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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 429835, 7 pages
Research Article

Numerical Fractional-Calculus Model for Two-Phase Flow in Fractured Media

1Department of Mathematics, Shanghai University, Shanghai 200444, China
2School of Mathematics and Statistics, Hubei Engineering University, Xiaogan, Hubei 432000, China

Received 17 May 2013; Revised 13 July 2013; Accepted 13 July 2013

Academic Editor: H. Srivastava

Copyright © 2013 Wenwen Zhong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.