A Robust Algorithm for Adaptive Chemical-Phase Equilibrium Calculations

Summary

Robust and efficient chemical-phase equilibrium (CPE) calculations are essential for modeling complex subsurface processes such as carbon dioxide (CO2) sequestration, enhanced oil recovery (EOR), and reactive transport in geologic formations. Many existing approaches rely on sequential or loosely coupled calculations of chemical and phase equilibria, which may suffer from convergence difficulties and inconsistent thermodynamic states. With this paper, we present a fully coupled Gibbs free energy minimization algorithm for multiphase chemical equilibrium calculations that can handle reactive and/or nonreactive systems. Unlike conventional nonstoichiometric methods that use component mole numbers as independent variables, the proposed formulation uses component mole fractions and phase amounts as independent variables. This formulation exploits the structure of the chemical potential expressions and results in a Hessian matrix that does not explicitly depend on phase amounts, improving numerical conditioning near phase boundaries and during phase transitions. The constrained minimization problem is solved using a Lagrange multiplier formulation combined with matrix reduction, constraint-handling, and line-search procedures. Numerical case studies of nonideal multiphase mixtures representative of CO2/brine/rock systems demonstrate that the proposed algorithm improves robustness and convergence compared with methods based on component mole numbers, particularly for trace components, phase transitions, and the precipitation of multiple solid phases. These capabilities become increasingly important in emerging technologies, such as CO2 mineralization and critical mineral recovery. The adaptivity and robustness make the algorithm suitable for integration into reactive transport simulators as a unified equilibrium framework for both reactive and nonreactive compositional simulations.