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Simulation of fracturing processes in porous rocks can be divided into twomain branches: (i) modeling the rock as a continuum which is enhanced withspecial features to account for fractures, or (ii) modeling the rock by adiscrete (or discontinuous) approach that describes the material directly as acollection of separate blocks or particles, e.g., as in the discrete elementmethod (DEM). In the modified discrete element (MDEM) method, the effectiveforces between virtual particles are modified in all regions, without failingelements, so that they reproduce the discretization of a first order finiteelement method (FEM) for linear elasticity. This provides an expression of thevirtual forces in terms of general Hook's macro-parameters. Previously, MDEMhas been formulated through an analogy with linear elements for FEM. We showthe connection between MDEM and the virtual element method (VEM), which is ageneralization of FEM to polyhedral grids. Unlike standard FEM, which computesstrain-states in a reference space, MDEM and VEM compute stress-states directlyin real space. This connection leads us to a new derivation of the MDEM method.Moreover, it gives the basis for coupling (M)DEM to domain with linearelasticity described by polyhedral grids, which makes it easier to applyrealistic boundary conditions in hydraulic-fracturing simulations. Thisapproach also makes it possible to combine fine-scale (M)DEM behavior near thefracturing region with linear elasticity on complex reservoir grids in thefar-field region without regridding. To demonstrate the simulation of hydraulicfracturing, the coupled (M)DEM-VEM method is implemented using the MatlabReservoir Simulation Toolbox (MRST) and linked to an industry-standardreservoir simulator.

Combining the Modified Discrete Element Method with the Virtual Element Method for Fracturing of Porous Media