The Optimal Design of a Reactor for the Hydrogenation of

14 Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on November 22, 2014 | http://pubs.acs.org Publication Date: December 9, 1984 | doi: 10.1021/bk-1984-0237.ch014

The Optimal Design of a Reactor for the Hydrogenation of Butyraldehyde to Butanol J.B.CROPLEY,L.M.BURGESS, andR.A.LOKE Union Carbide Corporation, South Charleston, WV 25303

The optimal design of a plant-scale catalytic reactor must effectively u t i l i z e capital, energy, and raw material resources to achieve the lowest possible product cost, consistent with constraints imposed by business plans and the overall plant environment. The paper illustrates an effective strategy that was used recently to develop the optimum reaction system design for a real process -- the hydrogenation of butyraldehyde to butanol -- in a total time of less than six months. The basic approach involved the development of Langmuir-Hinshelwood kinetics for the reaction from Berty autoclave data, incorporation of these kinetics into a tubular reactor simulation and optimization program, validation of the combined reaction and reactor models with data from an existing pilot-plant, and constrained optimization using easily-developed economic c r i t e r i a . The f i n a l design exhibited superior economic performance, largely as a result of greater catalyst productivity and more efficient energy u t i l i z a t i o n and integration.

Union Carbide manufactures normal- and i s o - b u t a n o l by the hydrogénation of the corresponding butyraldehydes produced by i t s rhodium-catalyzed, low-pressure Oxo process. The hydrogénation process has been noted f o r a long time as a h i g h l y - s e l e c t i v e , economical route to h i g h - p u r i t y b u t a n o l . Nevertheless, changes i n the r e l a t i v e costs of c a p i t a l , energy, and raw m a t e r i a l s over the l a s t s e v e r a l years l e d to a review of a l t e r n a t e technologies f o r the hydrogénation of butyraldehyde, followed by complete o p t i m i z a t i o n of some of the more promising candidates. T h i s paper describes the o p t i m i z a t i o n of one of these, the vapor-phase 0097-6156/84/0237-0255$06.00/0 © 1984 American Chemical Society

In Chemical and Catalytic Reactor Modeling; Dudukovi, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

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Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on November 22, 2014 | http://pubs.acs.org Publication Date: December 9, 1984 | doi: 10.1021/bk-1984-0237.ch014

c a t a l y t i c hydrogénation of butyraldehyde i n a shell-and-tube fixed-bed c a t a l y t i c converter. The o p t i m i z a t i o n study comprised s e v e r a l d i s t i n c t steps: ο

I d e n t i f i c a t i o n of the most s u i t a b l e c a t a l y s t ,

ο

Development of r e a c t i o n k i n e t i c s models f o r primary and byproduct r e a c t i o n s ,

ο

Development of r e a c t o r s i m u l a t i o n and o p t i m i z a t i o n computer programs s p e c i f i c a l l y f o r the vapor-phase tubular r e a c t o r system,

ο

V a l i d a t i o n of the s i m u l a t i o n models using e x i s t i n g c a t a l y t i c p i l o t - s c a l e equipment,

ο

Development of economic c r i t e r i a that could be evaluated r a p i d l y by the o p t i m i z a t i o n program, and f i n a l l y ,

ο

Reaction system design and o p t i m i z a t i o n .

I d e n t i f i c a t i o n of the Most S u i t a b l e C a t a l y s t The most important c h a r a c t e r i s t i c s of a hydrogénation c a t a l y s t are, f o r a p a r t i c u l a r r e a c t i o n , i t s p r o d u c t i v i t y and s e l e c t i v i t y to the d e s i r e d product over economical ranges of temperature and pressure. These ranges i n turn depend h e a v i l y upon the o v e r a l l plant context i n which the c a t a l y s t i s to be used. For example, the most economical pressure range f o r t y p i c a l vapor-phase processes i s between about f i v e and t h i r t y atmospheres, based on both equipment and energy c o s t s . S i m i l a r l y , the r e a c t i o n temperature should permit the heat of r e a c t i o n to be recovered as steam a t pressures between perhaps 3 and 45 atmospheres, corresponding roughly to 134 and 258°C. The u s e f u l and economical ranges f o r both the r e a c t i o n temperature and pressure vary widely w i t h i n these ranges from one p l a n t to another and so i t i s important when o p t i m i z i n g a process design f o r a p a r t i c u l a r l o c a t i o n to understand e x a c t l y how the process w i l l f i t i n t o the o v e r a l l p l a n t , e s p e c i a l l y from an energy conservation and u t i l i z a t i o n standpoint. I t i s apparent that optimum u t i l i z a t i o n of raw m a t e r i a l s , c a p i t a l , and energy resources w i l l i n f l u e n c e the choice of c a t a l y s t . C a t a l y t i c a c t i v i t y alone i s not a s u f f i c i e n t c r i t e r i o n . A h y p o t h e t i c a l c a t a l y s t might be wonderfully a c t i v e and s e l e c t i v e a t 25°C and one atmosphere, but i t would be d i f f i c u l t to b u i l d an economical process around i t . Union Carbide's Research and Development Department maintains a c t i v e programs i n c a t a l y s t research and screening f o r a number of major processes, and the candidate c a t a l y s t was s e l e c t e d f o r



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t h i s p r o j e c t on the basis of i t s chemical performance at a t t r a c t i v e temperatures and pressures. We have not discussed c a t a l y s t l i f e as one of the determinants i n the s e l e c t i o n of a c a t a l y s t , although i t obviously can be of c r i t i c a l importance. In the absence of poisoning, hydrogénation c a t a l y s t s f r e q u e n t l y l a s t f o r s e v e r a l years i n plant s e r v i c e , and c a t a l y s t costs are thus r e l a t i v e l y minor i n the o v e r a l l product cost breakdown. Candidate c a t a l y s t s that d i d not e x h i b i t e x c e p t i o n a l l i f e i n l a b o r a t o r y t e s t s were simply excluded from c o n s i d e r a t i o n f o r our purposes. Development of Reaction K i n e t i c s Models In r e a c t i o n engineering, k i n e t i c models are used to p r e d i c t r e a c t i o n rates at s p e c i f i e d c o n d i t i o n s of temperature and the p a r t i a l pressures or concentrations of reactants and products. The emphasis must be, t h e r e f o r e , upon accuracy of p r e d i c t i o n , even at the expense, i f need be, of mechanistic r i g o r . For t h i s reason, k i n e t i c models f o r design purposes should be developed using the same p e l l e t s i z e and geometry as w i l l be used i n the commercial process, and over the ranges of temperature and component p a r t i a l pressures expected f o r i t . F i n a l l y , the k i n e t i c s should be studied at r e a l i s t i c p l a n t - s c a l e gas v e l o c i t i e s so that the data are not i n f l u e n c e d by p h y s i c a l transport phenomena l i k e heat- and mass-transfer. Note that only temperature and p a r t i a l pressures or concentrations have been mentioned as v a r i a b l e s . For a c a t a l y t i c r e a c t i o n , these are the only v a r i a b l e s of importance from a k i n e t i c s standpoint. Time v a r i a b l e s l i k e s p a c e - v e l o c i t y , space-time, or residence-time, are r e a c t o r v a r i a b l e s rather than r e a c t i o n v a r i a b l e s , and w i l l be i n v o l v e d i n the development of the r e a c t o r s i m u l a t i o n model. The choice of experimental r e a c t o r i s important to the success of the k i n e t i c modeling e f f o r t . The short bench-scale r e a c t i o n tubes sometimes used f o r s t u d i e s of t h i s s o r t g i v e l i t t l e or no i n s i g h t i n t o best mathematical form of the k i n e t i c model, conduct the r e a c t i o n over v a r y i n g temperatures and p a r t i a l pressures along the tube, and i n e v i t a b l y operate at v e l o c i t i e s that are a small f r a c t i o n of those to be encountered i n the p l a n t - s c a l e r e a c t o r . Rate models from l a b o r a t o r y r e a c t o r s of t h i s s o r t r a r e l y scale-up w e l l . The l a b o r a t o r y d i f f e r e n t i a l r e a c t o r s u f f e r s from v e l o c i t y problems but does at l e a s t conduct the r e a c t i o n at known and r e l a t i v e l y constant temperature and p a r t i a l pressures. However, one u s u a l l y runs i n t o accuracy problems because c a l c u l a t e d r e a c t i o n r a t e s are based upon the small observed d i f f e r e n c e s i n concentration between the r e a c t o r i n l e t and o u t l e t . In recent years these problems have been l a r g e l y overcome with the development of gas-phase continuous back-mixed r e a c t o r s l i k e the Berty r e a c t o r . This r e a c t o r r e c i r c u l a t e s the gas




258

r a p i d l y through the c a t a l y s t bed and thus operates at uniform temperatures and p a r t i a l pressures, and g e n e r a l l y at rather high conversion l e v e l s . I t i s necessary, however, to c o n t r o l the o u t l e t concentrations of both reactants and products i n the course of the experimental program because the temperatures and p a r t i a l pressures i n s i d e the r e a c t o r are the same as those at the o u t l e t , r a t h e r than the i n l e t . G e n e r a l l y , i t i s necessary to feed r e a c t i o n products as w e l l as reactants to the r e a c t o r i n order to c o n t r o l both product and reactant concentrations independently. A Berty r e a c t o r was used i n the study described here. For more complete d i s c u s s i o n s of experimental r e a c t o r s the reader i s r e f e r r e d to S a t t e r f i e l d (1) and to Berty ( 2 ) (3)· The experimental program f o r the k i n e t i c study comprised only 17 experiments a l t o g e t h e r , but the formal program was not s t a r t e d u n t i l the a b i l i t y to o b t a i n q u a l i t y data had been e s t a b l i s h e d . This meant that we had fine-tuned a n a l y t i c a l methods and experimental procedures so that good m a t e r i a l balances could be obtained r o u t i n e l y at any d e s i r e d r e a c t i o n c o n d i t i o n s . A l s o , by the time the formal program was s t a r t e d , the c a t a l y s t a c t i v i t y i n the autoclave had d e c l i n e d to a r e l a t i v e l y constant l e v e l from the h y p e r a c t i v i t y c h a r a c t e r i s t i c of new hydrogénation c a t a l y s t s . The core of the experimental program comprised a small s t a t i s t i c a l l y - d e s i g n e d set of eleven experiments i n four variables: temperature, and the p a r t i a l pressures of hydrogen, butyraldehyde, and butanol. (For d i s c u s s i o n s of the design of k i n e t i c experiments, see Timoshenko and Cropley (.5).) Six a d d i t i o n a l experiments were made i n order to approach d e s i r e d c o n d i t i o n s more c l o s e l y , and u l t i m a t e l y a l l seventeen were used f o r model development. Both butyraldehyde and butanol were fed to c o n t r o l the o u t l e t p a r t i a l pressures a t the d e s i r e d l e v e l s . We used h i g h - p u r i t y mixed normal- and iso-butyraldehyde and butanol f o r our work. L i t t l e d i f f e r e n c e i n r e a c t i o n k i n e t i c s were observed with e i t h e r normal- or i s o - s p e c i e s . The k i n e t i c model developed from these data f o r the r e v e r s i b l e production of butanol i s of the form: , k

E

ο

/

R

T

e

r +

K

P

p

-E/RT

P - Î L H2 BAL K sa

1 BAL

+

K

P

2 B0H

+

ρ

K

P 3

H

BOL

2>

The expression f o r the e q u i l i b r i u m constant K q was developed from component standard f r e e energies of formation published by S t u l l (6^) and has the general form e

Keq = K e - A H / R 0

where Δ Η -

r

T >

i s the o v e r a l l heat of r e a c t i o n .



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The k i n e t i c parameters were evaluated n u m e r i c a l l y using the h e u r i s t i c procedures of Cropley (5)· The a l g e b r a i c form of the k i n e t i c model had been shown p r e v i o u s l y to describe adequately the k i n e t i c s of r e a c t i o n s of t h i s type. Note that i n s p i t e of i t s apparent complexity, only one parameter i s a s s o c i a t e d with each v a r i a b l e . The b a s i c two l e v e l experimental design i s thus adequate i f the form of the r a t e law i s f i x e d , though one might l i k e to have the time to develop a more complete data s e t . The o v e r a l l q u a l i t y of the model i s e x c e l l e n t , with a c o e f f i c i e n t of determination of 0.987 and a r e l a t i v e standard d e v i a t i o n of the e r r o r of 14.5 percent. Nonetheless, the values f o r K i , K2, and K3 are j o i n t l y confounded with one another and thus represent only one of many f a m i l i e s of values f o r the parameters that would f i t the data v i r t u a l l y e q u a l l y w e l l . This means that i n f e r e n c e s that these parameters r e a l l y represent chemisorption e q u i l i b r i u m constants are unwarranted, but the model i s nonetheless u s e f u l f o r i t s intended purpose. I f i t had been d e s i r a b l e to do so, a d d i t i o n a l experiments could have been run to narrow the j o i n t confidence i n t e r v a l s of these parameters. Simpler models f o r byproduct formation were developed from the same set of experiments. These models are of simple powers e r i e s or exponential form and serve adequately to p r e d i c t the small amounts of byproducts formed by the r e a c t i o n . Note that the mathematical form of the model i m p l i e s that the r a t e - l i m i t i n g step i s a d u a l - s i t e surface r e a c t i o n between chemisorbed hydrogen and chemisorbed butyraldehyde, and that the reverse r e a c t i o n i s the monomolecular dehydrogenation of chemisorbed butanol. Models of t h i s s o r t should not be overi n t e r p r e t e d from a mechanistic standpoint. K i n e t i c s models are at best ambiguous i n d i c a t o r s of mechanism i n that s e v e r a l models t y p i c a l l y f i t the data e q u a l l y w e l l . Although t h i s model i s e n t i r e l y adequate to f i t the data from which i t was developed, i t s form was s e l e c t e d f o r an e n t i r e l y d i f f e r e n t and even more pragmatic reason. Since the hydrogénation r e a c t i o n i s d e s i r a b l y conducted to v i r t u a l e x t i n c t i o n of the butyraldehyde to avoid problems and l o s s e s i n the r e f i n i n g system, the model must r e a d i l y c o l l a p s e to a p r e d i c t e d r a t e of zero a t e q u i l i b r i u m p a r t i a l pressures of hydrogen, butyraldehyde, and butanol. T h i s r e q u i r e s that a l l three components appear i n the numerator of the equation. I f i n f a c t some other r a t e c o n t r o l l i n g step p r e v a i l s e a r l y i n the r e a c t i o n , the model w i l l not p r e d i c t as w e l l a t that p o i n t . In a c t u a l f a c t , v a l i d a t i o n of the model i n the p i l o t - p l a n t showed that the model does a reasonably good job throughout the r e a c t i o n . Development of Reactor Simulation and O p t i m i z a t i o n Programs Numerical s i m u l a t i o n techniques were used to i n v e s t i g a t e the performance c h a r a c t e r i s t i c s of a l t e r n a t i v e fixed-bed r e a c t o r designs. The complexity of a model used f o r s i m u l a t i o n depends




260

l a r g e l y upon the o b j e c t i v e of the s i m u l a t i o n and the nature of the a v a i l a b l e data. For the hydrogénation p r o j e c t described i n t h i s paper, we used a r e l a t i v e l y simple one-dimensional simulat i o n that comprised a set of o r d i n a r y d i f f e r e n t i a l equations f o r a x i a l d i s t a n c e versus the mol f r a c t i o n s of hydrogen, i n e r t gases, butyraldehyde, butanol, p r i n c i p a l byproducts, water, r e a c t i o n temperature, coolant temperature, and mean molecular weight. This l a s t item i s important because i t leads to an easy way to accommodate the molar c o n t r a c t i o n of the gas as the r e a c t i o n proceeds. The program c a l c u l a t e s steady-state p r o f i l e s of each of these down the length of the tubular r e a c t o r , given the r e a c t i o n k i n e t i c s models, a d e s c r i p t i o n of the r e a c t o r and c a t a l y s t geometries, and s u i t a b l e i n l e t gas f l o w - r a t e , pressure and composition information. Reactor performance i s c a l c u l a t e d from the flow-rate and composition data a t the r e a c t o r o u t l e t . Other data, such as the c a l c u l a t e d pressure drop across the r e a c t o r and the heat of r e a c t i o n recovered as steam, are used i n economic c a l c u l a t i o n s . The methods of Dixon and Cresswell (7) are recommended f o r h e a t - t r a n s f e r c a l c u l a t i o n s . The equations comprising the s i m u l a t i o n model f o r the hydrogénation of butyraldehyde a r e : For each chemical species i : dY.

R.ntfD

2

Y.

d(MW)

For Reaction and Coolant dT 2 r nTfD —r=— = -r=7rdZ 4FC P dT

c-» „ > B .r . Δ Η . j j j A

nUttD(T -T ) r c' — FC P v

ni! DU ( T ~ T ) ( MODE )

c

dZ~

Temperatures:

r

=

c

F~C c c

For Pressure: dP dZ

-150uv (l.-e)

2

2

o

D

2 P

e

3

1.75,0 v ( l . - e ) U-2 /144./32.3/14.7 ^ 3 D e P o

+

For Mean Molecular Weight:

dZ

BAL dZ

H2 dZ

BOH

dZ


η dZ

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Although these equations incorporated the best information we had at the time of t h e i r development, the model had to be v a l i d a t e d before i t s accuracy could be r e l i e d upon f o r a c t u a l design and o p t i m i z a t i o n of the r e a c t i o n system.


Model V a l i d a t i o n The one-dimensional model i s by no means d e s c r i p t i v e of everything that goes on i n the r e a c t o r , because i t provides c a l c u l a t e d temperatures, concentrations, pressures, and so on only i n one dimension — lengthwise, down the a x i s of the tube. A c t u a l l y , transport processes and d i f f u s i o n cause v a r i a t i o n s and gradients not only a x i a l l y but a l s o r a d i a l l y w i t h i n tubes and w i t h i n 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 . Furthermore, the r e a c t o r may not a c t u a l l y operate a t steady-state, and so time might a l s o be included as a v a r i a b l e . A l l of these f a c t o r s can be described q u i t e e a s i l y by p a r t i a l d i f f e r e n t i a l equations i n as many as four dimensions (tube length, tube r a d i u s , p e l l e t r a d i u s , and time). But there are problems with multi-dimensional models. From a purely pragmatic standpoint, even two-dimensional models r e q u i r e too much computer time to be r e a l l y p r a c t i c a b l e f o r o p t i m i z a t i o n purposes. In a d d i t i o n , multi-dimensional models r e q u i r e values f o r parameters that are d i f f i c u l t or impossible e i t h e r to estimate with s u f f i c i e n t accuracy, or to measure. In p r a c t i c e , i t g e n e r a l l y w i l l be found that one-dimensional models are e n t i r e l y adequate f o r o p t i m i z a t i o n , provided that they are v a l i d a t e d i n some k i n d of p i l o t - s c a l e tubular r e a c t o r . V a l i d a t i o n comprises the adjustment of parameters i n the r e a c t o r model equations so that observed and p r e d i c t e d temperature and concentration p r o f i l e s match as c l o s e l y as p o s s i b l e . T y p i c a l parameters a r e the r e l a t i v e c a t a l y s t a c t i v i t y f a c t o r s B j and, i f necessary, the o v e r a l l h e a t - t r a n s f e r c o e f f i c i e n t , U. A s t a t i s t i c a l l y - d e s i g n e d s e t of experiments i n the p i l o t - p l a n t i s i n v a l u a b l e f o r model v a l i d a t i o n , and such a s e t was used i n t h i s project. Figure 1 i l l u s t r a t e s t y p i c a l performance of a v a l i d a t e d one-dimensional model i n the p r e d i c t i o n of temperature p r o f i l e s i n a p l a n t - s c a l e tubular hydrogénation r e a c t o r . Note that the major problem area i s i n the r e l a t i v e l y low-temperature region near the i n l e t . The peak temperature i s p r o p e r l y l o c a t e d i n the tube, but i s s l i g h t l y lower than the a c t u a l temperature. With r e a c t i o n s and r e a c t o r s of t h i s type, the major r e a c t i o n i s over s l i g h t l y a f t e r the peak temperature has been reached, and the remainder of the r e a c t o r i s described p r i m a r i l y by a c o o l i n g curve. The o u t l e t composition of the r e a c t o r w i l l be e s s e n t i a l l y at e q u i l i b r i u m with respect to the p r i n c i p a l r e a c t i o n . We have i d e n t i f i e d s e v e r a l probable causes of the "hook" phenomena — the f a i l u r e of the one-dimensional model to p r e d i c t the i n l e t temperature p r o f i l e a c c u r a t e l y , as shown i n Figure 1. The major causes a r e :




OBSERVED PROFILE

AXIAL DISTANCE

Figure 1. T y p i c a l temperature p r o f i l e s using a v a l i d a t e d one-dimensional r e a c t o r s i m u l a t i o n model.



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a)

D e a c t i v a t i o n of the c a t a l y s t i n the bed by progressive poisoning or d e a c t i v a t i o n or by condensation of l i q u i d s i n the smallest pores of the c a t a l y s t p e l l e t .

b)

A x i a l and r a d i a l thermal d i s p e r s i o n i n the c a t a l y s t bed.

c)

Non-uniform s h e l l temperatures, e s p e c i a l l y i n r e a c t o r s i n which both gas and r e l a t i v e l y c o o l steam condensate enter at the bottom.

There are other p o s s i b l e causes as w e l l , but i t i s e s s e n t i a l to point out that the e f f e c t has l i t t l e apparent impact on the o v e r a l l performance of the r e a c t o r or the model s a b i l i t y to p r e d i c t i t , based on o u t l e t composition and product d i s t r i b u t i o n . I f progressive d e a c t i v a t i o n i s a f a c t o r , i t may be d e s i r a b l e to describe the β a c a t a l y s t a c t i v i t y f a c t o r s as f u n c t i o n s of a x i a l distance ana c a t a l y s t age. In any event, the f i n a l design must be checked over a r e a l i s t i c range of c a t a l y s t a c t i v i t i e s to ensure o p e r a b i l i t y and performance over the p r o j e c t e d l i f e of the c a t a l y s t . In our judgment, i t i s not necessary that the exact geometry of the f i n a l r e a c t o r design be d u p l i c a t e d i n the p i l o t p l a n t to be used f o r v a l i d a t i o n , provided that appropriate ranges of mass and space v e l o c i t i e s , pressure, temperature, feed composition, and so on can be e f f e c t i v e l y matched, and that c r i t i c a l r e c y c l e loops can be c l o s e d . F o r t u n a t e l y f o r our p r o j e c t , a p i l o t - p l a n t s u i t a b l e f o r v a l i d a t i o n purposes was a v a i l a b l e as part of the R&D f a c i l i t i e s at the p r o j e c t e d plant s i t e . 1

Development of Economic Optimization

Criteria

In p r i n c i p l e , almost any economic parameter that r e f l e c t s changes i n the r e a c t i o n system may be used f o r o p t i m i z a t i o n . In p r a c t i c e there a r e c o n s t r a i n t s and l i m i t a t i o n s that h i s t o r i c a l l y have l i m i t e d the d i r e c t use of economic c r i t e r i a . The most common of these i s the complexity of economic e v a l u a t i o n s , which t y p i c a l l y have r e q u i r e d vast amounts of computer time i n t h e i r preparation. Nevertheless, i t i s e n t i r e l y p o s s i b l e and p r a c t i c a b l e to develop o p t i m i z a t i o n c r i t e r i a that are simultaneously r e l e v a n t to the r e a c t i o n system design and r e a d i l y c a l c u l a b l e . Most economic s t u d i e s of chemical processes show the p r o j e c t e d performance of the process with respect to some parameter l i k e r e t u r n on investment, p r o f i t on s a l e s , or net present value a t some future year. These studies are appropriate f o r p r o j e c t e v a l u a t i o n by management, and may include cost components r e l a t e d to c a p i t a l , energy, u t i l i t i e s , raw m a t e r i a l s , l a b o r , overhead, working c a p i t a l , and so on. They may or may not include s e n s i t i v i t y analyses of the e f f e c t s




264

of r e a c t o r s i z e , raw m a t e r i a l u t i l i z a t i o n , or reactant conversion. And they i n v a r i a b l y include sales p r i c e p r o j e c t i o n s . Reaction system o p t i m i z a t i o n seeks to reduce the cost of manufacturing a p a r t i c u l a r product, and i s t y p i c a l l y unconcerned with s a l e s p r i c e unless more than one s a l e a b l e product i s produced. For p l a n t design and o p t i m i z a t i o n , i t i s convenient to separate o v e r a l l product costs i n t o components that d i r e c t l y r e f l e c t the a t t r i b u t e s of the r e a c t i o n system. Thus instead of c a p i t a l , u t i l i t i e s , and raw m a t e r i a l u t i l i z a t i o n c o s t s , one c a l c u l a t e s costs that are r e l a t e d to r e a c t o r s i z e , gas r e c y c l e volume, raw m a t e r i a l i n e f f i c i e n c i e s and vent and purge l o s s e s . Each of these may have components r e l a t e d both to c a p i t a l and operating costs that are of i n t e r e s t to management but which are not p a r t i c u l a r l y u s e f u l f o r o p t i m i z a t i o n . I t i s d e s i r a b l e to summarize costs i n a way that i s simultaneously meaningful to management and to the r e a c t i o n system designer. One such way i s to prepare a t a b l e of the f o l l o w i n g type, to be used to summarize each of s e v e r a l base cases. The h y p o t h e t i c a l example shown here i s reproduced from an e a r l i e r paper ( 8 ) , but i t e f f e c t i v e l y i l l u s t r a t e s the kind of summary used i n t h i s p r o j e c t . The a c t u a l numbers f o r the butyraldehyde hydrogénation process, of course, are c o n f i d e n t i a l .

Sample Table of Base Summaries Capital il lb Reactor ( I n c l .

Catalyst)

Utilities i / l b

1.0

Raw Mat'ls i / l b 0.5

Total i / l b 1.5

Gas Recycle System Compressors Heat Exchangers

1.5 0.6

0.8 0.2

2.3 0.8

Product Recovery System

2.0

0.2

2.2

Raw M a t e r i a l A Losses to Byproducts P h y s i c a l Losses S t o i c h i o m e t r i c Req'ts Raw M a t e r i a l Β Losses to Byproducts P h y s i c a l Losses S t o i c h i o m e t r i c Req'ts

0.5

6.2 1.0 20.0

6.7 1.0 20.0

0.1

1.0 1.0 3.0

1.1 1.0 3.0

Semi-Fixed Costs (Labor, Inventory, Overhead, etc.)

2.0

1.0

Totals

7.7

2.2

3.0 32.7


42.6


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Armed with the summaries of s e v e r a l well-conceived case s t u d i e s , the r e a c t i o n system designer can r e a d i l y p l o t the economic impact of c a t a l y s t p r o d u c t i v i t y , product concentration, or r e a c t i o n s e l e c t i v i t y — the primary chemical responses of the r e a c t i o n system — as r e f l e c t e d by r e a c t o r s i z e , c y c l e gas volume, and raw m a t e r i a l u t i l i z a t i o n . As i t turns out, p l o t s of these responses are t y p i c a l l y simple monotonie f u n c t i o n s l i k e s t r a i g h t l i n e s or curves that are e a s i l y described a l g e b r a i c a l l y . Figure 2 i s t y p i c a l of the graphs and r e l a t i o n s h i p s used i n the o p t i m i z a t i o n of the butyraldehyde hydrogénation r e a c t o r . Given these, we e a s i l y determined the t o t a l cost of producing butanol from butyraldehyde by simply adding up the component costs and adding i n the s t o i c h i o m e t r i c cost requirements and semi-fixed c o s t s . The equations that describe these graphs are e n t i r e l y adequate to evaluate the production cost i n the o p t i m i z a t i o n program, and comprised a t o t a l of fewer than 50 FORTRAN s t a t e ments, even with p r o v i s i o n s f o r m u l t i p l e options and c o n s t r a i n t s . Obviously, the optimum r e a c t i o n system design w i l l r e f l e c t assumptions about the r e l a t i v e costs of c a p i t a l , energy, and raw m a t e r i a l s . These w i l l i n e v i t a b l y change as one s t u d i e s the optimum timing to b u i l d the new u n i t and i t s a c t u a l l o c a t i o n . But the economic c r i t e r i a developed here are r e a d i l y changed to r e f l e c t d i f f e r e n t assumptions. A strength of the method i s that i t can q u i c k l y lead to changes i n the optimum plant design based on p r o j e c t e d changes i n the o v e r a l l economic c l i m a t e . Optimization

of the Reaction

System

The business department e s t a b l i s h e d the production r a t e f o r the new system, and the plant context determined c e r t a i n other q u a n t i t i e s , such as the pressure and p u r i t y of the hydrogen feed stream. Given these, o p t i m i z a t i o n of the r e a c t i o n system was accomplished by i t e r a t i v e l y s o l v i n g the s i m u l a t i o n equations to a r r i v e at the lowest cost f o r the product butanol, which was c a l c u l a t e d according to the scheme described i n the l a s t s e c t i o n . The o p t i m i z a t i o n procedure u t i l i z e d a non-linear optimum-seeking algorithm, and involved the manipulation and c a l c u l a t i o n of search v a r i a b l e s , response v a r i a b l e s , and c o n s t r a i n t s . The search v a r i a b l e s included both reactor design and operating v a r i a b l e s . The former included q u a n t i t i e s l i k e the number of tubes i n the r e a c t o r and t h e i r diameter and l e n g t h . Operating v a r i a b l e s included q u a n t i t i e s l i k e the mol f r a c t i o n of aldehyde i n the r e a c t o r feed (and hence the c y c l e gas flow r a t e ) , r e a c t o r i n l e t and s h e l l temperatures, and r e a c t o r i n l e t pressure. The response v a r i a b l e s included v i r t u a l l y everything that one might observe i n a r e a l r e a c t o r — r e a c t o r maximum and o u t l e t temperatures, reactor o u t l e t concentrations of butyraldehyde, butanol, and byproducts, i n l e t and o u t l e t dewpoint temperatures, c a t a l y s t p r o d u c t i v i t y , r e a c t o r pressure drop, and so on.



266


P: SYSTEM PRESSURE A: STEAM REQUIRED FOR PREHEAT B: INTEGRATED PREHEAT - NO STEAM

* P, Û

3 /

^ ^

P

1'

B

P

2'

A

2'

B

P

GAS CYCLE VOLUME, MLBMOLS/HP.

Figure 2,

Incremental b u t a n o l cost v s . gas c y c l e volume.



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The c o n s t r a i n t s changed from one t r i a l c o n f i g u r a t i o n of the r e a c t i o n system to the next, but t y p i c a l l y included things l i k e the minimum coolant temperature to permit e f f i c i e n t u t i l i z a t i o n of the heat of r e a c t i o n as process steam, the maximum allowable aldehyde c o n c e n t r a t i o n i n the condensed crude product to avoid r e f i n i n g and product s p e c i f i c a t i o n problems, and a p r e s c r i b e d r e a c t o r pressure drop to i n s u r e adequate flow d i s t r i b u t i o n among the r e a c t o r tubes at a minimum energy c o s t . A l l of these are i m p l i c i t c o n s t r a i n t s — they e s t a b l i s h the maximum or minimum l e v e l s f o r c e r t a i n response v a r i a b l e s . Explicit c o n s t r a i n t s comprise the ranges f o r search v a r i a b l e s . We proceeded to develop the e n t i r e r e a c t i o n system network f o r the optimum case, by s e t t i n g i m p l i c i t and e x p l i c i t c o n s t r a i n t l e v e l s that r e a l i s t i c a l l y described each new v e r s i o n of the system as we perceived i t . Most of these v e r s i o n s i n v o l v e d changes e x t e r n a l to the r e a c t o r that were p r i m a r i l y concerned with the most e f f i c i e n t u t i l i z a t i o n of the heat of r e a c t i o n . But they f r e q u e n t l y n e c e s s i t a t e d changes i n r e a c t o r o u t l e t temperature or s h e l l temperature to a d j u s t the f r a c t i o n of the heat of r e a c t i o n to be generated as steam. These changes i n turn made changes necessary throughout the system, and the o p t i m i z a t i o n program determined the best combination of these. A s i m p l i f i e d flow diagram of a t y p i c a l hydrogénation system i s shown i n F i g u r e 3. The r e s u l t of the e f f o r t was a p r e c i s e d e f i n i t i o n of the values f o r a l l of the f i x e d , search, and response v a r i a b l e s f o r the optimum case, as w e l l as an economic breakdown of the c o s t s . We'll see how these compared with the previous technology i n the next s e c t i o n . Comparative Economics of the Optimized Vapor-Phase Tubular Reaction System At the outset of the p r o j e c t , we e s t a b l i s h e d as a y a r d s t i c k f o r economic comparison, an e n t i r e l y new u n i t based on the o l d hydrogénation process technology. No attempt was made to improve i t , e i t h e r i n the l i g h t of experience or knowledge gained from the study described i n t h i s paper. Dubbed i r r e v e r e n t l y the "Rubber Stamp", the o l d process, while chemically e f f i c i e n t , was c h a r a c t e r i z e d by s i g n i f i c a n t l y higher product costs than was the new optimized process. The comparative costs are shown i n Figure 4. Note that they exclude the s t o i c h i o m e t r i c requirements f o r butyraldehyde and hydrogen, as w e l l as the serai-fixed costs discussed e a r l i e r . The most s t r i k i n g r e d u c t i o n i n costs was achieved by energy i n t e g r a t i o n , s p e c i f i c a l l y by e s t a b l i s h i n g the recovery of usable energy and the m i n i m i z a t i o n of expended energy as important components of the o v e r a l l economic o p t i m i z a t i o n process. Raw m a t e r i a l usage was reduced l a r g e l y by lowering the hydrogen concentration i n the c y c l e gas i n order to reduce the


268

CHEMICAL AND CATALYTIC REACTOR MODELING PREHEATER

. PROCESS


STEAM

MAKEUP H?

, COLD STEAM CONDENSATE

Τ CYCLE-GAS' COMPRESSOR

cw

PRODUCT

JT

CONDENSER VENT GAS CONDENSED CRUDE PRODUCT

F i g u r e 3. Conceptual flow diagram f o r a t y p i c a l vaporphase hydrogénation r e a c t i o n system.

Figure 4. Economic comparison of e x i s t i n g "Rubber Stamp" and optimized t u b u l a r r e a c t i o n systems.



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Butyraldehyde

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hydrogen vented with the purge. (The "Rubber Stamp" process was already h i g h l y e f f i c i e n t from a purely chemical standpoint.) C a p i t a l costs were reduced v i r t u a l l y everywhere i n the r e a c t i o n system, but the u t i l i z a t i o n of a h i g h l y r e a c t i v e c a t a l y s t that was s u i t a b l e f o r o p e r a t i o n at economical temperatures and pressures was probably the most important s i n g l e f a c t o r . I t i s thus important to e s t a b l i s h economic c r i t e r i a f o r c a t a l y s t s e l e c t i o n or development e a r l y i n the development and design of a new process. As with most commodity chemicals, the s t o i c h i o m e t r i c chemical costs remain the dominant component of o v e r a l l process economics, but success i n the marketplace depends c r i t i c a l l y upon the most e f f i c i e n t u t i l i z a t i o n of c a p i t a l , energy, and raw m a t e r i a l resources to g a i n and r e t a i n the economic upper hand. Programs l i k e the one described i n t h i s paper are designed to do j u s t t h a t . Legend of Symbols C C D Dp Ε e F Δ H

Coolant heat c a p a c i t y , Btu/Lb/°C Gas heat c a p a c i t y , Btu/LbMol/°C Tube diameter, f t . C a t a l y s t p e l l e t diameter, f t . Reaction a c t i v a t i o n energy, Cal/Gmol C a t a l y s t bed v o i d f r a c t i o n Gas f l o w - r a t e , LbMols/Hr Heat of r e a c t i o n f o r r e a c t i o n j , Btu/LbMol

c

p

r

j k K q K-£ MODE Q

e

MW MW-£ η P^ rj R Rl T ,T T U v Y-£ Ζ ocij >Og Bj u r

c

0

Pre-exponential r a t e constant Reaction e q u i l i b r i u m constant (dimensionless) K i n e t i c parameter Heat t r a n s f e r mode: -1 f o r coolant countercurrent to gas 0 f o r isothermal s h e l l - s i d e +1 f o r coolant co-current with gas Mean molecular weight of gas, Lb/LbMol Molecular weight of component i , Lb/LbMol Number of tubes i n r e a c t o r P a r t i a l pressure of component i , atmospheres Reaction r a t e f o r r e a c t i o n j , LbMols/Ft^/Hr Gas constant, 1.987 Cal/Gmol°C Net r a t e of r e a c t i o n f o r component i , LbMols/Ft^/Hr Reaction temperature, °C Coolant temperature, °C O v e r a l l h e a t - t r a n s f e r c o e f f i c i e n t , Btu/Ft /Hr/°C S u p e r f i c i a l gas v e l o c i t y , f t / s e c . Mole f r a c t i o n of component i A x i a l d i s t a n c e from r e a c t o r i n l e t , f t . S t o i c h i o m e t r i c c o e f f i c i e n t f o r component i i n r e a c t i o n j Gas d e n s i t y , L b / f t Relative a c t i v i t y factor for reaction j Gas v i s c o s i t y , L b / f t - s e c . 2

3


270

C H E M I C A L AND C A T A L Y T I C R E A C T O R M O D E L I N G

Literature Cited 1.


2. 3. 4. 5.

6.

7. 8.

Satterfield, C. N. "Heterogeneous Catalysis in Practice," McGraw-Hill Book Company, New York, 1976. Berty, J. M. Chem. Eng. Prog. 1974, 5 (5). Berty, J. M. Catal. Rev.-Sci. 1979, 20, 76-96. V. I . Timoshenko, et a l . Kinetika i Kataliz, 1968, 9, 1358-1363. Cropley, J. B., in "Chemical Reaction Engineering Houston"; Weekman, V. W., Jr.; Luss, D., Eds; ACS SYMPOSIUM SERIES No. 65, American Chemical Society: Washington, D . C . , 1978; pp. 292-302. S t u l l , R. D.; Westrum, E. F., Jr.; Sinke, G. C. "The Chemical Thermodynamics of Organic Compounds," John Wiley and Sons: New York, 1969. Dixon, A. G . ; Cresswell, D. L . AIChEJ 1979, 25, 663-676. Cropley, J. B. Proc. Pittsburgh AIChE Section Reactor Engineering Industrial Applications Symposium, 1982.

R E C E I V E D August 22, 1983


The Optimal Design of a Reactor for the Hydrogenation of

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