# Generalized Multiscale Finite Element Method for the poroelasticity problem in multicontinuum media

## TL;DR

This paper develops a multiscale finite element method for simulating poroelasticity in complex heterogeneous multicontinuum media, enabling accurate solutions with fewer computational resources.

## Contribution

It introduces a generalized multiscale finite element method tailored for poroelasticity in multicontinuum media, including fracture networks, with demonstrated accuracy in 2D and 3D models.

## Key findings

- Accurate coarse grid solutions with few basis functions.
- Effective modeling of fractured porous media.
- Reduced computational cost for complex simulations.

## Abstract

In this paper, we consider a poroelasticity problem in heterogeneous multicontinuum media that is widely used in simulations of the unconventional hydrocarbon reservoirs and geothermal fields. Mathematical model contains a coupled system of equations for pressures in each continuum and effective equation for displacement with volume force sources that are proportional to the sum of the pressure gradients for each continuum. To illustrate the idea of our approach, we consider a dual continuum background model with discrete fracture networks that can be generalized to a multicontinuum model for poroelasticity problem in complex heterogeneous media. We present a fine grid approximation based on the finite element method and Discrete Fracture Model (DFM) approach for two and three-dimensional formulations. The coarse grid approximation is constructed using the Generalized Multiscale Finite Element Method (GMsFEM), where we solve local spectral problems for construction of the multiscale basis functions for displacement and pressures in multicontinuum media. We present numerical results for the two and three dimensional model problems in heterogeneous fractured porous media. We investigate relative errors between reference fine grid solution and presented coarse grid approximation using GMsFEM with different numbers of multiscale basis functions. Our results indicate that the proposed method is able to give accurate solutions with few degrees of freedoms.