Monolithic hydromechanical model for fluid flow and solid deformation incorporating solid contact

Abstract:

The characterization and modeling of hydromechanical properties of rocks are crucial for advancing various energy-related technologies, including underground hydrogen storage, CO2 sequestration, geothermal energy extraction, and deep radioactive waste disposal. Due to the scarcity of sample material from great depths, Digital Rock Physics has gained popularity as a non-destructive characterization approach to rocks. This consists of microstructure simulations that use finite element method (FEM) for fluid and solid, or hybrid approaches, which solve fluid dynamics with other methods in a staggered manner.

Here we develop a monolithic coupled FEM hydromechanical solver, that allows for large deformations through a Lagrangian formulation, and incorporates solid contact effects through an optimized Linear Complementarity Problem (LCP) method. The fluid flow is resolved based on the Navier-Stokes equation, stabilized with the Pressure-Stabilizing Petrov-Galerkin (PSPG) method. The stiffness matrix of the deformed geometry is updated based on the contact analysis, incorporating periodic boundary conditions to account for the repetitive nature of the porous structure. The numerical framework for solving the coupled fluid flow and solid deformation problem is integrated into the DEHydrate simulator, previously developed by the authors.

Using this framework, the influence of pore anisotropy ratio and porosity on the stiffness matrix is systematically analyzed, resulting in non-linear elastic behavior and induced anisotropy. Going beyond conventional permeability-porosity relationships, future 3D simulations are then expected to relate evolving pore structures to upscaled hydraulic properties.

Short bio:

Li Zhang is a postdoctoral researcher working at Navier with Jean Sulem and Philipp Braun since July 2024. Her research focuses on establishing a numerical framework to evaluate the macroscopic properties of rocks through microstructural simulations, incorporating coupled hydro-mechanical behavior with multiphase transport properties. In particular, she emphasizes the effect of deformation on transport properties. Li Zhang obtained his PhD in June 2024 from Tsinghua University in China. Her doctoral thesis proposed a comprehensive thermo-poro-elastoplastic theory and developed a highly nonlinear, fully coupled three-dimensional thermo-hydro-mechanical-chemical model, along with its computational simulator, DEHydrate, to describe the multiphysical behavior of hydrate-bearing sediments during gas hydrate dissociation.