Multiscale Extended Finite Element Method for the Simulation of Fractured Geological Formations

Abstract

In the prevailing context of the 21st century, characterized by a predominant reliance on oil and gas, or in the promising future where green energy shapes a human society committed to net-zero emissions, the role of underground fractured formations in energy production and storage remains pivotal and irreplaceable. Geological faults typically act as non-permeable sealing boundaries for reservoirs used in storage, including those for hydrogen and carbon dioxide. In contrast, artificial fractures can serve as highly permeable conduits for fluid flow into wellbores, particularly in applications such as enhanced geothermal reservoirs. In the past decade, the hazardous consequences of failing to predict the geomechanics behaviors of fractured formations have led to a pronounced focus on developing simulation strategies that are both accurate and efficient for fractured formations.
It is challenging to understand formations riddled with fractures. From a computational perspective, the complex fracture networks typically demand a way finer unstructured grid. However, using such an unstructured grid is impractical for real-world applications due to their high computational load. Conversely, coarser grids paired with strategies such as homogenization could result in loss of crucial details. Heterogeneous properties of geological formations that span on large length sizes require the simulation strategies to be scalable, in order to be relevant.
This thesis proposes a novel approach named as multiscale extended finite element method (MS-XFEM) to tackle these challenges. The challenges related to discretization are resolved by applying the extended finite element method (XFEM) which allows for the use of structured grids. This simplified mesh, however, leads to an augmented matrix size due to extra degrees of freedom (DOFs) introduced by enrichments. A multiscale approach is therefore combined with XFEM. The computational process is operated on the larger yet sparser coarse grids and then the coarse scale mesh solutions are interpolated back to fine scale mesh. The novelty of this work is to involve the fractures into basis functions only, thus the coarse scale system is constructed based on a finite element method. More importantly, this construction of basis functions is fully algebraic and can be updated locally and adaptively for the simulation of propagating fractures.
This method has been implemented and tested to prove its efficiency and accuracy. All tests results prove the good qualities of solutions computed from MS-XFEM when compared to fine scale XFEM solutions. Basis functions are constructed successfully with the algebraic method. These tests reveal the potential of the MS-XFEM in simulating real-world subsurface fractured formations.