Modeling piecewise planar fault discontinuities without element‐partitioning in 3D reservoir‐geomechanical models

Abstract

SummaryUsing the extended finite element method, faults can be introduced into a three‐dimensional reservoir‐geomechanical model without meshing to assess the potential for fault reactivation associated with industrial activities such as disposal of CO2 or fluid extraction. The residuals to the governing equations include basis functions formed from the enrichment functions for strong and weak discontinuities. The traditional spatial integration scheme is based on an algorithm that partitions each enriched element into a collection of subtetrahedra, which is time and storage intensive. To avoid element partitioning, we adopt the homogeneous numerical integration scheme (referred as HNI hereafter) where the integration of homogeneous monomials over each polyhedron is converted into the integration of the same monomials over the one‐dimensional edges of the polyhedron by using Stokes's theorem and Euler's homogeneous function theorem. The integrands for the strong and weak discontinuities are derived to implement the integration scheme in the three‐dimensional reservoir‐geomechanical model. An example of a jagged fault is presented to reveal the advantages of HNI scheme over the standard element partitioning approach. Several other examples that involve fluid flow, fault sliding, and fault sliding triggered by injection pressure are also presented to demonstrate that accurate and efficient computations are realized by the new integration scheme.