s i d e the tube, the dimensionless mass and energy balances, w i t h the u s u a l assumptions, become (J_, Z) f o r the s i n g l e main r e a c t i o n : Fluid Field. dc

Sî

. +

n G

2

«Φ ;P- - G dz 4

Λ

θ

2

/

_

η

e

(t-T) +

J

- ?

*P

2Nu * ™ -χ G

3

c

=

0

(T-T ) = C

( 3 )

0


(4)

18.

MCGREAVY

with i n i t i a l

A N D DUNBOBBIN

conditions:


Τ

c

217

Τ ζ

0

ζ

Ο

c

Reaction on the S o l i d . The r e a c t i o n r a t e on the c a t a l y s t can be e a s i l y c a l c u l a t e d i f t h e p e l l e t i s assumed t o be i s o t h e r m a l ( 1 , 2, 3 ) , a t a temperature g i v e n by:


Β Sh

A

(r-g) (5)

t = Τ + (sg + r ) T h i s equation must be solved i t e r a t i v e l y t o f i n d the temperature and hence the r e a c t i o n r a t e .

solid

D e t a i l s o f the method o f the s o l u t i o n can be found elsewhere (4), but the r e s u l t i n g p r o f i l e s g i v e d e t a i l e d information on t h e coolant temperature and c o n d i t i o n s i n t h e r e a c t o r tubes. It is a l s o p o s s i b l e t o see how heat i s e f f e c t i v e l y passed between tubes and hence which are most v u l n e r a b l e t o the development o f i n s t a b i l ities. Each case requires c a r e f u l scanning o f the r e s u l t s , but the f i n d i n g s can be summarized i n the manner i n d i c a t e d below. N e v e r t h e l e s s , i t should be noted that i t i s not p o s s i b l e i n general t o p r e d i c t , a p r i o r i , which p a r t o f the bundle c o n t a i n s the c r i t i c a l tube. I t w i l l a l s o depend on whether m a l d i s t r i b u t i o n e f f e c t s are present. The number o f c e l l s used w i l l c l e a r l y depend on the nature o f the problem, but f o r the system considered here, and t o c a r r y out a reasonable d e t a i l e d survey, i t i s necessary t o use about 10 c e l l s f o r each o f the c o o l a n t s i d e passes. T y p i c a l r e s u l t s f o r the dimensionless p r o f i l e s f o r tubes a t o p p o s i t e s i d e s o f t h e bundle are shown i n f i g u r e 2 i . e . i d e n t i f i e d as tubes 1 and 50: these are f o r the row o f tubes a c r o s s the d i a m e t e r . The very d i f f e r e n t c o n d i t i o n s i n s i d e the tubes a t these p o s i t i o n s i s apparent. Comparison o f Reactor C o n f i g u r a t i o n s The data i n t a b l e I are f o r the p a r t i a l o x i d a t i o n o f benzene and can be used t o explore how a l t e r n a t i v e mechanical c o n f i g u r a t i o n s a f f e c t the o p e r a t i o n . I n adopting t h i s approach, i t w i l l be appreciated t h a t a number o f d i f f e r e n t bases f o r t h e comparison are p o s s i b l e . For convenience a t t e n t i o n w i l l be confined t o those f a c t o r s a f f e c t i n g the o p e r a b i l i t y o f a g i v e n , f i x e d s i z e reactor u n i t . A l t e r n a t i v e c o n f i g u r a t i o n s are e a s i l y derived from t h i s by a p p r o p r i a t e changes a t the i n l e t and o u t l e t , together w i t h any a s s o c i a t e d r e l o c a t i o n o f the b a f f l e p l a t e s .



218

Table I G

2

G

3

G


= 0.0849;

0

= 10°

= 0.84

Β

= 4.602x1 θ"" ;

;

; 5

G

( inlet)

= 76.85 ; A

A

= 500.0 ;

Nu

=

1.0

= 98.25

G

0

4

Sh

Data used i n the case s t u d i e s

c w

= 14.6

;

Τ

= 0.03884 0

T o t a l No. o f tubes = 2,500.

The obvious d i f f e r e n c e between the heat t r a n s f e r mechanism o f the co- and c o u n t e r - c u r r e n t l y cooled r e a c t o r s i s t h a t the former operates w i t h a feed-forward and the l a t t e r a feed-back o f heat along the r e a c t o r tubes. Thus,co-current r e a c t o r s i n t r o d u c e the c o l d c o o l a n t where t h e r e i s a high r e a c t a n t c o n c e n t r a t i o n and heated coolant promotes r e a c t i o n i n the l e a n r e a c t a n t regions towards the tubeside e x i t . Counter-current r e a c t o r s on the o t h e r hand have pre-heated coolant a f f e c t i n g high r e a c t a n t c o n c e n t r a t i o n s and c o l d coolant i n t h e e x i t regions o f the t u b e s i d e . Thus, the r e a c t i o n i s e s s e n t i a l l y r e s t r i c t e d t o the i n i t i a l p o r t i o n s o f t h e bed. A l s o , because o f the h i g h e r coolant temperatures i n t h e r e g i o n o f t h e tube-side h o t s p o t s , the counter-current r e a c t o r g i v e s higher peak temperatures and conversions. However, because o f t h e s m a l l zone a v a i l a b l e f o r high r e a c t i o n , high con v e r s i o n o f t e n r e s u l t s i n temperature runaway on the t u b e s i d e , making the co-current system more a t t r a c t i v e i n many circumstances. Thus, w h i l e counter-current flow may reduce the s i z e o f r e a c t o r to achieve a given conversion, i t has u n d e s i r a b l e f e a t u r e s which can l e a d to d i f f i c u l t o p e r a t i o n . The above o b s e r v a t i o n s suggest an a l t e r n a t i v e c o n f i g u r a t i o n might make i t p o s s i b l e to improve designs. Thus, i f an arrange ment such as t h a t shown i n f i g u r e 3 i s used, i t r e q u i r e s no complex s h e l l - s i d e m o d i f i c a t i o n s and i s achieved very simply by having the coolant e n t e r i n g at pass 2 and l e a v i n g a t passes 1 and 4, a t the c o s t o f a s m a l l amount o f e x t r a p i p i n g . With t h i s scheme the counter-current stream i s heated by coolant pass 2 before e n t e r i n g pass 1, so t h a t the incoming reactant i s contacted by warm c o o l a n t . Since the flowpath i s not as long as i n a conventional counter-current r e a c t o r , the coolant i s not heated as much and so the very l a r g e temperature peaks o f these r e a c t o r s can be avoided. The co-current stream i s a l s o heated and causes r e a c t i o n i n the lower c o n c e n t r a t i o n regions o f the bed. I t there f o r e makes i t p o s s i b l e t o take advantage o f both the co- and counter-current systems, so t h a t the incoming r e a c t a n t s are con t a c t e d by warm c o o l a n t , thus ensuring t h a t a u s e f u l amount o f r e a c t i o n takes place e a r l y i n the bed, and any r e a c t a n t s l e f t i n the l a t t e r h a l f o f the r e a c t o r are a l s o contacted w i t h warmer c o o l a n t , which w i l l thus i n c r e a s e the r e a c t i o n r a t e . In e f f e c t ,


18.

MCGREAVY

AND

DUNBOBBIN


219

COOLANT IN

J

1-

OUT

L

RE ACTA NT

GASES

—I COOLANT PASS 1


TUBE NO.

COOLANT PASS 2

Figure 1. General representation of the reactor indicating the notation used in describing it

0.046i

coolant

velocity 0 . 0 5

m/sec

"

0.1

"

"

0.2

»

0.038!

Figure 2. Typical temperature profiles in reactor tubes at positions 1 and 50 for various flows

COOLANT OUT

C O O L A N T PASS: 1

Figure 3.

Mixed flow reactor



220

CHEMICAL

REACTION

ENGINEERING—HOUSTON

t h i s mixed-flow c o n f i g u r a t i o n i n t r o d u c e s the c o l d e s t coolant i n the p o s i t i o n where i t i s most e f f e c t i v e , namely a t the tubeside hotspot, and i t a l s o provides a reasonable degree o f f l e x i b i l i t y . Other methods o f i n c r e a s i n g the heat t r a n s f e r i n the r e g i o n o f t h e hotspot do not tend t o have the same degree o f a d a p t a b i l i t y during operation. P a r i s and Stevens (4) devised a complex s h e l l s i d e arrangement f o r a s i n g l e tube r e a c t o r and s e v e r a l workers (5, 6, 7) have considered u s i n g v a r i o u s s i z e d packings o r i n e r t spheres a t d i f f e r e n t p o i n t s i n the tubes. These methods, w h i l e o f t e n s u c c e s s f u l , assume t h a t design s p e c i f i c a t i o n s can, and w i l l be maintained. An advantage o f the above method i s t h a t i t can be used even w i t h e x i s t i n g tube bundles w i t h very l i t t l e s t r u c t u r a l change. Mixed Flow C o n f i g u r a t i o n s To see the inherent advantages o f the mixed f l o w system, i t i s u s e f u l to compare systems f o r each o f the main d i s t r i b u t i o n s i n each l o o p , a t constant t o t a l mass f l o w r a t e o f c o o l a n t . The u n i t s are a l s o taken t o be the same s i z e , the o n l y d i f f e r e n c e being the r o u t i n g o f the c o o l a n t f l o w . T h i s means t h a t although the residence time o f the c o o l a n t i s the same i n the co- and counterc u r r e n t r e a c t o r s , i t w i l l be s m a l l e r i n the mixed flow c o n f i g u r a tion. C o n t r o l can be e x e r c i s e d by a d j u s t i n g the r e l a t i v e flow r a t e s i n the c i r c u i t , and t h i s i s i l l u s t r a t e d by u s i n g the following distributions: 1.

\ the c o o l a n t flow from pass 2 flows c o u n t e r - c u r r e n t l y i n t o pass 1.

2.

% the coolant flow from pass 2 flows c o u n t e r - c u r r e n t l y i n t o pass 1.

3.

% the c o o l a n t f l o w from pass 2 flows c o u n t e r - c u r r e n t l y i n t o pass 1.

The f l o w r a t e through coolant pass 2 i s always the same as i n the co- and counter-current cases. The tubeside temperature p r o f i l e s o f tube 1 f o r the three types o f mixed flow system, together w i t h the p r o f i l e f o r the coand counter-current r e a c t o r s , are g i v e n i n f i g u r e 4. In a l l cases, the tube i n the bundle r e p r e s e n t i n g the 'worst c o n d i t i o n s has been used. An important o b s e r v a t i o n i s t h a t i t i s not always the same one. The lowest, and most s t a b l e , temperature p r o f i l e i s obtained from the co-current r e a c t o r , w i t h the l a r g e s t tempér ature peak being given by the counter-current. The three mixed f l o w p r o f i l e s are intermediate to these, w i t h t h e type 3 g i v i n g the f l a t t e s t p r o f i l e . F i g u r e 5 uses the Τ versus Β s t a b i l i t y p l o t s proposed by McGreavy and Adderley (S) t o examine the co1


18.

MCGREAVY


0.05

AND

DUNBOBBIN


221

r

Figure 4.

The co-current, counter-current, and mixed-flow tubeside tempera ture profiles for tube Una four-coolant pass reactor

0.05r

Figure 5.

Τ vs. Β stability plot comparing the co-current, counter-current, and mixedflow four-coolant pass reactors




222

c u r r e n t , counter-current and type 3 mixed f l o w systems a t a constant c o o l a n t f l o w r a t e expressed by the dimensionless parameter GG = 4.0. At t h i s v a l u e , the l a t t e r c o n f i g u r a t i o n i s a t the l i m i t o f s t a b i l i t y w i t h respect t o temperature runaway. To compare performance, i t i s s u f f i c i e n t t o look a t the conversions i n each case which correspond t o the l i m i t o f s t a b i l i t y , since t h i s i n d i c a t e s the most favourable conversions. Making use o f p l o t s s i m i l a r to f i g u r e 5, i t may be shown t h a t f o r the same parameter values and o p e r a t i n g c o n d i t i o n s , the l i m i t o f s t a b i l i t y o f the counter-current r e a c t o r i s GG = 5.0 and the co-current GG = 2.0 (1_). These would correspond w i t h a maximum temperature r i s e o f 25.1 Κ i n t h e mixed f l o w type 3 r e a c t o r a t GG = 4.0. Hence, a t these c o n d i t i o n s , the coolant temperature r i s e i s much higher f o r the co-current r e a c t o r , being over t w i c e t h a t f o r the counterc u r r e n t system, but w i t h a much lower coolant f l o w r a t e f o r the same conversion. The co-current r e a c t o r , w i t h i t s low coolant f l o w r a t e (low value o f GG) e x h i b i t s the best behaviour o f a l l the c o n f i g u r a t i o n s . The disadvantage i s the high coolant temperature r i s e (up to 30K). The main advantage o f the mixed flow system i s t h a t , w i t h c o o l a n t f l o w r a t e s lower than those f o r the counter-current system, con v e r s i o n s o f comparable magnitude can be o b t a i n e d , which, though they r e s u l t i n higher c o o l a n t temperature r i s e s , are s t i l l l e s s than those f o r co-current systems. Furthermore, although t h i s study i s i n terms o f a p a r t i c u l a r system, w i t h o n l y adjustment i n the coolant f l o w paths, f u r t h e r f l e x i b i l i t y i s p o s s i b l e by a s u i t a b l e choice o f the p o s i t i o n o f the b a f f l e s , but t h i s must be regarded as a design r a t h e r than an o p e r a t i o n a l v a r i a b l e . The need to i n t r o d u c e some co-current flow f o r the c o o l a n t , d e s p i t e i t s unfavourable e f f e c t on the s i z e o f the r e a c t o r i s to ensure t h a t the r e s u l t i n g a x i a l temperature p r o f i l e i n the tubes i s f l a t t e r , and so cause the thermal l o a d i n g t o be more evenly d i s t r i b u t e d along the l e n g t h . This i s an important advantage o f the mixed flow arrangement. The d e t a i l e d model must be solved to i d e n t i f y the tube which i s s u b j e c t t o the g r e a t e s t r i s k o f damage, however. U n f o r t u n a t e l y , i t i s not always p o s s i b l e t o assume i t w i l l be the same one, as the o p e r a t i n g c o n d i t i o n s change. Once i d e n t i f i e d , the i n f o r m a t i o n can be summarized i n diagrams such as f i g u r e 5. Other p l o t s can a l s o be prepared which g i v e v a l u a b l e i n f o r m a t i o n regarding the i n f l u e n c e o f the coolant flow r a t e parameter, GG ( 0 . Conclusions A comparison o f co- and c o u n t e r - c u r r e n t l y cooled has demonstrated t h a t , although co-current f l o w has some advantages, the temperature r i s e o f the coolant i s g r e a t e r , because o f t h e lower f l o w r a t e s which are p o s s i b l e . There i s a l s o g r e a t e r scope f o r a d j u s t i n g o p e r a t i n g c o n d i t i o n s . Using a mixed f l o w


18.

M C G R E A V Y A N D DUNBOBBIN

system, however, i t low coolant pumping temperature r i s e s . d i s t r i b u t i o n can be greater operational


223

i s p o s s i b l e t o take advantage o f r e l a t i v e l y c o s t s (lower flow rates) w i t h o u t excessive A t the same time, a more even temperature achieved w i t h t h e a d d i t i o n a l b e n e f i t o f flexibility.


Nomenclature A°

= Arrhenius pre-exponential f a c t o r .

Β

=

b C ,

= =

Q

B C

ο radius o f p e l l e t . reference concentration and f l u i d concentration respectively. s p e c i f i c heats o f f l u i d and coolant r e s p e c t i v e l y ,

C , C = ρ pc D

=

p

Ε e, e h g K

= a c t i v a t i o n energy o f r e a c t i o n . = voidage o f f i x e d bed and tube bundle r e s p e c t i v e l y . = p e l l e t t o f l u i d heat t r a n s f e r c o e f f i c i e n t , = tanh ( r ) . = effective i n t e r s t i t i a l radial conductivity i n f l u i d phase. = thermal c o n d u c t i v i t y o f c o o l a n t .

c

f

k

g

L L

c D

D L M c R R r s

=

f l u i d t o p e l l e t mass t r a n s f e r c o e f f i c i e n t ,

=

diameter o f tube bundle,

=

distance between b a f f l e p l a t e s .

= length o f r e a c t o r tube. = mass f l o w r a t e o f coolant, = =

r e a c t o r tube r a d i u s . gas constant.

V(2t))

= 0exp(=

= =

(Sh /2 - 1) P c o o l a n t , f l u i d and p e l l e t respectively. o v e r a l l f l u i d t o coolant heat t r a n s f e r c o e f f i c i e n t , f l u i d a n d coolant i n t e r s t i t i a l v e l o c i t y r e s p e c t i v e l y .

p,

=

d e n s i t y o f f l u i d and coolant

φ

= heat o f r e a c t i o n , = Q exp (-1/(2T)).

t T

effective radial diffusivity within catalyst pellet.

c

9

T

f

9T

A

=

c

U u, u

θ

p

c

T

e

m

e

r

a

t

u

r

e

=

V(A/D ).

=

1.5 S h

o

f

respectively.

p

A

( r - g)/ ( φ

2

(sg + r ) )



224

Dimensionless B

Groups D

C R

0

=

("ΔΗ)

C

=

concentration =

p

q

/(2bhE).

g

cVC . Γ

_ G

m

=

4nK e f


ο

C c pc L

B

GG

= G /G c c reference

G

2

=

(1 - e) L D / ( b ue)

G

3

=

R

G

4

=

(1 - e) 3hL/(bpue C )

Nu w

=

RU/(K^ e ) . f

Nu * w

=

4 Nu / ( 4 + Nu ) w w

9

; G . = 98.25. c reference

2

p

2

up C / ( L K ) f

Sh = 2bkg /D A Ρ Τ, T , t = f l u i d , coolant and p e l l e t temperature r e s p e c t i v e l y , T R/E, T R^/E, T R^/E. A

f

ζ

=

c

p

A x i a l position i n reactor.

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8.

Dunbobbin, B.R. Ph.D. Dissertation, University of Leeds (1976). Adderley, C.I. Ph.D. Dissertation, University of Leeds (1973). Thornton, J . M . Ph.D. Dissertation, University of Leeds (1970). Paris, J . R . and Stevens, W.F. Fourth European Symposium on Chemical Reaction Engineering, Brussels (1968), 73, Pergamon Press (1971). Brusset, H. et al, Chem.Eng.Sci. (1972), 27, 1945. Calderbank, P.H. et al. Fourth European Symposium on Chemical Reaction Engineering, Brussels (1968), 93 Pergamon Press (1971). Stewart, W.E. and Sorensen, J . P . F i f t h European/Second International Symposium on Chemical Reaction Engineering, Amsterdam (1972), B8-75. McGreavy, C. and Adderley, C.I., Chem.Eng.Sci. (1973) 28, 577.


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