Multiscale extended finite element method for deformable fractured porous media

Multiscale extended finite element method for deformable fractured porous media

Xu, F. (TU Delft Applied Mechanics)
Hajibeygi, H. (TU Delft Reservoir Engineering)
Sluys, Lambertus J. (TU Delft Materials- Mechanics- Management & Design)

Materials- Mechanics- Management & Design

2021

Deformable fractured porous media appear in many geoscience applications. While the extended finite element method (XFEM) has been successfully developed within the computational mechanics community for accurate modeling of deformation, its application in geoscientific applications is not straightforward. This is mainly due to the fact that subsurface formations are heterogeneous and span large length scales with many fractures at different scales. To resolve this limitation, in this work, we propose a novel multiscale formulation for XFEM, based on locally computed enriched basis functions. The local multiscale basis functions capture heterogeneity of th e porous rock properties, and discontinuities introduced by the fractures. In order to preserve accuracy of these basis functions, reduced-dimensional boundary conditions are set as localization condition. Using these multiscale bases, a multiscale coarse-scale system is then governed algebraically and solved. The coarse scale system entails no enrichment due to the fractures. Such formulation allows for significant computational cost reduction, at the same time, it preserves the accuracy of the discrete displacement vector space. The coarse-scale solution is finally interpolated back to the fine scale system, using the same multiscale basis functions. The proposed multiscale XFEM (MS-XFEM) is also integrated within a two-stage algebraic iterative solver, through which error reduction to any desired level can be achieved. Several proof-of-concept numerical tests are presented to assess the performance of the developed method. It is shown that the MS-XFEM is accurate, when compared with the fine-scale reference XFEM solutions. At the same time, it is significantly more efficient than the XFEM on fine-scale resolution, as it significantly reduces the size of the linear systems. As such, it develops a promising scalable XFEM method for large-scale heavily fractured porous media.

Extended finite element
Fractured porous media
Geomechanics
Multiscale
Scalable iterative solver

http://resolver.tudelft.nl/uuid:8ccc06af-42e1-47f5-b6a7-a3fac049faa8

https://doi.org/10.1016/j.jcp.2021.110287

0021-9991

Journal of Computational Physics, 436, 1-19

Institutional Repository

journal article

© 2021 F. Xu, H. Hajibeygi, Lambertus J. Sluys