Prediction of vapor‐liquid equilibria from the corresponding states principle

Abstract

A new ideal K value is defined which does not depend on the Lewis and Randall ideal solution rule but is derived only from composition dependent pseudo criticals and the corresponding states principle. Properties of the liquid and vapor mixtures are evaluated from either experimentally measured properties of closely related pure substances or from generalized tables of thermodynamic properties. A derivation of an improved pseudocritical expression applicable to liquids which may be approximated by simple spherical molecules is presented. The derivation illustrates the assumptions involved and points the way for a possible extension of the technique to more complex molecules. There are some advantages to this approach. It does not require the troublesome extrapolation of liquid properties into regions where no liquid can exist, a fact which is characteristic of K value calculations from the ideal solution rule. It is especially useful for systems in which an equation of state is not available for all of the components present. It avoids the difficulties in defining combination rules for complicated equations of state. Even for systems including very complex or moderately polar molecules it provides a base for subsequent empirical modification. This base follows the correct isotherm of In K vs. In P up to the actual critical of the system without the difficulties associated with defining a convergence pressure or evaluating the extremely large activity coefficient corrections to the ideal solution rule in the critical region. For mixtures of simple molecules the calculated ideal K value is within about 10% of the experimental value in both the low pressure and in the critical region. The entire calculation may be expressed completely analytically for use on a digital computer and may be coupled with an equilibrium flash calculation so that the ideal K values may be determined from a given overall composition, temperature, and pressure.

Phase Behavior of Light Gases in Hydrogen and Aqueous Solvents

“…The comparisons are shown in terms of deviations (δx) of the solubilities (liquid mole fraction nitrogen) from values predicted using the PR EOS, using temperature independent C ij and D ij values determined from the present data. 8 The figure facilitates a sensitive analysis of differences in data sets. The difference in the deviations between data sets (not the magnitude of the deviation of either set from the reference EOS model) is of interest in these data comparisons.…”

“…Figure 1. The one-fluid approach, introduced by van der Waals, is the most commonly used method for extending equations of state to nonpolar mixtures (8). This approach assumes that the properties of a mixture are equivalent to those of a hypothetical pure component at the same temperature and pressure, with the characteristic constants properly averaged over the composition (8).…”

Theory of infinite dilution chemical potential

“…2. To correct for this deficiency we use the mean density approximation (Leland et al, 1962;Mansoori and Leland, 1972) of the pair correlation function which is known to be accurate in representing the dependence of the pair correlation function on the energy parameter (Hoheisel and Lucas, 1984). The mean density approximation assumes the following: g12@/~12?…”

Pseudocritical constants

“…It can be justified empirically for van der Waals fluid mixtures whenever the a and b terms for the mixture are given by the empirical P 8 x*xjulj and P 8 XIXjbzj. In this case van der Waals equation can be rearranged as follows in the form of Equation (13) after the distribution functions have been approximated by (15) and (16) :…”

“…This assumption in Equations (15) and (16) considerably modifies the dependence of the radial distribution function on composition. I t assumes that in addition to r and T the distribution function is dependent only on the force parameters of the molecules in the pair and the average reduced density of the mixture around the pair.…”