MODELING CHEMICAL MASS-TRANSFER IN GEOCHEMICAL PROCESSES - THERMODYNAMIC RELATIONS, CONDITIONS OF EQUILIBRIA, AND NUMERICAL ALGORITHMS

The problem of chemical mass transfer-calculation of complete and/or r estricted chemical equilibrium states in multiphase and multiaggregate systems-is reduced to the convex programming problem. A related set-t heory notation is introduced for complex physico-chemical models. It i s used to represent the explicit analytical expressions for chemical p otentials of species or dependent components both in symmetric and asy mmetric 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 m olar quantities of dependent components, Such restrictions permit to s imulate the metastable the states for individual. species, phases, and subsystems in the system under study. The chemical equilibrium proble m is solved both for prime variables (sought-for molar quantities of d ependent 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 to ol 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 defined by the number of independ ent components, By means of the same algorithm, a feasible initial app roximation can always be computed automatically from the entire list o f dependent components that may be potentially present in equilibrium, The approach to the global minimum point is explicitly identified whe n the necessary and sufficient Kuhn-Tucker conditions are met, The min imization of total Gibbs free energy in highly nonideal systems is mad e persistent and fast by introducing a smoothing parameter that restri cts increments of activity coefficients of dependent components as fun ctions of system composition between subsequent iterations of IPM. The oretical considerations are illustrated by numerical examples. The cal culation of total equilibrium in the highly non-ideal case is presente d for a very rigid system including silicate melt Parametric minimizat ion of Helmholtz potential under conditions of total and restricted eq uilibria is shown by an example of the system containing aqueous solut ion, gas phase, liquid hydrocarbon mixture, and solid carbon.