Energy transition extends the range of geological settings and physical processes to be considered in subsurface reservoir modeling. Numerous applications consider essentially anisotropic reservoirs or require advanced gridding that can not be resolved consistently by conventionally used Two Point Flux Approximation (TPFA). The presence of anisotropy and heterogeneity can occur in both Permeability (porous media) and Stiffness tensor (linear elasticity). Just like any subsurface formation, geothermal reservoirs can have fluvial channels, sand lenses, and spatial heterogeneity in permeability which will not give an accurate solution on non-K-orthogonal grids. A Finite Volume (FV) framework forms the basis for this project due to the local mass conservation property while solving the flow problem. When there are full tensor material properties, multipoint methods provide a good approximation of flux across interfaces. But these methods are known to be non-monotone which can introduce new types of numerical errors. So, we present a Nonlinear Two Point Flux Approximation (NTPFA) based on gradient reconstruction and homogenization function, and a Nonlinear Two Point Stress Approximation where the linear elasticity equation is solved in FV framework using the Nonlinear discretization technique instead of a multipoint approach. Currently, we treat both the models independently but the main idea of this kind of approximation is to integrate flow and mechanics in a unified nonlinear framework with minimal degrees of freedom, and we can derive the coupled equation for a poro-mechanical simulation. Reducing monotonicity in our primary variables can improve the accuracy of the traction component at the interface which is especially useful when we model displacement along the fault.

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