Model-Order Reduction of Coupled Flow and Geomechanics in Ultra-Low Permeability ULP Reservoirs

Abstract

This work focuses on the development of accurate and fast simulation models for Ultra-Low Permeability (ULP) reservoirs, i.e., tight-sands and shales. ULP plays are the main unconventional resources that concentrate the bulk of production activity in the US. ULP challenge conventional simulators because they require multiphysics couplings, e.g., flow and geomechanics couplings, which poses a severe burden regarding computational efforts. We, thus address these challenges by developing accurate reduced-order models for coupled flow and geomechanics. We rely on projection-based Model-Order Reduction (MOR) and hyper-reduction (POD-DEIM) techniques to reduce the ULPs computational cost. More specifically, we perform the standard offline training stage on displacements as primary variables to create local basis using Proper Orthogonal Decomposition (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 (POD-DEIM) on the non-linear functions. Preliminary results, that focus on linear and nonlinear thermo-poroelasticity, show that our MOR algorithm provides substantial single and double digits speedups, up to 50X if we combine with multi-threading assembling and perform MOR on both physics. We highlight the remarkable MOR compression ratio above 99.9% for mechanics. The approach is particularly useful to speed up solving the sparse system for the inner iteration in convolution like problems which produces significant time savings compared to the serial full-order model (FOM). The latter is also true for problems that exhibit long serial times, for instance, while assembling the Jacobian and Residual for both physics and post-processing to compute stresses, if the serial-time per iteration is shorter that solving the sparse system of equations. These MOR results are promising in the sense that for most coupled flow and mechanics problems, the above condition holds. We formally compare FOM and reduced-order model (ROM) and provide time data to demonstrate the speedup of the procedure. Examples cover elasticity and rate-independent plasticity one-way coupled with the two-phase flow and the energy equation. We employ continuous Galerkin finite elements for the mechanics.