A Review of Process Synthesis - ACS Publications - American

3 A Review of Process Synthesis ARTHUR W. WESTERBERG

Downloaded by UNIV OF AUCKLAND on May 3, 2015 | http://pubs.acs.org Publication Date: May 30, 1980 | doi: 10.1021/bk-1980-0124.ch003

Department of Chemical Engineering, Carnegie-Mellon University, Pittsburgh, PA 15213

The purpose of the paper is to present a review of the area of chemical process synthesis. As two earlier review articles on synthesis have already appeared (Hvalecek (1978) and Hendry, Rudd and Seader (1973)), this paper will l i s t most but will not review all previous synthesis publications. This paper will respond to the often asked question, Has anything really useful come from the research activity called process synthesis?" n

A Definition

of

Synthesis

We shall start by defining the term "synthesis." The activities of design are 1) synthesis — the step where one conjectures the building blocks and their interconnection to create a structure which can meet stated design requirements, 2) analysis — the activity of modeling and then solving the resulting equations to predict how a selected structure would behave if it were constructed, 3) evaluation — the activity of placing a worth on the structure where the worth might be its cost, its safety, or its net energy consumption, and 4) optimization — the systematic searching over the allowed operating conditions to improve the evaluation as much as is possible. The design engineer moves iteratively through each of these activities, developing more and more details and/or a better understanding about the design with each iteration. Synthesis is the inventive step in the design of a process. It is often the most enjoyable one. The primary research question is: Can the synthesis activity be automated and, if so, to what extent? An interesting paradox occurs because if "synthesis" as an activity is automated, is the activity correctly labeled "synthesis?" Using a dictionary definition, synthesis should be based on inductive (going from the particular to the general) reasoning whereas analysis is deductive (going from the general to the particular). If process design follows a series of automatic steps, leading more or less to a preordained solution, was not this solution deduced from the given problem definition? We may only be arguing semantics here, but this point 0-8412-0549-3/80/47-124-053$08.75/0 © 1980 American Chemical Society In Computer Applications to Chemical Engineering; Squires, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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l e a d s one t o r e s t a t e the important q u e s t i o n i n process s y n t h e s i s : How much o f the s t r u c t u r e can be deduced from the statement o f the d e s i g n requirements f o r a problem? Stated t h i s way the a c t i v i t y may no longer appear so mysterious an a c t i v i t y . The com puter should indeed be able t o i n v e n t process s t r u c t u r e when that s t r u c t u r e can be deduced from the problem statement. I t i s ques t i o n a b l e i f the computer can be used w i t h a h i g h degree o f success t o d i s c o v e r a u t o m a t i c a l l y a d e s i g n r u l e by s o l v i n g s e v e r a l p a r t i c u l a r " s y n t h e s i s problems and from these d i s c o v e r i n g an u n a n t i c ipated rule. I n c o n t r a s t , the human i s o f t e n v e r y s u c c e s s f u l a t this activity. R e s t a t i n g , the computer should be e f f e c t i v e i n developing s t r u c t u r e based on w e l l - d e f i n e d technology, where the h e u r i s t i c r u l e s which guide i t t o f i n d s u c c e s s f u l designs q u i c k l y are p r o v i d e d as p a r t o f i t s programming. An example i s f o r the computer to s e l e c t a heat exchanger network t o exchange heat among s e v e r a l hot and c o l d streams t o minimize or reduce the use o f u t i l i t i e s . The s e l e c t i o n o f such a network amounts t o a c l e v e r search among a v e r y l a r g e number o f reasonably w e l l - d e f i n e d a l t e r n a t i v e s . The computer should be i n e f f e c t i v e i n a u t o m a t i c a l l y developing a new r u l e which might be obvious t o an engineer a f t e r performing a l a r g e number o f heat exchanger network d e s i g n s . Such a r u l e might be that the b e s t networks normally r e s u l t when one attempts a t each step t o minimize the temperature d r i v i n g f o r c e s w i t h i n each exchanger, i . e . when one attempts t o minimize i r r e v e r s i b i l i t i e s . C l e a r l y the engineer and the computer can complement each other, and one should be s t r i v i n g f o r s y n t h e s i s t o o l s where they do. Such a view o f s y n t h e s i s suggests that the r i g h t s y n t h e s i s computer programs are those which permit the d e s i g n e r t o put new h e u r i s t i c s i n t o them as he or she (and very l i k e l y not the com puter) d i s c o v e r s them. The computer can s t i l l be used i n t h i s manner t o f i n d unex pected s o l u t i o n s . F o r example, Johns (1977) proposed an i n t r i g u i n g use o f s y n t h e s i s which uses the s t r e n g t h o f the computer t o search q u i c k l y f o r a l t e r n a t i v e s u s i n g known technology but w i t h the hope o f f i n d i n g new s o l u t i o n s . He suggested a l l o w i n g the com puter t o use an i n f e a s i b l e step a t no c o s t i n developing a s o l u t i o n . F o r example, known technology may not i n c l u d e a method t o separate component A from component B. Thus, i f A and Β are not to end up mixed, the computer must e i t h e r avoid mixing them, o r , i f allowed one i n f e a s i b l e step, i t c o u l d develop a s t r u c t u r e which i n c l u d e s the i n f e a s i b l e step o f s p l i t t i n g A from B. I f t h i s i n f e a s i b l e step reduces the c o s t by $7 m i l l i o n / y r , one c o u l d then decide i f t h a t makes i t worth l o o k i n g f o r new technology t o s p l i t A from B. Douglas (1977, 1979) has been pursuing a q u i t e d i f f e r e n t ap proach t o process s y n t h e s i s . He has been developing techniques which permit the designer t o analyze and optimize a l t e r n a t i v e con f i g u r a t i o n s q u i c k l y and by hand. H i s " s y n t h e s i s " s t r a t e g y i s t o teach people t o recognize v a l i d approximations f o r the problem at hand; i t has proved a r a t h e r c o n t r o v e r s i a l e x e r c i s e s i n c e people


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c l a i m i t i s not new i n concept. Indeed, i t i s not s i n c e hand approximations were the t o o l s o f design before the computer. However, Douglas i s attempting t o push these techniques even f u r t h e r than before t o g a i n problem i n s i g h t as w e l l as good f i r s t approximations t o the s o l u t i o n o f a process design problem. We have a l s o used the approach (Westerberg (1978)) t o d e v e l op a s e t o f hand a n a l y s i s techniques, which we use i n our undergraduate design course. T h i s approach works. V a l i d designs a l most always r e s u l t . We s h a l l not be s t r e s s i n g these ideas here, however, since the purpose o f t h i s paper i s t o examine automatic s y n t h e s i s techniques. We only mention these ideas here t o make people t h i n k twice about i g n o r i n g the t a l e n t s o f the engineer when developing a s y n t h e s i s t o o l . The a c t i v i t y o f s y n t h e s i s occurs throughout a design, from o r i g i n a l process conception t o c o n s t r u c t i o n and o p e r a t i o n . Examples are 1) the s y n t h e s i s o f a c o n t r o l system f o r f i x e d p l a n t c o n f i g u r a t i o n , 2) the s y n t h e s i s o f a s t a r t - u p procedure f o r a new process, 3) the s e l e c t i o n o f m a t e r i a l s o f c o n s t r u c t i o n and 4) the layout o f the p l a n t t o improve s a f e t y . A l l o f these a c t i v i t i e s i n v o l v e d i s c r e t e d e c i s i o n making; t h i s aspect i s a common denominator o f a l l synthesis a c t i v i t i e s . A more formal d e f i n i t i o n o f process s y n t h e s i s i s p o s s i b l e . I t i s f o r m a l l y a n o n l i n e a r mixed i n t e g e r and continuous v a r i a b l e o p t i m i z a t i o n problem, g e n e r a l l y a v e r y l a r g e one. The s e l e c t i o n o f the b u i l d i n g b l o c k s and how they are t o be interconnected may be formulated as a s e t o f d i s c r e t e d e c i s i o n s represented by a s e t of zero/one v a r i a b l e s . F o r a p a r t i c u l a r s e t o f d i s c r e t e d e c i sions one must determine the optimal operating l e v e l s f o r the c o r responding process s t r u c t u r e ; these l e v e l s are represented gene r a l l y by continuous v a r i a b l e s . C e r t a i n d i s c r e t e decisons d i s a l low others which may be f o r m a l l y s t a t e d u s i n g i n e q u a l i t y cons t r a i n t s among the d i s c r e t e v a r i a b l e s . We could continue, but by now the correspondence should be e v i d e n t . The Research Problems o f Synthesis The p r i n c i p a l r e s e a r c h problems o f s y n t h e s i s were s t a t e d by Simon (1969) i n an essay on design. They are 1) r e p r e s e n t a t i o n o f the a l t e r n a t i v e s , 2) a n a l y s i s and e v a l u a t i o n o f each a l t e r n a t i v e and 3) the s t r a t e g y o f searching among the a l t e r n a t i v e s . The r e p r e s e n t a t i o n problem can be s t a t e d b r i e f l y as: Can a r e p r e s e n t a t i o n be developed which i s r i c h enough t o a l l o w a l l a l t e r n a t i v e s t o be i n c l u d e d and c l e v e r enough t o exclude automatic a l l y r i d i c u l o u s options? Simon argues by example that the d i s covery o f a c o r r e c t r e p r e s e n t a t i o n may o f t e n convert what appears t o be a v e r y d i f f i c u l t problem i n t o one f o r which the s o l u t i o n i s e a s i l y s t a t e d . To appreciate the r e p r e s e n t a t i o n problem, consider the d i f f i c u l t y o f uniquely r e p r e s e n t i n g an a r b i t r a r y organic mole c u l e . Beside g i v i n g a unique r e p r e s e n t a t i o n , i t should a l s o a l low one t o d i s c o v e r q u i c k l y f u n c t i o n a l groups on a molecule. A




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second example i s t o develop a s u i t a b l e unique r e p r e s e n t a t i o n f o r a sequence o f s e p a r a t i o n u n i t s , a l l o w i n g f o r t h e r m a l l y coupled d i s t i l l a t i o n columns among the a l t e r n a t i v e s . What i s needed i n each case i s a r e p r e s e n t a t i o n which a i d s i n s o l v i n g the s y n t h e s i s problem. The a n a l y s i s and e v a l u a t i o n problem i n v o l v e s modeling the a l t e r n a t i v e s i n an a p p r o p r i a t e f a s h i o n and then developing an e v a l u a t i o n c r i t e r i o n so t h a t one can compare them t o each other. De v e l o p i n g a s u i t a b l e c r i t e r i o n i s o f t e n a n e a r l y impossible t a s k . How does one compare the s a f e t y o f two processes? F o r the problem of r e a c t i o n path s y n t h e s i s , how does one compare a l t e r n a t i v e chem i c a l r o u t e s t o the same molecule when one cannot p r e d i c t k i n e t i c s ? I f i t proves p o s s i b l e t o develop a s u i t a b l e e v a l u a t i o n f u n c t i o n , then one must s t i l l be able t o do the a n a l y s i s and e v a l u a t i o n q u i c k l y . One i s u s u a l l y faced w i t h an enormous number o f a l t e r n a t i v e s i n s y n t h e s i s , and a trade o f f i s necessary between a n a l y s i s and e v a l u a t i o n speed and accuracy. L a s t l y , the search s t r a t e g y problem i s t o develop a s t r a t e g y to l o c a t e q u i c k l y the b e t t e r a l t e r n a t i v e s without t o t a l l y enumer a t i n g a l l o p t i o n s . While s y n t h e s i s problems are f i n i t e , one i s faced w i t h an enormous number o f a l t e r n a t i v e s even f o r simple problems. To i l l u s t r a t e , one can enumerate 47 d i f f e r e n t s t r u c t u r e s f o r exchanging heat among two h o t and two c o l d streams where one d i s a l l o w s the s p l i t t i n g o f any o f the streams, where no two streams may exchange heat between them more than one time, and where each match must i n v o l v e heat t r a n s f e r r i n g o n l y from a h o t stream t o a c o l d stream. The s t r u c t u r e s i n c l u d e the " n u l l " s t r u c ture (no exchange) , four s t r u c t u r e s w i t h o n l y a s i n g l e heat ex change, e i g h t w i t h two exchanges which both i n v o l v e the same stream, e t c . I f one has three c o l d and two h o t streams, the num ber o f a l t e r n a t i v e s i s 847. A r e a l i s t i c process may i n v o l v e 20 streams and an i n c r e d i b l e number o f a l t e r n a t i v e s t r u c t u r e s . I n d u s t r i a l p r a c t i c e allows one to s p l i t a stream and t o rematch streams so the a c t u a l s y n t h e s i s problem i s much l a r g e r than even these numbers i n d i c a t e . Simple s e p a r a t i o n sequences g i v e r i s e t o s i m i l a r r e s u l t s . Thompson and King (1972) developed a formula f o r p r e d i c t i n g the number o f d i f f e r e n t s t r u c t u r e s which e x i s t f o r simple s e p a r a t i o n sequences. A simple separator i s one which s p l i t s a multicomponent mixture i n t o two p r o d u c t s , the two products having no common components. F o r such a problem the number o f s t r u c t u r e s p o s s i b l e i s (2(N-1))! S " / ( ( N - 1 ) ! N!) where Ν i s the number o f components i n the multicomponent mixture and S the number o f d i f f e r e n t sepa r a t i o n methods. The f o l l o w i n g t a b l e i n d i c a t e s the s i z e o f t h i s problem. The two s t r u c t u r e s f o r N=3 components (say A, Β and C) and S=l method ( d i s t i l l a t i o n ) are 1) separate A from BC i n the f i r s t column and then separate Β from C i n the second and 2) sepa r a t e AB from C i n the f i r s t and then A from Β i n the second. Thus, one must develop a s t r a t e g y t o l o c a t e q u i c k l y the b e t t e r a l t e r n a t i v e s f o r these v i r t u a l l y i n f i n i t e problems, a s t r a t e g y which cannot r e q u i r e one t o enumerate a l l o p t i o n s . N

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C l a s s i f i c a t i o n o f Synthesis Problems A problem a r i s e s when one attempts t o c l a s s i f y the v a r i o u s approaches t o s y n t h e s i s because a t l e a s t three c l a s s i f i c a t i o n schemes e x i s t . The s y n t h e s i s approaches might be c l a s s i f i e d as being predominantly h e u r i s t i c or predominantly a l g o r i t h m i c . An h e u r i s t i c approach i s one which r e l i e s on r u l e s o f thumb t o search q u i c k l y among the a l t e r n a t i v e s . For example, one may s e l e c t the s e p a r a t i o n sequence based on simple d i s t i l l a t i o n columns which a l ways makes the l e a s t c o s t l y next s p l i t at each step through the column sequence. An a l g o r i t h m i c approach i s one which s t a t e s the exact s y n t h e s i s problem t o be solved and then guarantees t o f i n d the best s o l u t i o n among the a l t e r n a t i v e s p o s s i b l e . The exact s y n t h e s i s problem i s u s u a l l y a much s i m p l i f i e d one and one whose s i z e i s o f t e n s i g n i f i c a n t l y reduced f i r s t using h e u r i s t i c s . A second c l a s s i f i c a t i o n f o r s y n t h e s i s schemes, and the one we s h a l l use here, i s by the nature o f the s y n t h e s i s p r o b l e m — h e a t exchanger networks, s e p a r a t i o n schemes, r e a c t i o n paths, c o n t r o l systems, f a u l t t r e e s , t o t a l flowsheets, e t c . The t h i r d c l a s s i f i c a t i o n i s based on whether the s y n t h e s i s method being proposed 1) begins w i t h a f e a s i b l e flowsheet and the method seeks to improve i t or 2) begins w i t h no s t r u c t u r e and the method seeks t o f i n d a good i n i t i a l candidate. For c l a s s (1) the methods f r e q u e n t l y en countered i n c l u d e e v o l u t i o n a r y ones, where one makes small changes to the s t r u c t u r e i n the search f o r improvements, and embedding, where one proposes a superstructure which i n c l u d e s a l l p o s s i b l e alternatives. O p t i m i z a t i o n i s used i n embedding t o f i n d the "best" substructure which solves the s y n t h e s i s problem. F o r c l a s s (2) one w i l l encounter h e u r i s t i c based methods and a l g o r i t h m i c methods based on i n t e g e r programming (e.g. branch and bound) or dynamic programming, e t c . We s h a l l now examine s e v e r a l areas o f s y n t h e s i s , d i s c u s s i n g the key c o n t r i b u t i o n s f o r each. We s h a l l s t a r t w i t h the s y n t h e s i s of heat exchanger networks, an area f o r which i n d u s t r i a l l y s i g n i f icant results exist. Heat Exchanger Network S y n t h e s i s . The t y p i c a l problem f o r heat exchanger network s y n t h e s i s i s s t a t e d as f o l l o w s . Given a set o f hot streams t o be cooled and another s e t of c o l d streams t o be heated p l u s a set o f a v a i l a b l e h e a t i n g and c o o l i n g u t i l i t i e s , develop the l e a s t c o s t network of heat exchangers t o accomplish



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the r e q u i r e d h e a t i n g and c o o l i n g . The c o s t s i n c l u d e the annual cost o f buying the u t i l i t i e s and the cost o f purchasing the equip ment. F o r t h i s problem one i s g i v e n the process stream flow r a t e s and t h e i r i n l e t and e x i t temperatures, the heat t r a n s f e r c o e f f i c i e n t s f o r a l l p o s s i b l e matches, the i n l e t and e x i t temperature f o r a l l u t i l i t i e s , the c o s t o f each u t i l i t y and the cost on an an nual b a s i s o f a heat exchanger versus i t s area. S e v e r a l r e p r e s e n t a t i o n s e x i s t f o r a heat exchanger network problem. The temperature ( o r d i n a t e ) versus stream heat content (e.g. k j / s ) diagram i s one o f the o l d e s t . The heat content i s on a r e l a t i v e b a s i s so each stream once drawn may be moved r i g h t or l e f t r e l a t i v e to any other. F i g u r e 1 i l l u s t r a t e s .

kJ/s Figure 1.

Stream heat content diagram

A second and very u s e f u l r e p r e s e n t a t i o n i s the s o - c a l l e d area o r i e n t e d "heat content" diagram of N i s h i d a , Kobayashi and Ichikawa (1971). I t i s a p l o t o f Τ (ordinate) versus heat con tent per degree ( k j / s K ) , and the heat content o f each stream i s represented as an area. F i g u r e 2 i l l u s t r a t e s . The area i s equal to the amount (e.g. k j / s ) o f heat a v a i l a b l e or needed by each stream. The f i r s t r e p r e s e n t a t i o n i s the i n t e g r a l o f the second. A t h i r d r e p r e s e n t a t i o n which i s not r e l a t e d to these two i s by L i n n h o f f and Flower (1978) and i s one which shows the s t r u c t u r e of the network as w e l l as the r e l a t i v e temperatures o f the streams. I t does not d i r e c t l y show the q u a n t i t y o f heat i n each stream except by l a b e l i n g i t . F i g u r e 3 i l l u s t r a t e s .

FC ,kJ/sK p

Figure 2.

"Area-oriented" heat content diagram


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Figure 3. Linnhoff and Flower heat exchanger network representation The f i r s t paper t o d i s c u s s the heat exchanger network synt h e s i s problem appears t o be that by Hwa (1965) who used separable programming techniques. K e s l e r and Parker (1969) and o t h e r s s i n c e (Kobayashi e t a l . (1971); Cena e t a l . (1977)) have formulated the problem as an a s signment problem i n l i n e a r programming. I n an assignment problem f o r m u l a t i o n , each stream i s p a r t i t i o n e d s e r i a l l y i n t o a sequence of small substreams, each r e q u i r i n g the exchange o f Q u n i t s o f heat. Q i s chosen so the heat requirement f o r each process stream i s , t o an adequate approximation, an i n t e g e r m u l t i p l e o f Q. A b i n a r y (zero/one) v a r i a b l e i s a s s o c i a t e d w i t h each p o t e n t i a l match o f a h o t substream or u t i l i t y w i t h a c o l d substream or w i t h a cold u t i l i t y . U n d e s i r a b l e o r i n f e a s i b l e matches are r e a d i l y excluded w i t h c o n s t r a i n t s or a r t i f i c a l l y h i g h c o s t s . The d i f f i c u l t y w i t h t h i s approach i s posing the o b j e c t i v e f u n c t i o n . The r e a l o b j e c t i v e f u n c t i o n cannot be l i n e a r because a l a r g e heat exchanger i s much l e s s expensive per u n i t area than a small one. The method cannot account f o r t h i s nonconvexity o f cost versus area. Thus the method w i l l i n g l y c r e a t e s networks w i t h l a r g e numbers o f heat exchangers. Nonetheless i t appears t o generate good r e s u l t s e a s i l y even f o r q u i t e large problems p a r t i c u l a r l y when u t i l i t y c o s t s dominate. The u s u a l approach t o reduce the number of exchangers i s t o make a sequence o f small changes manually t o the network which the program produces. Masso and Rudd (1969) proposed the next a l g o r i t h m , one i n which the computer was t o l e a r n how t o c o n s t r u c t a heat exchanger network. Masso and Rudd conjectured t h a t the b e t t e r networks c o u l d be found by making a sequence o f d e c i s i o n s about matching streams. They suggested a l i s t o f p l a u s i b l e h e u r i s t i c s which could be used t o make the next stream/stream heat exchange d e c i s i o n . Once made, as much heat as p o s s i b l e was exchanged between the two s e l e c t e d streams. Then the l i s t o f h e u r i s t i c s was used again t o s e l e c t the second stream/stream match. Scores were gene r a t e d a u t o m a t i c a l l y f o r the h e u r i s t i c s by s o l v i n g the complete network problem r e p e a t e d l y , r a i s i n g the h e u r i s t i c scores used f o r each step i f the r e s u l t was a b e t t e r network, lowering them i f a worse one. Thus a b e s t f i r s t match h e u r i s t i c was found, a b e s t second match h e u r i s t i c and so f o r t h . The r e s u l t s demonstrated how d i f f i c u l t i t i s t o get the computer t o do p a t t e r n matching as t h i s approach was i n t e r e s t i n g but not v e r y s u c c e s s f u l .



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S e v e r a l a r t i c l e s f o l l o w e d i n quick s u c c e s s i o n u s i n g a v a r i ety of a l g o r i t h m s — b r a n c h and bound, h e u r i s t i c s , e t c . Some r e s t r i c t the problem s o l u t i o n to no stream s p l i t t i n g and/or t o no rematching o f streams. Another c l a s s o f a l g o r i t h m s , as w i t h the l i n e a r programming approach, c r e a t e s networks w i t h an enormous number o f s p l i t streams and exchangers. The h e u r i s t i c based a l gorithms are v e r y f a s t and o f t e n s u c c e s s f u l but are a l s o o f t e n very u n s u c c e s s f u l . One might c l a s s i f y s e v e r a l of these heat exchanger network s y n t h e s i s algorithms i n t o two broad c l a s s e s . There are s e v e r a l algorithms which view the s y n t h e s i s problem as one which s e l e c t s the next hot process stream/cold process stream match to make. The d i f f i c u l t i s s u e s are the d e f i n i t i o n of a match and which match to make next. Masso and Rudd (1969), Lee, Masso and Rudd (1970) and Pho and Lapidus (1973) s t a r t a match w i t h the two stream i n l e t cond i t i o n s and exchange a l l the heat p o s s i b l e , t e r m i n a t i n g when one stream reaches i t s t a r g e t o u t l e t temperature or when a temperature p i n c h o c c u r s . Ponton and Donaldson (1974), Donaldson, Paterson and Ponton (1976) and Grossmann and Sargent (1978) s t a r t a match at the hot end o f both streams (or as c l o s e to the hot end of the c o l d stream as p o s s i b l e ) . The i d e a i s to i n t r o d u c e necessary u t i l i t i e s at t h e i r l e a s t c o s t l e v e l w h i l e exchanging as much heat as p o s s i b l e . Rathore and Powers (1975) do both, g e t t i n g two a l t e r n a t i v e matches and o b v i o u s l y many more a l t e r n a t i v e networks. To solve a problem of t h i s f i r s t c l a s s i s to perform a t r e e search. Ponton and Donaldson use h e u r i s t i c s t o s e l e c t each next match and f i n d o n l y one s o l u t i o n , o f t e n a good one but not a l ways. Pho and Lapidus propose a t o t a l enumeration scheme, but, for v e r y large problems (10 streams), suggest a f a l l i b l e lookahead s t r a t e g y t o e l i m i n a t e branches. Lee, Masso and Rudd, Rathore and Powers, and Grossmann and Sargent propose u s i n g branch and bound s t r a t e g i e s . The enormous number o f a l t e r n a t i v e s generated by Rathore and Powers l i m i t s t h e i r a l g o r i t h m . A f t e r l o c a t i n g the b e t t e r s t r u c t u r e u s i n g a branch and bound a l g o r i t h m Grossmann and Sargent perform a continuous v a r i a b l e o p t i m i z a t i o n , s e v e r a l times reducing c o s t s by 10 to 30%. Note they have p a r t i t i o n e d the problem i n t o one of f i n d i n g the b e t t e r d i s c r e t e dec i s i o n v a r i a b l e v a l u e s f i r s t , u s i n g h e u r i s t i c s to s e t the v a l u e s for the continuous v a r i a b l e s . Then, with f i x e d d i s c r e t e v a r i a b l e s , they optimize the continuous v a r i a b l e s . For problems o f t h i s f i r s t c l a s s , stream s p l i t t i n g i s not permitted. The second c l a s s o f algorithms merge a l l heat sources or s i n k s o p e r a t i n g at the same temperature l e v e l . Thus i f p a r t s o f two or more hot streams have heat a v a i l a b l e over the same temperature range, those p a r t s are merged and t r e a t e d as one l a r g e r heat source i n that temperature i n t e r v a l . The f i r s t or outer l e v e l d e c i s i o n s are to s e l e c t which merged heat sources supply



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heat t o which merged heat s i n k s . These f i r s t l e v e l d e c i s i o n s e f f e c t i v e l y p a r t i t i o n the problem i n t o a s e t of smaller ones. I n each o f these small problems one must s e l e c t which stream p a r t s w i t h i n the merged streams are t o exchange heat. With t h i s second approach, one should expect to develop networks which are more thermodynamically r e v e r s i b l e because they w i l l have a more u n i form average ΔΤ d r i v i n g f o r c e throughout than r e s u l t s when u s i n g the f i r s t approach. Stream s p l i t t i n g i s r e a d i l y accommodated. The networks w i l l l i k e l y have more heat exchangers too however, a disadvantage. Algorithms f a l l i n g i n t o the second c l a s s i n c l u d e those by N i s h i d a , Kobayashi and Ichikawa (1971) , Hohmann and Lockhart (1976) and L i n n h o f f and Flower (1978a,b). In a sense the assignment problem i n l i n e a r programming based algorithms belong t o t h i s second c l a s s o f algorithms. The r e a l l y s i g n i f i c a n t r e s u l t s f o r the heat exchanger net work s y n t h e s i s problem have been g i v e n f i r s t by Hohmann (1971) and then l a t e r by L i n n h o f f and Flower and others ( L i n n h o f f and Flower (1979a), Flower and L i n n h o f f (1978), L i n n h o f f , Mason and Wardle (1979)). These r e s u l t s are as f o l l o w s . 1)

One can r e a d i l y determine the minimum amount of each type o f u t i l i t y needed to e f f e c t the needed h e a t i n g and c o o l i n g w i t h out having t o develop a heat exchanger network t o accomplish it.

2)

One can e a s i l y p r e d i c t the l i k e l y l e a s t number o f heat ex changers r e q u i r e d i n t h i s network.

A l l the example problems i n the l i t e r a t u r e demonstrate that the b e t t e r networks, from an annualized cost p o i n t o f view, use the minimum amount of u t i l i t i e s and the fewest exchangers. Thus i t i s a s i g n i f i c a n t i n s i g h t to see that one can c a l c u l a t e these bounds before developing a network. The u t i l i t y usage bounds are d i s c o v e r e d q u i t e e a s i l y by u s i n g the temperature versus heat content ( k j / s ) r e p r e s e n t a t i o n (see F i g u r e 1). One simply merges (see Umeda, I t o h and Shiroko (1978)) a l l the hot streams i n t o one super hot stream and a l l the c o l d streams i n t o a super c o l d stream. These merged super streams are each t r e a t e d as a s i n g l e stream and are moved t o the r i g h t or l e f t u n t i l the minimum v e r t i c a l approach d i s t a n c e of the c o l d beneath the hot stream j u s t equals the allowed minimum ΔΤ (say 5°C) f o r the network. Exchange o f heat can occur between the hot and c o l d streams where the hot stream i s d i r e c t l y above the c o l d on t h i s diagram. The l e f t o v e r p o r t i o n s o f each must be dealt with using u t i l i t i e s . The fewest exchangers u s u a l l y needed i s N - l , where Ν i s the t o t a l number o f both process and u t i l i t y streams i n v o l v e d i n the network. S e v e r a l schemes suggest themselves f o r u s i n g these bounds. Obviously one can develop any network he or she chooses s u b j e c t to s a f e t y c o n s t r a i n t s , c o n t r o l l a b i l i t y c o n s t r a i n t s , e t c . , and



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then compare the r e s u l t s to these bounds. I f the network i s on these bounds, one probably has found an economic network. I f f a r from these bounds, one should attempt to improve the network he or she has developed. A second scheme i s to use these bounds as a means t o e s t i mate q u i c k l y the p o t e n t i a l heat exchanger network c o s t s f o r a flowsheet. Thus s e v e r a l d i f f e r e n t process flowsheets might be compared q u i c k l y without developing the exchanger network i n detail. A t h i r d scheme developed by Flower and L i n n h o f f (1978) i s to generate d i r e c t l y a l l networks having the two p r o p e r t i e s o f m i n i mum u t i l i t y usage and fewest exchangers. Remarkably few (under 10) networks r e s u l t f o r the example problems they use t o i l l u s t r a t e t h e i r approach. These are considered then as prime c a n d i dates f o r being the optimal network. L i n n h o f f and Flower (1978a) note t h a t , i f a p i n c h p o i n t occurs f o r a network, then i t e f f e c t i v e l y decomposes the heat exchanger s y n t h e s i s problem i n t o two d i s j o i n t s y n t h e s i s problems. No heat can be exchanged between two streams where one i s above the p i n c h and the other i s below i f one wishes to use the minimum amount o f u t i l i t i e s . Note t h a t t h i s p a r t i t i o n i n g may i n c r e a s e the fewest exchangers p o s s i b l e as each p a r t i t i o n must be t r e a t e d separately. Cerda and Westerberg (1979) have g e n e r a l i z e d the s o l u t i o n to the minimum u t i l i t y usage problem by showing how to s o l v e i t when p a r t i c u l a r hot stream/cold stream matches are f o r b i d d e n i n t o t a l or i n p a r t . I n t h i s form, the d e s i g n engineer can d i s c o v e r the e f f e c t o f f o r b i d d i n g a p a r t i c u l a r match or s e t o f matches on the minimum u t i l i t y c o s t s . The a n a l y s i s i s extremely f a s t and i s r e a d i l y implemented as an i n t e r a c t i v e program. Hohmann (1971) and l a t e r Umeda, N i i d a and Shiroko (1979) and Urneda, Harada and Shiroko (1979) i n d i c a t e how to use the heat content diagram (see F i g u r e 1) t o f i n d the m o d i f i c a t i o n s which l e a d t o improvements i n the heat i n t e g r a t i o n f o r a g i v e n flowsheet c o n f i g u r a t i o n . A t o t a l c o o l i n g curve f o r a l l heat sources i s drawn against a t o t a l h e a t i n g curve f o r a l l heat s i n k s , i n cluding a l l u t i l i t i e s . These curves are then moved together unt i l they reach an allowed minimum approach temperature. This moving together t r a n s l a t e s i n t o a heat i n t e g r a t i o n among the sources and sinks s i n c e i t w i l l show where c e r t a i n sources can be used t o heat c e r t a i n s i n k s . Moré i m p o r t a n t l y i t a l s o shows where the curves " p i n c h , " that i s , the p o i n t s on the t o t a l h e a t i n g and c o o l i n g curves which produce the l i m i t i n g approach temperature. The next step i s to modify the flowsheet (done manually) i n such a way that the p a r t i c u l a r streams i n v o l v e d i n the p i n c h move apart on the temperature versus heat content diagram, w h i l e c r e a t i n g no p i n c h c o n d i t i o n s elsewhere on the diagram. Changes i n clude i n c r e a s i n g a d i s t i l l a t i o n column p r e s s u r e so the condenser becomes a h o t t e r source stream, r e d u c i n g a column pressure so the r e b o i l e r becomes a c o l d e r heat s i n k , i n t r o d u c i n g a p o r t i o n of the



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r e b o i l e r duty to a column p a r t way up the column (see Peterson and Wells (1977)) and thus a t a lower temperature, and running a r e a c t o r s l i g h t l y h o t t e r o r c o l d e r . A f t e r making process a l t e r n a t i o n s t h a t move apart the temperatures which c r e a t e the p i n c h , the two curves on the temperature versus heat content diagram can be moved together even more u n t i l another p i n c h p o i n t occurs. Again, t h i s p i n c h p o i n t suggests the p l a c e where u s e f u l m o d i f i c a t i o n s might be made. T h i s process continues u n t i l no f u r t h e r m o d i f i c a t i o n s e x i s t , which h o p e f u l l y occurs when the curves p i n c h i n s e v e r a l p l a c e s along t h e i r e n t i r e l e n g t h . Each m o d i f i c a t i o n probably c o s t s money which can be balanced a g a i n s t the savings i n utilities. The engineer can stop when the m o d i f i c a t i o n c o s t s more than the savings or when he o r she does not l i k e the process r e s u l t i n g from the heat i n t e g r a t i o n . There i s no doubt t h a t these i n s i g h t s lead t o u s e f u l t o o l s for the design engineer, and i n d u s t r y can no longer a f f o r d t o ignore them. I f no other r e s u l t s came from the s y n t h e s i s l i t e r a t u r e , these alone would j u s t i f y i t s e x i s t e n c e . Future s y n t h e s i s questions t o be answered i n energy i n t e g r a t i o n should i n c l u d e mechanical energy as w e l l as heat energy. For example, the energy c o n s e r v a t i o n schemes r e q u i r e d f o r an ammonia p l a n t r e q u i r e one t o c o n s i d e r t u r b i n e s as w e l l as heat exchangers. S e p a r a t i o n System S y n t h e s i s . The f i r s t paper which d e a l s w i t h s e p a r a t i o n system s y n t h e s i s appears t o be t h a t by Lockhart (1947). The next was by Herbert (1957) and t h i r d by Rod and Marek (1959). Then a f l o o d o f papers s t a r t e d around 1970. The m a j o r i t y o f these papers d e a l w i t h f i n d i n g s e p a r a t i o n sequences comprising simple separators o n l y ; t h a t i s , each component i n the feed t o a separator leaves the separator i n only one o f i t s two product streams. A second assumption made i s t h a t each separator method, e.g. simple d i s t i l l a t i o n , e x t r a c t i v e d i s t i l l a t i o n w i t h e x t r a c t i v e agent S i , or e x t r a c t i v e d i s t i l l a t i o n w i t h e x t r a c t i v e agent S2, imposes an o r d e r i n g on the components i n the feed mixture t o the problem. That i s , each separator method has i t s own component o r d e r i n g , where the f i r s t component i n the o r d e r i n g i s the most " v o l a t i l e " and the l a s t the l e a s t " v o l a t i l e . " Splits u s i n g a p a r t i c u l a r method can only occur between adjacent components on the ordered l i s t f o r t h a t method, and a l l those components above the s p l i t on the ordered l i s t go t o one product, a l l those below t o the other. The r e p r e s e n t a t i o n used f o r t h i s problem i s always some v a r i a t i o n o f the s p l i t l i s t , o r i g i n a l l y d e s c r i b e d by Hendry and Hughes (1972). F i g u r e 4 i l l u s t r a t e s . Thompson and King (1972) presented a computer program t o invent s e p a r a t i o n system flowsheets based e n t i r e l y on simple sepa r a t o r s . The program i s e n t i r e l y h e u r i s t i c , i s very f a s t when i t works, but has a problem w i t h c y c l i n g and thus not always t e r m i n a t i n g w i t h an answer.




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Figure 4.

Split-list representation for simple separation sequence

Simultaneous w i t h the above paper, Hendry and Hughes (1972) presented an a l g o r i t h m f o r the same problem but based on dynamic programming. F o l l o w i n g these were a number o f papers f o r the same problem u s i n g branch and bound algorithms (Westerberg and Stephanopoulos (1975), Rodrigo and Seader (1975), Gomez and Seader (1976)) and e v o l u t i o n a r y search (Stephanopoulos and Westerberg (1976)). Of the algorithms f o r " l i s t s p l i t t i n g " sequences, one which seems r a t h e r s u c c e s s f u l even when a p p l i e d by hand combines heur i s t i c s and e v o l u t i o n (Seader and Westerberg (1977)). F i r s t a set o f h e u r i s t i c s i s g i v e n i n a rank o r d e r i n g , w i t h the h e u r i s t i c deemed most e f f e c t i v e by the authors g i v e n f i r s t , the one which i s deemed next most e f f e c t i v e second, e t c . To s o l v e a s e p a r a t i o n s y n t h e s i s problem, these h e u r i s t i c s are used to invent a good f i r s t s o l u t i o n . Often the h e u r i s t i c s are i n c o n f l i c t , but the h i g h e r ranked ones are used i n p r e f e r e n c e to the lower ranked ones i n i t i a l l y . Then, u s i n g a s e t o f e v o l u t i o n a r y r u l e s , the des i g n e r invents a complete s e t o f neighboring s t r u c t u r e s t o h i s f i r s t solution. (A much improved s e t o f r u l e s t o develop neighbors i s g i v e n by Westerberg i n the notes f o r the AlChE advanced seminar on Process Synthesis (Motard and Westerberg (1978)). The neighbors are p l a c e d onto an ordered l i s t , where the o r d e r i n g i n d i c a t e s the rank o f the c o n f l i c t i n g h e u r i s t i c which suggests t h i s neighbor might be b e t t e r . Next t h i s l i s t o f neighbors i s searched i n sequence u n t i l e i t h e r a neighbor g i v e s an improved s t r u c t u r e or u n t i l no neighbor g i v e s an improvement. I n the f i r s t case, the neighbor g i v i n g an improvement becomes the next candidate sol u t i o n ; i n the second case the search stops. A v a r i a t i o n t o r e duce the e f f o r t i s to drop a l l neighbors from the l i s t not supp o r t e d by any h e u r i s t i c . Nath and Motard (1978) present a c l o s e l y r e l a t e d a l g o r i t h m but a l s o i n c l u d e an h e u r i s t i c a l l y invented s c r e e n i n g f u n c t i o n t o order the l i s t o f neighbors. They a l s o invent a neighboring


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11

s t r u c t u r e by d e s t r o y i n g a l l "downstream s t r u c t u r e from the p o i n t where the change occurs and using the h e u r i s t i c s to i n v e n t the needed a d d i t i o n a l s t r u c t u r e . Another c l a s s of s e p a r a t i o n problem attacked has been that o f d e s i g n i n g the most e f f e c t i v e t h e r m a l l y coupled d i s t i l l a t i o n column arrangement to separate a multicomponent mixture. Sargent and Gaminibandara (1975) present a general column s u p e r s t r u c t u r e which they optimize. Imbedded i n the s u p e r s t r u c t u r e are a l l the a l t e r n a t i v e thermally coupled and o r d i n a r y column sequences to be considered. The o p t i m i z a t i o n e l i m i n a t e s those p o r t i o n s of the s u p e r s t r u c t u r e which are not economic l e a v i n g , h o p e f u l l y , the optimal substructure. Tedder and Rudd (1978) present the r e s u l t s of a study of the economics of s e p a r a t i n g a v a r i e t y of three component mixtures u s i n g a v a r i e t y of thermally coupled and o r d i n a r y columns. T h e i r g o a l was to expose trends. They show which feed c h a r a c t e r i s t i c s favor which column s t r u c t u r e . No one as y e t has developed an a l g o r i t h m s u i t a b l e f o r a gene r a l s e p a r a t i o n problem which uses f l a s h u n i t s , b l e e d streams, mixers, e t c . , as w e l l as " l i s t s p l i t t e r " columns i n the s o l u t i o n . Such an a l g o r i t h m would have to handle p a r t i a l s p l i t s . A t b e s t the algorithms f o r a t o t a l flowsheet might give an approach but not a s o l u t i o n to t h i s much more g e n e r a l problem. Synthesis o f Separation Systems w i t h Heat I n t e g r a t i o n . A v a r i a t i o n on the s y n t h e s i s of s e p a r a t i o n systems which leads to an even more complex s y n t h e s i s problem i s t o synthesize such s y s tems while a l s o attempting to reduce the use of u t i l i t i e s i n the r e b o i l e r s and condensers. A r e b o i l e r i s a heat s i n k or, i n our e a r l i e r terminology, a c o l d stream which needs to be heated. A condenser i s a heat source, that i s a hot stream. W i t h i n a s i n g l e column, the c o l d stream ( r e b o i l e r ) i s at a higher temperature than the hot stream (condenser). To get a match between them r e q u i r e s the expenditure of work, which i s of course the i d e a behind a vapor recompression c y c l e . On the other hand the condenser of one column can become the source of heat f o r a r e b o i l e r o f another. A l s o the column temperature l e v e l s can be i n c r e a s e d or decreased by i n c r e a s i n g or decreasing column p r e s s u r e . Increasi n g pressure w i l l u s u a l l y reduce the r e l a t i v e v o l a t i l i t i e s , thus i n c r e a s i n g the number o f stages and the r e f l u x r a t e s needed to o b t a i n a g i v e n s e p a r a t i o n . We t h e r e f o r e have the i n t r i g u i n g problem of s e l e c t i n g the best i n t e r n a l flows, p r e s s u r e s , and c o l umn sequence to accomplish the d e s i r e d s e p a r a t i o n task while savi n g to the extent p o s s i b l e on the use of u t i l i t i e s . The f i r s t e f f o r t s a t h a n d l i n g t h i s problem were by Rathore and Powers (1974a, 1974b). They developed a h i g h l y c o m b i n a t o r i a l approach based on dynamic programming. Sophos, StephanopouloÎ and Morari (1978) have developed a r e l a t e d approach but advocate an branch and bound a l g o r i t h m based on dual bounding through the use o f Langrangian techniques.


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F a i t h and Morari (1979) f u r t h e r develop the ideas o f u s i n g dual bounding through the use of Lagrangian techniques f o r t h i s problem. They d e s c r i b e refinements which a l l o w one to make a good f i r s t estimate to the Lagrange m u l t i p l i e r s (needed f o r the bounding) and to develop r a t h e r e a s i l y a "lower lower bound. They s t i l l need to apply these ideas to s e v e r a l examples to demonstrate t h e i r e f f e c t i v e n e s s . A subproblem t o the above i s t o f i x the s e p a r a t i o n sequence and attempt to improve the heat i n t e g r a t i o n by a d j u s t i n g p r e s sures, u s i n g intermediate column r e b o i l e r s ( r e b o i l e r s p a r t way up the column) and intermediate condensers, u s i n g vapor recompress i o n , e t c . King, Gantz and Barnes (1972) very s u c c e s s f u l l y developed by hand a sequence of e v o l u t i o n a r y steps to improve heat i n t e g r a t i o n w i t h i n a demethanizer column. The ideas we d i s c u s s e d e a r l i e r o f Umeda, N i i d a and Shiroko (1979) were f i r s t a p p l i e d to heat i n t e g r a t i o n o f columns and p r o v i d e a r e a l t o o l f o r t h i s subproblem. Thermally coupled columns are a l s o a means to heat i n t e g r a t e column sequences, and, while not mentioned y e t i n the l i t e r a t u r e s p e c i f i c a l l y as p a r t o f a s y n t h e s i s s t r a t e g y , i t i s c l e a r they should be. One s e r i o u s d i f f i c u l t y a s s o c i a t e d w i t h such column arrangements has been the l a c k of s h o r t c u t d e s i g n procedures f o r them so one can q u i c k l y i n v e s t i g a t e among the a l t e r n a t i v e s . Cerda (1979) has produced a s u i t e o f i n t e r a c t i v e programs f o r t h i s problem and w i l l be r e p o r t i n g on them at the November AlChE meeti n g t h i s year (Cerda and Westerberg (1979a)).


11

R e a c t i o n Path S y n t h e s i s . For the m a t e r i a l i n t h i s s e c t i o n the author i s r e l y i n g h e a v i l y on m a t e r i a l o r i g i n a l l y prepared by Motard (Motard and Westerberg (1978)). The u s u a l s y n t h e s i s problem here i s t o f i n d a sequence of r e a c t i o n s which can be used to reach a g i v e n t a r g e t molecule from a catalogue of a v a i l a b l e raw m a t e r i a l s . Almost a l l the work on t h i s problem has been done by o r g a n i c chemists w i t h the dominant names i n the f i e l d being Corey (see Pensak and Corey (1977)), Wipke (see Wipke e t a l . (1977, 1978)), G e l e r t n e r ( a computer s c i e n t i s t — s e e G e l e r t n e r e t a l . (1977)), Hendrickson (1976) and Ugi (see Brandt e t a l . (1977)). I n chemical e n g i n e e r i n g , Govind, Blower and Powers (1976) and A g n i h o t r i and Motard (1978) have been the most a c t i v e r e s e a r c h e r s . T h i s s y n t h e s i s problem has problems with every aspect: r e p r e s e n t a t i o n , e v a l u a t i o n and s t r a t e g y , w i t h e v a l u a t i o n probably being the most d i f f i c u l t . B a s i c a l l y three r e p r e s e n t a t i o n s e x i s t . The ones by Corey, Wipke and G e l e r t n e r are r a t h e r d i r e c t , u s i n g e s s e n t i a l l y l i n k e d l i s t s and a v a r i e t y of f u n c t i o n codes to encode the molecule. Hendrickson has a more g e n e r a l i z e d represent a t i o n i n which he c l a s s i f i e s each carbon atom i n a molecule by the types o f bonding i t has w i t h other carbon atoms and by the types of heteroatoms attached to i t . H i s r e p r e s e n t a t i o n does not d i s t i n g u i s h among heteroatoms, except t o note i f they are more or l e s s e l e c t r o n e g a t i v e than carbon. With t h i s r e p r e s e n t a t i o n a



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number of molecules are t r e a t e d as e q u i v a l e n t i f they have the same s t r u c t u r e and the same g e n e r a l f u n c t i o n a l i t y groups attached. Govind, Blower and Powers extend t h i s r e p r e s e n t a t i o n and use i t i n t h e i r work. The l a s t r e p r e s e n t a t i o n i s that by Ugi where a molecule i s represented by a bond e l e c t r o n connection m a t r i x . The bond e l e c t r o n connection m a t r i x (BECM) i s a symmetric m a t r i x whose rows and columns are the i n d i v i d u a l atoms i n each o f the molecules being c o n s i d e r e d . A p a r t i c u l a r molecule i s represented by m a t r i x elements a.. where a . i s the number of e l e c t r o n s i n the bond between t h e ^ w o atoms I and j . A r e a c t i o n i s represented by a m a t r i x which when added t o the BECM f o r the r e a c t a n t s y i e l d s the BECM f o r the p r o d u c t s . U g i shows that these r e a c t i o n matrices are r e s t r i c t e d as t o t h e i r s t r u c t u r e . A g n i h o t r i and Motard use U g i s representation. 1

As i n d i c a t e d e a r l i e r , e v a l u a t i o n i s probably the most d i f f i cut problem. How does one conjecture the value o f an a r b i t r a r y r e a c t i o n ? Thermodynamics can t e l l one how f a r a r e a c t i o n may p r o ceed, but no one can y e t p r e d i c t how f a s t a r e a c t i o n w i l l proceed since the r a t e depends on such things as the e f f e c t of c a t a l y s t s . A l s o a s s e s s i n g the p r o c e s s i n g c o s t s i s a complex e x e r c i s e . Gen e r a l l y , e v a l u a t i o n i s done very i n d i r e c t l y i n these programs by allowing the use o n l y o f named chemistry and then, f o r those r e a c t i o n s which might work, other e f f e c t s such as s t e r e o hindrance are sometimes examined. The s y n t h e s i s s t r a t e g y i s almost always to s t a r t from the t a r g e t molecule and work backwards t o the source m a t e r i a l chem icals. I n t h i s manner one s e l e c t s the source m a t e r i a l chemicals indirectly. To synthesize a t a r g e t molecule by working forward from a p r e s c r i b e d s e t o f source m a t e r i a l chemicals may be p o s s i b l e i f one has p a r t i c u l a r l y good i n s i g h t , but such an approach w i l l g e n e r a l l y be l e s s e f f i c i e n t and may l e a d t o no s o l u t i o n i f one guesses i n c o r r e c t l y on which m a t e r i a l s to use i n i t i a l l y . The one i m p l i c i t h e u r i s t i c encoded i n almost a l l the p r o grams produced so f a r i s that each step backward from the t a r g e t molecule must be from a source molecule which i s s t r u c t u r a l l y no more complex than the immediate t a r g e t . Thus r e a c t i o n paths are not found which pass through complex intermediate molecules. The search s t r a t e g i e s seem to be v a r i a t i o n s on two: develop the a l t e r n a t i v e s 1) by l o o k i n g a t f u n c t i o n a l i t y and 2) by l o o k i n g at s k e l e t a l s t r u c t u r e o f the molecule. To look at f u n c t i o n a l i t y i s to look f o r such t h i n g s as double bonds, -COOH groups, -OH group and the l i k e . To look at the s k e l e t a l s t r u c t u r e on the other hand i s t o look f o r p a t t e r n s i n the molecules, l i k e r e peated r i n g s . The f i r s t i s a m i c r o s c o p i c view and the second a macroscopic view. Hendrickson p r e f e r s the l a t t e r w i t h most others the former. I n the former, t y p i c a l l y a computer r o u t i n e or equiv a l e n t i s w r i t t e n f o r each r e a c t i o n type, w i t h perhaps 300 to 500 such r o u t i n e s e x i s t i n g . Each r o u t i n e has a check l i s t at the be g i n n i n g . The check l i s t looks at the t a r g e t molecule to see i f i t has the c o r r e c t f u n c t i o n a l groups, to see i f the carbon " β " t o the



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reaction site has the right appendages, etc. I f that l i s t can be passed through successfully with a target molecule, the reac tion becomes a candidate. For each step backward from a target molecule, each of the 300 to 500 reactions i s rated and only those with the higher ratings are kept. In one set of programs the user i s then presented with the preferred options, and he or she interactively selects those he or she wishes to pursue. Hendrickson prefers applying his method by hand. He has written a book on his method which contains a very long l i s t of so-called half reactions and a general synthesis tree that one uses to de velop his or her reaction paths. Some of the computer programs developed to do reaction path synthesis apparently are very impressive. Subject to the above r e s t r i c t i o n forbidding complex intermediates, some of them may well out-perform many organic chemists for the class of problems they can handle. May and Rudd (1976) present a very interesting paper on r e action path synthesis for a special class of inorganic reactions which they t i t l e d solvay clusters. A solvay cluster i s a se quence of reactions equivalent to one overall net reaction which refuses to go at reasonable industrial conditions. To be a cluster the reaction sequence must make use of other species which are f i r s t used and then fully recovered later i n the se quence, an example being 2HC1 + Mn 0 + 2MnCl = 2MnO + H 0 + 2MnCl 2

Cluster

3

3

***h

2

3 2 2MnO + CO - Μ η 0 + C =

2 M n C l

+

£

2

m

C

l

' 2 H

+

C l

C l

3

C + H 0 = CO + H Reaction

4

2

2

Each of the reactions i n a successful cluster w i l l proceed at reasonable industrial conditions. May and Rudd show that clusters are very conveniently rep resented p i c t o r i a l l y using what they term "nested polygons." Thus one can quickly generate alternative solvay clusters. They also describe a convenient method to represent p i c t o r i a l l y the free energy of the reactions versus reaction conditions (T and P). Using this representation one can quickly select reactions sequences which form a thermodynamic a l l y viable solvay cluster. Included i n the article are some clever ways to extend the l i s t of potential reactions. As May and Rudd point out, their approach only allows one to find a thermodynamically plausible cluster, but one w i l l need further evaluation methods to see i f the reactions rates are adequate and i f the implied processing problems can be reasonably solved.



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T o t a l Flowsheet S y n t h e s i s . S e v e r a l approaches to t o t a l flowsheet s y n t h e s i s appear i n the l i t e r a t u r e . The f i r s t was the AIDES system developed by S i i r o l a , Powers and Rudd (1971). A second i s the BALTAZAR system by Mahalec and Motard ( 1977a,b). The l a t e s t and one which seems t o be v e r y i n t r i g u i n g i s by Johns and Romero (1979). I n these e f f o r t s the problem s o l v e d i s to develop an e n t i r e process flowsheet g i v e n the r e a c t i o n s t o be a l lowed, d e s i r e d product streams and a v a i l a b l e raw m a t e r i a l s . The programs a u t o m a t i c a l l y invent the e n t i r e s t r u c t u r e needed from a f u n c t i o n a l p o i n t of view i n c l u d i n g s e p a r a t o r s , r e a c t o r s , s p l i t t e r s , mixers, pressure changers, temperature changers, and the r o u t i n g of a l l flows i n c l u d i n g r e c y c l e s where a p p r o p r i a t e . I t i s probably f a i r to say t h a t these programs do a reasonable job on many problems but that they cannot y e t compete w i t h a competent design engineer. The r e p r e s e n t a t i o n f o r a t o t a l flowsheet i s handled s i m i l a r l y by AIDES and BALTAZAR. T h e i r view i s to transform streams d e f i n e d by temperature, p r e s s u r e , t o t a l flow, s t a t e , chemical species and t h e i r mole f r a c t i o n s by a p p l y i n g a sequence o f tasks such as temperature changing ( h e a t e r s , c o o l e r s ) , pressure changing ( v a l v e s , pumps, compressors), composition and flow changing ( s e p a r a t o r s , m i x t e r s , s p l i t t e r s ) and k i n d o f s p e c i e s ( r e a c t o r s ) . Johns and Romero view streams more c r u d e l y . They use b i n a r y (0 or 1) f l a g s to note the presence or absence o f a component or to note that a stream i s at h i g h or low pressure or h i g h or low temperature or t o note the presence or absence o f a contami n a n t , e t c . T h e i r d e s c r i p t i o n of a process i s to l i s t a l l poss i b l e streams represented by t h e i r b i n a r y f l a g p a t t e r n and then to work out a s t r u c t u r e which connects them " o p t i m a l l y " to meet the s t a t e d design g o a l s . I n each case the e v a l u a t i o n of a flowsheet i s done very c r u d e l y , w i t h such g u i d e l i n e s as minimum mass flow i n t o separat i o n tastes being used. Of course such crude e v a l u a t i o n i s a l l that can be done i n the p r e l i m i n a r y stages because one i s not able to evaluate on an economic b a s i s u n t i l the process i s f u l l y s y n t h e s i z e d and the equipment s e l e c t e d ; these programs stop short of s e l e c t i n g a c t u a l equipment. For these programs the problem i s to c r e a t e a s t r u c t u r e which can transform raw m a t e r i a l s sources i n t o d e s i r e d product streams. BALTAZAR uses b a s i c a l l y a depth f i r s t s t r a t e g y f o l lowed by e v o l u t i o n to d i s c o v e r i t s s o l u t i o n . AIDES on the other hand uses a breadth f i r s t s o l u t i o n , s e l e c t i n g the b e t t e r a l t e r n a t i v e s by doing a one step look ahead at each d e c i s i o n s t e p . Johns and Romero view the s y n t h e s i s problem as one which enumerates a l l streams, and, whenever a t r a n s f o r m a t i o n i s needed between two streams, t h e i r approach i s t o look a t a l l process options capable of doing that transform and p i c k i n g the b e s t . I f one has three a l t e r n a t i v e simple s e p a r a t i o n methods (e.g. d i s t i l l a t i o n , e x t r a c t i v e d i s t i l l a t i o n with e x t r a c t i v e agent S i , and c r y s t a l l a t i o n ) to separate a 10 component mixture, the Thompson



70

and King (1972) formula mentioned earlier predicts over 9.5x10^ alternative configurations. However, only 1023 distinct process streams can ever occur i n a l l these processes. Thus the Johns and Romero strategy i s to represent a process by the total l i s t of a l l the streams i t can produce, viewing the streams crudely so only a small number of them exist. They estimate the problem size w i l l grow by 3 where η i s the number of binary flags used to describe a stream. They conjecture about 12 such flags can readily be handled and that this w i l l be sufficient for most preliminary synthesis problems. BALTAZAR starts with a product stream and makes i t the f i r s t goal to meet. I t searches among the source streams ( i n i t i a l l y , the raw material sources) to see i f they can supply this goal i n terms of species and their amounts. Sources are rank ordered depending on how close they are to the goal—is i t exactly what i s needed except for amount, does i t have only species needed i n the goal and no others, does i t have any species needed plus others which are not needed, etc. The closest stream i s selected as the source and appropriate s p l i t t e r s , mixers and separator tasks are invented to transform this source stream into the goal stream. While working on these transformations other goals and sources are l i k e l y created. Goals arise because the source may only provide part of the orig i n a l product stream; the part not provided becomes a new goal. Sources arise because a source may have left over portions not needed for the goal. These goals and sources are l i s t e d , with the last goal l i s t e d being the next one to be satisfied. I f a species i n a goal i s missing from a l l sources, a reaction must be selected which has the missing specie as a reaction product. The reactor feed becomes a new goal. In this manner an entire struc ture i s created which can produce the f i r s t product before the second product i s looked at, thus i t can be viewed as a depth f i r s t strategy. When developing the structure needed for the second product, a l l the streams of the existing structure can be used as sources thus the second product knows of the f i r s t , but not the reverse. BALTAZAR i s therefore sensitive to the order i n which i t looks at the products. To remove this dependence, BALTAZAR goes into an evolutionary mode, where a l l structure for the f i r s t product i s destroyed. Then the structure i s reinvented, but this time the structure for the other products exists. The structure i s r e peatedly destroyed and reinvented for each product i n sequence u n t i l the structure does not change. Few iterations seem to be required to get the structure to s t a b i l i z e , and the result seems not to depend on the original order i n which the products were listed. AIDES has to be given the particular reactions to be used for the process. Its f i r s t step i s to select which raw materials i t w i l l use and how much of each by selecting those which cost the least overall. I t assumes a l l reactant species w i l l be r e cycled and ultimately converted when selecting the amounts needed.


n



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Next, i t does a species allocation, deciding in one step where a l l species shall pass through the flowsheet. A scoring function is created for eachspecies going from a source to each potential destination. This scoring function attempts to account for potential separation costs which might result i f the match were made. Which separation tasks w i l l occur depends on a l l matches made so this scoring step cannot be done exactly. The essential idea is that after working out a l l possible species source/destination matches, developing a score for each, the total species matching is done a l l at once (by solving a linear program). The matching is then fixed. Next the separation tasks which actually result are looked at and solved. These result from having different species in a source stream matched to different destination streams. AIDES uses this look ahead, scoring, and then making of a l l match decisions at once as its way of developing the better flowsheets. It can be viewed as a breadth f i r s t algorithm therefore. From the evidence, i t is not yet possible to say which approach is better, that used by AIDES or that by BALTAZAR. Of i n terest is that two such different approaches exist, and both seem to get reasonable structures. Johns and Romero use a very different strategy to create a flowsheet. As stated earlier their approach is based on finding the best transformations among the small number of streams which can exist, regardless of the process structure. Obviously they need a crude definition for a stream to keep the number of streams small. For separation sequences, where each separator sharply splits the feed into two products, each of which have no species in common, the crude stream approximation is in fact accurate and was the f i r s t problem solved using this approach (Johns (1977)). The synthesis starts with a single specified feed and a l i s t of acceptable process output streams. It also starts with a l i s t of possible unit transformations. The units are defined by conditions which must be met by the input streams and limitations which describe the outputs in terms of inputs. No more than two input or two output streams are allowed for a unit. A crude cost correlation is also required for each unit. The algorithm is one which starts with the specified input stream and systematically works its way through a process to a l lowed output streams. Using a mixture of branch and bound and dynamic programming based arguments, the algorithm locates the least cost flowsheet structure. In essence, any time a pair of streams within the process can be connected by a unit, then a l l units are examined which can make that connection and the least cost one selected. The calculations associated with the enormous number of alternative structures are very significantly reduced by this two level approach. Johns and Romero discuss how the program may be used to solve a variety of synthesis problems including reactors, multiple


72


(more than two) input and/or output units, processes with recycles and/or bypass streams. Each involves using the program by being clever on the unit input/output restrictions and/or the a l lowed process products. In some instances one risks generating unrealizable flowsheets, particularly for the recycle case, but they give "gambits" for overcoming such d i f f i c u l t i e s . Johns and Romero justify their very crude stream definition by arguing that the program is for very early process synthesis, to discover the general structure l i k e l y to be needed. The a l gorithm appears both interesting and restricted by the approach, but one might guess many of the restrictions may disappear when one finds a clever way around them, s t i l l within the "spirit of the program. It seems unlikely the method can deal effectively with a heat exchanger network synthesis problem. It is clear that i t can deal very well with synthesizing a sequence of sharp simple separators. Friedler, Blickle, Gyenis and Tajan (1979) describe an a l gorithm for generating a l l alternative flowsheets which can be produced from given raw materials, products and single step transformations. The method uses an abstract algebraic method. They define as the basic "operand" in their algebra, a process stream at a given set of conditions so, i f the temperature or flow rate or composition is altered, one has a different operand. Like Johns and Romero, i t appears they must use a crude stream definition ( i . e . they must judiciously discretize the continuous variables) to prevent an explosive growth in the number of operands and a resulting combinatorial growth in the number of flowsheets. While i t is interesting to be able to generate a l l possible flowsheets, one must s t i l l remember that, for most synthesis problems, the problem is that there are far too many for total enumeration to be practical. It is d i f f i c u l t to assess the power of the approach u n t i l some example problems are presented. Another class of total flowsheet synthesis algorithms is that of "embedding," where (as stated earlier) a superstructure is invented which contains a l l the desired flowsheet arrangements as substructures within i t . Optimization is used to remove those portions of the superstructure which are not worthwhile, leaving the optimal flowsheet. This approach s t i l l requires one to invent the superstructure before i t is similar in capability to the three algorithms just described. However, as with the Romero and Johns view, a superstructure may be relatively small because of the limited number of streams possible. Several papers on this approach convert the optimization problem to one using continuous "structural parameter" variables (Umeda, Hirai and Ichikawa (1972); Umeda, Shindo and Tazaki (1972); Osakada and Fan (1973); Ichikawa and Fan (1973); Mishra, Fan and Erickson (1973a,b); Himmelblau (1975); Sargent and Gaminibandara (1975)). Here the idea is to s p l i t the exit flow of each unit into part-flows to each of the potential target


11



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Process Synthesis

units for that output, with the s p l i t fractions being continuous variables ranging in value from zero to one and adding to unity. These s p l i t fractions are labeled structural parameters and, i f optimized to zero, indicate the associated stream does not exist in the final flowsheet. The hope that one has converted the dis crete problem of including or deleting portions of a structure in the final flowsheet to a continuous variable optimization problem is fraught with danger as shown by Shah and Westerberg (1977). Without considerable care inequality constraints may defeat the approach because they may cause discontinuities to occur at the boundaries of the feasible region. In essence the discrete de cisions are often really s t i l l present. The method may also suffer from the presence of local optima (Westerberg and Shah (1978); Shah and Westerberg (1979)). Such optima are almost guaranteed i f the same substructure can be created from the su perstructure in more than one way. Grossmann and Santibanez (1979) suggest that the approach of embedding can be very effectively and quite generally handled by reformulating the problem as a mixed integer linear program. This approach brings back memories of quite early work in the o i l industry where the same tool was used for similar problems. One's first reaction is to reject the adequacy of casting the problem as a linear one, but, as Grossmann and Santibanez show, the use of discrete (zero/one) decisions allow one to include to a very good approximation many of the nonlinearities. For ex ample, a zero/one variable can be associated with the existence or non-existence of a unit. In the cost function that discrete variable can cause one to add in a fixed charge for the unit only i f i t exists. Also one can define a continuous "flow" variable for the unit which can be forced to zero i f the unit does not ex i s t by the linear constraint: Flow

£ Discrete Variable

χ Maximum Flow

A variable cost for the unit can be assessed proportional to the continuous flow variable. Note that a fixed cost plus variable cost for a unit is not a convex function. Mixed integer linear programming codes exist which can solve very large problems of that type (several thousand constraints). They generally use branch and bound algorithms. Grossmann and Santibanex solve two very different synthesis problems using em bedding and a mixed integer linear programming formulation. The results are impressive. Control System Synthesis. The synthesis problem for control systems is to select the controllers needed to meet specified control goals for a fixed plant configuration. The designer se lects his goals by stating which variables he wishes controlled. The synthesis algorithm selects which variables to measure, which to manipulate and what type of controllers to use.



74


Govind and Powers (1976, 1978) have developed a synthesis algorithm which deliberately uses very crude process models. Their idea i s to see how well one can automatically generate a control scheme using essentially no more information than control engineers currently appear to use. The controllers permitted are conventional PID controllers. The control schemes include simple, cascaded and s p l i t range structures, using both feed-forward and feed-back schemes. The crude process models are called causeand-effect models. They allow only certain directions of information flow, reflecting that which the units being modeled permit. For example, the temperature of the inlet to a heat exchanger is allowed to affect the outlet temperature but not the reverse. The models include process gains to indicate i f a small change in a "causal" variable w i l l lead to a large or small, posi t i v e or negative change in each affected variable. Also, process delay times are estimated and are part of the models. Using these models, alternative sets of variables are generated which can be measured to allow an estimate of each v a r i able whose value is to be controlled. Similarly the system generates alternative sets of variables whose manipulation permits control of each variable to be controlled. Clearly i f the controlled variable can be measured and manipulated inexpensively and accurately, i t i s . Otherwise alternative sets are generated and ranked. Long delay times or poor gains between a measured or manipulated variable and the desired control variable w i l l give that choice a low rating. Govind and Powers also state a number of qualitative rules for liking or disliking various options for variables to be measured or manipulated, and these rules aid i n selecting which ones to choose. Cascading is tried i f the cascaded loops have different expected response times so they w i l l not fight each other. Stephanopoulos and Morari (1976, 1977) developed ideas related to those of Govind and Powers. They developed a modified view to selecting the manipulated and measured variables, aided by the concepts of "structural controllability" and "structural observability." Structural controllability and structural observability are similar to controllability and observability except they are based only on the zero/nonzero pattern of the appropriate matrices. The question asked is i f any numbers were to be allowed in these matrices, would the system be controllable or observable. Their other heuristic arguments for accepting or rejecting alternatives are very similar to those of Govind and Powers. Umeda and Kuriyama (1978) describe a two level approach to control system synthesis. At the inner level control schemes are developed for each unit in the flowsheet. While these schemes would work for the unit i n isolation, they likely w i l l fight each other i f used together. Thus an outer level coordinating step examines and modifies these schemes to eliminate undesirable i n teractions. The two levels of activity are repeated u n t i l they both give the same structure.



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75

Brosilow and coworkers (Weber and Brosilow (1972); Easterday (1973); Joseph and Brosilow (1978a); Brosilow and Tong (1978); Joseph and Brosilow (1978b)) present another control synthesis technique. They term i t linear inferential control, and i t s purpose is to select which variables to measure when developing a control scheme. This problem is obviously only part of that for the general control system synthesis problem. The proposed method ignores dynamics. They select the variables from among a given candidate set by examining the steady state sensitivity and the noise, and usually they pick more than one measurement for each control loop. Stephanopoulos and Morari (1977) add dynamic compensation considerations to this approach. Mellefont and Sargent (1978a) deal with selecting the measurement variables also, only they pose the problem as one to minimize a quadratic performance index for a linear stochastic system. The index included a quadratic term for cost of the controllers. They use a branch and bound algorithm to search for the best measurements to make. Mellefont and Sargent (1978b) also treat a more general problem in which the measurement subsets change during the cont r o l interval. Shinsky (1979) uses a relative gain matrix to select which variables to manipulate and measure. Again dynamics are ignored. The method allows one to find which variables influence which others the most i f they were put into a feedback control loop. Using embedding with a structural parameter formulation, Nishida, Liu and Ichikawa (1976) state the necessary conditions for optimality for both the structure and the control of a dynamic process system. They also permit some of the system parameters to take on uncertain values from within allowed ranges. The problem is stated as a minimax problem, where the maximum value of the performance index with respect to selection of the uncertain parameter values is minimized with respect to the cont r o l variables, the design decisions and the structural parameters. This problem is obviously a large one in that i t includes a l l the problems of optimal control with uncertain parameters as well as embedding in synthesis. Two example problems are given, with one i l l u s t r a t i n g that the minimax structure may well be different from the steady-state optimal structure. Arkun, Stephanopoulos and Morari (1978) have added a new twist to control system synthesis. They developed the theory and then demonstrated on two example problems how to move from one control point to another for a chemical process. They note that the desirable control point is l i k e l y at the intersection of a number of inequality constraints, the particular set being those that give optimal steady-state performance for the plant. Due to process upsets or slow changes with time, the point may move at which one wishes to operate. Also, the inequality constraints themselves may shift relative to each other. Arkun, Stephanopoulos and Morari provide the theory to decide when to move, and then develop alternative paths along which to move to the new



76


t a r g e t . The a l t e r n a t i v e paths i n v o l v e f o l l o w i n g d i f f e r e n t cons t r a i n t s . As new c o n s t r a i n t s become a c t i v e and o l d ones are r e leased along a path, new c o n t r o l s t r u c t u r e s may be needed; i . e . new loops must be s t r u c t u r e d dynamically. The s y n t h e s i s problem i s to s e l e c t the o r i g i n a l c o n t r o l s t r u c t u r e , to s e l e c t the path to t r a v e l and to r e s t r u c t u r e the c o n t r o l l e r s as one moves. This paper introduces what may become a v e r y i n t e r e s t i n g t o p i c i n control. Other Synthesis problems. One r e c e n t s y n t h e s i s p u b l i c a t i o n by N i s h i t a n i and Kunugita (1979) i s d i f f i c u l t to c l a s s i f y under the above headings. I t deals w i t h s e l e c t i n g the optimal vapor/ l i q u i d flow p a t t e r n s t o use f o r a m u l t i p l e e f f e c t evaporator system. The two obvious p a t t e r n s are cocurrent (the l i q u i d and vapor proceed through the system together) and counter c u r r e n t . Other p a t t e r n s are p o s s i b l e and o f t e n s i g n i f i c a n t l y improve the economics. The authors pose the problem as a m u l t i p l e o b j e c t i v e funct i o n problem, and, i n t h e i r example, consider the two competing o b j e c t i v e s o f t o t a l evaporator heat exchanger area and steam usage. The paper i s r e a l l y a c l e v e r way of e l i m i n a t i n g a number o f flow p a t t e r n s as never being candidates f o r the optimal s o l u t i o n r e g a r d l e s s of the r e l a t i v e importance of the c o s t f o r area versus steam c o s t s . For a p a r t i c u l a r t r i p l e e f f e c t example problem, they show t h a t , depending on the l i q u i d feed temperature, 3, 4 and even 5 of the p a t t e r n s out of 6 can be e l i m i n a t e d . The paper s i m p l i f i e s the a n a l y s i s r e q u i r e d f o r each c o n f i g u r a t i o n by e l i m i n a t i n g a l l continuous v a r i a b l e o p t i m i z a t i o n problems. ( T h i s sounds f a m i l i a r , does i t not?) Most notably they r e q u i r e a l l evaporator areas to be equal and add other s p e c i f i c a t i o n s s u f f i c i e n t i n number to absorb a l l the degrees of freedom. One might view some of these added s p e c i f i c a t i o n s as " h e u r i s t i c s . " F i n a l Comments Synthesis i s an a c t i v e r e s e a r c h area. S i g n i f i c a n t r e s u l t s have emerged from t h i s a c t i v i t y , p a r t i c u l a r l y i n heat exchanger network design. The a b i l i t y to e s t a b l i s h bounds on u t i l i t y usage and number o f exchangers r e q u i r e d and the use of the temperature versus heat content diagram to f i n d p i n c h p o i n t s are v e r y s i g n i f i c a n t t o o l s f o r design. A l s o very competent computer p r o grams now e x i s t to a i d i n organic r e a c t i o n path s y n t h e s i s . A number o f the other s y n t h e s i s s t r a t e g i e s must be f u r t h e r developed to make them u s e f u l f o r a wide range of i n d u s t r i a l problems. Separation system s y n t h e s i s , f o r example, needs to handle a wider c l a s s of s e p a r a t o r s . Many o f the c o n t r o l system synthes i s ideas which e s t a b l i s h the t o t a l c o n t r o l s t r u c t u r e are as y e t u n t r i e d on r e a l problems. The t o t a l flowsheet s y n t h e s i s a l g o rithms are as y e t only a beginning.



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Process Synthesis

77

Synthesis research has caused a number of people to organize their approach to process design. People now ask the right ques tion about design even i f the answers as yet are lacking. How does one locate the best structure for a process? How does one teach another person to do synthesis? The past emphasis i n teaching design has been on the analy sis of a given process. The current emphasis i s moving toward teaching how to invent the structure, and the synthesis tools give a framework from which to teach. The author has available a suite of interactive analysis programs including flash units, shortcut d i s t i l l a t i o n and absorption. I f students are not taught a design strategy, few w i l l systematically examine a l l the a l ternatives for a separation scheme. On the other hand, i f they are given the slightest insight into the synthesis problem and the established heuristics, they readily do a respectable job at inventing a flowsheet. Abstract Synthesis is the step in design where one conjectures the building blocks and their interconnection to create a structure which can meet stated design requirements. This review paper first defines chemical process synthesis and indicates the na ture of the research problems—to find representations, evalua tion functions and search strategies for a potentially nearly infinite problem. It then discusses synthesis research and the most significant results in each of six areas—heat exchanger networks, separation systems, separation systems with heat inte gration, reaction paths, total flowsheets and control systems. The main conclusions of the review are that industrially significant synthesis results now exist in energy conservation and reaction path synthesis and that the area of synthesis is a valuable research area. As a research area, it will produce significant results, though many of those available now are of limited usefulness on real problems. Literature

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RECEIVED November 5, 1979.


A Review of Process Synthesis - ACS Publications - American

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