Reactive flash for ideal multiphase mixtures: Unified formulation and efficient computation
Abstract
Multiphase chemical equilibrium problems lead to nonlinear systems with complementarity constraints, which become particularly challenging when phases may vanish. We introduce a new algebraic formulation of the equilibrium problem based on extended mole fractions, derived from the subdifferential of the Gibbs free energy, and establish its equivalence with the classical minimization problem. Our analysis provides new conditions ensuring the uniqueness of solutions, even when some phases disappear. Building on this formulation, we propose two parametrized Newton-based strategies: one reformulates the relation between species quantities and chemical potentials, while the other parametrizes the complementarity conditions directly. Numerical experiments on a system with 72 species and 22 phases confirm the robustness and efficiency of the proposed methods. In tests with randomized inputs, both strategies achieve success rates above 90% with moderate iteration counts, outperforming established approaches such as the Newton-min and Fischer-Burmeister complementarity functions, and interior-point methods.
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BibTeX
@article{jonval2026reactive,
title = {{Reactive flash for ideal multiphase mixtures: Unified formulation and efficient computation}},
author = {Maxime Jonval and Ibtihel Ben Gharbia and Clément Cancès and Thibault Faney and Quang Huy Tran},
journal = {Journal of Computational Physics},
year = {2026},
month = oct,
url = {https://hal.science/hal-05393808v2},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - JOUR
TI - Reactive flash for ideal multiphase mixtures: Unified formulation and efficient computation
AU - Maxime Jonval
AU - Ibtihel Ben Gharbia
AU - Clément Cancès
AU - Thibault Faney
AU - Quang Huy Tran
PY - 2026
DA - 2026/10/20
JO - Journal of Computational Physics
UR - https://hal.science/hal-05393808v2
AB - Multiphase chemical equilibrium problems lead to nonlinear systems with complementarity constraints, which become particularly challenging when phases may vanish. We introduce a new algebraic formulation of the equilibrium problem based on extended mole fractions, derived from the subdifferential of the Gibbs free energy, and establish its equivalence with the classical minimization problem. Our analysis provides new conditions ensuring the uniqueness of solutions, even when some phases disappear. Building on this formulation, we propose two parametrized Newton-based strategies: one reformulates the relation between species quantities and chemical potentials, while the other parametrizes the complementarity conditions directly. Numerical experiments on a system with 72 species and 22 phases confirm the robustness and efficiency of the proposed methods. In tests with randomized inputs, both strategies achieve success rates above 90% with moderate iteration counts, outperforming established approaches such as the Newton-min and Fischer-Burmeister complementarity functions, and interior-point methods.
SN - 0021-9991
SN - 1090-2716
ER -