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The conventional Gibbs energy minimization methods apply elemental amounts of system components as conservation constraints in the form of a stoichiometric conservation matrix. The linear constraints designate the limitations set on the components described by the system constituents. The equilibrium chemical potentials of the constituents are obtained as a linear combination of the component-specific contributions, which are solved with the Lagrange method of undetermined multipliers. When the Gibbs energy of a multiphase system is also affected by conditions due to immaterial properties, the constraints must be adjusted by the respective entities. The constrained free energy (CFE) minimization method includes such conditions and incorporates every immaterial constraint accompanied with its conjugate potential. The respective work or affinity-related condition is introduced to the Gibbs energy calculation as an additional Lagrange multiplier. Thus, the minimization procedure can include systemic or external potential variables with their conjugate coefficients as well as non-equilibrium affinities. Their implementation extends the scope of Gibbs energy calculations to a number of new fields, including surface and interface systems, multi-phase fiber suspensions with Donnan partitioning, kinetically controlled partial equilibria, and pathway analysis of reaction networks.

Multicomponent equilibrium models for aqueous salt solutions have been developed with the novel ChemSheet program. The calculations are based on the minimization of the Gibbs free energy of the reaction mixtures. For the excess Gibbs energies of the solute species, the Pitzer interaction model with temperature-dependent parameters was used. The results of the ChemSheet multiphase calculations have been verified with experimental or reference data. With the presented modeling technique, reaction kinetics can also be taken into account for specific systems using the Gibbs energy approach. These methods have been applied to the aqueous chemistry of calcium carbonate and sulfate in the wet-end solutions of papermaking. ChemSheet models are applicable in spreadsheets and can be customized for the needs of an industrial user.

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