%0 Journal Article
%T Numerical Fractional-Calculus Model for Two-Phase Flow in Fractured Media
%A Wenwen Zhong
%A Changpin Li
%A Jisheng Kou
%J Advances in Mathematical Physics
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/429835
%X Numerical simulation of two-phase flow in fractured porous media is an important topic in the subsurface flow, environmental problems, and petroleum reservoir engineering. The conventional model does not work well in many cases since it lacks the memory property of fracture media. In this paper, we develop a new numerical formulation with fractional time derivative for two-phase flow in fractured porous media. In the proposed formulation, the different fractional time derivatives are applied to fracture and matrix regions since they have different memory properties. We further develop a two-level time discrete method, which uses a large time step for the pressure and a small time step size for the saturation. The pressure equation is solved implicitly in each large time step, while the saturation is updated by an explicit fractional time scheme in each time substep. Finally, the numerical tests are carried out to demonstrate the effectiveness of the proposed numerical model. 1. Introduction Numerical simulations for multiphase flow in fractured porous media are very important in the subsurface flow, environmental problems, and petroleum reservoir engineering. Compared to usual heterogenous porous media, the fractured media have two spaces with two distinct scales: the fracture and the matrix. The fractures possess the higher permeability than the matrix, but their volume is very small when compared to the matrix. Several conceptual models [1¨C11] have been developed to simulate the multiphase flow in porous media, for example, the single-porosity model, the dual-porosity/dual-permeability model, and the discrete-fracture model. The review for these models can be found in [4]. These models can deal well with the two-phase flow with constant physical parameters. However, the fluid flow may perturb the porous formation by causing particle migration resulting in pore clogging or chemically reacting with the medium to enlarge the pores or diminish the size of the pores [12]. As a matter of fact, the porosity and permeability often depend on the fluid pressure and saturation. For incompressible two-phase flow in petroleum reservoir engineering, the porosity varies small with respect to the pressure. However, the injection fluids can change the porosity to a great extent. In the displacement process of oil by water, the injected water will make the media wet, and then the porosity will be enlarged, along with the change of permeability. As a result, the variability of the physical parameters should be considered in modeling realistic two-phase flow. For flow in
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