Computational methods for reactive transport modeling: An extended law of mass-action, xLMA, method for multiphase equilibrium calculations

• Published in: Advances in water resources 2016-10, Vol.96, p.405-422
• Main Authors: Leal, Allan M.M., Kulik, Dmitrii A., Kosakowski, Georg, Saar, Martin O.
• Format: Article
• Language: English
• Subjects: Algorithms; Energy conservation; Equilibrium; Gibbs energy minimization; LMA; Mathematical models; Minimization; Modelling; Multiphase; Optimization; Phases; Reactive transport; Speciation; Transport
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/j.advwatres.2016.08.008

•We present a multiphase chemical equilibrium method based on an extended law of mass-action (xLMA) approach directly derived from the fundamental Gibbs energy minimization problem.•The proposed xLMA method inherits traits of Gibbs energy minimization algorithms that allow it to naturally detect the phases present in equilibrium.•The xLMA method is tested in reactive transport simulations to demonstrate its efficiency and reliability in performance-critical applications.•Only a few iterations are necessary when using warm-start strategies for equilibrium calculations in reactive transport simulations. We present an extended law of mass-action (xLMA) method for multiphase equilibrium calculations and apply it in the context of reactive transport modeling. This extended LMA formulation differs from its conventional counterpart in that (i) it is directly derived from the Gibbs energy minimization (GEM) problem (i.e., the fundamental problem that describes the state of equilibrium of a chemical system under constant temperature and pressure); and (ii) it extends the conventional mass-action equations with Lagrange multipliers from the Gibbs energy minimization problem, which can be interpreted as stability indices of the chemical species. Accounting for these multipliers enables the method to determine all stable phases without presuming their types (e.g., aqueous, gaseous) or their presence in the equilibrium state. Therefore, the here proposed xLMA method inherits traits of Gibbs energy minimization algorithms that allow it to naturally detect the phases present in equilibrium, which can be single-component phases (e.g., pure solids or liquids) or non-ideal multi-component phases (e.g., aqueous, melts, gaseous, solid solutions, adsorption, or ion exchange). Moreover, our xLMA method requires no technique that tentatively adds or removes reactions based on phase stability indices (e.g., saturation indices for minerals), since the extended mass-action equations are valid even when their corresponding reactions involve unstable species. We successfully apply the proposed method to a reactive transport modeling problem in which we use PHREEQC and GEMS as alternative backends for the calculation of thermodynamic properties such as equilibrium constants of reactions, standard chemical potentials of species, and activity coefficients. Our tests show that our algorithm is efficient and robust for demanding applications, such as reactive transport modeling, where it