A Fully Mass Conservative Numerical Method for Multiphase Flow in Fractured Porous Reservoirs

Numerical methods that are mass conservative, computationally stable, and efficient are essential for simulating multiphase flow in fractured porous reservoirs. In this paper, a fully mass conservative numerical method that meets these requirements is proposed and analyzed. Unlike in the implicit pressure and explicit saturation (IMPES) method, in this method, the pressure and saturation equations are solved sequentially in each iteration step. In this framework, the calculation of the saturation-related parameters no longer depends on the initial conditions of the current time step, but on the results of the current and previous iterations. Through this treatment, the discontinuities of the saturation and capillary pressure in the pre- and post-two time steps can be overcome to achieve fully mass conservation. Two numerical examples are designed to verify the robustness and efficiency of the presented method. The numerical results indicate that this new method is fully mass conservative, computationally more stable, and more efficient than the IMPES method. Furthermore, the proposed method is suitable not only for reservoirs with homogeneous permeability distributions but also for reservoirs with heterogeneous permeability distributions, which greatly improves the applicability of the new method.