Comments on "Flash calculations for continuous or semicontinuous mixtures using an equation of state"

Abstract

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

Multicomponent flash algorithm for mixtures containing polydisperse polymers

“…For unimodal molecular-weight distribution curves, pseudocomponents are generated by matching the statistical moments of the distribution to those of the pseudocompo-Ž . nents to be determined Tork et al, 1999 or by discretizing a continuous distribution function using Gaussian quadrature Ž method Cotterman et al, 1985Cotterman et al, , 1986Cotterman and Praus-. nitz, 1985 .…”

Asymptotic effects using semicontinuous vis-a-vis discrete descriptions in phase equilibrium computations

“…Cotterman and Prausnitz (1985), Cotterman et al (1985a,b;1986), Behrens and Sandler (1988), and Shibata et al (1987) have used this approach. Some of these efforts have been explicitly restricted to specific physicochemical models such as Raoult's law or specific applications such as polymers.…”

Regression Analysis and C7+ Description for Accurate PVT Data Calculations with Equations of State

“…Cotterman an d Prau snitz use a gamma distribution function, b ut the method for setting up the nodes a n d the (111-8) re lat ion of [9] a re not accurate . The above menti oned a uth ors co me back to the prob l em witti an accurate solution of t h e quadrature [101, but l imited only to semi-infini te distrib utions .…”