| Title: |
Reactive flash for ideal multiphase mixtures: Unified formulation and efficient computation |
| Authors: |
Jonval, Maxime; Ben Gharbia, Ibtihel; Cancès, Clément; Faney, Thibault; Tran, Quang Huy |
| Contributors: |
Laboratoire Jean Alexandre Dieudonné (LJAD); Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA); Centre Inria d'Université Côte d'Azur; Institut National de Recherche en Informatique et en Automatique (Inria); IFP Energies nouvelles (IFPEN); Reliable numerical approximations of dissipative systems (RAPSODI); Laboratoire Paul Painlevé - UMR 8524 (LPP); Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centre Inria de l'Université de Lille; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria); This work was jointly supported by IFPEN and Inria.; ANR-23-EXMA-0010,MATHSOUT,Mathématiques Souterraines(2023); ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011) |
| Source: |
https://hal.science/hal-05393808 ; 2025. |
| Publisher Information: |
CCSD |
| Publication Year: |
2025 |
| Collection: |
IFP Énergies nouvelles: HAL-IFPEN |
| Subject Terms: |
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]; [CHIM]Chemical Sciences |
| Description: |
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. |
| Document Type: |
report |
| Language: |
English |
| Availability: |
https://hal.science/hal-05393808; https://hal.science/hal-05393808v1/document; https://hal.science/hal-05393808v1/file/Article_Maxime_Jonval_Multiphasique.pdf |
| Rights: |
info:eu-repo/semantics/OpenAccess |
| Accession Number: |
edsbas.6B9AC313 |
| Database: |
BASE |