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In this paper, we consider a poroelasticity problem in heterogeneousmulticontinuum media that is widely used in simulations of the unconventionalhydrocarbon reservoirs and geothermal fields. Mathematical model contains acoupled system of equations for pressures in each continuum and effectiveequation for displacement with volume force sources that are proportional tothe sum of the pressure gradients for each continuum. To illustrate the idea ofour approach, we consider a dual continuum background model with discretefracture networks that can be generalized to a multicontinuum model forporoelasticity problem in complex heterogeneous media. We present a fine gridapproximation based on the finite element method and Discrete Fracture Model(DFM) approach for two and three-dimensional formulations. The coarse gridapproximation is constructed using the Generalized Multiscale Finite ElementMethod (GMsFEM), where we solve local spectral problems for construction of themultiscale basis functions for displacement and pressures in multicontinuummedia. We present numerical results for the two and three dimensional modelproblems in heterogeneous fractured porous media. We investigate relativeerrors between reference fine grid solution and presented coarse gridapproximation using GMsFEM with different numbers of multiscale basisfunctions. Our results indicate that the proposed method is able to giveaccurate solutions with few degrees of freedoms.

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