Geomechanical Modeling Using Variable Order Spectral Element Method at Non-Conformal Meshes

Abstract

The paper considers an overview of the problems of mathematical modeling of geomechanical processes occurring in rocks during the geological exploration and development of reservoirs and well boring process. The mathematical formulation is based on the theory of repeated superposition of large deformations. A numerical discretization of the posed boundary problems of interacting solids is performed using a discontinuous spectral element method and multi-point constraints at non-matching mesh interfaces between interacting solid rock structures. Several industrial applications of the developed approach are considered. Seismic wave propagation in the heterogeneous media with initial geomechanical stresses is considered. A modelling of an induced anisotropy is performed by the superposition of dynamic deformations onto initial generally finite strains. Use of variable order spectral elements at non-conformal meshes allows one to simplify the process of unstructured mesh generation for the discretization of complex geological models and to set the local spatial order of the SEM discretization depending on the speed of seismic waves in geological structures, which significantly reduces the computational costs when conducting numerical modeling and lowers the requirements to the model preprocessing and mesh quality. The considered approach allows predicting in more detail the behavior of the rock during reservoir development, taking into account different stages of the field deformations. In particular, the redistribution of accumulated deformations during multistep loading and / or changes in the structure (topology) of the loaded body, as well as contact conditions of adhesion / sliding at the interlayer boundaries and bonded contacts are taken into account. These problems were solved using CAE Fidesys software, which allows solving static and dynamic problems of geomechanics and geophysics using finite (FEM) and spectral (SEM) element methods of a variable approximation order in space at non-conformal unstructured meshes.