Simulation of coupled multiphase flow and geomechanics in porous media with embedded discrete fractures

Abstract

In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using uncoupled methods. In recent years, significant research has focused on discretization strategies for these coupled systems, particularly in the presence of complicated fracture network geometries. In this work, we explore a finitevolume discretization for the multiphase flow equations coupled with a finiteelement scheme for the mechanical equations. Fractures are treated as lower dimensional surfaces embedded in a background grid. Interactions are captured using the embedded discrete fracture model (EDFM) and the embedded finite element method (EFEM) for the flow and the mechanics, respectively. This nonconforming approach significantly alleviates meshing challenges. EDFM considers fractures as lower dimension finite volumes that exchange fluxes with the rock matrix cells. The EFEM method provides, instead, a local enrichment of the finite-element space inside each matrix cell cut by a fracture element. Both the use of piecewise constant and piecewise linear enrichments are investigated. They are also compared to an extended finite element approach. One key advantage of EFEM is the element-based nature of the enrichment, which reduces the geometric complexity of the implementation and leads to linear systems with advantageous properties. Synthetic numerical tests are presented to study the convergence and accuracy of the proposed method. It is also applied to a realistic scenario, involving a heterogeneous reservoir with a complex fracture distribution, to demonstrate its relevance for field applications.

Mixed-dimensional poromechanical models of fractured porous media

“…This expands on similar results for the single-phase case in [16]. Finally, we mention also the work of Cusini et al, which address numerical method for this coupled problem [17]. While they consider geometric complexity, they limit their discussion to quasi-static, small-strain kinematics.…”

Phase‐field modeling of rock fractures with roughness

“…When dealing with stationary fractures-a fairly common scenario in rock mechanics applications-Equation (5) needs to be solved only once for obtaining an initial phase field that suitably represents the preexisting fractures. It is noted that such stationary fractures have also been well modeled by embedded discontinuity methods (e.g., [40][41][42] ). Compared with these methods, the phase-field method entails more computation time as it requires a quite fine discretization around the discontinuity.…”

Modeling fracture propagation in a rock‐water‐air system with the assumed enhanced strain method

“…26,27 The XFEM enriches FE shape functions with discontinuous functions through the standard partition of unity method, 28 and therefore XFEM introduces new degrees of freedom into the global system to represent displacement jumps. The AES method enriches the strain tensor with the fracture-related discontinuous modes which may be statically condensed at the element level, [29][30][31][32][33][34][35] so the method does not introduce additional enriched degrees of freedom in the implementation. Interested readers can refer to References 22 and 36 for more detailed information on the analyses and comparisons between the two types of enrichment methods.…”