A block preconditioner for thermo-poromechanics with frictional deformation of fractures

Abstract

The numerical modeling of fracture contact thermo-poromechanics is crucial for advancing subsurface engineering applications, including CO2 sequestration, production of geo-energy resources, energy storage and wastewater disposal operations. Accurately modeling this problem presents substantial challenges due to the complex physics involved in strongly coupled thermo-poromechanical processes and the frictional contact mechanics of fractures. To resolve process couplings in the resulting mathematical model, it is common to apply fully implicit time stepping. This necessitates the use of an iterative linear solver to run the model. The solver’s efficiency primarily depends on a robust preconditioner, which is particularly challenging to develop because it must handle the mutual couplings between linearized contact mechanics and energy, momentum, and mass balance. In this work, we introduce a preconditioner for the problem based on the nested approximations of Schur complements. To decouple the momentum balance, we utilize the fixed-stress approximation, extended to account for both the porous media and fracture subdomains. The singularity of the contact mechanics submatrix is resolved by a linear transformation. Two variations of the algorithm are proposed to address the coupled mass and energy balance submatrix: either the Constrained Pressure Residual (CPR) or the algebraic multigrid method (AMG) for systems of equations. The preconditioner is evaluated through numerical experiments of fluid injection into fractured porous media, which causes thermal contraction and subsequent sliding and opening of fractures. The experiments show that the preconditioner performs robustly for a wide range of simulation regimes governed by various fracture states, friction coefficients and Peclétnumber. The grid refinement experiments demonstrate that the preconditioner scales well in terms of GMRES iterations, in both two and three dimensions.