A unified Element-based Finite Volume Method for linear and nonlinear geomechanics and compositional reservoir simulation

This work presents an unstructured grid-based formulation for compositional reservoir simulation coupled with elastic, elastoplastic, and viscoplastic geomechanical models. Implemented in the UTCOMPRS simulator using the Element-based Finite Volume Method (EbFVM), the proposed approach explicitly solves both flow and mechanical equations on unstructured grids. It supports nonlinear models, such as Mohr-Coulomb, Drucker-Prager, and a Perzyna-based viscoplastic criterion to represent material yield. Five case studies are conducted to verify the geomechanical implementation: Prandtl’s benchmark validates the plastic and viscoplastic models; primary production matched results from a commercial simulator; WAG injection and CO 2 storage cases demonstrated the influence of the geomechanical model on production forecast, reservoir pressure, and rock deformation; and a Pre-Salt reservoir proxy tested computational efficiency, and numerical accuracy of the EbFVM across multiple grid refinements. Results show that the EbFVM captures nonlinear deformation while delivering solutions comparable to fine meshes using significantly coarser grids. The proposed formulation provides a robust and versatile tool for simulating complex reservoir-geomechanical problems. • A unified Element-based Finite Volume Method (EbFVM) is developed for coupled flow-geomechanics. • The formulation handles elastic, elastoplastic, and viscoplastic constitutive behaviors. • Flow and mechanical equations are solved on the same unstructured grid framework. • Validation includes benchmarks, WAG injection, CO 2 storage, and Pre-Salt reservoir cases. • The EbFVM achieves fine-grid accuracy with lower computational cost and higher scalability.