508
Ind. Eng. Chem. Process Des. Dev. 1980, 79, 508
CORRESPONDENCE Applicability of the UNIFAC-FV Model
Sir: Recently Oishi and Prausnitz (1978) proposed a new method of estimating solvent activities in polymer solutions. Their approach is based on a group-contribution method (UNIFAC) with a free-volume correction. This model, termed here the UNIFAC-FV model, was applied to predict the weight-fraction Henry's constants of hydrocarbons in polystyrene. The weight-fraction Henry's constant, H1, can be given by
*I
- 2o
Exp(lwaieta1.)
--- UNIFAC-FV (b=1.28,cl=l.l)
- UNIFAC-FV(bl28, c@O)
where subscript 1 refers to the volatile component and subscript 2 refers to the polymer; ymis the infinite dilution activity coefficient; M is the molecular weight; and fOL is the fugacity of pure liquid solute. The infinite dilution activity coefficient can be estimated by eq 1 and eq 14 of their paper. The fugacity of pure liquid can be calculated by the correlation of Maloney and Prausnitz (1976). Oishi and Prausnitz find that good agreement is obtained with normal solvents when b (a factor in the evaluation of reduced volume) = 1.28 and 3cl (number of external degrees of freedom per molecule) = 3.3, i.e., c1 = 1.1. Comparison of calculated results with our experimental data (Iwai et al., 1980) shows that the UNIFAC-FV model ( b = 1.28; el = 1.1)gives somewhat smaller values of H1(see Figure 1 for benzene). As discussed by Oishi and Prausnitz, a larger value of c1 may be required. Indeed, we find that the UNIFAC-FV model ( b = 1.28; c1 = 2.0) represents well the experimental results as shown in Figures 1 and 2. In the present calculation, the specific volume of a volatile hydrocarbon was estimated using a corresponding states correlation (Hildebrand et al., 1970) and that of polystyrene was given by experiment (Moriyama, 1977) as (t°C - 83.2)] above the u(cm3/g) = 0.973 [l + 6.37 X glass transition point. The UNIFAC-FV model proposed by Oishi and Prausnitz seems to be a very useful correlation method for the weight-fraction Henry's constants of volatile hydrocarbon-polymer systems.
Literature Cited Hildebrand, J. H., Prausnitz, J. M.,Scott, R. L., "Regular and Related Solutions", Appendix 5, Van Nostrand-Reinhold, New York, 1970. Iwai, Y., Nagafuji, M., Arai, Y., J. Jpn. Pet. Insf., in press, 1980. Maloney, D. P., Prausnitz, J. M.,AIChEJ., 22, 74 (1976).
0196-4305/80/1119-0508$01 .OO/O
150
200
175
Ternp.('C)
225
Figure 2. Weight-fraction Henry's constants of normal paraffinic hydrocarbons in polystyrene (data for dodecane were obtained here).
Modyam, Y., Graduation Thesis, Department of ChemicalEngineering, Tohdtu University, 1977. Oishi, T., Prausnitz, J. M., I&. Eng. Chem. Rocess Des. Dev., 17, 333 (1978).
Department of Chemical Engineering Kyushu University Fukuoka 812, J a p a n
0 1980 American
Chemical Society
Yasuhiko AraP Yoshio Iwai
