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Title: MODELING CHEMICAL MASS TRANSFER IN GEOCHEMICAL PROCESSES: THERMODYNAMIC RELATIONS, CONDITIONS OF EQUILIBRIA, AND NUMERICAL ALGORITHMS
Author(s): Igor K. Karpov, Konstantin V. Chudnenko, Dmitri A. Kulik
Annotation: The problem of chemical mass transfer-calculation of complete and/or restricted chemical equilibrium states in multiphase and multiaggregate systems-is reduced to the convex programming problem. A related set-theory notation is introduced for complex physico-chemical models. It is used to represent the explicit analytical expressions for chemical potentials of species or dependent components both in symmetric and asymmetric reference scales. The necessary and sufficient conditions for the complete and metastable equilibrium states are formulated as Kuhn-Tucker conditions of the convex programming problem, including one- or two-sided restrictions that may be imposed on some or all sought-for molar quantities of dependent components. Such restrictions permit to simulate the metastable states for individual species, phases, and subsystems in the system under study. The chemical equilibrium problem is solved both for prime variables (sought-for molar quantities of dependent components) and dual variables (sought-for values of chemical potentials of stoichiometric units, or independent components, in the system). An Interior Points Method (IPM) algorithm is an efficient tool for Gibbs free energy numerical minimization regarding one- and two-sided restrictions without increase in the dimensionality of the itera-tional equations system of the order denned by the number of independent components. By means of the same algorithm, a feasible initial approximation can always be computed automatically from the entire list of dependent components that may be potentially present in equilibrium. The approach to the global minimum point is explicitly identified when the necessary and sufficient Kuhn-Tucker conditions are met The minimization of total Gibbs free energy in highly non-ideal systems is made persistent and fast by introducing a smoothing parameter that restricts increments of activity coefficients of dependent components as functions of system composition between subsequent iterations of IPM. Theoretical considerations are illustrated by numerical examples. The calculation of total equilibrium in the highly non-ideal case is presented for a very rigid system including silicate melt Parametric minimization of Helmholtz potential under conditions of total and restricted equilibria is shown by an example of the system containing aqueous solution, gas phase, liquid hydrocarbon mixture, and solid carbon.
Bibliographical description: MODELING CHEMICAL MASS TRANSFER IN GEOCHEMICAL PROCESSES: THERMODYNAMIC RELATIONS, CONDITIONS OF EQUILIBRIA, AND NUMERICAL ALGORITHMS Igor K. Karpov, Konstantin V. Chudnenko, Dmitri A. Kulik - AMERICAN JOURNAL OF SCIENCE, VOL. 297, OCTOBER, 1997, P. 767-806
Publication's type: статья
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