They obtained the parameters for binary systems at 101.3 kPa (1 atm) from best fits of the experimental T-y-x equilibrium data by setting OV and OL to their ideal-gas, ideal-solution limits of 1.0 and Psat/P respectively, with the vapor pressure Psat given by a three-constant Antoine equation, whose values they tabulate. Extensive listings of binary-interaction parameters for use in all but the UNIFAC equation are given by Gmehling and Onken (op. Six popular expressions are the Mar-gules, van Laar, Wilson, NRTL, UNIFAC, and UNIQUAC equations. Jin, Greenkorn, and Chao present a revised correlation for the standard-state liquid fugacity of hydrogen, applicable from 200 to 730 K.įor mixtures containing polar substances, more complex predictive equations for ytL that involve binary-interaction parameters for each pair of components in the mixture are required for use in Eq.
Conf., Frankfurt, June, 1963) for the OL expression permit application of the CS correlation to higher temperatures and pressures and give improved predictions for hydrogen. Revised coefficients of Grayson and Streed (Gs) (Pap. Five pure-component constants for each species (Tc, Pc, ffl, 8, and vL) are required to use the CS method, which when applied within the restrictions discussed by Lenoir and Koppany gives good results. 13-19 for the heptane-toluene system at 101.3 kPa (1 atm). (13-4) by using an empirical expression for OL based on the generalized corresponding-states PVT correlation of Pitzer et al., the Redlich-Kwong equation of state for OV, and the regular solution theory of Scatchard and Hildebrand for The predictive ability of the last-named theory is exhibited in Fig. (13-4) that uses Henry's law is sometimes applied.įor mixtures of hydrocarbons and light gases, Chao and Seader (CS) applied Eq. (13-4) is hypothetical for any components that are supercritical. (13-4) can be applied, the former is generally preferred because it involves only a single equation of stateĪpplicable to both phases and thus would seem to offer greater consistency. At low to moderate pressures, accurate prediction of the latter is crucial to the application of Eq. Where different equations of state may be used to predict the pure-component liquid fugacity coefficient Of and the vapor-mixture fugacity coefficient, and any one of a number of mixture free-energy models may be used to obtain the liquid activity coefficient y,L. Īn alternative K-value formulation that has received wide application to mixtures containing polar and/or nonpolar compounds is The Wong-Sandler mixing rules for cubic equations of state now permit such equations to be extended to mixtures of organic chemicals, as shown in a reformulated version by Orbey and Sandler. Similar results are achieved with the PR correlation. The ability of the SRK correlation to predict K values even when the pressure approaches the convergence pressure is shown for a multicomponent system in Fig. Computer programs for K values derived from the SRK, PR and other equations of state are widely available in all computer-aided process design and simulation programs. The Starling extension of the BWR equation (Fluid Thermodynamic Properties for Light Petroleum Systems, Gulf, Houston, 1973) predicts K values and enthalpies of the normal paraffins up through n-octane, as well as isobutane, isopen-tane, ethylene, propylene, nitrogen, carbon dioxide, and hydrogen sul-įide, including the cryogenic region. The SRK and PR equations belong to a family of so-called cubic equations of state. These equations include those of Bene dict-Webb-Rubin (BWR), Soave (SRK), who extended the remarkable Redlich-Kwong equation, and Peng-Robinson (PR). (13-3) have been restricted to mixtures of nonpolar compounds, namely, hydrocarbons and light gases. Until recently, equations of state that have been successfully applied to Eq. Consistent equations for enthalpy can similarly be derived. Where the mixture fugacity coefficients L for the liquid and ,V for the vapor are derived by classical thermodynamics from the PVT expression.
When a single pressure-volume-temperature (PVT) equation of state is applicable to both vapor and liquid phases, the formulation used is Preferred analytical correlations are less empirical in nature and most often are theoretically based on one of two exact thermodynamic formulations, as derived in Sec. 13-14 K values (K = y/x) in light-hydrocarbon systems.