Thermodynamic formulations of thermo-hydro-mechanical-chemical coupling for multiphase flows in porous media

This PhD subject aims to develop a thermodynamically consistent model for thermo-hydro-mechanical-chemical (THMC) coupling in a porous medium subjected to multiphase flows. This term refers to a model in which the cross-effects between phenomena of different natures are taken into account based on a fundamental physical principle that ensures a form of robustness in terms of entropy. The development of such a coupling model is crucial for applications such as CO₂ or H₂ storage, geothermal energy, or radioactive waste.
More specifically, our objective is to model the interaction between mechanical deformation and chemical alteration, in particular irreversible compaction linked to the dissolution of intergranular cement. The thermodynamic framework allows for a unified formulation of physical processes at different scales. The planned work is divided into three tasks: mathematical modeling, algorithm development, and numerical simulations. The model will be expressed in the form of “gradient flows” with convex potentials. The algorithms will be implemented in BRGM's ComPASS platform. Progressive test cases will validate the models, including one based on a CO₂ injection experiment.
This project is part of the MathSout program of the MathVives PEPR, with strong interdisciplinary potential. It draws on the expertise of BRGM, IFPEN, and INRIA. The doctoral student will be hired by and based at BRGM, with periods spent at partner institutions. Funding is provided by PEPR, and the subject area is in line with the priorities of the ENERGIE and GEONUM programs.

Keywords: porous medium, multiphase flow, thermodynamic formulation

Academic supervisor    Prof. Clément CANCÈS, Inria Lille, ORCID : 0000-0002-7682-1695
Doctoral School    ED631 MADIS, Université de Lille
IFPEN supervisor    Dr. HDR Quang Huy TRAN, ORCID :  0000-0001-7771-3154
BRGM supervisor    Dr. Farid SMAI, ORCID : 0000-0002-8065-3196
PhD location    BRGM, Orléans, France
Duration and start date    3 years, starting in the fourth quarter 2026 (Novembre 2)
Employer    BRGM
Funding    PEPR Maths-Vives, project MathSout
Academic requirements    Master’s degree in scientific computing, numerical analysis, modeling
Language requirements    English level B2 (CEFR)
Other requirements    Python, C++ ou Fortran

To apply, please send your cover letter and CV to the IFPEN supervisor indicated here below.