A VEM application to geomechanical simulations for underground fluid storage

In this paper, we discuss how to describe the geomechanical behavior of geological formations used for underground fluid storage through the application of the Virtual Element Method (VEM) on conforming polyhedral meshes for the solution of stress-strain equilibrium equations. Under the assumption of small deformations, the solution algorithm for an Isotropic Linear Elastic (ILE) constitutive law coupled with the Mohr-Coulomb perfectly plastic yield criterion is implemented. The solution is then tested on a geological scenario with simplified geometry but realistic rock parameters. Results are compared with the solution of a first-order FEM obtained from a commercial solver, showing a good agreement in terms of displacement and stress maps. In the current implementation, a stabilization term of the VEM projectors is tailored to the elastoplastic law, paving the way for the generalization to polyhedral grids and the introduction of domain discontinuities such as faults