Kroepelin, H., Winter, E., “Thermodynamic and Transport Parent, J. R., ScD thesis in Chemical Engineering, Laval Univ., Properties of Gases, Liquids and Solids,” ASLIE Symposium on Thermal Properties, McGraw-Hill, Sew York, NY (1959).

Kubert, R. B., Stephanou, S. E., “Extension to Multiphase Tremblay, D., SA1 thesis in Chemical Engineering, Laval Systems of the .Rand Method for Determining Equilibrium ComDositions.” in “Kine tics. Eauilibria and Performance of White. W. B.. Johnson. S. 11.. Dantzie. G. B.. J . Chem. Phws..

QUE, Canada (1966).

Univ., QUE, Canada (1970).

Plooster, 11. N., Reed, T. B., J . Chem. Phys., 31, 66 (1939).

- High:Temperature Systems,” G’ S. Bahn, E. E. Zukoski, Eds., Butterworths, London, England (1960).

Lafond, R., SM thesis in Chemical Engmeering, Laval Univ., QUE, Canada (1968).

Oliver, R. C., Stephanou, S. E., Baier, R. W., Chem. Eng., 69 (4), 121 (1962). of Canada.

28, 751 (1958). RECEIVED for review July 1, 1971

ACCFPTED Sovember 8, 1971 Financial support was given by the Sational Research Council

Systematic Evolutionary Process Synthesis

C. J. King,l D. W. Gantz, and F. J. Barnes Department of Chemical Engineering, Cnioersity of California, Berkeley, Calif. 94720

A strategy of systematic evolutionary process synthesis is described, wherein process configurations are successively improved by changing particular elements of the process. Heuristics are invoked to determine the portion of the process to b e modified and the modification to be made. Two examples of the use of this strategy are described. The first involves generation of demethanizer tower configurations for an ethylene plant, and leads to two novel processing improvements. One improvement consists of the generation of inter- mediate reflux in an amount which allows the overhead reflux to be generated by autorefrigeration; the other involves the introduction of solvent with the feed. The second example is implemented entirely on the computer and concerns the synthesis of a sequence of improved processes for methane liquefaction.

Process design has often been described as a succession of alternating steps of synthesis and analysis. Analysis typically involves calculating the outputs from a known process, given the input conditions (Figure 1). Sometimes one or more out- put variables may be specified, in which case the analysis may determine values of one or more input variables. Syn- thesis, on the other hand, requires the conception of a process which will transform given inputs into given outputs. Again, some but not all of the inputs and outputs may be unknown. Analysis characteristically involves deductive logic, while synthesis utilizes inductive logic. Alternative steps of syn- thesis and analysis imply first conceiving a process, then evaluating its capabilities and cost requirements, then using the information gained plus new ideas to generate a new process, then evaluating tha t process, and so forth.

Our capabilities of analysis in chemical process engineering are quantitative and highly developed. Process synthesis, by contrast, is an a r t involving thinking which has not been codified or even well-identified. I t is a much more difficult matter to structure inductive reasoning than it is for deductive reasoning. Nevertheless, the logic of synthesis is deserving of much more attention than i t is receiving, both because of its present underdeveloped state and because i t is the keystone of process development and design.

The logic required for systematic process synthesis is similar, on the surface a t least, to that involved in artificial intelligence or heuristic programming, which has been applied to such diverse problems as chess-playing, theorem-proving,

1 To whom correspondence should be addressed.

investment portfolio selection, and synthesis of large organic molecules (Feigenbaum and Feldnian, 1963; Corey and Wipke, 1969). The complexity of these problems and of pro- cess synthesis problems leads to the use of heuristics, which are rules of thumb capable of reducing the number of alter- natives to be explored by a considerable factor. A heuristic, however, cannot be proved to lead necessarily to the optimal solution; the efficiency which i t gives to the search must be balanced against its presumed likelihood of leading to the optimal or a near-optimal solution. Heuristics are often based on one’s physical knowledge of the system under con- sideration or on intuition. An algorithmic solution, on the other hand, can be shown necessarily to lead to the optimal solution, but is likely to be considerably more time-consuming than a heuristic solution.

There have been a few recent studies which are first steps toward placing the synthesis of chemical processes on a more systematic basis. Yearly all of these studies have dealt with the synthesis of heat exchange networks, a problem that is well-defined, is close-ended, and requires oiily a small number of basic processing concepts. Masso and Rudd (1969) de- scribe a heuristic approach for building a heat exchange network fixing one exchanger a t a tinie, in succession, using synthesis rules of thumb repeatedly chosen from a weighted list of rules. Kesler and Parker (1969) divided the heat ex- change duties of different streams into small increments and repeatedly carried out a linear programming solution to arrive a t the most desirable heat exchange network. Lee e t al. (1970) utilized concepts of branching and bounding the problem to arrive a t an efficient, algorithmic solution to heat

Ind. Eng. Chem. Process Des. Develop., Vol. 11, No. 2, 1972 271

INPUT (OUTPUT) PROCESS --+

A N ALYS I S

-I OUTPUT r------ -1 (PROCESS) I-

L _ _ _ _ _ _ _ J

SYNTHESIS

Figure 1. Contrast between analysis and synthesis

exchange network synthesis problems. Siirola e t al. (1971) investigated ways of assembling processing schemes by in- corporating recycle streams and simple separation steps about specified chemical reactors.

Evolutionary Process Synthesis

The previous approaches to systematic chemical process synthesis have been one-shot methods which are designed to utilize a single set of rules and generate a single process by a logical method well-suited to computer implementation. No particular effort has been made to imitate human process synthesis logic or to make use of analyses of past syntheses to generate an improved synthesis of a new process. An exception of sorts is the heuristic synthesis method of lfasso and Rudd (1969), who derived new weighting factors for their various heuristics based on their past success in improving the ob- jective function, and used updated weighting factors for repeated resyntheses of the entire process, starting from the beginning.

A human design engineer is most likely to approach process synthesis through an evolutionary strategy, wherein he de- vises a processing scheme, analyzes that scheme, changes the scheme in one or more ways to improve it, analyzes the re- vised scheme, improves it, etc. Such an approach directly maintains the good points of previously synthesized versions of the process during the search for better versions. I t is analogous to hill-climbing search techniques for optimization problems involving continuous variables; however, a synthesis problem necessarily involves discrete variables which can change in identity from one processing scheme to another. As is the case for the hill-climbing optimization techniques, the optimum reached by any evolutionary process synthesis strategy will necessarily be the best of the particular "hill" or class of processes to which the initially considered design eventually leads; it is not necessarily a global optimum process. On the other hand, it is questionable whether one can even speak of a global optimum design for an open- ended process synthesis problem, and in any event, the con- siderable amount of efficiency in the synthesis procedure which can be obtained by the heuristic of an evolutionary approach in many cases should offset the risk of missing a substantially better process configuration.

The idea of an evolutionary strategy is not totally new in heuristic programming, although it does not appear to have been used previously in any highly systematic way for chemical process synthesis. .in evolutionary strategy was employed, for example, by Kuehn and Hamburger (1963) for the problem of locating warehouses for product distribution over a wide area. They first synthesized a system of ware- houses, building the system up one-by-one from the start by applying particular heuristics-e.g., that only urban areas should be considered, that the next warehouse to be included should be the one which produces the greatest cost savings for the entire system, and that the potential warehouses to

Pressure, psia Temp, "F Flow, lb mol/hr

Hydrogen Methane Ethylene Ethane Propylene Propane

Total

Table 1. Demethanizer Specifications

Feed Vapor distillote Total Liquid Vapor product

460 65 - 20 - 150

1 , 770 45 1 , 725 1,770 2 , 980 375 2,605 2,965 3,080 1 , 246 1,834 X

740 377 363 . . . 1 , 290 1 , 007 283 . . .

140 113 27 , . . ~ ~

10,000 3 , 163 6 , 837 4,735 + z

Murphree vapor eff in tower = Refrigeration

Level

Ethylene -90'F Ethvlene - l5O'F

Materials Temp range

Carbon steel above -20°F Killed carbon steel 31/& Nickel steel

-70" t o -20°F -150" to -70°F

304 Stainless steel below - 150°F 50%

cost

$ 2 . lOimillion Btu $3 80/million Btu

Cost i f steam in reboiler = $0 50/million Btu Cost of ethylene lost in tail gas = 2 0 cents/lb Cost of recycled propane = 0 265 cents/lb

(available a t -80'F, 460 psia)

Bottoms product

460 about 50

15 3,080 - z

740 1,290

140 5,265 - x

272 Ind. Eng. Chem. Process Des. Develop., Vol. 11, No. 2, 1972

be considered each time should be that group of N sites \yhich would result in the greatest saving considering only local demand. Once a first netlvork of warehouses had been con- structed using this set of heuristics until no further cost- saving resulted, Kuehn aiid Hamburger then used a bump and shift rout'ine, in which they bumped any warehouse which was no longer economical because of subsequent additions and tested shifting each warehouse to a different site within the same general territory. The bump and shift procedure is clearly an evolutionary design strategy, while the means of synthesizing the first network is more similar to the heuristic network building strategy investigated by Masso and Rudd (1969) for heat exchangers. It may be tha t the evolutionary strategy is most suitable for t'he closing game, where the basic type of process has been established by some opening strategy, and improvements of that basic processing approach are now being sought as a final step.

I n this paper, two specific applications of systematic evolutionary process synthesis are presented. One is im- plemented entirely on the digital computer, while the other involves computer-implemented calculations, but the execu- tive design strategy is applied ment'ally. Both involve the same basic evolutionary strategy, as follows: A first, very simple process to accomplish the given task is soniehow synthesized. The weakest portion of that process is identified by an ap- propriate criterion. The portion of the process so identified is then modified through steps which are generated through other appropriate criteria. The same strategy is then repeat- edly applied to achieve more complex arid hopefully more desirable processes. Two levels of heuristics are required to implement this strategy-one to identify the portion of the process to be modified each time, and t'he other to generate the appropriate modification of that portion. Ai third level of heuristic may then be required to readapt the modified portion to the remainder of the previous process.

Synthesis of Demethanizer Configurations

The first synthesis problem Considered is t'he generation of improved designs for the deniethanjzer tower in an ethylene plant. This is a problem of considerable importance to industry. Xfter ainmonia, ethylene is t'he largest volume petrochemical, with a large amount of growth foreseen in the years to come. The design of the demet'lianizer column is one of the most critical aspects of the process, since demethaii- ization is expensive, and considerable savings are possible through good design (Fair et al., 1958; King, 1958; Frank, 1968). The function of the demethanizer tower is to remove hydrogen and methane from ethylene and heavier hydro- carbons as one of the first steps in product separation. Ue- cause of the light overhead stream, operation a t a high pres- sure aiid extensive use of refrigeration are required. 1 pres- sure of 40&500 psia is generally chosen for distillation if ethylene is the coldest refrigerant employed, representing the closest approach to the crit'ical conditions that can reliably be made.

Design Basis. The specifications established for the deniethaiiizer in the present study are given in Table I . The feed flow aiid conipositioti are typical of a large, modern plant receiving a naphtha feed to the pyrolysis furnaces. The factor 2 in the material balance represents the amount of ethylene lost with the tail gas, a dependent variable. The lo\Ter pressure allowed for the overhead vapor product (tail gas) stems from routing this stream to EL fuel h e . TKO available levels of ethylene refrigeration are postulated. The coldest of these corresponds to maiiiteiiaiice of a slight positive pressure 011

the refrigeration compressor suct'ion, a practice which may be conservative in a number of modern installations. All heat exchangers were designed to have a minimum approach temperature difference of IOOF. The demethanizer column in all cases was operated a t an overhead reflux flow equal to 1.25 t,imes the calculated minimum overhead reflux. For the calculation of the minimum reflux, the L-nderwood equations as adapted for multiple-feed towers (Barn& et al., 1972) were used, along with an enthalpy balance relating internal flows a t the controlling feed point to the overhead reflux flow. Postulation of a lower minimum ethylene refrigeration temperature, of a different minimum approach temperature difference in heat exchangers, or of a different factor relating the operating reflux to the minimum reflux will change the numerical results, but will not alter the synthesis logic or the general economic ordering of the different process con- figurations.

I n any real plant, the tail gas would be used in a number of heat exchangers for prechilling the feed or the overhead vapor, or for other purposes. This heat exchange would be common in all the processes considered, however, aiid \yould therefore not affect the cost difference between different process configurations. Because of this, the process boundaries were defined so that the feed was taken to be available a t - 20°F (the postulated coldest level of propane refrigerant), aiid the tail gas was released to the succeeding common heat exchange purposes a t - 150°F. Expansion engines were not considered as possible process steps.

The procedures used for sizing and determining costs of heat exchangers and the tower are described elsewhere (Barn&, 1970). The costing procedure was essentially that given in the 1959 AIChE Student Contest Problem (AIChE, 1959), modified for the June 1969, Chemical Engineering cost indices.

The thermodynamic properties of the components listed in Table I and their mixtures were supplied as subroutines to the computer. Details of these procedures are given elselvhere (Bards , 1970). Low-pressure vapor-phase enthalpies were provided as fourth-order polynomials in temperature. The combined low-pressure enthalpy for a mixture was corrected for pressure through the Kilson equat'ioii of state (Kilson, 1966; Chueh and Prausnitz, 1968). Liquid enthalpies were obtained in the same way, using bhe equation of state to give the effects of both pressure aiid the latent heat of condensa- tion. This procedure was found to give excellent agreement with the experiment'al enthalpy data of Tully aiid Edmister (1967). The parameters of the TTilsoii equation were obtaiiied using the mixing rules and prediction equations of Chueh and Prausnitz (1968). Vapor-liquid equilibrium data, es- pressed as K i = (yi/zt) a t equilibrium, were obtained by the method of Chao and Seader (1961), with two modifications (Barnh , 1970) : The Kilson equation was used rather than the Redlich-Kwong equation for the calculation of vapor fugacity coefficients, and the liquid fugacity for hydrogen was calculated using the unsymmetrical activity coefficient convention aiid a mixing rule for Henry's Law constants for binary systems involving hydrogen, as giveii by Chueh and Prausnitz (1968). The predicted Kt agreed well with the experinieiital data of Cohen et al. (1967) aiid Hanson et al. (1958).

Mass and heat balances for each process configuration were obtained by computer calculations, iterative in most cases, using the therniodynamic property subroutines. The results of the economic analyses following the sizing of equipment, are show1 in Table 11. An efficient stage-to-stage procedure for

Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 2, 1972 273

2 0

8 9 0

v) ml

0 9

3

9 0

I3

l r i

i

I3

l r i

w q 14OoF -143OF

I

Figure 2. Scheme 2: tail-gas autorefrigeration

calculating the plate requirement of the tower was pro- grammed, following a Lewis-Matheson type of approach (Bards , 1970). The results of these calculations, coupled with sizing calculations for tower diameter and materials selection for different sections of the tower, showed that the tower cost was a small and insensitive contributor to the total cost (Table 11); hence for simplicity, the tower cost was held constant from case to case. Four stages were taken above the topmost feed to the tower in all cases. Because of the high volatility of methane relative to ethylene, the four stages gave a close approach to a pinch. The annual fixed costs of the plant are computed allowing for numerous factors and are taken equal to 1.55 times the purchased cost of the basic equipment items.

Logic of Synthesis. The pattern of logic which may be followed for the evolutionary synthesis of successive de- methanizer designs is shown in Table 111, and will be ex- panded on here. The process that serves as a starting basis is the simplest that can be conceived, subject to the problem specification. This is Scheme I, a simple distillation with a partial condenser supplied with refrigeration a t the level iiecessary to generate reflux. The tail gas is released a t tower pressure. The economic evaluation of Scheme 1, shown in Table 11, reveals that the principal costs are associated with the loss of ethylene in the tail gas and the consumption of - 150'F refrigerant.

A key point to be realized a t this juncture is that the loss of ethylene in the tail gas is governed completely by the temperature of the separator drum where the tail gas is generated. The tail gas contains fixed amounts of hydrogen and methane and is a t the specified tower pressure when it is generated. Hence the temperature of that separator uniquely determines the amount of ethylene which must be included with the tail gas to make i t a saturated vapor stream leaving the separator. Generation of the tail gas a t a lower pressure will increase the ethylene loss; generation a t a higher pressure than tower pressure would require an expensive compressor and could give phase separation problems. Nodifying Scheme 1, a lower temperature for tail gas generation can be achieved by obtaining additional cooling beyond the -150'F con- denser through adiabatic expansion of the tail gas and heat exchange of the tail gas with the -140'F vapor. This auto- refrigeration effect will also slightly reduce the duty of the - 150'F condenser Jyhich is required to generate the requisite amount of overhead reflux. This modified process is Scheme 2 (Figure 2 ) . The separator drum has been cooled another 3'F.

I n Scheme 2 , the principal costs are still associated with the loss of ethylene and the consumption of -150'F re- frigerant. The consumption of - 150'F refrigerant can be

274 Ind. Eng. Chem. Prbcess Des. Develop., Vol. 11, No. 2, 1972

Table 111. logic of Synthesis for Demethanizer Designs

Scheme Means no.

. . . 1

Step

A

B

C

D

E

F

G

Weak point(s) Goal

Start

C2H4 loss and - 150°F re- frigeration

C2H4 loss and - 150'F re- f rigeration

-90°F re- f rigerant cost

CzH4 loss

Lower temp of tail-gas genera- tion; achieve refrigeration from process

Lower temp of tail-gas genera- tion; reduce overhead reflux requirement

Lower consumption of -90'F refrigerant

Same as C

CzH4 loss Same as C

CzH4 loss Lower temp of tail-gas genera- tion; decrease volatility of streams a t - 140°F stage

Autorefrigerate (expand) 2

Chill feed 3

Remove liquid before 4 feed chiller

Additional chilling and 5 and feed separation

Intermediate reflux 7 generation

Recycle propane 8

Process change

Simple distillation with - 150°F refrigerant partial condenser

Expand tail gas and exchange vs. effluent from -150°F conden- ser (Figure 2)

-90'F chiller for feed before tower

Separator drum before -90°F feed chiller; second feed to tower

Separator drum and - 150'F chiller following -90°F feed chiller; three feeds to tower (Figure 3)

Recycle vapor from tower through final feed prechiller [combines final feed prechiller with inter- mediate condenser (Figure 4)] ; eliminate - 150'F overhead chiller altogether

chiller (Figure 5 ) ,4dd propane before final feed

reduced if some way is found to reduce the required amount of overhead reflux. Furthermore, reducing the overhead reflux requirement will also lower the separator temperature and thereby reduce the loss of ethylene. The lowering of the separator temperature would come from the fact that the tail-gas stream is very nearly a fixed flow rate, and hence a nearly constant amount of cooling duty is available from the expansion of the tail gas. If the overhead reflux requirement is less, the amount of material being cooled by the expanded tail gas in the autorefrigeration heat exchanger will be less, and that stream can therefore reach a lower temperature.

One way to lower the overhead reflux requirement is to cool the feed to the tower. Simple reasoning with a binary McCabe-Thiele diagram reveals that additional liquefaction of a feed of fixed composition reduces the slope of the recti- fying section operating line for minimum reflux, and hence reduces the operating overhead reflux requirement. Scheme 3, then, involves a modification of Scheme 2, wherein the tower feed is passed through a -90°F refrigerated chiller before entering the tower. Table I1 shows that the improvement is considerable: The overhead reflux is reduced by more than a factor of 2; total refrigeration costs are less; the separator is cooled another 3°F; and there is an important saving in ethylene loss.

I n Scheme 3, a major cost is now associated with the - 90°F feed chiller. About '/3 of the duty of that exchanger comes from subcooling of liquid which was already present in the tower feed a t -20°F (Table I ) . A logical step, then, is to separate the liquid formed a t -20"F, pass only the vapor from that separator through the -90°F chiller, and have two feeds, each introduced a t its optimal location to the torver. Table I1 shows that this modification, Scheme 4, reduces the - 90°F refrigerant cost substantially; holvever, the fact that the upper tower feed now contains less liquid than the single tower feed in Scheme 3 and the fact that the pinches near the upper feed are controlling a t minimum reflux now cause

the reflux requirements to be somewhat higher, with con- comitant additional - 150'F refrigerant requirements, higher overhead separator temperature, and greater ethylene loss. The net result is still a gain, however. S o t e also that the separation of feeds to the tower is only advantageous if the vapor portion from the feed separator is further chilled, as is done in Scheme 4.

I n Scheme 4, the ethylene loss is still the dominant cost, and the next logical step is to make use of additional feed- chilling capabilities in an effort to reduce the required over- head reflux still further and thereby generate the tail gas a t a lower temperature to lessen the ethylene loss. The additional feed-chilling capability comes from the - 150°F refrigerant, which can be used as a coolant for vapor generated by a separabor following the -90°F feed chiller of Scheme 4. This design is Scheme 5, which is shown in Figure 3. The -150°F coolant cost is not much increased, and the over- head reflux drops by almost a factor of four, giving 5°F additional cooling in the overhead separator and a consequent lower ethylene loss.

Nonetheless, in Scheme 5, the costs are still dominated by ethylene loss. Again, the route toward improvenient is through reduced overhead reflux and therefore more cooling of the overhead vapor past the - 150°F chiller. In addition to feed chilling, the overhead reflux may also be reduced through the use of intermediate reflux. Since the minimum reflux requirement is set by a pinch in the vicinity of a feed, it is possible to achieve effective fractionation a t points some distance above the pinch with a lesser reflux flow than is required a t the pinch, while generating more reflux a t a lower point in the tower to satisfy the needs in the pinch zone. Khen there is a large temperature gradient in the tower, such as for the demethanizer, the intermediate reflux may be generated a t a less cold temperature than is required to generate the overhead reflux. The concept of intermediate reflux is not new (Robinson and Gilliland, 1950; King, 1971); however, the

Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 2, 1972 275

- I 5OoF

Figure 3. Scheme 5: prechilling of feed with separation of liquid portions

I t -2OoF,

'r 7 -Q-- Figure 4. Scheme 7: intermediate reflux coupled with feed prechilling

incentive considered has classically been the less severe temperature level required for the interniediat'e reflux. I n the present situat'ion where some overhead autorefrigeration is available, a much more important benefit also accrues from the use of intermediate reflux; the refrigerated overhead coii- denser can be eliminated altogether.

Intermediate reflux can be generated with either or both the -90" or -150°F refrigerant. Use of the -150°F refrigerant is made in Scheme 7 , shown in Figure 4. Scheme 7 is a modi- fication of Scheme 5 in which the intermediate reflux is generated by drawing off vapor from the tower at a stage with a temperature above -140"F, passing the vapor through a - 150°F refrigerant chiller, and returning it to the tower partially liquefied. I n Figure 4 aiid Scheme 7 , the inter- mediate reflux condenser and final feed prechiller are com- bined in a single exchanger. The other important step taken in Scheme 7 is that the intermediate reflux generation is made great enough so that the overhead reflux can be sup- plied entirely by the autorefrigeration exchanger. This elimi- nates the - 150°F overhead condenser aiid allows the stages in the topmost section to accomplish fractionation of t'he key coniponents beyond the ratio of keys which corresponds to the - 140°F temperature. The autorefrigeration is capable of giving enough reflux so that the additional fractionation is substantial, and the chilled overhead vapor now reaches -160"F, a temperature 10°F lower than in Scheme 5 . The

ethylene loss is cut by more than a factor of two, aiid the cost savings are large.

Even with the much reduced ethylene loss, the dominant cost in Schenie 7 is still the ethylene loss. Consequently, we would like to generat,e the t,ail gas a t a still lower temperature. The elimination of the - 150°F overhead condenser made in Scheme 7 now allows us another opportunity for lowering the temperature of the overhead separator. The reflux in the topmost section generated by the autorefrigerated condenser will give a certaiii amount of fractionation beyond whatever rat'io of key components is present 011 the stage fed by the effluent from the -150°F chiller. If the ratio of key com- ponents on the top feed stage could be altered somehow so as to give a lower rat'io of ethylene to methane, then the fraction- ation above the top feed stage would lead to a lower ratio of ethylene to methane in the tail gas. The volatilities of the liquid and vapor on t,he top feed stage may be lowered by adding a relatively nonvolatile component to the top feed stage. In an ethylene plant, likely nonvolatile components for this purpose would be recycled propane, a propylene-propane mixture, or even ethane. The addition of the heavy component to the feed stage will lessen the ratio of ethylene to methane required to give sat'uration of the vapor arid liquid on that stage, and this lessening of t,he key conipoiieilt ratio is the desired goal. Figure 5 shows Schenie 8, in lvhich propane is used as the heavy component. I t is important that the pro-

276 Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 2, 1972

C3H8 I -175OF

I - 14OoF

-14OOF

-8OOF -2OOF

Figure 5. Scheme 8: addition of recycle propane to top feed before final prechilling

pane be added before the final feed prechiller, especially since heat is liberated on mixing the propane with the feed stream. The propane is a heavy nonkey component and hence is rapidly removed from the stages above the top feed by fractionation. The overhead vapor contains very little propane, and hence the temperature corresponding to any particular ethylene/methane ratio is much lower than in the presence of propane. Calculated costs are shown in Table I1 for various propane flows. I n all four cases, the propane flow is large enough so tha t the recycle of vapor from the tower (intermediate reflux generation) is no longer needed to eliminate the need for a refrigerated chiller overhead. For the economics used, the optimal propane addition rate is about 0.05 mol/mol of tower feed. The ethylene loss has finally been reduced to a very low level, and the process cost is correspondingly further reduced.

The pattern of logic followed in Table I11 is not the only one possible for obtaining the same results. Figure 6 shows some alternative paths. Rather than following Scheme 3 with the modification wherein the liquid formed a t - 20" was separated from the vapor before the -90°F feed chiller, one could take the step of sending the effluent from the -90°F chiller in Scheme 3 through a - 150°F feed chiller, with there still being only a single feed to the tower. This is denoted as Scheme 4 d in Figure 6 and leads to Scheme 5 whereiii the liquids are removed when formed as the next logical modi- fication. Furthermore, when Scheme 2 is being modified to reduce the overhead reflux requirement, one could turn im- mediately to the intermediate reflux concept rather than feed prechilling. This would give a modification of Scheme 2 wherein a -90°F cooler was used four stages below the top to generate part of the reflux. This modification is denoted as Scheme 6, and costs for it are shown in Table 11. The costs for Scheme 6 are much the same as those for Scheme 4, indi- cating that it does not much matter whether the -90°F re- frigerant is used for generating intermediate reflux or for feed prechilling after liquid feed separation. Similarly, a modifica- tion of Scheme 7 with very similar costs is Scheme 'id, wherein there is no feed prechilling, but there are two inter- mediate condensers above the feed, using -90'F and - 150°F refrigerant, and the autorefrigeration coiide~iser assumes the entire overhead reflux generation duty.

The logical structuring of this synthesis problem can also help with the evaluation of suggested designs which are not directly generated by the logic. For example, Figure 7a s h o ~ ~ s

Scheme I

I A 2 -

_. 7 - 3

1' 8

Figure 6. Synthesis routes for demethanizer designs

an approach which has been used industrially, wherein the vapor remaining after the coldest feed prechilliiig is diverted from the tower and joined with the overhead tail gas. I n such a process, there must be very little ethylene remaining in this vapor from the final feed prechiller; hence the auto- refrigeration cooling is most needed for final feed prechilling rather than generation of overhead reflux. Examinntioil of this process reveals that it' will be advantageous to contact the liquid formed in the final feed prechilling with the high- pressure tail gas in a fractionator, as showi in Figure 7b. The process of Figure 7b is entirely equivalent to Scheme 7 shown in Figure 4, and hence Scheme 7 represents an im- provement over processes where the noncondeiisables in the feed are diverted from the t'ower.

The concepts involved in Schemes 7 and 8 are the subject of a patent application (King and Barn&).

Synthesis of Methane liquefaction Processes

The second application of evolutionary process synthesis was carried out using the digital computer to document and implement the synthesis logic, as well as to carry out the process analysis calculations. This approach was taken to ensure forcibly that all necessary steps of logic were ac- counted for.

The problem is the synthesis of methane liquefaction

Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 2, 1972 277

Figure 7. Schemes in which noncondensable portion of feed is diverted from tower

I T = 7OoF I

I / I I

l / i I I I H

Figure 8. feed and product states

Log pressure vs. enthalpy for methane, showing

processes. The goal is to improve the process in such a way as to reduce the energy consumption per unit quantity of methane liquefied. The problem is an outgrowth of the discussion given by Sherwood (1963). Strictly speaking, minimum cost would be a more realistic design objective; however, searching for reduced energy consumption will lead generally to lower cost for liquefaction processes of modest complexity and thus will lead to processes of in- creasing complexity which warrant more detailed consid- eration. Furthermore, the objective of reduced energy con- sumption allows equipment sizing and cost calculations to be avoided and permits the analysis to be based solely on thermo- dynamic calculations. I n this application, a well-known processing problem is being considered, and no attempt is made to synthesize a totally new processing scheme.

I n this case, the thermodynamic properties of methane were represented by: (1) the Redlich-Kwong (1949) equation of state, (2) a low-pressure heat capacity equation, (3) an independently specified vapor-liquid saturation equation, and (4) the critical temperature, 344.2OR. The enthalpy and

Table IV. Available Elements for Synthesis of Methane liquefaction Processes

Element

Cooler

Heat exchanger

Constant variable Direction

c

P

P I f Joule-Thompson valve H

Phase separator P

Mixing junction . . .

H Compressor s f

Table V. Available Coolants for Methane liquefaction

Refrigerant temp, O F

Water 70 Prop an e 0 Propane - 40 Ethylene - 70 Ethylene - 105 Ethylene - 150

Coolant Thermodynamic

eff, V R

1.00 0.87 0 .74 0.68 0.75 0.69

entropy of vaporization were related through the Clapeyron equation to the saturation pressure-temperature relationship and the liquid and gas volumes. The saturation equation could have been omitted since the equation of state gives a prediction of saturation conditions (as was used in the de- methanizer problem). The thermodynamic equations were not used in a way that would allow different predictions of state properties when reached by different paths.

The synthesis problem may be viewed as one of devising an appropriate path, with recycle flows where warranted, to convert gaseous methane a t 70°F and 800 psia into liquid methane saturated a t 15 psia (- 26OOF). The feed and prod- uct conditions are shown in Figure 8. Table IV shows the different basic process elements which are available to be used in the synthesis. Each element corresponds to a path on Figure 8 where one of the state variables is held c o n s t a n t either pressure ( P ) , enthalpy ( H ) , or entropy (S). The phase separator splits a two-phase mixture into gaseous and liquid effluents, and the mixing junction combines two or more streams a t the same pressure while conserving mass and enthalpy. Nost of the elements are unidirectional. A given type of element may be used repeatedly within a process.

The coolers can be provided with various coolants; the list for the example problem is indicated in Table V . A thermo- dynamic efficiency, V R = reversible work with heat source a t 70°F divided by actual work, was assigned to each level on a somewhat arbitrary basis. In both coolers and process-to- process heat exchangers, the full amount of heat transfer allowed by the Second Law was taken-Le., an infinite-area heat exchanger was assumed. Joule-Thompson valves were taken to be isenthalpic, and compressors to be isentropic.

Each process synthesized may be described by a listing of the constituent process streams, identified by: an arbitrary stream number; the temperature, pressure, specific vol- ume, specific enthalpy, and specific entropy of that stream; the type of element from which the stream emanated; the stream(s) entering the element which forms the stream; and

278 Ind. Eng. Chem. Process Der. Develop., Vol. 1 1 , No. 2, 1972

Table VI. Stream listing for Simple Liquefaction Cycle Stream(s) Stream(s)

Source entering leaving Stream s, Btu/ element source succeeding

no. r, O R P, psia V, f t3/ lb H, Btu/lb Ib-OR type" element element b 1 530 800 0.40 -1,560 2.24 0 . . . 2

2 530 800 0.40 -1,560 2.24 1 1, 7 3 3 355 800 0 .13 -1,709 1 .89 2 2 4, 5 4 200 15 0.04 -1,918 1.17 4 3 . . .

6 550 800 0.42 -1,540 2.26 5 5 7 7 530 800 0 .40 -1,560 2.24 2 6 2

c

5 200 15 8 .00 -1,698 2 .26 3 3 6

a Key to types of source element: 0 = feed, 1 = mixing junction, 2 = cooler, 3 and 4 = J-T expansion followed by phase separator ( 3 = gaseous product; 4 = liquid product), 5 = compressor, 6 and 7 = process-process heat exchanger (6 = hot stream, 7 = cold stream). * Feed. c Product.

M i x i n g I

Feed 1 r T 1

21 _ I + ' I Refr ig . Cooler

-105'F 7

Seporatorl-1 4 , L i q u i d P roduc t

Figure 9. Simple cycle for methane liquefaction

the stream(s) leaving the element to which the stream flows. One simple liquefaction cycle is shown in Figure 9, and the stream listing for it is shown in Table VI.

Logic of Synthesis. The basic logic diagram for com- puterized evolutionary synthesis of methane liquefaction processes is shown in Figure 10. The procedure s b r t s with a particular simple process. A mass balance is performed to obtain stream flow rates, using the lever rule for stream enthalpies surrounding the Joule-Thompson expansion and phase separator elements.

The nest step is to identify the element in the process which should be modified in the current iteration of the evolutionary synthesis procedure. I n the present work, only a single heuris- tic was implemented for this st'ep. For all process elements except compressors, the loss of available energy ( - A B = --AI[ + T O A S , where To = 530'R) of the streams passing through the element was taken as evidence of the degree to which that process element was causing the work re- quirement of the entire process to be large. For refrigerated coolers, the auxiliary refrigeration cycle was considered as }'art of the element; hence ( - A B ) for a cooler was ( - A B ) for the process stream plus ( - A B ) / ~ R for the refrigerant stream passing through the cooler. For a compressor, a doniparable criterion of the degree to which the compressor configuration was contributing to the work requirement of t'he entire process was taken to be (W - TTimi,) or ( + A B - TtTmin), where W m i n is an ideal work of compression. Various

EQ. OF STATE

EAT CAPACITY - - - - - - - - THE RMODY N AM IC

PROCESS EQUATIONS SEQUENCE ~~

J b 1

ADAPT TO

REVIOUS PROCESS BALANCE REMAINDER OF

SELECT ELEMENT TO HEURISTIC CRITERION (+I)

BE REPLACED [e. g.9 MAX. ( - A B ) ]

SELECT

ELEMENTS REPLACEMENT HEURISTIC CRITERIA (+e)

I 1 - EVOLUTIONARY DESIGN

Figure 10. Logic diagram for automated evolutionary synthesis of gas liquefaction processes

definitions of W,,, were considered; the one that is used in the example is the isothermal, reversible J\-ork of compression, AG, a t the compressor inlet temperature, assuming that liquid could be formed by reversible condensation as neces- sary. Table VI1 shows the criterion for each type of process element. AIixing junctions were not considered as candidates for being modified. The element with the largest value of the criterion was identified as the element to be modified. h second level of heuristics then guided the selection of the

new elements to replace or augment the element identified to be modified. I t would be desirable to use one or more general

Table VII. Criteria for Selection of Process Element to Be Modified

1. Cooler

2. Process-to-process heat exchanger

3.

4. Compressor

( - A B ) = T,(FiAS, + F2AS2)

Joule-Thompson valve and phase separator ( - A B ) = T,[FG(Sr - Sin) + F L ( S L - SLJI

AB - W,,, = FITln(S~,,t,~,, - Sin) + ( H o u t - H ~ o ~ t , T J I

Ind. Eng. Chem. Process Des. Develop., Vol. 11, No. 2, 1972 279

Table VIII. Criteria for Selection of N e w Elements and Adaptation to Remainder of Previous Process Type of element with largest ( -AB)

1. Refrigerated cooler

2. Process-to-process heat exchanger

3. Joule-Thompson valve

4. Compressor

1A.

1B.

1c.

2A.

3A.

3B.

3c.

4A.

4B.

Heuristica

New Element: Precede with cooler using warmest refrigerant in range TL < T R <

Feasibility : Existence of refrigerant in this range Size: Cool to TR Adaptation: L - 1 + new cooler -+ L New Element: Heat exchange vs. vapor recycle stream to replace all or part of duty

Feasibility: Existence of vapor recycle stream with T < TL--1 Size: hlaximum allowed by Second Law, countercurrent, with AT = 0 a t one end Adaptation: L - 1 -+ (HEx)hOt + L; insert HEX),,^^ into vapor recycle a t point

Go to element with next highest (- AB) Feasibility: If 1A and 1B both infeasible Go to element with next highest (-AB) Feasibility : dlways New Element: Additional J-T expansion, taking input to L and expanding it to

Feasibility: ( T L - ~ + T L ) / ~ 5 304’R Size: Outlet pressure such that T = (TL-I + T L ) / ~ Adaptation: Follow J-T expansion with phase separator. Liquid from separator

is feed to previous J-T expansion (Element L). Find an existing nonrecycle ele- ment, N , with S,v < S of vapor from new separator. Compress vapor to PN, followed by cooling with warmest possible coolant to TN. Combine this stream in a mixing element with stream from A;

New Element : Precede existing J-T expansion with cooler using refrigerant with T R next below (TL-l - 20°F)

Feasibility: (TL--l + T L ) / ~ > 304”R; existence of refrigerant Size: Cool to T R Adaptation: L - 1 -+ new cooler + L Go to element with next highest (- AB) Feasibility: If 3A and 3B both infeasible Yew Element : Additional compressor and intercooler (staging of compression) Feasibility: Existence of coolant with T < outlet temperature from first new com-

Size:Outlet P = (PL--~ . P L ) ” ~ Adaptation : Cool compressor outlet with TR next below outlet vapor temperature - 50°F. Effluent from new cooler fed to second compressor with outlet pressure = PL. Cool outlet from second compressor with coolant of T 2 T L + ~ . L + new cooler -+ second new compressor + second new cooler -+ L + 2

(TL--1 - 20°F)

of L

selected

intermediate pressure

pressor

Go to element with next highest (- AB) Feasibility: If 4A infeasible

Q Element L is element of largest available energy criterion.

types of heuristic on this level, as was done for the identi- fication of the element to be modified; however, more specific heuristics were used. Table VI11 shows the replacement elements used for each type of removed element in the ex- ample which will be described. Each heuristic has been chosen on the basis that i t has the capability of reducing the available energy criterion for the element which has been flagged. When several different heuristics are given for replacing a given type of element, some logic must be provided for picking the particular type of replacement element to use each time. h learning procedure and/or weighting factors could be used in a more sophisticated program; however, neither of these approaches was used here. In the example to be described, when a cooler was to be replaced, Heuristic 1A was used mhen- ever i t was feasible; otherwise, Heuristic 1B was used. Vhen a Joule-Thompson valve was to be replaced, a choice between Heuristics 3A and B was made, depending upon whether the average of the inlet and outlet temperatures of the offending Joule-Thompson valve was greater or less than -156’F. A phase separator was always inserted as the process element following a Joule-Thompson expansion.

If none of the replacement heuristics for a particular type of element with largest (- AB) were feasible, the synthesis pro- ceeded to the element of next largest (-AB) as the element to be replaced. This step is represented by Heuristics lc, 2A, 3C, and 4B. KO replacement heuristics were supplied for the case {There a process-to-process heat exchanger had the largest (- AB), and the program automatically went to the element tvith the next largest (- AB).

The outlet conditions from the replacement element must be defined by two thermodynamic state variables. One of these is established by the nature of the path (constant 8, constant P ) . The other is defined by a sizing heuristic. Sizing heuristics for each replacement element are also shown in Table VIII.

Further heuristic procedures are necessary to adapt the altered process to the remaining elements in the previous process. The logic through which this was accomplished in each case is also shown in Table VIII. An effort was made to devise adaptation procedures which would result in the deletion of the least number of elements from the previous process.

280 Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 2, 1972

Table IX. logical Steps for Methane liquefaction Process Synthesis Illustrative Example M a x (-AB)b Second largest, (-AB)*

pro- Work, Btu/lb producta cess Com- no. pression

1 3,002

2 296

3 85

4 85

5 94

6 140

7 140

8 140

9 132

Refrig- erotion

1 , 956

395

355

327

332

292

280

275

279

Total Element

4,958 JT-4,5

691 JT-8,9

440 Cool-3

412 Cool-13

426 Cool-13

432 Cool-3

420 cool-13 Cool-3

415 COOI-13 Comp-6

411 Cool-13 JT-4,5

(AB), Btu/lb

3,340 Comp-6 prod. Element

276 Comp-10

8 8 . 5 Cool-13

79 .5 Cool-3

76 .3 Cool-3

69 Cool-13

55 Cool-3 50 .3 Comp-6

55 Comp-6 49 .8 J T 4 , 5

55 J T 4 , 5 40 .2 COOL-3

(-AB), Btu/lb Heuristic prod. applied Process modification

2,885 3A

217 3B

79 .5 1A

69 1B

69 1B

55 1A

50 .3 1C 4 9 . 8 121

49.8 IC 4 0 . 2 4A

40 .2 1C 38 .1 3A

Insert JT-8,9 before JT-4,5. Liquid (Str. 8) to JT-4,5. Vapor (Str. 9) to Comp-10, then to Cool-11, and then to Mix-12 to blend with Str. 3.

Insert Cool-13, using - 150°F refrigerant before JT-8,9

Insert Cool-14, using 0°F refrigerant before Cool- 3

Exchange heat between Str. 9 and Str. 12, produc- ing Strs. 15 and 16

Exchange heat between Str. 5 and Str. 15, produc- ing Strs. 17 and 18

Insert Cool-19, using -40°F refrigerant before

Ignore (-AB) of cool-13 Insert Cool-20, using - 70°F refrigerant before

Ignore (-AB) of Cool-13 Stage Comp-6: Change coolant in cool-7 from

water to 0°F refrigerant. Insert Comp-21 after Cool-7. Insert Cool-22, using water, after Comp-21. Effluent from Cool-22 blends with Feed-1 in Mix-8

Cool-3

COOI-3

Ignore (- AB) of Cool-13 Another stage of J-T expansion

a Reversible work = 212 Btullb product. Except for compressors, where criterion = AB -

The final step required in the logic of Figure 10 before the evolutionary synthesis procedure can be repeated is the calculation of the remaining thermodynamic state variables which are unknown a t various points in the new process. Calculations of values of one or more thermodynamic state variables from known values of two other variables are also required a t various stages during the application of the re- placement heuristics. When P and !/' were known, V was obtained by use of the procedure described by Edmister (1968a) for finding the desired root of the Redlich-Kwong equation. H and S were found by first using the low-pressure heat capacity equation and then applying the algebraic corrections for pressure derived from the Redlich-Kwong equation and given by Edniister (1968b). P was always one of the two known variables. When T was unknown, i t was necessary to iterate on values of T until convergence was obtained to match the specified value of the second known variable.

Illustrative Example. Table IX gives the results of an illustrative example, using the heuristics of Table VI11 and starting with the process shown in Figure 9 and Table VI, which is identified as process 1. Process 9, which is reached after eight evolutionary synthesis iterations, is shown in Figure 11. The stream numbers in Figures 9 and 11 are those referred to in Table IX. Process elements are named through their effluent streams-e.g., JT-4,5 is the Joule-Thompson expansion plus phase separator which produces Streams 4 and 5.

I n process 1, the largest degradation of available energy occurs in the Joule-Thompson valve. Since the average of the inlet and outlet temperatures is below 304"R, the logic selects Heuristic 3A, which puts in a second stage of Joule-Thompson expansion, with the intermediate pressure being 178 psia,

which corresponds to saturation a t the average temperature of 277.5"It. The work requirement of the process is reduced sharply (by a factor of over 10) largely because the conditions for process 1 were chosen to achieve the workable process using the least severe level of refrigeration. Consequently, process 1 produced a very low amount of liquid (5%) in the expansion and involved a large vapor recycle. The second stage of expansion reduces the recycle flows considerably, since the first expansion forms 17y0 liquid and the second forms 69y0 liquid.

I n process 2, the higher pressure Joule-Thompson ex- pansion degrades the most available energy. Since the average of the inlet and outlet temperatures is above 304"R, the logic follows Heuristic 3B, and a - 150°F cooler is inserted before that expansion valve. This change brings the inlet stream to the expansion in process 3 to a much lower enthalpy and thereby increases the liquid formation in the first expansion to 74% The available energy criterion then identifies the -105°F chiller as the element to be modified, and the logic follows Heuristic lil to insert a 0°F chiller before that exchanger, giving process 4.

Next the - 150°F chiller preceding the first expansion valve is flagged. Heuristic 1A cannot be followed now, how- ever, since there exists no refrigerant with a temperature intermediate between the inlet and outlet temperatures of this exchanger. Hence the logic must resort to Heuristic lB , and search for a cold vapor stream which may be used to assume part of the duty of the -150°F cooler. The stream found is Stream 9, with a temperature of - 182.5"F, and it is used to assume about 8y0 of the duty of the -150°F chiller. The work requirement of the process increases, however, since Comp-10 must handle a stream of greater specific volume and Cool-11 must provide more aftercooling.

Ind. Eng. Chem. Process Des. Develop., Val. 1 1 , No. 2, 1972 281

MIX 1 Feed n 1

22

cooler, 00

d6 , I ,415

G1-L Liauid Product

Figure 1 1 . Methane liquefaction process evolved for illustrative example, after eight iterations

Again in process 5, the -150'F chiller is marked as the element of greatest degradation of available energy. The only other sufficiently cold vapor (Stream 5 a t -260'F) is found and is used ahead of the - 150'F chiller to assume about 19% of its duty from process 5. Again the conipression of a warmer stream in process 6 causes the net work requirement of the process to increase, even though the work associated with Cool-13 is decreased.

In process 6, the available energy loss in Cool-13 has been reduced enough to make Cool-3 the controlling element now, and hence the logic follows Heuristic lrl to insert a -40'F cooler ahead of cool-3. Process 7 , with this change made, now flags cool-13 as the element to be modified. I n this case, however, Heuristic 1A cannot be followed because no inter- mediate refrigerant exists, and Heuristic 1B also cannot be followed since there is no other cold vapor stream. As a result, the logic must follow Heuristic IC and move to the element of second highest ( - A B ) , which is cool-3. Heuristic I d is then followed to insert a cooler with the one remaining level of refrigerant, -70'F, ahead of cool-3 in process 8. Again Heuristic 1C ignores cool-13 and moves to the element of next highest value of the available energy criterion, which is now Comp-6. Comp-6 is then staged in process 9 (Figure 11), using 0°F refrigerant for intercooling. If the synthesis were to be carried further, Heuristic 38 would add another stage of expansion, and in a subsequent iteration, the vapors from the heat exchangers would be used to assume part of the - 105'F cooling duty.

Discussion. There are several aspects of the synthesis In the illustrative example n hich warrant discussion, since they bear on the effectiveness of the evolutionary synthesis scheme and the particular heuristics given in Table VIII. First, it should be noted that the heat exchangers in Figure 9 are placed before the chillers; whereas if they were after the

chillers they could bring the stream to a lower temperature, giving a greater percentage liquefaction in the expansion and thereby introducing an effect tending to reduce the work requirement. Such a location would not reduce the duty of the preceding cooler, however, and thus cannot result from a heuristic which is chosen to reduce the available energy loss of the cooler. Perhaps location of a heat exchanger im- mediately before an expansion could be one of the heuristics responding to a flagged Joule-Thompson expansion. Alter- natively, a separate step in each iteration through the syn- thesis loop could search for the most efficient heat exchange locations.

Another problem is the need of some means for removing the results of any change that turned out not to be well- chosen. One approach would be to disallow any change reached by the logic which increased the 17voi-k requirement rather than reducing it. Thus processes 5 and 6 in Table IX would not be allowed. On the other hand, the compressor inter- cooling achieved in process 9 alleviates much of the dis- advantage caused by introducing the second heat exchanger in process 6. Compressor intercooling and heat exchange against cold recycle vapor are synergistic process changes in that the two together tend to help the process more than either change does by itself. Some facility must be included in a synthesis routine to allolv for such synergistic effects.

4 s might be expected, the modification called for by the element of largest available energy degradation is not always the single change which would be most beneficial to the pro- cess. =is an example, the inclusion of a - 150GF chiller before the expansion valve in process 1 is a more effective modifi- cation than the introduction of a second stage of expansion, as was actually done to reach process 2. Process 1 with a -150'F cooler before the expansion would have a work re- quirement of 451 Btu/lb product, which is better than the 691 Btu/lb product work requirement of process 2. Hence it would appear that the 304'R criterion between Heuristics 3 8 and B should be reduced or changed altogether.

Finally, i t should be noted that this synthesis procedure is capable of generating elements of duplicate function, such as the -105'F coolers in Figure 11. Some mechanism should be incorporated for combining such units iiito single, larger elements

Conclusion

Results and concepts presented in this paper serve as a progress report on some early steps toward systematic syn- thesis. The principal value may lie more in helping the design engineer to structure his thinking better, rather than in the prospect of an ultimate totally computerized synthesizer. The computer will be most useful for process synthesis as an on-line, interactive partner of the process design engineer.

Acknowledgment

The University of Colorado and the h'ational Center for -1tmospheric Research, Boulder, Colo., provided facilities to one of the authors (C. J. K.) during the preparation of the paper. Computer time was supplied by the Computer Center of the University of California, Berkeley, Calif.

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RECEIVED for review July 2, 1971 ACCEPTED October 15, 1971

Presented at the Division of Industrial and Engineering Chemis- try, 161st hleet,ing, ACS, Los Angeles, Calif., March 1971. Financial support was supplied to one of the authors (D. W. G.) by a Sational Science Foundation Traineeship and to another of the authors (F. J. B.) by Consejo Nacional de Ciencia y Tecnologia of Mexico.

Catalytic Reduction of Calcium Sulfate to Calcium Sulfide with Carbon Monoxide

Thomas W. Zadick,’ Ronanth Zavaleta, and F. P. McCandless2 Department of Chemical Engineering, Montana State University, Boreman, Mont. 69’715

The reduction of calcium sulfate to calcium sulfide with carbon monoxide was studied using various catalysts. Ferric oxide, stannous sulfate, and vanadium pentoxide were found to have a pronounced catalytic effect on the reduction reaction. The ferric oxide was the most active catalyst and resulted in about 9770 reduction of the calcium sulfate in 45 min at 680°C when at the optimum concentration of about 9 wt Yo. The system at 660°C showed reproducible oscillations of SO? content with time. In addition, calcium sulfide was found to autocatalytically favor its own rate of formation. A mechanism involving the formation of active carbon monoxide is postulated.

T h e reduction of calcium sulfate has been extensively studied as a first step in various processes for the winning of elemental sulfur from gypsum (George et al., 1968). A number of ieduc- ing agents such as coal, coke, CH,, CO, and H2 can be used, but temperatures of 900’ to 1000°C with reaction times of 1 hr or more are reported as requirements to obtain near stoichiometric conversions. Apparently catalysts to promote the reduction reaction have not been investigated in the past because of the extreme conditions required to make the un- promoted reaction proceed. However, the reduction is ther- modynamically feasible even a t quite lo^ temperatures, and this fact promoted this study on the use of catalysts to pro- mote the reduction reaction.

Thermodynamic Study

A brief thermodynamic study was made of various possible reducing agents using existing data. Table I summarizes this study. Several interesting conclusions can be drawn

Present address, Shell Oil Co., Midland, Tex. 79701. To whom correspondence should be addressed.

from this table. First, t’he reduction reactions are highly endothermic except for CO and HI which are exothermic. Also, a favorable free energy change, A F Z , was calculated for all reducing agents above about 200”C, but a t the lower temperatures, CO is best from a standpoint of equilibrium and free energy driving force. Finally, Reactions 5 and 6 in which SO2 is liberated become t,hermodynamically feasible only a t temperatures above 1000°C. Therefore, high tem- peratures must be avoided if CaS is the desired product’.

Experimental

All experimental runs were made in a semibatch fluidized bed reactor, the details of which are shown in Figure 1. The reactor was constructed from a 12-in. length of I-in. schedule 40 stainless steel pipe. The bottom 8 in. of the pipe were packed with small stainless steel wire rings (Fenske rings) to increase the heat transfer area, The last 4 in. constituted the fluidized bed reaction chamber, and this was contained between two porous stainless steel plates. In operation, the reactor was mounted in a tubular electric furnace capable of

Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 2, 1972 283