A method for multicomponent equilibrium calculations by using dew point pressure‐vapor composition data

Abstract

Numerical integration of total vapor pressure-liquid composition curves with the Gibbs-Duhem equation is an established tool for calculating vapor-liquid equilibria of binary systems (1 to 9). The procedure is usually employed with isothermal data, since isobaric data may require accurate values of the heat of mixing. In contrast, it has only rarely been used for multicomponent systems. This is largely explained by the increasing complexity of the calculational procedures and the greater quantity of data required as the number of components is increased beyond 2.Mixon et al. (10) have given a general procedure for isothermal multicomponent total pressure-liquid composition data. It is essentially a generalization of the method of Tao (9) in which nj refers to constant mole numbers for all components except component 1, and + is a correction for gas phase nonideality. The derivatives are taken such that all mole fractions except XI remain in a fixed ratio as XI is varied. It can be shown that this is exact for an ideal liquid phase. Unfortunately, it is not correct for nonideal liquid phases in multicomponent systems, as will be explained later. DEW POINT PRESSURE METHODAll the above methods, both binary and multicomponent, employ bubble point pressures and composition with the Gibbs-Duhem equation for the calculation of the vapor-phase composition. There is no reason, however, why dew point pressures and vapor-phase compositions cannot be used. While the equipment for dew point measurements is more complex, such apparatus have been constructed, and variations could easily be designed.Generally, the sample would be vaporized and the isothermal pressure-volume relations recorded until condensa-R. James is at Massachusetts Institute of Technology. Cambridge, Massachusetts.tion occurred, as noted by a break in the pressure-volume curve; if the pressure rise is rapid as compared with heat transfer, the process will be nearly adiabatic. Then AT/AP = u/CP Since the apparent heat capacity will include the latent heat, it will show a large change at the dew point. An obvious bonus from this procedure would be the byproduct pressure-volume data from which fugacity coefficients could be calculated. The unavailability of the latter is frequently the weakness in the total pressure method. Fortunately, there is also an enormous simplification in the resulting equations as compared with the corresponding liquid-phase calculations. where nj represents %. n3, ---n~. Now