1497
Znd. Eng. Chem. Res. 1989,28, 1497-1503
diction of the extent and rate of migration. In this paper, we have described the measurement of the solubility and diffusion coefficient of methylene chloride in polycarbonate using 14C-tagged methylene chloride. Extremely small partial pressures of tagged material could be used, resulting in measurements at very low concentrations of methylene chloride in the polymer. We have determined values of K and D with an independent experiment in which methylene chloride was sorbed from a dilute aqueous solution into clean polycarbonate (Stanley and Alger, 1989). Sorption was monitored through measurements of the aqueous-phase concentration of methylene chloride. The results of the sorption technique are in close agreement with the results of the 14Cexperiment we report here. We conclude with a few brief comments about the relative merits and general applicability of the two techniques. First, the 14Cexperiment is the more flexible. It can be used with any carbon containing gas or vapor, and a very broad range of permeabilities and diffusion coefficients can be measured by varying the film thickness, diffusion area, and tagged gas charge. The sorption experiment is less universally applicable; good sensitivity is realized only for systems in which the partition coefficient is sufficiently large that the liquid-phase concentration changes appreciably. Also, very low polymer-phase concentrations can be explored only when very sensitive detectors are available. A GC equipped with an electroncapture detector allowed us to equal the sensitivity of the 14C experiment for methylene chloride, but we are restricted to halogenated solutes with this detector. Second, the sorption experiment gives the parameters of direct interest in packaging applications-the diffusion coefficient and the partition coefficient of the solute between the polymer and the external liquid phase. The 14Cexperi-
ment, on the other hand, yields a Henry’s law constant from which the partition coefficient must be calculated (using a liquid-phase activity coefficient). Third, tagged solutes used in the 14Cexperiment are expensive compared to untagged ones used in the sorption experiment. Finally, the 14Cexperiment was relatively difficult to establish; the sorption experiment was easy. Both experiments require a great deal of care to set up and run to ensure accurate measurements. Registry No. CHZClz,75-09-2.
Literature Cited Alger, M. M.; Ward, W. J. Measurement of COz Diffusion in Polymer Films. J. Plas. Film Sheet 1987, 3, 33. Alger, M. M.; Ward, W. J.; Stanley, T. J. 14C02and COz Transport in Polycarbonate: Measurement of the Time Lag and Permeability. J . Polym. Sci., Polym. Phys. 1989, 27, 97. Crank, J. The Mathematics of Diffusion; Oxford University Press: London, 1975. Fazio, T. FDA’s View of Extraction Testing Methods for Evaluation of Food Packaging Materials. Food Technol. 1979, April, 61. Koros, W. J.; Hopfenberg, H. B. Small Molecule Migration in Products Derived from Glassy Polymers. Znd. Eng. Chem. Prod. Res. Dev. 1979,18, 353. Reid, R. C.; Schwope, A. D.; Sidman, K. R. Modelling the Migration of Additives from Polymer Films to Food and Food Simulating Liquids. Fourth International Symposium on Migration, Hamburg, Germany, 1983. Schwartz, P. S. Migration and the Regulation of Indirect Food Additives: A Reassessment. Fourth International Symposium on Migration, Hamburg, Germany, 1983. Stanley, T. J.; Alger, M. M. Methylene Chloride Migration in Polycarbonate Packages: Effect of Initial Concentration Profile. Znd. Eng. Chem. Res. 1989,28, 865.
Received for review January 26, 1989 Accepted July 10, 1989
Effect of Retrograde Solubility on the Design Optimization of Supercritical Extraction Processes Miriam L. Cygnarowiczf and Warren D. Seider* Department of Chemical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 192 04
A general strategy to design cost-efficient supercritical extraction processes is applied to a process to dehydrate acetone with supercritical carbon dioxide. The extractor, distillation column, heat exchangers, and compressors in the process flow sheet are simulated, and a nonlinear program is used to locate the optimal designs with respect to both the utility and annualized costs. As the design variables are varied, the strategy overcomes the difficulties in maintaining the proper phase distribution in the near-critical distillation tower. When the cost of utilities only is minimized, local and global minima are identified. The local minima arise due to the retrograde solubility effect associated with supercritical fluids. Minimization of the annualized cost is shown to be preferred for the design of SCE processes, since the equipment costs are an appreciable fraction of the total cost. Furthermore, the annualized cost appears to possess a unique (global) optimum. Supercritical extraction (SCE) is an increasingly important technology in the food and pharmaceutical industries because it allows the substitution of nontoxic, environmentally safe solvents, like COz, for traditional liquid solvents like methylene chloride and hexane. At the present time, this is most applicable in the food and
* Author t o whom correspondence should be addressed. Employed by the U.S. Department of Agriculture, Eastern Regional Research Center, Philadelphia, PA, while completing a doctoral program a t the University of Pennsylvania, Department of Chemical Engineering.
0888-58851 8912628-1497$0l.50/0
pharmaceutical industries where the use of toxic solvents is regulated. However, more stringent regulations regarding toxic waste disposal may, in the future, broaden the significance of this technology to include many segments of the chemical process industry. In Europe and, on a more limited scale, in the United States, SCE is used commercially to decaffeinate coffee and tea and to extract hops and spices. These commercial successes indicate that SCE is a viable alternative for the preparation of some food products. Its feasibility is determined by the scale of the process, the value of the product, the need for a nontoxic solvent, etc. Design 0 1989 American Chemical Society
1498 Ind. Eng. Chem. Res., Vol. 28, No. 10, 1989
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Previous Work Our approach for designing cost-efficient SCE processes involves the development of a model for the process flow sheet and the creation of a nonlinear program to minimize either the utility or the annualized cost. The strategy was applied to the dehydration of acetone using supercritical COP,even though acetone is a commodity chemical and is not a prime candidate for recovery by SCE. This system was chosen because extensive, high-pressure, phase equilibria data are available (Panagiotopoulos and Reid, 1987) and the physical properties (i.e., critical temperatures and pressures, acentric factors) are known, making it a good system for the development of design methodologies. The Group-Contribution Equation of State (GC-EOS) of Skjold-Jorgensen (1984) was used to predict the phase equilibria and to estimate the heating, cooling, and compression loads. This model was chosen for its ability to predict the composition of both the vapor and liquid phases of polar and nonpolar species. Figures 1and 2 show experimental and predicted values for the vapor and liquid phases of the CO2-HZ0and COz-acetone binaries, over a range of pressures representative of a SCE process. The model fits the experimental data well, even in the liquid phase, providing confidence in its use to predict the phase
1500
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3000
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PRESSURE (ATM)
Figure 1. Phase equilibria for the system acetone-C02 at 313 K.
studies properly weigh these factors and allow the identification of the most promising SCE processes for a particular application. They provide the best designs upon which to base the decision to invest in SCE processes. Simulation and optimization methodologies are widely used for process design studies in the chemical industry to reduce the experimental work required. Simulation allows a broad range of operating conditions and process configurations to be explored quickly and easily, and optimization provides a means of systematically determining the most favorable design parameters for a given economic objective. The use of these techniques is particularly advantageous for the design of SCE processes, since there are many design parameters, and since the costs associated with the construction and operation of pilot plants are high. In this paper, the optimization strategy introduced by Cygnarowicz and Seider (1988) for locating cost-efficient designs for SCE processes is reviewed briefly. Implementation of the strategy is complicated by the retrograde solubility behavior exhibited by supercritical fluids, and this paper demonstrates how this effect may lead to local minima in the utility cost.
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100.0
150.0
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Figure 2. Phase equilibria for the system C02-H20 a t 323 K. X and Yare mole fractions.
equilibria. Errors are introduced, however, when such an EOS model is used to estimate the heating, cooling, and compression requirements, especially at high pressures. Todd and Howat (1988) investigated these errors for the separation of butadiene and isoprene with supercritical trifluoromethane and showed that the heat and work loads predicted by the Peng-Robinson EOS exceed the predictions of a more accurate PVT-based correlation by 1O-40%. Since the EOS model overestimates the load in every case, its use provides conservative overdesigns that can be improved upon through the use of the PVT-based correlation in the final design stages. The SEPSIM system of Andersen and Fredenslund (1987) was utilized for the steady-state simulation. The system includes subroutines to simulate staged extractors and distillations columns, as well as programs to perform two-phase isenthalpic and isentropic flash calculations and to compute phase envelopes and critical points. The latter programs use the methods of Michelsen (1980,1982a,b), which have been shown to be very reliable in the critical region, the region in which SCE processes are designed to operate. A flow sheet for the dehydration of acetone, annotated with typical operating conditions, is shown in Figure 3. The extractor is modeled with equilibrium stages, with the dilute acetone stream entering continuously at the top and
Ind. Eng. Chem. Res., Vol. 28, No. 10, 1989 1499 90.w
OVERHEAD
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I
b 10.0 Ace 90.0 H 2 0
SUPERCRITICAL EXTRACTOR
200.00
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TEMPERATURE (K)
103 Atm .
250
COMPRESSOR
.
468.2 K
COMPRESSOR
17Atm
I
MAKE-UP SOLVENT
Figure 3. Process to dehydrate acetone with supercritical C02 (case 2).
the supercritical C02 at the bottom. As the C02 flows through the extractor, it preferentially dissolves the acetone, leaving the bulk of the water in the raffinate. Upon leaving the extractor, the C02-acetone stream is expanded across a valve and fed to a distillation column where the acetone is concentrated in the bottoms with nearly pure C02 in the distillate. The C02 stream is recompressed, mixed with the make-up stream, and recycled to the exprocess streams are heat-integrated whenever practical.
Design Optimization The variables that have the greatest impact on the process cost and performance are the extractor pressure (P,) and temperature (T,), the flow rate of the recirculated solvent (FE&), the distillation tower pressure (Pd), the reflux ratio in the distillation column, and the number of stages in the extractor and distillation column. In our approach, several of these variables are fixed to make the optimization more tractable. For example, the number of stages in the extractor and distillation column are specified because their inclusion as design variables would require the solution of a mixed-integer, nonlinear program (with the number of stages as integer variables), which would significantly increase the computational complexity of the problem. Although the reflux ratio is a continuous design variable, in our experience, it is normally reduced to its lower bound and need not be varied continuously in the optimization. The distillation tower pressure is an important variable in two respects. As illustrated in our previous work, P d determines whether or not expensive refrigeration is needed in the condenser. In addition, the range of feasible values for P d is tightly constrained. Figure 4 is a phase envelope calculated with the GC-EOS for a mixture with composition typical of the feed to the tower. Note that, at such compositions, the two-phase region exists only at high pressures (close to the critical point) over a narrow range. The unavoidable proximity to the critical point makes the simulation of the distillation tower
Figure 4. Phase envelope of a typical feed to the distillation column.
difficult. The Newton-based method that solves the MESH equations is extremely sensitive to the initialization, and convergence failures are common. For this reason, P d is fixed, and the optimal design is located at discrete values of this variable. The SCE flow sheet is optimized with the “infeasible path” strategy (Biegler, 1985) in which the tear equations are included directly as equality constraints. This formulation greatly decreases the computational expense, as compared to the “feasible path” strategies in which the tear variables are converged during each iteration of the optimization algorithm. Since the objective function and many of the constraints are nonlinear, a general-purpose, nonlinear program solver is used. The successive-quadratic programming algorithm (SQP)developed by Powell (1977) and improved by Biegler and Cuthrell(l985) was used in this study. The infeasible path algorithm was implemented with the outlet of the recycle compressor as the tear stream and P,, T,,and the flow rate of the solvent make-up, as the design variables. The flow rate of the solvent makeup was chosen as a design variable, rather than the solvent-to-feed ratio, because it simplifies the evaluation of the residuals of the tear equations using subroutines that solve the equations for each process unit given specifications for their feed streams and equipment parameters. The nonlinear program has seven variables (Te,Pe, F$?, E&, F$io, T,,,), four equality constraints (the tear equations), two inequality constraints, and upper and lower bounds on the variables. The inequalities include a product recovery constraint and a constraint limiting the water in the extract stream. In this study, two objectives are considered to minimize the utility and annualized costs. The utility cost was minimized because other researchers (Brignole et al., 1987; Moses et al., 1982) have shown that SCE can be competitive with conventional separation techniques when energy consumption is the sole criterion. However, since highpressure processes operate under extreme conditions and require specialized equipment, a more realistic assessment can be made when the capital cost is included in the criterion for locating optimal SCE processes.
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Minimum Utility Cost In the process to dehydrate acetone with supercritical C02,the utility costs arise in compressing the solvent and makeup streams, preheating the feed stream, cooling the
1500 Ind. Eng. Chem. Res., Vol. 28, No. 10, 1989 Table I. Design for Minimum Utility Cost with Minimum Recovery of Acetone at 98%. Initial Guesses in Parentheses case 1 case 2 65 Pd, atm 65 1.8 reflux ratio 1.8 Pe, atm 105 (80) 103 (80) 350 (333) 310 (310) Te, K 391 (772.4) 200 (400) Fb&, mol/min F E e ,mol/min 27.1 (30.9) 30.1 (30.9) flow rate of product, mol/min 28.1 25.6 co, acetone 9.80 9.80 1.23 water 3.81 heating 1.25 x 105 1.58 x 105 load, kJ/h 1950 2460 cost, $/year cooling 1.49 x 105 1.08x 105 load, kJ/h 180 248 cost, $1year compression 2.77 x 104 1.92 x 104 load, kJ/h 2240 cost, $/year 3230 refrigeration 9.71 x 104 1.92 X lo5 load, kJ/h cost, $/year 258 000 131000 263 000 operating costs, $/year 135000 cost/kg of acetone 0.92 0.47
solvent fed to the extractor, and removing and supplying the heat duties of the condenser and reboiler of the distillation column. When the cost of the utilities is minimized, the objective function is a linear sum of the heating, cooling, compression, and refrigeration requirements, multiplied by the appropriate cost coefficients. The values of the coefficients used in this study are given in the Appendix. In the examples that follow, the flow rate of the feed is 100 mol/min (10% acetone, 90% water), T, 1 310 K, P, > Pd + 5 (atm),Fz& > 200 mol/min, the minimum recovery of acetone is specified as 98% of the acetone in the feed stream, and the minimum recovery of water in the extract is 6% of the water in the feed stream. The distillation tower pressure is 65 atm, the reflux ratio is 1.8, the extractor has four stages, and the distillation column has eight (excluding the condenser and reboiler). In the first case, P, is initialized at 80 atm, T, at 333 K, @ ,; at 772.4 mol/min, and E@at 30.9 mol/min. The solution, found after 19 iterations of the SQP algorithm, is detailed in Table I. The minimum cost of utilities computed for these specifications is $263 000/year or $0.92/ kg of acetone. At the solution, P, is 105 atm, T, is 350 K, and Fz;,is 391 mol/min. The product recovery constraint, and the constraint limiting the water in the extract stream are active, and T, and P, are at their upper bounds. A different minimum is located, however, when P, is initialized at 80 atm, as before, but T,is initialized at 310 K, and FC"*at 400 mol/min. The minimum cost of utilities for this case is $135000/year or $0.47/kg of acetone, as given in Table I. At this solution, P, is 103 atm, T, is 310 K, and lT$, is 200 mol/min. The product recovery con,; are at their lower bounds. straint is active, and T, and @ The lower utility costs (as compared to case 1)are due to the lower solvent recirculation rate, which reduces the demand for compression, and the lower extractor temperature, which decreases the refrigeration requirements in the condenser of the distillation tower, since the liquid fraction of the feed to the tower is increased. It can be concluded that this solution is the global minimum in utility cost for these specifications, since the product recovery constraint is active and the solvent recirculation rate is driven to its lower bound.
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t
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Figure 5. Moles of acetone extracted as a function of T,and P,. The solvent-to-feed ratio = 8.
The occurrence of local minima in the utility cost is a result of the "retrograde effect" that is associated with supercritical fluids. This effect is a manifestation of the complex relationship between the solubility and the solvent temperature and density. At a fixed pressure, the solubility decreases with increasing temperature close to the critical point due to a decrease in the density of the solvent but increases with increasing temperature far from the critical point due to the increased vapor pressure of the solute. A more fundamental explanation of this phenomenon is given by Debenedetti and Kumm (1988), who show that the retrograde solubility can be related to the clustering of solvent molecules around solute molecules. In addition, Chimowitz and Pennisi (1986) have developed guidelines for the synthesis of processes that exploit this effect to separate mixtures of solid isomers. The retrograde effect leads to the two utility cost minima in Table I. This is clearly demonstrated by plotting the moles of acetone extracted as a function of T,and P,, as shown in Figure 5. This surface was generated by simulating the extractor at numerous temperatures and pressures, with the solvent-to-feed ratio fixed at 8. Note that there are two solutions for the recovery of 9.8 mol of acetone, with P, equal to approximately 100 atm; one at a high T, (near 350 K) and the other at a low T,(near 310 K). Thus, the solution obtained by the optimizer depends on the initial guess for T,. The existence of local minima is expected in such nonconvex, nonlinear programs, and unfortunately, there is no way to predict a priori the location of these minima. However, as this example demonstrates, because supercritical systems exhibit unusual solubility behavior in the retrograde region, local minima in utility cost should be expected, and design optimizations should be executed with caution. Minimum Annualized Cost In this case, the objective function is the annualized cost; that is, the sum of the installed cost of equipment multiplied by the rate of return on investment (assumed to be 15%) and the cost of the utilities. The correlations for the installed cost of the equipment are given in the Appendix. The initial guesses for this case are identical with those for case 1; i.e., P, is 80 atm, T,is 333 K, and Fc%zis 772.4
Ind. Eng. Chem. Res., Vol. 28, No. 10, 1989 1501 Table 11. Design for Minimum Annualized Cost with Minimum Recovery of Acetone at 98% for Case 3. Initial Guesses in Parentheses 65 Pd,atm 1.8 reflux ratio 103 (80) P., atm 310 (333) 200 (772.4) 30.1 (30.9) F*, mol/min flow rate of product, mol/min 28.1 COP 9.8 acetone 1.23 water heating 1.58 x 105 load, kJ/h 2460 cost, $/year cooling 1.49 x 105 load, kJ/h 248 cost, $/year compression 1.92 x 104 load, kJ/h 2240 cost, $/year refrigeration 9.71 x 104 load, kJ/h 131000 cost, $/year 135000 operating costa, $/year cost/kg of acetone 0.47 installed cost of equipment 123000 cost of heat exchangers, $ cost of extractors 2 number 1.87 diameter, m 216 000 cost, $ cost of distillation columns 4 number diameter, m 2.55 670 OOO cost, $ 145000 cost of compressors 309 000 annualized cost, $/year 1.08 cost/kg of acetone
molfmin. However, at the minimum annualized cost, the utility cost is at its global minimum (Table 11). When the fixed cost is included in the objective function, there is a great incentive to decrease the sizes of the extractors and distillation columns as much as possible. This is accomplished by reducing FZ& to its lower bound. When F%, is at its lower bound (i.e., the solvent-to-feed ratio is 2), the surface of the moles of acetone extracted as a function of T, and P, (Figure 6) is quite different from that at higher solvent-to-feed ratios. Because the solubility is reduced, it is no longer possible to extract 9.8 mol of acetone at the “high” extractor temperature (near 350 K), and only the “low”-temperature solution (near 310 K) exists. Thus, the minimum annualized cost formulation not only provides a more realistic assessment of the feasibility of the proposed SCE process but also appears to exhibit a unique (global) minimum. A conclusion of the design optimizations is that SCE is not competitive with conventional separation techniques for the dehydration of acetone. In the examples discussed in this paper, the distillation pressure was set at 65 atm, which requires refrigeration to be used in the condenser of the distillation column. The cost of refrigeration is prohibitive for this separation since it raises the utility cost to $0.47/kg of acetone. In our previous work (Cygnarowicz and Seider, 1988), a design was considered in which P,-Jwas raised to 70 atm to eliminate the need for refrigeration. The minimum utility cost for this specification was favorable, only $0.014/kg of acetone. Note, however, that 70 atm is very close to the critical point of pure COz, and the densities of the two contacting phases approach each other, resulting in small flooding velocities. This sharply increased the volume required to disengage the vapor and
Figure 6. Moles of acetone extracted as a function of T,and P.. The solvent-to-feed ratio = 2. Table 111. Overall Heat-Transfer Coefficients exchanger U,J/(m2s K) feed preheater 3985 feed-raffinate exchanger 1200 condenser 540 reboiler 910 200 solvent cooler
liquid phases and raised the equipment cost significantly. Thus, despite the low operating costs for this design, the minimum annualized cost ($1.07/kg of acetone) was nearly identical with that of case 3, previously discussed. The savings in utility cost realized by eliminating refrigeration is negated by an increase in the cost of the equipment.
Conclusions Design optimization is a valuable tool for assessing the feasibility of using SCE for a particular application. Care must be taken, however, when optimizing these systems since the retrograde solubility effect may lead to local minima. Minimization of the annualized cost is a more realistic criterion for optimality than minimization of the utility cost, since the capital costs are a significant fraction of the total cost. Furthermore, the annualized cost appears to possess a unique (global) minimum. Acknowledgment The SEPSIMsystem was provided by Aa. Fredenslund and M. L Michelsen, Danmarks Tekniske Hojskole, and the OPT subroutine which implements the successive quadratic programming algorithm was provided by L. T. Biegler, Carnegie-Mellon University. The use of both programs is gratefully acknowledged.
Nomenclature A = heat-exchanger area, m2 Cmmp = installed cost of compressors, $ Ccw = cost coefficient for cooling water, $/kJ/h Cex = installed cost of heat exchangers, $ Celt = installed cost of extractors, $ C H = cost coefficient for heating, $/kJ/h C ref = cost coefficient for refrigeration, $/kJ/h CbW = installed cost of distillation columns, $ D = tower diameter, m
1502 Ind. Eng. Chem. Res., Vol. 28, No. 10. 1989
D, = maximum tower diameter, m
fl5 = flow rate of solvent makeup, mol/min
Free = flow rate of recycle compressor outlet, mol/min h = latent heat of vaporization of steam, kJ/kg Ht = tray spacing, m Ksb = Souders-Brown constant, m/s Nt = number of trays P = stream pressure, atm P, = extractor pressure, atm Pd = distillation pressure, atm Pi= suction pressure of compressor, atm T'" = recycle stream temperature, K T, = extractor temperature, K Tref= refrigerant temperature, K U = overall heat-transfer coefficient, J/(m2sK) usg= flooding velocity in tower, m/s V = maximum vapor flowrate in tower, mol/s W , = shaft work of compressor, kW Greek Symbols pg = vapor pI = liquid
density, mol/L density, mol/L +(D)= tower cost penalty term
= ( W,0.4006+ 8501.2)(4.620
+ O.O1322P,)
The installed cost of the heat exchangers is given as a function of the area, A (m2),and the pressure, P (atm) Cex = (A0.6489+ 506.2)(3.6023 + 0.00251P) The overall heat-transfer coefficients assumed for the heat exchangers are given in Table 111. To compute the cost of the extractors and distillation columns, a tray spacing, Ht = 0.5 m, is assumed. Hence, the tower height is height (m) = HJV, where Nt is the number of trays. To compute the tower diameter, the flooding velocity (u,) is given by the Souders-Brown correlation: usg
=
Ksb(
$(D) = C(D - Dmd2 D > Dmax =o D IDm, where C is a large constant. Given the diameter, D(m), the number of trays, N,, and the pressure, P, (atm), the extractor cost is calculated from Cext = 2.4Nt(D1.1g4 228.6) + (5.90 + 0.00536Pe)(D0~70s33 + 7413.4)
+
Appendix Utility Cost Coefficients. The following coefficients were used in minimizing the total cost of utilities. The values are based on 8400 operating h/year. Steam cost: low-pressure steam, 411 K, 3.40 atm, h = 2149.0 kJ/kg, $4.0/ton, C H = $0.0156/kJ/h. Cooling water cost: Ti,= 300 K, To,, = 322 K, $0.07/gal, Ccw= $0.00167/kJ/h. Electricity cost: $0,05/kWh, Celec = $0.1167/kJ/h. Refrigeration cost: Tref= 244.1 K, $300/ton, Cref= $1.343/kJ f h. Equipment Cost Correlations. The equations for the cost of the equipment were correlated with the graphical data in Ulrich (1984). The installed cost of the compressors as a function of the shaft work, W, (kW), and the suction pressure, Pi (atm), is given by C "p
of the flooding velocity. Because the extractors and distillation columns for these designs operate at high pressures, slightly below the critical point, the densities of the two contacting phases in the towers approach each other, making the flooding velocity very small and the tower diameter very large. To keep the tower diameters at a reasonable size, several columns are used in parallel. In this formulation, the numbers of extractors and distillation columns are fixed to avoid discontinuities in the objective function. A penalty term is added to the capital cost to ensure that the solutions have tower diameters less than the maximum specified by the designer. The penalty term is of the form
T P1 ) Pg
112
In this relationship, Ksb is the Souders-Brown constant, density, and p1 is the liquid density on the top tray. KBbis assumed to be 0.10 m/s. The tower diameter may then be calculated from
p g is the vapor
where V is the maximum molar vapor flow rate in the column. The tower diameters are calculated using 80%
The above equation was derived with graphs of the cost data for process vessels in Ulrich (1984). Data for the cost as a function of the diameter at fixed height (2 m) were correlated. In all of the case studies, four trays, spaced 0.5 m apart, are used for the extractor. Similarly, the distillation tower cost is CmW= 1.88N,(D'.194+ 228.6) + (5.90 + 0.00536Pd)(D0.M246 + 9513.4) where Pd (atm) is the tower pressure. Here, the cost correlation was determined for a tower height of 4 m. All case studies involved eight trays, spaced 0.5 m apart. Registry No. COB,124-38-9;acetone, 67-64-1.
Literature Cited Andersen, P. M.; Fredenslund, Aa. Process Simulation with Advanced Thermodynamic Models. Proc. Chem. Eng. Fund., XVIII Cong., Sicily, 1987. Biegler, L. T. Improved Infeasible Path Optimization for Sequential Modular Simulators I: The Interface. Comput. Chem. Eng. 1985 9(3), 245-256. Biegler, L. T.; Cuthrell, J. E. Improved Infeasible Path Optimization for Sequential Modular Simulators-11: The Optimization Algorithm. Comput. Chem. Eng. 1985,9(3),257-267. Brignole, E. A.; Andersen, P. M.; Fredenslund, Aa. Supercritical Fluid Extraction of Alcohols from Water. Ind. Eng. Chem. Res. 1987,26,254-261. Chimowitz, E. H.; Pennisi, K. J. Process synthesis concepts for supercritical gas extraction in the crossover region. MChE J. 1986, 32,1665-1676. Cygnarowicz, M. L.; Seider, W. D. Optimal Design of Supercritical Extraction Processes. In Proc. Znt. Symp. Supercrit. Fluids; Perrut, M., Ed.; Societe Francaise de Chimie: Nice, France, 1988. Debenedetti, P. G.; Kumar, S. K. The Molecular Basis for Temperature Effects in Supercritical Extraction. MChE J. 1988,34, 645-657. Katayama, T.; Ohgaki, K.; Maekawa, G.; Goto, M.; Nagano, T. Isothermal Vapor-Liquid Equilibria of AcetoneCarbon Dioxide and Methanol-Carbon Dioxide Systems at High Pressures. J. Chem. Eng. Jpn. 1975,8, 2. Michelsen, M. L. Calculation of Phase Envelopes and Critical Points for Multicomponent Mixtures. Fluid Phase Equilib. 1980,4,1-10. Michelsen, M. L.The Isothermal Flash Problem. Part I: Stability Analysis. Fluid Phase Equilib. 1982a,9,1-19. Michelsen, M. L. The Isothermal Flash Problem. Part 11: Phase Split Calculation. Fluid Phase Equilib. 198213,9, 21-40. Moses, J. M.; Goklen, K. E.; deFilippi, R. P. Pilot Plant Critical Fluid Extraction of Organics from Water. Presented a t the AIChE Annual Meeting, Los Angeles, 1982;Paper 127c. Panagiotopoulos, A. Z.; Reid, R. C. High Pressure Phase Equilibria in Ternary Mixtures with a Supercritical Component. In SU-
Ind. Eng. Chem. Res. 1989,28, 1503-1507 percritical Fluids: Chemical and Engineering Applications; Paulaitis, M. E., Ed.; American Chemical Society: Washington, DC, 1987. Powell, M. J. D. A Fast Algorithm for Nonlinearly Constrained Optimization Calculations. AERE (Harwell) 1977. Skjold-Jorgensen, S. Gas Solubility Calculations 11: Application of a New Group Contribution Equation of State. Fluid Phase Equilib. 1984,16, 317-351. Todd, J. N.; Howat, C. S. Sensitivity of Supercritical Fluid Extraction Process Design to Phase Equilibria and PVT Data. In Proc.
1503
Znt. Symp. Supercrit. Fluids; Perrut, M., Ed.; Societe Francaise de Chimie: Nice, France, 1988. Ulrich, G. D. A Guide to Chemical Engineering Process Design and Economics, 1st ed.; Wiley: New York, 1984. Wiebe, R.; Gaddy, V. L. Phase Composition of Carbon DioxideWater Mixtures at Various Temperatures and Pressures to 700 atm. J. Am. Chem. SOC.1941,63,475-477. Received for review December 27, 1988 Accepted June 6 , 1989
Studies in Petroleum Composition. 2. Scale-up Studies for Separating Heavy Feedstocks by Adsorption Robert B. Long Long Consulting Znc., Rural Route 2, Box 1271, Stowe, Vermont 05672
James G . Speight* Western Research Institute, P.O. Box 3395, University Station, Laramie, Wyoming 82071
The composition of petroleum has been the subject of many studies even since it was first discovered that petroleum could be fractionated by passage through a column of adsorbent. Throughout all of these studies, the objective has been to determine the petroleum composition in terms of broad generic fractions and to apply this knowledge to petroleum processability. In a prior publication, a commencement was made to understand the chemical and physical nature of various feedstocks, leading ultimately to relating composition to behavior in a more definitive form. The composition “maps” reported therein can be used to locate the properties of various subfractions of a feedstock by, for example, showing the effects of molecular weight and polarity on these properties. The current work is a continuation of these investigations in which the separation of whole feedstocks was scaled up to ensure that larger size samples could be achieved to produce larger samples for conversion and composition studies. Attapulgus clay was used in open vessels as well as in 1-,2-, 6-, and lZin.-diameter columns that were 40-53-in. long. In addition, the residence time of the feed to contact with the adsorbent was found to be a critical influence in the quality of the products. The composition of petroleum has been the subject of many studies ever since it was first discovered that petroleum could be fractionated by passage through a column of adsorbent.’ Throughout all of these studies, the objective has been to determine the petroleum composition in terms of broad generic fractions and to apply this knowledge to petroleum processability. These endeavors represented important advances in the relationship of petroleum compositional studies and were deemed worthy of more detailed investigation. For example, in a previous publication,2 an asphaltene composition “map” was presented in terms of molecular weight and relative polarity of the constituents. This was the first attempt to define petroleum (or a fraction thereof) using parameters such as polarity and molecular weight. Further work3took this knowledge several steps further and lead to relating feedstock composition to behavior in a more definite form. The composition maps reported therein can be used to locate the properties of various subfractions of a feedstock by writing them on the map and showing the effects of molecular weight and polarity on these properties. On the basis of this knowledge, it was essential to understand the application of the concept to petroleum processing since the early findings of composition studies were that the behavior and properties of any material are dictated by compositi~n.~-~ Although the early studies primarily focused on the composition and behavior of asphalt, the techniques developed for those investigations have provided an excellent means of studying heavy feedstock~.~J~ The original method of clay treating was to percolate a petroleum fraction through a tower containing coarse clay 0888-5885/89/2628-1503$01.50/0
pellets.’l As the clay adsorbed impurities from the petroleum fraction, the clay became less effective. The activity of the clay was periodically restored by removing it from the tower and burning the adsorbed material under carefully controlled conditions so as not to sinter the clay. The percolation method of clay treating was widely used for lubricating oils but has been largely replaced by clay contacting. Thus, the potential exists for application of the current concept to refinery operations.12 However, the first step is to assess the effects of scale-up on the separation procedure. The present work is a report of the outcome of these investigations in which the separation of whole feedstocks was achieved using Attapulgus clay to produce larger samples for conversion and composition studies and to ensure that these samples matched the smaller laboratory samples in character. Open vessels were used as well as 1-,2-, 6-, and 12-in.-diameter columns that were 4053-in. long. Experimental Procedures Feedstocks. The principal feedstock reported here was a heavy crude oil. Other feedstocks were also used to test the concept but are not reported here. Feedstock Separation. (1) General. All of the studies reported here are adsorption-elution studies at atmospheric pressure. Both batch techniques in a single-stage stirred vessel and chromatographic column techniques using gravity feed for the eluting solvent are reported. In general, when the feedstock to be separated included large amounts of asphaltenes, the adsorbent was preloaded with feed. For the batch operation, the entire adsorbent charge was preloaded with feed. In all cases, the adsorbent was 0 1989 American Chemical Society
