An Efficient Discrete Fracture Model Applicable for General Purpose Reservoir Simulators

Abstract

Abstract A simplified discrete fracture model suitable for use with general purpose reservoir simulators is presented. The model handles both two and three-dimensional systems and includes fracture-fracture, matrix-fracture and matrix-matrix connections. The formulation applies an unstructured control volume finite difference technique with a two-point flux approximation. The implementation is generally compatible with any simulator that represents grid connections via a connectivity list. A specialized treatment based on a "star-delta" transformation is introduced to eliminate control volumes at fracture intersections. These control volumes would otherwise act to reduce numerical stability and time step size. The performance of the method is demonstrated for several example cases including a simple two dimensional system, a more complex three-dimensional fracture network, and a model of a strike-slip fault zone. The discrete fracture model is shown to provide results in close agreement with those of a reference finite difference simulator in cases where direct comparisons are possible. Introduction Flow through fractured porous media is typically simulated using dual-porosity models. This approach, although very efficient, suffers from some important limitations. One drawback is that the method cannot be applied to disconnected fractured media. In addition, dual-porosity models are not well suited for the modeling of a small number of large-scale fractures, which may dominate the flow. Another shortcoming is the difficulty in accurately evaluating the transfer function between the matrix and the fractures. For these reasons, discrete fracture models, in which the fractures are represented individually, are beginning to find application in reservoir simulation. These models can be used both as stand-alone tools as well as for the evaluation of transfer functions for dual-porosity models. Such models can also be used in combination with the dual-porosity approach. To accurately capture the complexity of a fractured porous media it is usually necessary to use an unstructured discretization scheme. There are, however, some effective procedures based on structured discretization approaches. For example, Lee et al.1 presented a hierarchical modeling of flow in fractured formations. In this approach the small fractures were represented by their effective properties and the large-scale fractures were modeled explicitly. In the case of unstructured discretizations there are two main approaches - finite element and finite volume (or control volume finite difference) methods. Baca et al.2 were among the early authors to propose a two-dimensional finite element model for single phase flow with heat and solute transport. In a more recent paper Juanes et al.3 presented a general finite element formulation for two- and three-dimensional single-phase flow in fractured porous media. There has been some work on the extension of the finite element method to handle multiphase flow. For example, Kim and Deo4 and Karimi-Fard and Firoozabadi5 presented extensions of the work of Baca et al.2 for two-phase flow. They modeled the fractures and the matrix in a two-dimensional configuration with the effects of capillary pressure included. The two media (matrix and fractures) were coupled using a superposition approach. This entails discretizing the matrix and fractures separately and then adding their contributions to obtain the overall flow equations.