Modified Extended Finite Element Methods for Gas Flow in Fractured Reservoirs: A Pseudo-Pressure Approach

Abstract

Fluid flow in fractured porous media has always been important in different engineering applications especially in hydrology and reservoir engineering. However, by the onset of the hydraulic fracturing revolution, massive fracturing jobs have been implemented in unconventional hydrocarbon resources such as tight gas and shale gas reservoirs that make understanding fluid flow in fractured media more significant. Considering ultralow permeability of these reservoirs, induced complex fracture networks play a significant role in economic production of these resources. Hence, having a robust and fast numerical technique to evaluate flow through complex fracture networks can play a crucial role in the progress of inversion methods to determine fracture geometries in the subsurface. Current methods for tight gas flow in fractured reservoirs, despite their advantages, still have several shortcomings that make their application for real field problems limited. For instance, the dual permeability theory assumes an ideal uniform orthogonal distribution of fractures, which is quite different from field observation; on the other hand, numerical methods like discrete fracture network (DFN) models can portray the irregular distribution of fractures, but requires massive mesh refinements to have the fractures aligned with the grid/element edges, which can greatly increase the computational cost and simulation time. This paper combines the extended finite element methods (XFEM) and the gas pseudo-pressure to simulate gas flow in fractured tight gas reservoirs by incorporating the strong-discontinuity enrichment scheme to capture the weak-discontinuity feature induced by highly permeable fractures. Utilizing pseudo-pressure formulations simplifies the governing equations and reduces the nonlinearity of the problem significantly. This technique can consider multiple fracture sets and their intersection to mimic real fracture networks on a plain structured mesh. Here, we utilize the unified Hagen–Poiseuille-type equation to compute the permeability of tight gas, and finally adopt Newton–Raphson iteration method to solve the highly nonlinear equations. Numerical results illustrate that XFEM is considerably effective in fast calculation of gas flow in fractured porous media.