Ind. Eng. Chem. Res. 1994,33,1580-1584
1580
Rational Solvent Selection for Cooling Crystallizations Kathryn K. Nass Chemicals Development Division, Eastman Kodak Company, Building 820, Floor 6, RL, Rochester, New York 14650-2112
The development of a successful crystallization process for purification and isolation of an organic compound requires the selection of a suitable solvent or solvent mixture; to date, no logical method has been established for determining the best solvent combination. The process chemist or engineer often employs a trial-and-error procedure to identify an appropriate solvent system, the success of which is dependent on experience and intuition. This paper describes a strategy for choosing crystallization solvents based upon equilibrium limits. The approach utilizes a group-contribution method (UNIFAC) to predict a value for the activity coefficient of the solute in a given solvent system a t the saturation point. This value is then used to calculate the solubility of the solute a t a "high" temperature and a "low" temperature. The resulting solubility values determine the maximum theoretical yield for the process. Both quantities are used to rank order solvents and/or their mixtures relative to one another according to their solvent power and potential process yield. Several examples illustrating the successful application of this method are described, and potential improvements to the algorithm are discussed. Implementation of this strategy will reduce product cycle time, minimize solvent usage, and allow identification of cheaper solvent alternatives.
Introduction Solution crystallization continues to be an important technique for purification and isolation of a wide variety of industrial chemicals. Specialty chemical manufacture, in particular, often relies upon crystallization to provide a solid product of high purity and yield at an economically competitive cost. Design of such processes must include selection of a suitable solvent or solvent mixture, but to date no logical method has been developed for determining the best solvent combination. Selection of a crystallization solvent system is often a trial-and-error procedure, the success of which is dependent upon the experience and intuition of the process chemist or engineer. Methods for selecting solvents for other purification techniques have appeared in the recent literature. Gani and Brignole (1983) describe a method for synthesizing molecular structures with specific solvent properties for separation of aromatic and paraffinic hydrocarbons by liquid-liquid extraction. The algorithm searches for potential combinations of functional groups, as defined by the group contribution concept of UNIFAC, that will optimize selectivity and solvent power. A number of constraints are introduced to limit the number of possible groups, and a set of combination rules dictates how the selected groups can be recombined into molecular structures. Brignole et al. (1986) further refine this approach and suggest its use for other separation techniques, such as extractive distillation. Naser (1991) describes a similar method for selection of extraction solvents, but the final list of solvents is determined by matching molecular formulas to databases of actual solvents, rather than by using combination rules. Selection of solvents for other fluid-fluid separations such as extractive or azeotropic distillation have been treated by Magnussen et al. (1979) and Kolbe et al. (1979), among others. This paper describes a strategy for choosing crystallization solvents based upon equilibrium limits. The approach utilizes a group-contributionmethod (UNIFAC) to predict a value for the activity coefficient of the solute in a given solvent system at the saturation point. This value is then used to calculate the solubility of the solute at a selected temperature from the thermodynamic criteria for solid-liquid phase equilibrium. Since the activity
coefficient is also a function of composition (i.e., solubility), the algorithm employs an iterative technique to converge to a final solubility value. The solubility is calculated at a high temperature and a low temperature, and these values are then used to determine the maximum theoretical yield. Both quantities are used to rank order solvents and/or their mixtures relative to one another according to their solvent power and potential process yield. Note that the strategy as described here applies specifically to batch cooling crystallizations; however, extension of this concept to other types of crystallizations is straightforward. Several examples illustrating the successful application of this method are described, and potential improvements to the algorithm are discussed below.
Model Development We start with the general criterion for solid-liquid equilibrium (Prausnitz et al., 1986), written in terms of fugacities as ?;(solid) = ?$liquid)
(1)
If we assume the formation of a pure solid, then fi(solid) = fi(solid) and by definition, Ti(liquid) = xiylfio From eq 1, we can then write xiyi= fi(solid)/fio
(2)
Here x i is the solubility (mole fraction) of the solute i in the solvent, yi is the activity coefficient of the solute i in solution, fi(so1id) is the fugacity of the pure solid, and fi" is the standard-state fugacity to which yi refers. The ratio of the fugacities can then be related to measurable thermodynamic properties by calculating the Gibbs free energy change for the thermodynamic cycle shown in Figure 1(Prausnitz et al., 1986). The resulting expression for the solubility is given by
0888-5885~94/2633-1580$04.50/0 0 1994 American Chemical Society
Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994 1581
1 Operating Temperature T l a- - - - -
-
Read Parameters Initial Guesses Tolerance
t I
Calculate y, from UNIFAC
- - - - - - - - - - - - - -d
Liquid
Solid
4
Figure 1. Thermodynamic cycle for calculating the fugacity of a pure subcooled liquid. (Reprinted with permission from Prausnitz et al. (1986). Copyright 1986 Prentice-Hall.)
xi =
4
Calculate x, from Eqn. 2
(l/ri)exp[(Ahf/RTt)(l- Tt/T) - (Acp/R)(l- T J T )(AcdR) ln(T,/T)I (3)
where Ahf is the heat of fusion a t the triple point temperature of the solute, Tt is the triple point temperature, T i s the temperature of the system, and R is the gas constant. Here we have assumed that the standard state is that of a pure subcooled liquid, the effect of pressure on the solid and subcooled liquid is negligible, and no solid-solid phase transitions occur during the thermodynamic cycle. Further simplifications can be made if we assume that the triple point temperature can be approximated by the melting point temperature, the heat of fusion is approximately the same a t the triple point and melting point temperatures, and the terms containing changes in heat capacities are small compared to the heat of fusion term. The expression for the solubility then becomes
x i = (l/ri)exp[(Ahf/RT)(T/Tm)l
I
output value of
I-
Figure 2. Iteration scheme for determining xi at a fixed temperature using UNIFAC. Table 1. Summary of Key Equations in UNIFAC
In yi = In y;
+ In y:
(5)
(4)
Note that the activity coefficient yi is the only quantity that is a function of the solute i i n solution, as opposed to a pure-component property. The heat of fusion and melting temperature are easily obtained from experimental data for the pure solute; the activity coefficient, however, must reflect solute/solvent interactions and is therefore difficult to determine for each solvent without extensive experimentation. UNIFAC, a predictive group-contribution method, provides an alternative method for evaluating the activity coefficient of solute i. Fredenslund et al. (1975) first developed UNIFAC as a method for predicting liquid-phase activity coefficients for systems in vapor-liquid equilibrium. Numerous papers have since appeared in the literature demonstrating the successful application of UNIFAC, e.g., Skjold-Jorgensen et al. (1979), Magnussen et al. (1981), and Hansen et al. (1991),among others. Gmehlinget al. (1978) demonstrate the use of UNIFAC for prediction of solubilities of typical nonelectrolyte solids in solvents with good results. Details of the UNIFAC model development can be found in many of the references given here, and are not repeated for the sake of brevity. A summary of the key equations appears in Table 1. The algorithm described in this paper utilizes Procedure 6A subroutine licensed from the AIChE Design Institute for Physical Property Research (DIPPR);this subroutine contains code for evaluation of activity coefficients by UNIFAC, as well as available interaction parameters. Since the activity coefficient is a function of composition itself, an iterative method must be used to determine the solubility from eq 4. Figure 2 outlines the steps required for convergence to the solubility value a t a fixed tem-
In y; = 1n(ai/xi) + ( z q i / 2 )1n(Oi/ai)+ li - ( Q i / x i ) ~ x j l j ( 6 )
n
-
,P
I"\
perature. Two guesses for the composition are initially required; for most applications, the upper and lower bounds of 0 and 1 are satisfactory. The algorithm then employs the method of Van Wijngaarden-Dekker-Brent
1582 Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994
(Press et al., 1986)to determine a new value, which is then compared to the old value. The iteration continues until the difference between the values is less than a specified tolerance. Solubility values are determined at a high temperature (e.g., 333 K) and alow temperature (e.g., 293 K), and these values are then used to calculate the maximum theoretical yield, given as
Y = (1- (S*/S*))x 100
(15)
m
13
0.6 1
2 3 4 5
Q,
.->
. I -
and Sz are the solubility values at the high and low temperatures, respectively. The maximum theoretical yield represents the maximum amount of solute that can be expected to be removed from solution between those two temperatures as defined by the equilibrium limits. Note that it is important to use the same temperature range for each solvent in order to make a fair comparison. A good crystallization solvent (or solvent mixture) is one which results in relatively high solubility at the high temperature, but also exhibits a high theoretical yield. A good nonsolvent also exhibits a high theoretical yield, but the solubility of the solute is minimal over the whole temperature range. The solubility values should not be used as absolute numbers; instead, they are used to determine a relative ranking of the solvent power of each candidate solvent, e.g., the solute is more soluble in acetone than in heptane. Comparisons on a relative basis reduce the potential error associated with missing functional groups in the UNIFAC database. Once the relative solubilities and maximum theoretical yields are determined for each solvent or solvent mixture of interest, the solvents are rank ordered accordingto their potential as a good crystallization system. The usefulness of the top candidates should then be verified through experimentation in the laboratory; this predictive algorithm is not meant to replace solubility measurement in the laboratory, but rather to narrow the list of potential solvents so that experimentation time is minimized. Note also that the algorithm in its present form does not provide information on the final purity of the solid; selection of a solvent is based solely on potential yield. The algorithm can be used to consider purity, however, by using the same approach for the impurity of interest, but selecting a solvent system that easily solubilizes the impurity over the entire temperature range. The second example in the following section illustrates this concept.
6 7 8
SI
Examples and Discussion Example 1. Development of a process for producing a new organic photographic chemical (termed here as compound A) was interrupted when it was determined that the crystallization solvent (tetrahydrofuran) formed a solvate with compound A. The residual solvent could not be removed by drying, and the presence of the solvent could not be tolerated in the end use of the product. In addition, tetrahydrofuran is a relatively expensive solvent, which added to the cost of compound A. The solubility of compound A in toluene, isopropyl ether, heptane, isopropylamine,2-ethyl-1-hexanol, dimethyl sulfoxide, isopropyl acetate, 1,2-dichloroethane, acetonitrile, isopropyl alcohol, ethyl acetate, tetrahydrofuran, carbitol, diethylene glycol, methyl isobutyl ketone, cumene, and propionic acid was predicted using the method described here over the temperature range from 293 to 343 K. These values were then used in eq 15 to calculate the maximum theoretical yields. Figure 3 summarizes the predicted results for compound A. Note that a good crystallization
9
0.0 0
Acetonitrile Isopropanol Diethylene Glycol 1, 2 - Dichloroethane IsopropylAmine PropionicAcid Ethvl Acetate Dimethyl Sulfoxide Tetrahydrofuran
10 Methyl lsobutvl Ketone 11. lscpiopylAceiale 12. Carbitol 13. 2 Ethvl - 1 - Hexanol 14. Toluene 15. isopropyl Ether 16. Cumene 17 Heptane I
I
I
I
I
20
40
60
80
15 16
100
Maximum Theoretical Yield Figure 3. Relative solubilities and maximum theoretical yields of compound A in selected solvents.
solvent will lie in the upper-right-hand quadrant of the plot (high solubility at high temperature, high yield), while a good nonsolvent will lie in the lower-right-hand portion of the graph (low solubility, high yield). The majority of the solvents are essentially indistinguishable, in terms of solubility and maximum theoretical yield. The exceptions include toluene, which is clearly the best choice of the solvents considered here, as well as cumene, isopropyl ether, and heptane. Cumene and isopropyl ether are suitable in terms of potential yield, but their solubilities are somewhat low, and they may be more appropriately used in a nonsolvent role. Heptane is clearly the strongest nonsolvent; indeed, it may be so strong that excessive spontaneous nucleation (and excessive fines in the product) could occur during the crystallization. Interestingly, the algorithm does not select tetrahydrofuran as being any better a choice than the majority of solvents considered. We suggested that toluene be examined as a potential crystallization solvent based on these results, as well as its relatively inexpensive cost. Laboratory evaluation of toluene as the crystallization solvent proved our prediction to be correct; the crystallization yield was high and somewhat improved over that from tetrahydrofuran. Pilot-scale runs successfullyproduced compound A in good yield, although retention of solvent in the product remains a problem. Example 2. A new synthetic method for a high-volume organic chemical (compound B) provided an opportunity for a more robust process at a lower cost. Recovery of compound B from the reaction mixture by crystallization is complicated, however, by the presence of 43 wt % propionic acid, which is produced as part of the reaction. The process development team identified sec-butyl alcohol or isobutyl alcohol as potential crystallization solvents, and indeed these solvents give products of high purity and excellent yield in the laboratory. The cost of both solvents is quite high, however, and additional tankage would need to be added to the production facility to handle mother liquor wastes. We were asked to use our algorithm to identify an alternative solvent system that minimizes cost, eliminates the need for capital expenditure, and makes use of our existing line solvents, without compromising product quality and yield. The solubility of compound B in acetone, isopropyl alcohol, toluene, methanol, ethyl acetate, heptane, and isopropyl ether was predicted using the algorithm over the temperature range from 263 to 313 K (313K was chosen as an upper limit in this case because the product is
Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994 1583 1.o
E‘
2 m
0.8
v
a,
f
Table 3. Comparison of Solubility Predictions and Experimental Data for Compound C in Ethyl Acetate
I I
methanol
4 .
acetone Y
f=
toluene
ethyl acetate
isopropanol I I I
heptane
0.2
[r
isopropyl 0.0
40 60 80 100 Maximum Theoretical Yield Figure 4. Relative solubilities and maximum theoretical yields of compound B in selected solvents.
0
20
Table 2. Comparison of Solvent Volume and Solvent Cost for Crystallization of Compound B (Basis: 40 000 kg/yr Product) 100% isobutyl alcohol
20% ethyl acetate/ 80 % heptane
total solvent volume (m3) price ($/m3) total solvent cost ($)
349 634” 221 300
123 343” 42 200
total reduction in solvent usage (m3/yr) total savings ($/yr)
226 179 100
Based on 1987 figures.
unstable at elevated temperatures). Maximum theoretical yields were then calculated from eq 15. Figure 4 presents these results in terms of solubility a t 313 K and maximum theoretical yield. The solubility of propionic acid a t 243 K was also estimated in the same solvents. Note that the UNIFAC prediction method is strictly not applicable below 293 K, but these results provide some indication of the relative affinity of propionic acid for each solvent. Since the melting point of propionic acid is well below the final crystallization temperature, precipitation of the acid is not expected to affect product purity. Indeed, the algorithm predicted that all of the solvents except heptane have reasonably high affinity for the impurity. These results suggest that toluene, or a mixture of ethyl acetate and heptane, would provide excellent yield and purity of compound B. Laboratory studies confirmed that 20% ethyl acetate/80% heptane is an excellent choice for crystallizing compound B. Table 2 details the cost savings from replacing isobutyl alcohol with ethyl acetate/heptane, based on the difference in price between the solvents and the amount of solvent required in each case (this does not take into account the additional savings in capital expenditure because no new tankage is required for handling ethyl acetate and heptane). Use of the algorithm resulted in cost savings of nearly $180 000 annually and reduced the amount of solvent needed by 226 m3.
Model Improvements The accuracy of this method for choosing crystallization solvents depends strongly on the accuracy of the UNIFAC prediction for the activity coefficient. The UNIFAC database sometimes lacks the appropriate parameters between functional groups and sometimes lacks a required functional group altogether. We assessed the impact of missing interaction parameters by determining values for
~~
solubility (wt % ) temp (K)
exptl data
predicted without regressed params
predicted with regressed params
282.3 294.2 294.6 303.1 313.7 313.8 323.5 332.6 333.6 343.5
6.36 8.85 8.86 11.12 15.77 15.94 22.10 28.77 29.32 37.90
7.54 11.38 11.52 14.83 19.47 19.49 24.16 28.80 29.30 34.53
5.47 8.91 9.05 12.21 16.84 16.86 21.64 26.46 26.98 32.46
Table 4. Comparison of Relative Solubilities of Compound C in Selected Solvents at 323.5 K (Listed as Most to Least Soluble) exptl acetone ethyl acetate isopropyl alcohol toluene heptane
predicted without regressed params acetone isopropyl alcohol ethyl acetate to1u en e heptane
predicted with regressed uarams acetone isopropyl alcohol ethyl acetate toluene heptane ~~
the missing parameters from experimental solubility data and then using the values for those parameters to predict solubility and maximum theoretical yield. We chose a binary system (compound C in ethyl acetate) for which the predicted and experimentally measured relative solubilities differed. Values for the two missing parameters were determined by nonlinear regression of experimental solubility data at 303.1, 313.8, and 333.6 K. The determined values were then incorporated into the UNIFAC database, and the solubility of compound C in ethyl acetate was predicted. Table 3 summarizes the solubility predictions with and without the parameters and compares both predictions to experimental data. The absolute solubility values predicted with the determined parameters are in better agreement with experimental data than those predicted without the parameters at the lower temperatures. The agreement is not as good, however, at the higher end of the temperature range. Recall, however, that the algorithm described here utilizes relative solubilities, rather than absolute solubilities to select a solvent. Table 4 lists the relative solubilities of compound C as determined with and without the missing interaction parameters for ethyl acetate, as well as the relative solubilities based on experimental values. Inclusion of the additional parameter values makes no difference in the relative solubilities; the error associated with missing parameters can therefore be minimized by comparing solubilities, rather than by examining absolute solubilities. Future improvements to this method include the “design”of a solvent molecule to crystallize a given solute, similar to the method proposed by Naser (1991)for liquidliquid extraction. The functional groups in the solute molecule would dictate what functional groups should be included in the solvent molecule. Other criteria such as cost, availability, and safety could be included to narrow a list of potential solvents. A method for design of solvent mixtures would also need to be developed. The algorithm in its current form strictly applies to nonelectrolyte compounds. Expansion of the algorithm to treat ionic species would require inclusion of a different model for the excess Gibbs energy, such as that proposed by Chen and Evans (1986). The expression for the solubility (eq 4) might need to be modified since some
1584 Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994
ionic species do not have true heats of fusion (e.g., amino acids decompose upon melting). Design of a solvent molecule in this case would be complicated and might better be handled by the approach outlined in this paper, i.e., comparison of solvents based on relative solubilities and theoretical yield.
2 = final or low temperature Superscripts
c = combinatorial (i) = species i in reference solution at temperature T O = standard state r = residual = property in solution
Summary
A
An algorithm for determining the optimal solvent or solvent mixtures has been developed and described. The utility of this approach is demonstrated through two actual industrial examples. Potential model improvements are discussed and limitations of the approach are detailed. Implementation of this algorithm will reduce product cycle time, minimize solvent usage, and allow identification of cheaper solvent alternatives.
Literature Cited
Acknowledgment A. Svereika provided excellent technical assistance with the generation of solubility data. Nomenclature a,,, = group interaction parameter (K) Ac, = difference in heat capacity between
liquid and solid (Jl(mo1 K)) f i = fugacity of species i (N/m2) Ahf = heat of fusion of solute at Tt (J/mol) 1, = defined as (z/2)(ri- qi) - (ri - 1) Q k = group area parameter for group k qr = molecular surface area of species i R = universal gas constant (J/(mol K)) Rk = group volume parameter for group k r, = molecular van der Waals volume of species i S = solubility T = temperature (K) T,,, = melting temperature (K) Tt = triple point temperature (K) X, = mole fraction of group m in mixture x , = mole fraction (solubility) of species i Y = maximum theoretical yield (76) z = coordination number Greek Symbols
rk
= residual activity coefficient of group k y = activity coefficient 8, = area fraction of species i Uk = number of groups of type k
Brignole, E. A.; Bottini, S.; Gani, R. A Strategy for the Design and Selection of Solvents for Separation Processes. Fluid Phase Equilib. 1986, 29, 125. Chen, C.-C.; Evans, L. B. A Local Composition Model for the Excess Gibbs Energy of Aqueous Electrolyte Systems. AIChE J . 1986, 32, 444. Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. Group-Contribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures. AIChE J . 1975, 21 (6), 1086. Gani, R.; Brignole, E. A. Molecular Design of Solvents for Liquid Extraction Based on UNIFAC. Fluid Phase Equilib. 1983, 13, 331. Gmehling, J. G.; Anderson, T. F.; Prausnitz, J. M. Solid-Liquid Equilibria Using UNIFAC. Ind. Eng. Chem. Fundam. 1978,17 (4), 269. Hansen, H. K.; Rasmussen, P.; Fredenslund, A.; Schiller, M.; Gmehling, J. Vapor-Liquid Equilibria by UNIFAC Group Contribution. 5. Revision andExtension. Ind. Eng. Chem. Res. 1991, 30 (lo), 2352. Kolbe, B.; Gmehling, J.; Onken, U. Selection of Solvents for Extractive Distillation Using Predicted and Correlated VLE Data. Institution of Chemical Engineers Symposium Series; Inst. Chem. Eng.: London, 1979; Vol. 56. Magnussen, T.; Michelsen, M. L.; Fredenslund, A. Azeotropic Distillation Using UNIFAC. Institution of Chemical Engineers Symposium Series; Inst. Chem. Eng.: London, 1979; Vol. 56. Magnussen, T.; Rasmussen, P.; Fredenslund, A. UNIFAC Parameter Table for Prediction of Liquid-Liquid Equilibria. Ind. Eng. Chem. Process Des. Deu. 1981,20 (2), 331. Naser, S. F. LEMDS: Software to Select Alternative Optimum Extraction Solvents, the System and Results. Presented at the Summer National Meeting of the American Institute of Chemical Engineers, Pittsburgh, PA, August 1991; paper 9G. Prausnitz, J. M.; Lichtenthaler, R. N.; de Azevedo, E. G. Solubility of Solids in Liquids. In Molecular Thermodynamics of Fluid Phase Eouilibria, 2nd ed.: Prentice-Hall: Enalewood Cliffs, NJ, 1986; pp-415-420. Press, W. H.; Flannery,B. P.;Teukolsky, S. A.; Vetterling, W. T. Van Wiineaarden-Dekker-Brent Method. In Numerical Recipes: -The Art of Scientific Computing; Cambridge University Press: Cambridge, 1986; pp 251-254. Skjold-Jorgensen, S.;Kolbe, B.; Gmehling, J.; Rasmussen, P. VaporLiquid Equilibria by UNIFAC Group Contribution. Revision and Extension. Ind. Eng. Chem. Process Des. Dev. 1979,18 (4),714.
9,= molecular volume fraction of species i
Received for review October 26, 1993 Revised manuscript received February 15, 1994 Accepted March 9, 1994'
$ = group interaction parameter Subscripts
i, j = species or components k, m, n = group 1 = initial or high temperature
Abstract published in Advance ACS Abstracts, April 15, 1994.
