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cubic equation is far better than the virial equation even though both have precisely the same constants. This result is expected, since the virial equation is known to be inapplicable at these conditions. One last point should be made about the cubic equation of state even though it does not directly involve the second virial coefficient. If one starts with eq 4 and endeavors to find the best set of constants to fit the PVT data over a wide range rather than to fit the second virial coefficient data with great precision, he can come up with a slightly better equation than (20) by making small changes in the Constants. Thus, the equation 27/64 TI PI = (22) zcVI- 0.075 T,0.75(Z,Vr 0.05)2
+
is slightly better, as noted by the comparisons in Table 14. Clearly (22) leads to a second virial coefficient correlation
which follows from eq 9. It is good, but not quite as good as eq 19, in fitting the second virial coefficient data. The principal conclusion from this study is that the best cubic equation of state can be utilized to develop a simple correlation for the generalized second virial coefficient of great precision. The constants in that correlation can then be used in the cubic equation of state to predict PVT data over extended ranges of temperature and pressure or density. Nomenclature b = translation constant in cubic equation of state B = second virial coefficient, usually in cm3/g-mol M = slope of vapor pressure at the critical point, dP,/dT, n = exponent on TI in temperature function
N = number of carbon atoms in a normal alkane P = pressure; in this work, bar R = gas constant; in this work 83.144 cm3 bar/g-mol K T = absolute temperature; in this work cm3/g-mol Z = compressibility factor, PV/RT a = constant in temperature function ,8 = constant in temperature function w = Pitzer’s acentric factor = 2-chart sum Subscripts c = at the critical point r = reduced property, Le., P, V, or T divided by corresponding
property at the critical point Literature Cited Berthelot, D. Trav. mem. bur. Intern. pdds measures, 1907, No. 13. Dymond, J. H.; Smith, E. B. ”Vlrial Coefficients of Qases: A Critical Compilatlon”; Oxford University Press, NJ, 1980. Qoodwin. R. D.; Roder, H. M.: Straty, 0. C. ”Thermophysicai Properties of Ethane, from 90 to 600 K at Pressures to 700 Bar“, NBS Techn/ca/ Note 684 Aug 1976. Martin, J. J. Chem. Eng. Rog. Symp. Ser. 1963, 59(44), 120. Martin, J. J. Ind. Eng. Chem. 1067, 59(12), 34. Martin, J. J. Ind. Eng. Chem. Fundam. 1979, 18(2),81. McGlashen, M. L.; Potter, D. J. B. Roc. R. Soc. London. Ser. A 1962,
A267, 478. Pltzer, K. S.; Curl, R. F., Jr. J . Am. Chem. Soc. 1957, 79, 2369. Rathman, D.: Bauer, J.: Thompson, P. A. “A Table of Mlscellaneous Thermodynamic Propertles for Various Substances, with Emphasls on the Critical Properties". Max-Planck-Institutefor Stromungsforschung. Wtthgen, Germany, June 1978.
Received for review March 29, 1982 Revised manuscript received March 2, 1984 Accepted April 23, 1984
Supplementary Material Available: Tables similar to Table I for argon, nitrogen, methane, ethylene, carbon tetrafluoride, propane, carbon dioxide, benzene, normal pentane, normal hexane, and water have been developed (31 pages). Ordering information is given on any current masthead page.
Influence of Heat and Mass Transfer Resistances on the Separation Efficiency in Molecular Distillations Arljlt Bose Department of Chem/cal Englneerlng, UnlversnY of Rhode Islend, Klngston, Rhode Island 0288 1
Harvey J. Palmer’ Department of C h e m l d Englneerlng, Unlverslty of Rochester, Rochester, New York 14627
A general theoretical analysis of unsteady evaporation of a binary mixture into a partial vacuum is presented which accounts for the resistances to heat and mass transfer in the bulk liquid as well as the kinetic constraints on mass exchange at the vapor-liquid Interface. I n particular, the coupling between interfacial coollng and surface depletion of the more volatile component is explicitly included in the analysis. Calculations reveal that separation factors approach thermodynamic and kinetic limits only at low temperatures and correspondingly low distillation rates. At higher temperatures, the separation factor decreases sharply to values which may be nearly half the theoretical maximum. These trends are in complete agreement wlth the experimental results of numerous investigators. Computations also reveal that surface depletion Is the domlnant factor responsible for thls reduction in separation factor with Increasingtemperature. Surprisingly, interfacial coollng partially compensates for the effect of surface depletion. I f interfacial cooling Is ignored separation factors may be underestlmated by 25% or more.
Introduction Vacuum distillation is a commercially important technique for purifying low volatility, high molecular weight
materials. By lowering the pressure, the relative volatility of components is increased and the operating temperature is reduced, which minimizes heat losses and permits the
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use of cheaper energy sources for heating. Often vacuum distillation is the only practical recourse for thermally sensitive compounds such as fat-soluble vitamins which will degrade or denature if distilled a t higher pressures. Over the past 30 years, several experiments and theoretical analyses have been done to identify and characterize the important parameters which determine the performance of these processes. These investigations clearly show that the actual degree of separation achieved in a molecular distillation process depends not only on the relative volatility of the components but also on the transport resistances in the liquid phase and their interaction with the intrinsic interfacial resistance to evaporation that exists because of kinetic-molecular constraints that become important at these low pressures (
