Black-Oil Simulations for Three-Component -- Three-Phase Flow in Fractured Porous Media

Abstract

Abstract Discrete-fracture modeling and simulation of two-phase flow in realistic representations of fractured reservoirs can now be used for the design of IOR and EOR strategies. Thus far, however, discrete fracture simulators fail to include a third compressible gaseous phase. This hinders the investigation of the performance of gas-gravity drainage, water alternating gas injection, and blow-down in fractured reservoirs. Here we present a new numerical method that expands the capabilities of existing Black-Oil models for three-component - three-phase flow in three ways:It utilizes a finite element - finite volume discretization generalized to unstructured hybrid element meshes.It employs higher-order accurate representations of the flux terms.Flash calculations are carried out with an improved equation of state allowing for a more realistic treatment of phase behavior. We illustrate the robustness of this numerical method in several applications. First, quasi-1D simulations are used to demonstrate grid convergence. Then, 2D discrete fracture models are employed to illustrate the impact of mesh quality on predicted production rates in discrete fracture models. Finally, the proposed method is used to simulate three-component - three-phase flow in a realistic 2D model of fractured limestone mapped in the Bristol Channel, U.K. and a 3D stochastically generated discrete fracture model. Introduction Approximately sixty percent of the world's remaining oil reserves are located in fractured reservoirs. These are often subject to complex production histories, unpredictable coupling of wells, rapidly changing flow rates, early water breakthrough, and a low final recovery.1 Experimental data on fracture permeability, water breakthrough, or relative permeability obtained on cores cannot be extrapolated to the field scale. Instead, computer simulations allow us to study the effects of viscous, capillary, and gravitational forces during two-phase flow in fractures at intermediate scales and develop more realistic models for the reservoir scale. In recent years, the limitations of dual-porosity models 2-4 that have been used traditionally to simulate two-phase flow in connected fractures were overcome by the development of discrete-fracture models. Discrete-fracture models were first introduced for single-phase flow applications 5-7 and have since been extended to simulate two-phase fluid flow including gravity and capillary effects.8-16 Based on the concept of cross-flow equilibrium between the fluids at the fracture and adjacent matrix nodes, it is possible to reduce the dimensionality of the fractures from n to n-1, representing them as lines in 2D or surfaces in 3D. This approach has two distinct advantages. First, the contribution of individual fractures to fluid flow can be simulated accurately. Second, the methods are computationally efficient because high-aspect ratio fractures with very small apertures do not need to be discretized as volumes. The spatial discretization in discrete-fracture simulations are based on either Galerkin finite element methods, finite volume methods, or a combination of both. Temporal discretizations usually employ fully-coupled implicit or implicit pressure - explicit saturation (IMPES) time-stepping. The spatial discretization of non-orthogonal and complexly intersecting and interconnecting lower-dimensional fractures with a suitable mesh is still a challenge. An obvious choice for unstructured discretizations is the use of triangular finite elements in 2D and tetrahedral elements in 3D. Significant reduction of memory requirements and CPU time, however, can be achieved when using so-called hybrid element meshes.14, 17 These employ a variety of element types: tetrahedra, hexahedra, pyramid, and prism elements in 3D and triangular and quadrilateral elements for 2D surfaces. This reduces the number of nodes (i.e. unknowns) and hence computational costs.