High-performance modeling of coupled hydro-mechanical behavior with graphical processing units

Proper consideration of the complexity of coupled processes is essential for accurate assessment of outcomes of geoenergy projects. The potential applications include evaluation of the sealing capacity of caprock, storage potential of the reservoir formation, fluid transport, and induced seismicity risks. The numerical implementation of the governing equations for thermo-hydromechanical-chemical response is challenging due to the substantial contrast between the characteristic times of coupled processes. Furthermore, addressing the heterogeneity and anisotropy of geological formations requires development of representative three-dimensional models, which can reach billions of grid points. These challenges are addressed by implementation of pseudo-transient iterative method with the use of graphical processing units (GPU) to achieve low-level parallelization. The implemented numerical codes are formulated in consistent modular structure allowing to enable modules based on the desired applications and are presented for the case of hydro-mechanical coupling. Hydro module handles single- and two-phase flow coupled with the mechanical component. The foundational constitutive framework of mechanical response is Biot's poroelasticity that can be expanded to incorporate viscous- and plastic- deformation. Resolving the governing equations of coupled hydro-mechanical (HM) response with high resolution is a bandwidth-limited problem, highlighting that effective management of memory access is essential for scalability of parallel computations. All the modules are implemented in the single executable file, allowing to limit unnecessary memory access, and resulting in up to 50x performance increase in single-GPU implementation compared to single CPU. The accuracy of HM solver is benchmarked with known analytical solutions for uncoupled and coupled processes.