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Computational methods for reactive transport modeling: An extended law of mass-action, xLMA, method for multiphase equilibrium calculations
- Source :
- Advances in Water Resources. 96:405-422
- Publication Year :
- 2016
- Publisher :
- Elsevier BV, 2016.
-
Abstract
- 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 converges within 1–3 iterations in most cases. The proposed xLMA method is implemented in Reaktoro, a unified open-source framework for modeling chemically reactive systems.
- Subjects :
- Activity coefficient
Physics
Thermodynamic equilibrium
Thermodynamics
Context (language use)
010103 numerical & computational mathematics
010502 geochemistry & geophysics
01 natural sciences
Law of mass action
Chemical species
symbols.namesake
Lagrange multiplier
symbols
Statistical physics
0101 mathematics
Reactive system
Equilibrium constant
0105 earth and related environmental sciences
Water Science and Technology
Subjects
Details
- ISSN :
- 03091708
- Volume :
- 96
- Database :
- OpenAIRE
- Journal :
- Advances in Water Resources
- Accession number :
- edsair.doi...........ad3ce82d2bb3ac9051820ab3edd412f5