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The convex programming minimization of five thermodynamic potentials other than Gibbs energy in geochemical modeling

^* Institute of Geochemistry, P. O. Box 4019, Favorskii str. 1a, 664033, Irkutsk, Russia
^** Waste Management Laboratory, Paul Scherrer Institute, CH-5232, Villigen PSI, Switzerland (on leave of absence from State Scientific Center of Environmental Radiogeochemistry, National Academy of Science, Palladin Prospect 34a, 03680 Kyiv, Ukraine)

An approach is suggested for computation of complete or metastable equilibrium states in the multicomponent, multiphase, and multiaggregate systems with parameters of state other than fixed temperature T and pressure P. It consists in computation of a series of isobaric-isothermal equilibrium states by Gibbs energy minimization. Thus, the general problem of minimization of thermodynamic potentials other than Gibbs energy G(T,P) is reduced to a sequence of simpler problems of two- or three-criteria parametric minimization of either of five thermodynamic potentials [isochoric-isothermal or Helmholtz energy A(T,V); isochoric-isentropic or internal energy at isochoric conditions U(S,V); isobaric-isentropic or enthalpy H(P,S); negative entropy at isobaric conditions and fixed enthalpy –S(P,H); and negative entropy at isochoric conditions and fixed internal energy –S(V,U)]. The computational scheme is simple, efficient, and reliable, because in any case it uses the IPM (Interior Points Method) algorithm for searching minimum of the non-linear total Gibbs energy function whereby one- or two-sided restrictions may be imposed on some or all dependent components in the system (Karpov and others, 1997). The new approach provides a rigorous basis for the formulation and numerical solution of the problems of chemical mass transfer under factors of state other than isobaric-isothermal.

The developed algorithms and their implementation in Selektor-C program package can be used in a wide variety of scientific and practical applications. The numerical tests and examples illustrate the new technique on a model of irreversible oil-water interaction in hydrocarbon reservoirs (system Ca-Mg-C-O-H).