Model-Order Reduction for Coupled Flow and Linear Thermal-Poroplasticity with Applications to Unconventional Reservoirs

This work focuses on the development of model reduction workflows for coupled flow and geomechanics arising in Ultra-Low Permeability (ULP) reservoir simulation. ULP challenges conventional simulators because they require multiphysics couplings, e.g., flow, thermal, and geomechanics couplings, which poses a severe burden regarding computational efforts. We tackle this problem by implementing a workflow for a two-step Proper Orthogonal Decomposition/Discrete Empirical Interpolation Method (POD-DEIM) model reduction approach for flow and geomechanics. More specifically, we perform the standard offline training stage on displacements as primary variables to create a basis for each primary variable using POD. During the online phase, we project the residual and Jacobian that arise from both poroelasticity and rate-independent poroplasticity into the given basis to reduce one-way coupled flow and geomechanics computations. We approximate the tensors, for the energy equation, to minimize the serial-time. We consider the role of the heterogeneity and material models such as Von Mises and investigate the benefits of hyper-reduction via DEIM on the nonlinear functions. Our results, which focus on linear and nonlinear thermo-poroelasticity, show that our Model-Order-Reduction (MOR) algorithm provides substantial single and double digits speedups, up to 50X if we combine with multi-threading assembling or DEIM and perform MOR on both physics.