Heat-Exchanger Network Analysis. 2. Steady-State ... - ACS Publications

Then one can use the Problem Table Analysis and the pinch design method to generate alternatives for a more detailed evaluation. The apparent iterativ...
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I n d . Eng. C h e m . Res. 1987,26, 691-696

generated by various network alternatives, indicating that the approximate model adequately represents the economics of the network. Similarly, when we compare the values of the optimum design variables for each process, we normally find that the values from the approximate model are in the middle of the range of values for the various alternatives. This indicates that the approximate model provides a good starting point for screening studies. For each process the approximate model differs in cost or profit from the most profitable alternative by no more than 5%. Economic factors in the cost models are uncertain, however, so that one can use the approximate model to obtain a first estimate of the optimum design conditions. Then one can use the Problem Table Analysis and the pinch design method to generate alternatives for a more detailed evaluation. The apparent iterative analysis can thus be solved sequentially at the conceptual stage of a design. For final design calculations, the procedure of Duran and Grossmann (1986) can be used for the optimization. Conclusions In this work we have shown that optimizing the process flows and temperatures has a greater impact on process profitability than HEN alternative generation. Also, the approximate model of Townsend and Linnhoff (1984) provides an adequate energy integration model for obtaining good estimates of the optimum flows and temperatures without having to specify a network. Since a variety of HEN alternatives seem to have about the same costs, the final selection of a network should also consider the operability of the process, as well as other similar considerations. Acknowledgment We are grateful to the Department of Energy for supporting the work in these two papers (DOE Contract DEAC02-8ER10938).

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Literature Cited Boland, D.; E. Hindmarsh, E. Chem. Eng. Prog. 1984, 80(7), 47. Cerda, J.; Westerburg, A. W. Chem. Eng. Sci. 1983, 38(10), 1723. Cerda, J.; Westerburg, A. W.; Mason, D.; Linnhoff, B. Chem. Eng. Sci. 1983, 38(3), 373. Douglas, J. M.; Woodcock, D. C. Znd. Eng. Chem. Process Des. Dev. 1985, 24, 970. Duran, M. A.; Grossmann, I. E. AZChE J . 1986, 32, 123. Dwyer, F. G.; Lewis, P. J.; Schneider, F. H. Chem. Eng. 1976,83(1), 90. Fisher, W. R.; Doherty, M. F.; Douglas, J. M. AZChE J . 1985, 31, 1538. Hindmarsh, E. submitted for publication in Chem. Eng. Sci. 1983. Hohmann, E. C. Ph.D. Dissertation, University of Southern California, Los Angeles, 1971. Linnhoff, B.; Dunford, H.; Smith, R. Chem. Eng. Sci. 1983,38,1175. Linnhoff, B.; Flower, J. R. AZChE J. 1978a, 24, 633. Linnhoff, B.; Flower, J. R. AZChE J. 197813, 24, 642. Linnhoff, B.; Hindmarsh, E. Chem. Eng. Sci. 1983, 38, 745. Linnhoff, B.; Townsend, D. W.; Boland, D.; Hewitt, G. F.; Thomas, B. E. A.; Guy, A. R.; Marsland, R. H. A User Guide on Process Integration for the Efficient Use of Energy; The Institution of Chemical Engineers: Rugby, England, 1982. Linnhoff, B.; Vredeveld, D. R. Chem. Eng. Prog. 1984, 80(7), 33. McKetta, J. J., Ed. Encyclopedia of Chemical Processing and Design; Marcel Dekker: New York, 1977; Vol. 4, p 182. McKetta, J. J., Ed. Encyclopedia of Chemical Processing and Design; Marcel Dekker: New York, 1984; Vol. 20, p 77. Papoulias, S. A.; Grossmann, I. E. Comput. Chem. Eng. 1983a, 7 , 707. Papoulias, S. A.; Grossmann, I. E. Comput. Chem. Eng. 198313, 7, 723. Terrill, D. L. P b D . Dissertation, University of Massachusetts, Amherst, 1985. Terrill, D. L.; Douglas, J. M. Ind. Eng. Chem. Res. 1987, 26, 175. Terrill, D. L.; Douglas, J. M. Znd. Eng. Chem. Res. 1987, following paper in this issue. Townsend, D. W.; Linnhoff, B. AZChE J . 1983a, 29, 742. Townsend, D. W.; Linnhoff, B. AZChE J . 1983b,29, 748. Townsend, D. W.; Linnhoff, B., Presented at the Annual Meeting of the Institution of Chemical Engineers, Bath, U.K., April 1984. Umeda, T.; Itoh, J.; Shiroko, K. Chem. Eng. Prog. 1978, 74(9), 70.

Received for review August 8, 1985 Revised manuscript received May 19, 1986 Accepted January 5, 1987

Heat-Exchanger Network Analysis. 2. Steady-State Operability Evaluation D. L. T e r r i l l and J. M. Douglas* Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003

In cases where the optimum design of heat-exchanger network alternatives have about the same processing costs, the selection of the network for the final design may be based on process operability or other considerations. Most heat-exchanger networks are not operable at the optimuin steady-state design conditions; i.e., normally they can tolerate disturbances that decrease the loads but not those that increase loads and there are not an adequate number of manipulative variables to be able to satisfy the process constraints and to optimize all of the significant operating variables. These types of operability limitations can be identified by using only steady-state considerations, and normally these operability limitations can be overcome by installing an appropriate amount of overdesign and by installing bypasses around the exchangers. Dynamic operability studies will be significantly simplified if these steady-state operability limitations are removed before a dynamic study is undertaken. In part 1 of this series, we considered the optimum design of two, typical petrochemical processes, with two alternatives for each process and with a variety of heatexchanger network alternatives for each process alterna0888-5885/87/2626-0691$01.50/0

tive. The focus of the study was on the screening of process alternatives at the conceptual stage of a process design, so that short-cut procedures were used in the analysis. The results indicated that there were large differences among 0 1987 American Chemical Society

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process alternatives, but that the total processing costs for any process alternative were about the same for a variety of heat-exchanger network alternatives at the optimum design conditions. In cases of this type, where screening calculations do not clearly differentiate among alternatives, the selection of the heat-exchanger network to use in a final design may be based on process operability or other considerations (Le., safety, simplicity, ease of start-up, etc.). Since energy integration introduces additional coupling in a process flow sheet, it is essential to evaluate the process operability. A complete operability analysis requires a dynamic study, but a preliminary operability evaluation can be based only on steady-state considerations. That is, if the plant cannot operate satisfactorily at steady-state conditions when disturbances enter the process, normally it is better to modify the design rather than to attempt to develop a sophisticated control system to compensate for the disturbances.

Previous Work Both Linnhoff and Turner (1980) and Townsend and Linnhoff (1983) have stated that none of the industrial case studies they considered have led to unusually difficult control problems. However, Marselle et al. (1982), Saboo and Morari (1984),and Grossmann and Morari (1983) have identified some network designs that are inoperable for certain disturbances, and they have developed techniques for evaluating the resilience and flexibility of heat-exchanger networks. In addition, Marselle et al. (1982) have developed techniques for heat-exchanger network designs and steady-state control that account for variations in inlet flow rates and temperatures. Halemane and Grossmann (1983) and Swaney and Grossmann (1985a) have developed a procedure for evaluating the effect of overdesign on process flexibility. Saboo and Morari (1984) and Saboo et al. (1985) have defined a resilience index which is the largest arbitrary disturbance load that can be shifted through every exchanger in a heat-exchanger network without violating a specified percentage of maximum energy recovery or a specified minimum approach temperature. Thus,new methods for steady-state operability studies are rapidly becoming available. Most of these studies for analyzing the flexibility or resiliency of heat-exchanger networks have abstracted the heat-exchanger network from a process flow sheet and have assumed that the process flows, as well as the inlet and outlet temperatures, can vary arbitrarily. However, in a process flow sheet, these changes are almost always correlated. For example, if the production rate is changed, many of the process flows increase or decrease directly proportional to the production rate variation. Similarly, if the temperature of the flash drum shown in Figure 1 decreases (due to a decrease in the cooling water inlet temperature to the partial condenser), the decreased target temperature for the product stream obviously is identical (for an isothermal flash) with the inlet temperature changes for the gas and liquid recycle streams. Moreover, this change in the flash drum temperature causes a change in the vapor and liquid flows leaving the flash drum. Thus, it is necessary to evaluate the effects that these correlated changes have on the heat-exchanger network (it should be noted that the recent paper of Saboo and Morari (1984) considers correlated variations). Since the studies discussed above abstract the heat-exchanger network from the flow sheet, it is difficult to understand the interaction between the operability of the heat-exchanger network and the remainder of the process.

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Figure 1. HDA process with a diphenyl byproduct-alternative

1.

For example, Fisher et al. (1987a) found that the optimum steady-state designs of most processes were not operable even at steady-state conditions when disturbances enter the process. That is, the plant could tolerate disturbances that decreased the load on the process but could become inoperable if the loads were increased. Similarly, they found that often there were not an adequate number of manipulative variables in order to be able to satisfy the process constraints and to optimize all of the operating variables as disturbances enter the plant. However, they found that normally it was fairly simple to restore the operability of the process by either (a) modifying the flow sheet to introduce new manipulative variables (bypasses, purge streams, auxiliary heaters and coolers, etc.), (b) designing away from process constraints so that the constraint never becomes active over the complete range of anticipated disturbances, or (c) neglecting the least significant optimization variables. Each of these alternatives has an associated economic penalty, and we want to find the alternative having the lowest cost. Of course, a complete operability analysis requires a dynamic study, but if these steady-state operability limitations are removed before the dynamic study is undertaken, then the dynamic analysis is simplified. Goals of This Research The costs required to remove any steady-state operability limitations for different process alternatives and for different heat-exchanger networks for any particular process alternative will be different. Thus, in some cases, these incremental costs might change the selection of the least expensive process alternative based only on steadystate considerations. In order to get some “feeling” for these cost penalties, we considered two, typical petrochemical processes, with two alternatives for each process. The optimum steady-state designs of these processes were discussed in part 1 of this series, and a variety of heatexchanger network alternatives were considered for each process alternative. In this paper, we consider the steady-state operability limitations of the various alternatives, and we evaluate the use of overdesign and the installation of bypasses around heat exchangers as a way of resolving any steady-state operability limitations. Perhaps it should be emphasized that our focus is on the screening of process alternatives at the preliminary stages of a process design. For final designs, after the number of alternatives has been reduced to a small number, the rigorous procedures described by Halemane and Grossmann (1983) and Swaney and Grossmann (1985a,b) would provide better solutions. Also, it is important to

Ind. Eng. Chem. Res., Vol. 26, No. 4, 1987 693 remember that a dynamic analysis is required to make a final evaluation of process operability.

Disturbances The optimum steady-state design must be able to tolerate disturbances entering the plant or else the design must be modified so that these disturbances can be tolerated. The disturbances enter the plant through its connections with the environment (Douglas, 1981), and therefore the disturbances may correspond to (a) production rate, (b) composition, temperature, and pressure of all raw materials streams, (c) composition,temperature, and pressure of all utility streams, and, (d) internal disturbances such as catalyst deactivation, heat-exchaner fouling, etc. Some of these disturbances have a much greater impact on the operability of the process and a heat-exchanger network alternative than others, and we would like to restrict our attention to the most significant disturbances in order to simplify our analysis. When the production rate is changed to meet changes in demand, normally all of the other process flows are changed proportionally, and therefore the heat duty of essentially every exchanger changes. Thus, production rate changes are almost always an important disturbance. For processes where the raw material streams have impurity levels of less than 1% , changes in the impurity concentrations normally only have a very small effect on the process flows. The impurities often have a chemical nature similar to the reactant, so that heat capacities and boiling points also don’t change very much with the impurity concentrations. Oil refineries and some natural gas-liquids plants on the other hand experience much more severe changes in feed compositions. Small pressure variations in raw material streams also are usually easily compensated. Temperatures of feed streams vary with ambient conditions, so that the heat loads change. However, for processes with large gas recycle flows, such as we are considering, the variation in the heat loads is quite small. Disturbances in steam and fuel supplies can be compensated simply by changing the utility flow rate, so that these variations can usually be kept from propagating through a heat-exchanger network. However, changes in cooling water temperatures fed to partial condensers preceding flash drums often cause a significant change in the vapor and liquid flows leaving the flash drum. Thus, cooling water variations often represent a significant disturbance. Heat-exchanger fouling is a relatively slow phenomenon, and it is common practice to accommodate the fouling by overdesign of the exchanger. Catalyst deactivation also usually is a relatively slow phenomenon (for cases where the deactivation is rapid, a fluid bed reactor with continuous catalyst regeneration is used to maintain a constant activity), but in some cases the changes in flows or changes in reactor temperature used to compensate for the deactivation may be significant. The design of the heat-exchanger network when there is a catalyst deactivation obviously depends on the strategy chosen to compensate for the deactivation; see Douglas et al., (1980). In summary, for the HDA and EB processes that we are considering, we expect that the most important disturbances are the production rate, the inlet cooling water temperature to the partial condenser (because of its effect on the temperature of the flash drum), and possibly the feed composition of Hz in the HDA plant. For the purposes of this study, we consider production rate variations of f14% for the HDA process and f20% for the EB process, as well as cooling water temperature changes from 283 K in the winter to 305 K in the summer.

0

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20

30

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ENTHALPY (MM watts)

Figure 2. Temperature-enthalpy diagram for the limiting overdesign policies.

Overdesign The optimum steady-state designs discussed in part 1 of this series normally cannot tolerate increases in the production rate above the nominal design value. Many of the heat-exchanger network alternatives also cannot tolerate the increased liquid load on the distillation train that corresponds to the lowest possible cooling water temperature. Hence, we consider the use of equipment overdesign to be able to accommodate the disturbances. Many authors have studied overdesign to compensate for parameter uncertainty or disturbances (Kittrell and Watson, 1966; Nishida, et al., 1974; Swaney and Grossmann, 1985a; Halemane and Grossmann, 1983; Saboo and Morari, 1984). Recently, Fisher et al. (1987b) have shown that different process units fall into one of three categories, depending on their economic response to disturbances: (a) the operating costs vary linearly, so that no overdesign can be justified; (b) the operating costs rapidly become unbounded as the optimum steady-state design capacity is exceeded, so that usually overdesign at the worst-expected conditions is justified; (c) the operating costs vary nonlinearly with the disturbances, so that the “expected” operating costs must be minimized. For screening calculations, where we are still attempting to fix the flow sheet, for the processes we are considering, a “reasonable” (i.e., simple and yet bounds the optimum) overdesign policy is to use the “worst-case”production rate and nominal values for all of the other operating variables. When we consider the overdesign of the heat-exchanger network, we have the options of trying to place all of the overdesign in the utility heaters and coolers, to overdesign only the intraprocess heat exchangers, or to use some combination of the two extremes. The results for the HDA process with a diphenyl byproduct indicated that it was not possible to accommodate all of the overdesign in the intraprocess heat exchangers while maintaining a positive driving force in each of the exchangers. However, we could modify the optimum steady-state design to correspond to minimum approach temperatures at the pinch that exceed the optimum steady-state values. Then, the two limits of overdesign become (a) overdesign in the utility exchangers and (b) overdesign in the network based on AT,,. The temperatureenthalpy diagrams for these two limits are shown in Figure 2 for the HDA process with a diphenyl byproduct. The results for both limiting cases are pres-

694 Ind. Eng. Chem. Res., Vol. 26, No. 4, 1987 i

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Figure 6. HDA process with diphenyl recycled-alternative ( I

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ented later. However, the two curves are so similar that there seems to be little incentive for determining the optimum amount of overdesign. Operability Evaluation Once the appropriate amount of overdesign has been added to the optimum steady-state design, we can evaluate the effects of the disturbances. Now the worst-case conditions correspond to the lowest energy demand, i.e., the lowest anticipated production rate and winter cooling water temperatures. The results indicate that each network that requires more than a feed-effluent heat exchanger and a pressure-shifted column is inoperable at these worst-case conditions. In an attempt to alleviate this operability

limitation, bypass streams were installed on each intraprocess heat exchanger; i.e., the number of manipulative variables was increased. After the bypass streams were installed, the operability was evaluated again, and the results are shown in Figures 1and 3-5 for the HDA process with a diphenyl byproduct, in Figures 6-8 for the HDA process with diphenyl recycled, and in Figures 9-11 for the EB process with steam exported. The results for the other cases can be found in Terrill (1985). As shown in the figures, for each unit, one of the following calculations was made: (a) for intraprocess exchangers, the percent bypass; (b) for a furnace, the percentage of maximum fuel usage; (c) for a partial condenser, the percentage of maximum cooling water flow. These

Ind. Eng. Chem. Res., Vol. 26, No. 4, 1987 695

Y E N T

Table I. Operability Criterion Results for Alternative 4 of the EB Process with Steam Exported exchanger description feed-effluent heat exchanger benzene column reboiler DEB column condenser DEB column reboiler

BENZENE

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UA/(FC,)DES 2.4 0.52 2.7 0.00098

All of the alternatives were found to be operable, with the exception of alternative 4 of the EB process, Figure 11, which will be discussed below. Not all of the alternatives are shown (see: Terrill, 1985),but the results are representative. The 0% bypass on some exchangers is the result of minimizing the utility usage when a range of operable conditions exists, so that any exchanger with the 0% bypass is used to its maximum capacity. No bypass valves are included when a condenser is used to drive a reboiler because the condenser duty can be changed by allowing the liquid level in the condenser to vary; see Shinskey (1977). General Results The results indicate that bypass streams often provide a simple way of overcoming steady-state operability limitations after an appropriate amount of overdesign has been included. Other alternatives could be explored, and structural variations in the heat-exchanger network could be considered, but for the processes under study there seems to be little economic incentive to undertake additional steady-state studies. However, no definitive conclusion as to the operability can be made until the dynamic effects of shifting the heat loads through the network have been determined.

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Figure 10. EB process with steam exported-alternative 3. \VENT

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-

Inoperable Exchanger The case of the one inoperable alternative, i.e., alternative 4 for the EB process (Figure 111, corresponds to a situation where the DEB column reboiler is driven by the reactor product stream. For this case, the reactor product stream is so large compared to the reboiler heat duty that 99.83% of the stream would have to bypass the exchanger, which is unrealistic. However, this apparent difficulty is easily overcome simply by splitting the stream and using only part of it to supply the reboiler load. An alternative approach would be simply to leave the reboiler out of the energy integration scheme because its load is so small. This approach is confirmed by the optimization results (Table I11 in part 11, where there is no significant differences in costs between alternatives 3 and 4. Approximate Criterion for Operability A simple way of identifying operability problems caused by imbalanced heat loads as described above is to require that

ETHYLENE FEED

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Figure 11. EB process with steam exported-alternative 4.

values are shown in the figures. The terms in brackets in Figures 1 and 3-5 represent the case where the overdesign is in the utility exchangers, whereas the terms in parentheses correspond to an overdesign based on AT,,. Because the results for the limiting cases were so similar for the HDA process with a diphenyl byproduct, only overdesign based on AT,, was considered for the other two case studies.

This criterion is based on the assumption that the minimum flow through an exchanger for the worst-case disturbance must be at least 10% of the design flow rate. It is also assumed that disturbances affect the heat duties but do not have much affect on the target temperatures. Table I shows the values of eq 1for the various exchangers in alternative 4 of the EB process. Conclusions The optimum steady-state designs of most processes are not operable. Some operability limitations, such as an

Ind. Eng. Chem. Res. 1987,26,696-699

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inadequate number of manipulative variables and inadequate capacity to tolerate disturbances that increase the load on the process, can be identified from steady-state considerations. There are a number of alternative ways of restoring the steady-state operability, and short-cut procedures can be used to estimate the cost penalties. A t the preliminary stage of a process design, we normally look for a low-cost alternative, rather than the optimum solution. However, a dynamic study is necessary to make definitive conclusions about operability. Acknowledgment We are grateful to the Department of Energy for supporting this work (DOE Contract DE-AC02-8ER10938). Nomenclature A = heat-exchanger area, ft2 C = heat capacity, BTU/(lb O F ) lf= flow rate, lb/h Q = heat duty, BTU/h AT,, = log-mean temperature difference, OF U = overall heat-transfer coefficient, BTU/(h ft2 O F ) Literature Cited Douglas, J. M. Presented a t the Proceedings of the Engineering Foundation Conference on Chemical Process Control 11, Sea Island, GA, 1981; p 497.

Douglas, J. M.; Reiff, E. W.; Kittrell, J. R. Chem. Eng. Sci. 1980,35, 322. Fisher, W. R.; Doherty, M. F.; Douglas, J. M. submitted for publication in Ind. Eng. Chem. Res. 1987a. Fisher, W. R.; Doherty, M. F.; Douglas J. M. submitted for publication in Ind. Eng. Chem. Res. 1987b. Grossmann, I. E.; Morari, M. Presented at the Proceedings of the 2nd International Conference on Foundations of Computer-Aided Process Design, Snowmass, CO, June 19-24, 1983. Halemane, K. P.; Grossmann, I. E. AIChE J . 1983, 29, 425. Kittrell, J. R.; Watson, C. C. Chem. Eng. Prog. 1966, 62(4), 79. Linnhoff, B.; Turner, J. A. Chem. Eng. (London) 1980, 363, 742. Marselle, D. F.; Morari, M.; Rudd, D. F. Chem. Eng. Sci. 1982, 37, 259. Nishida, N.; Ichikawa, A.; Tazaki, E. Ind. Eng. Chem. Process Des. Dev. 1974, 13, 209. Saboo, A. K.; Morari, M. Chem. Eng. Sci. 1984 39(3), 579. Saboo, A. K.; Morari, M.; Woodcock, D. C. Chem. Eng. Sci. 1985,40, 1552. Shinskey, F. G. Distillation Control for Productivity and Energy Conservation; McGraw-Hill: New York, 1977. Swaney, R. E.; Grossmann, I. E. AIChE J . 1985a, 31, 621. Swaney, R. E.; Grossmann, I. E. AIChE J . 1985b, 31, 631. Terrill, D. L. Ph.D. Dissertation, University of Massachusetts, Amherst, MA, 1985. Terrill, D. L.; Douglas, J. M. Ind. Eng. Chem. Res. 1987, preceding paper in this issue. Townsend, D. W.; Linnhoff, B. AIChE J . 1983, 29, 742.

Received f o r review August 8, 1985 Revised manuscript received May 19, 1986 Accepted J u n e 13, 1986

Extraction of Ethanol from Aqueous Solution. 1. Solvent Less Volatile than Ethanol: 2-Ethylhexanol Francisco Ruiz,* Vicente Gomis, and Rogelio F. Botella DivisiBn de Ingenieria Q u h i c a , Universidad de Alicante, Alicante, Spain

Liquid-liquid equilibrium data for the ternary system water-ethanol-2-ethylhexanol have been determined experimentally at 25 "C and correlated simultaneously together with vapor-liquid equilibrium data by using the UNIQUAC model. A suitable extraction process for separating ethanol and water using 2-ethylhexanol as the solvent has been chosen, and the design calculations have been carried out t o determine the energetic requirements. The properties which another solvent should offer t o decrease these energetic requirements have been studied. The fermentation process and its recent developments have led to the efficient production of dilute alcohol-water mixtures. The conventional method, distillation and azeotropic distillation, for recovering anhydrous ethanol from the fermentation broth consumes 50-80% of the energy used in a typical fermentation ethanol manufacturing process and is frequently cited in criticizing the potential of biomass-derived ethanol as a liquid fuel (Ladisch and Dyck, 1979). However, new technologies for separating alcohol from water solutions soon may lower significantly the cost of producing ethyl alcohol by fermentation. Liquid-liquid extraction is one possible means of accomplishing this separation. Several investigators have obtained experimental data of distribution coefficients and separation factors at high dilution of ethanol for a wide range of solvents (e.g.: Roddy, 1981; Roddy and Coleman, 1981; Munson and King, 1984). However, the design calculations cannot be done using only these data of one tie line for each system, because they depend on the ethanol concentration.

In this work, liquid-liquid equilibrium data covering the whole range of the heterogeneous region of a ternary system water-ethanol-solvent have been determined experimentally. The new data have been integrated into the total needed data set in order to carry out the calculation of the solvent circulation rates and energetic requirements of a suitable extraction process and to examine what properties the solvent should offer in order to decrease these requirements. Depending upon the volability of the solvent, these extraction processes can be divided into two types: those using a solvent less volatile than ethanol (part 1) and those using a solvent more volatile than ethanol (part 2). The solvent chosen in part 1 is 2-ethylhexanol. Ternary liquid-liquid equilibrium (LLE) data for the water (W)-ethanol (E)-2-ethylhexanol (EH) system have been measured at 25 "C and correlated simultaneously together with vapor-liquid equilibrium (VLE) data for the systems water-ethanol and ethanol-2-ethylhexanol. The results obtained allow the design calculations of an extraction process of the type reported by Munson and King (1984). 0 1987 American Chemical Society