Multiscale extended finite element method (MS-XFEM): Analysis of fractured geological formations under compression

Abstract

The activation of fracture networks poses significant risks and raises safety concerns for projects involving such geological structures. Consequently, an accurate and efficient simulation strategy is essential for modeling highly fractured subsurface formations. While the extended finite element method (XFEM), coupled with the penalty method, effectively models slip-stick conditions along fracture surfaces and fracture propagation under compression, its efficiency declines when handling dense fracture networks. To address this challenge, a multiscale XFEM (MS-XFEM) approach is developed and presented. MS-XFEM approximates fine-scale displacement field by interpolating solutions on a coarser-scale mesh using algebraically constructed basis functions. All extra degrees of freedom (DOFs) are incorporated within the basis functions matrix, rendering the coarse-scale system a standard finite element-based system. In each propagation step, basis functions are algebraically and locally updated to capture fracture propagation. Through four proof-of-concept test cases, the accuracy and efficiency of MS-XFEM in simulating fractured geological formations are demonstrated, emphasizing its potential for real-world applications.