  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.
