Automatic implementation of thermodynamic models for reliable parameter estimation using computer algebra

Abstract

An existing computer program for the automatic implementation of thermodynamic models, Thermath, was extended to allow the implementation of code compatible with the intbis/ intlib package for the solution of sets of nonlinear equations using interval arithmetic. Using the extended program, we developed the scalar and interval subroutines needed to fit interaction parameters of the Wilson and UNIQUAC excess Gibbs free energy models. We could then use these codes to perform a reliable parameter estimation for these models, i.e. guaranteeing that the global minimum of the objective function was achieved inside an initially specified range for each model parameter. Our observations in the estimation of parameters for the Wilson model in binary systems confirm those of [Nonlinear parameter estimation using interval analysis, presented at FOCAPD-98, Snowbird, UT, USA (1998)] and [Fluid Phase Equilibria 168 (2000) 1], who found that the parameters presented for some systems in the Dechema Vapor–Liquid Equilibrium Data Collection [vol. I, Parts 1–8. Frankfurt/Main, Germany: DECHEMA (1977–1990)] do not correspond to the global optimum of the objective function used in that reference. Our experience with UNIQUAC allowed us to reach the same conclusion for this model.