A General Boundary Integral Solution for Fluid Flow Analysis in Reservoirs With Complex Fracture Geometries

Abstract

Modeling fractured reservoirs, especially those with complex, nonorthogonal fracture network, can prove to be a challenging task. This work proposes a general integral solution applicable to two-dimensional (2D) fluid flow analysis in fractured reservoirs that reduces the original 2D problem to equivalent integral equation problem written along boundary and fracture domains. The integral formulation is analytically derived from the governing partial differential equations written for the fluid flow problem in reservoirs with complex fracture geometries, and the solution is obtained via solving system of equations that combines contributions from both boundary and fracture domains. Compared to more generally used numerical simulation methods for discrete fracture modeling such as finite volume and finite element methods, this work only requires discretization along the boundary and fractures, resulting in much fewer discretized elements. The validity of proposed solution is verified using several case studies through comparison with available analytical solutions (for simplified, single-fracture cases) and finite difference/finite volume finely gridded numerical simulators (for multiple, complex, and nonorthogonal fracture network cases).