This work presents a phenomenological correction to improve a classical equation of state for representing phase equilibria and densities in the vapor‐liquid critical region. This correction consists of two steps. The first step is a volume translation which locates the correct critical point; this volume translation also improves density predictions for pure fluids and mixtures. The second step provides a near‐critical contribution to the residual Helmholtz energy which accounts for aomalous behavior near the critical point. For pure fluids, the near‐critical contribution flattens the coexistence curve and pressure‐density isotherms near the critical point. For mixtures, the near‐critical contribution has only a small effect on the calculated coexistence curve; this effect is often masked by the choice of binary parameters in the classical equation which have a more profound effect on the calculated results.

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Sir: In our recent article (Cotterman and Prausnitz, 1985), we report a numerical procedure using Gaussian quadrature to calculate phase equilibria for a continuous or semicontinuous mixture. We describe the composition of a continuous mixture by a continuous distribution function F(Z) where the distributed variable Z is some characterizing property such as molecular weight. The phase-equilibrium equations contain integrals of this distribution function.In Appendix I11 of our article, we discuss Laguerre-Gauss quadrature for integrating semiinfinite distribution functions and we present a relation (eq 111-8) to scale tabulated quadrature points to match the range of the distributed variable. Equation 111-8 was developed empirically for simple, unimodal distribution functions.A more appropriate integration procedure for semiinfinite distributions, called "generalized Laguerre-Gauss quadrature" (see, e.g., Davis and Rabinowitz, 1984; Stroud and Secrest, 1966)) has been suggested by Vincent Van Brunt, Department of Chemical Engineering, University of South Carolina. This procedure eliminates the need for eq 111-8 and provides a rational method to determine quadrature points and weighting factors for integrating semiinfinite distributions. We discuss briefly here the implementation of generalized Laguerre-Gauss quadrature for calculating phase equilibria for a continuous or semicontinuous mixture.Generalized Laguerre-Gauss quadrature approximates a semiinfinite integral of an arbitrary function f(u) by a weighted sum of function evaluations with the weighting function ua-le-u. The n-point quadrature formula is

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