Multiscale Extended Finite Element Method for Modelling Mechanical Deformation in Porous Media with Propagating Fractures

Altering the state of the stress of the subsurface reservoirs can lead fractures to slip and extend their lengths (i.e., to propagate). This process can even be engineered, in many applications, e.g., enhanced geothermal systems. As such, accurate and efficient simulation of the mechanical deformation of the subsurface geological reservoirs, allowing for fracture propagation, is at the core of many geoscientific operational designs. Subsurface reservoirs entail many fractures at multiple scales. Implementation of 3D complex grids on these complex fractured systems, for mechanical deformation analyses, is extremely challenging. An alternative approach can be developed by using extended finite element methods (XFEM). XFEM allows for capturing the fractures effects on a conveniently-generated structured matrix mesh. The cracks are introduced by extra degrees of freedom (DOFs) on the nodes of the matrix rock mesh. For geoscientific applications, however, XFEM results in too many DOFs which are beyond the scope of simulators. Additionally, for propagating fractures, these DOFs need to be updated in response to the dynamic extension of the fractures in the domain. The propagation process not only adds to the sensitivity of the outputs to the accuracy of the estimated stress field, but also increases the size of the linear systems. In addition to these, matrix rocks are often highly heterogeneous, at high resolutions. In this work, we present a novel multiscale procedure for propagating fractures in heterogeneous geological reservoirs. For the first time in the community, we present the highly fractured systems at coarser resolutions via XFEM-based basis functions, which also account for the propagating effects. Fractures are allowed to extend their scale and the enriched basis functions are locally updated. Using these bases, the coarse scale system is obtained in which no extra DOFs due to fractures exist. This significantly reduces the computational complexity. As a significant step forward compared with our recently-published journal paper [Xu, Hajibeygi, Sluys, Journal of Computational Physics, 2021], in this conference contribution we allow the fractures to propagate. Specially, we introduce a local-global-based approach, in which fracture propagation is treated only at local stage; while the stress and deformation are modelled at global scale. In the search of convenient implementation, the procedure is presented algebraically. Through several test cases, we demonstrate the applicability of the method for complex fractured media. Specially we demonstrate that propagation can be modeled at local scale, while accurate stress and deformation fields are obtained at global scale.