Minimization of gibbs free energy in geochemical systems by convex programming

Calculation of complete and constrained chemical equilibrium in multicomponent multiphase and heterogeneous systems is reduced to the problem of convex programming. A set-theory system of notation is introduced for physicochemical models. Analytical expressions are provided for the chemical potentials of dependent components in symmetric and asymmetric reference states. Necessary and sufficient conditions are formulated for complete and metastable equilibrium using the Kuhn-Tucker conditions of the problem of convex programming, when one- and/or two-sided constraints can be set on part or all sought-for values of mole quantities of dependent components. The prime solution values of the convex programming problem are sought-for values of the molar quantities of dependent components, while the dual solution values are sought for values of the chemical potentials of independent components of the system related to stoichiometric units. The use of the chemical potentials of independent components allows solving the problem of the determination of the Gibbs free energy of formation of compounds from their known contents in the systems and, vise versa, the concentrations of dependent components in solution phases from the known Gibbs free energies of formation and chemical potentials of independent components in representative subsystems. Dual solutions related to a balance constraint on the electric charge of the system permit explicit calculation of the redox potential of the system, Eh (pe), without considering the partial pressure of oxygen or hydrogen and pH.