In this paper we consider fully mass-conservative numerical schemes for the simulation of incompressible and immiscible two-phase flow in porous media with capillary pressure. Compared with two kinds of conventional IMplicit Pressure Explicit Saturation (IMPES) schemes, the new schemes deserve a merit that the conservation of mass of both phases can be obtained. The total conservation equation is obtained by the summation of the discretized conservation equation for each phase. This approach is quite different from the conventional IMPES schemes. We present two kinds of fully mass-conservative IMPES schemes to solve the coupled systems for pressure, auxiliary velocity and saturation of each phase. The upwind mixed finite element methods are used to solve the pressure–velocity systems which can be decoupled, and the problems in the decoupled systems can be proved to be well-posed. Moreover, the new schemes are unbiased and the saturation of each phase can be proved to be bounds-preserving if the time step size is smaller than a certain value. The new schemes can also be applied to approximate the incompressible and immiscible two-phase flow in heterogeneous porous media with different capillarity pressures. Several interesting examples of incompressible and immiscible two-phase flow in porous media are presented to demonstrate the robustness of the new algorithms.
|Original language||English (US)|
|Number of pages||23|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|State||Published - Mar 21 2019|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): BAS/1/1351-01
Acknowledgements: The work of Huangxin Chen was supported by the National Natural Science Foundation of China (Grant Nos. 11771363, 91630204, 51661135011), the Fundamental Research Funds for the Central Universities (Grant No. 20720180003) and Program for Prominent Young Talents in Fujian Province University. The work of Shuyu Sun and Tao Zhang was supported by funding from the National Natural Science Foundation of China (No. 51874262) and the Research Funding from King Abdullah University of Science and Technology (KAUST) through the Grants BAS/1/1351-01.