A MPFA-D Finite Volume Scheme for 2-D Simulation of Two-Phase Flow in Naturally Fractured Reservoirs Using a Lower-Dimensional Fracture Model
Cavalcante, Túlio de M.1; Angelim, Kelly C. L.1; Brum, Braian S.1; Contreras, Fernando R. L.1; Lyra, Paulo R. M.1; Carvalho, Darlan K. E.1
1 Federal University of Pernambuco
doi:10.20906/CPS/CILAMCE2017-0674
Resumo
The two-phase flow in heterogeneous and anisotropic naturally fractured petroleum reservoirs, after considering some simplifying hypotheses, can be described, as a system of nonlinear partial differential equations, composed by an elliptic pressure equation and a hyperbolic transport equation. The modeling of this problem is a great challenge, due to the complexity of the depositional environments including inclined layers, channels, and the random spatial distribution of fractures of different sizes and shapes. In such cases, it is particularly complex to construct structured meshes which are capable of properly model the reservoir. In this work, as far as we know, for the first time, we adapt a cell-centered Finite-Volume Method with a Multi-Point Flux Approximation that uses the so called "diamond stencil" (MPFA-D) to deal with a Lower-Dimensional Fracture Model (LDFM). The method is very robust and is capable of dealing with highly heterogeneous fractured domains using any polygonal meshes and with full permeability tensor representation for the rock matrix. The hyperbolic saturation problem is solved by the First Order Upwind Method (FOUM). The pressure-saturation coupling is done through a segregated implicit strategy, in which both, the pressure and the saturation equations are sequentially solved implicitly. The LDFM uses an additional equation associated to the fracture which is treated as a geometric entity with a smaller dimension than the original problem, i.e., for 3-D problems fractures are represented by surfaces (2-D) and for 2-D problems fractures have only one dimension in space. This strategy reduces considerably the number of degrees of freedom of the model. The mesh which discretizes the domain must adapts itself to the position and orientation of the fractures, so that these are associated to the edges of the finite volumes in 2-D, therefore, the calculation of the fluxes in these control surfaces is dependent on the pressures in fractures and in the adjacent volumes. The proposed formulatio
Palavras-chave: Two-Phase Flow of Oil and Water; Heterogeneous and Ansisotropic Reservoirs; Naturally Fractured Reservoirs; Lower-Dimensional Fracture Model; MPFA-D