|
Multiphase flow in porous media is an important research topic in the field of oil and gas reservoir development. Due to the complex geological conditions in China, properties of rocks, such as permeability and porosity, are complex and heterogeneous. The numerical solution for the complex multiphase flow problems needs to overcome challenges such as the system’s multiple variables, strong nonlinearity, large computational cost, and the preservation of physical properties. For the traditional incompressible and immiscible two-phase flow model, the IMplicit Pressure Explicit Saturation (IMPES) semi-implicit scheme is a widely-used important algorithm for solving such problems, where the pressure equation is solved implicitly, and the saturation is updated explicitly. However, the traditional IMPES scheme requires the calculation of saturation gradients when updating the saturation. Therefore, it is not suitable for solving the two-phase flow problems in complex heterogeneous media. Hoteit and Firoozabadi proposed an improved IMPES method, allowing the method to reproduce discontinuous saturation in heterogeneous media. However, these two IMPES methods only update the saturation through the mass conservation equation of one phase of fluid, they cannot guarantee that the other phase of fluid also satisfies the local mass conservation property. The derivations of the pressure equations for these two IMPES methods are obtained by adding the volume conservation equations of each phase at the continuous level of partial differential equations, and then using incompletely matched spatial discretization methods for the pressure equation and the saturation equation. Therefore, it is impossible to simultaneously ensure the local mass conservation of each phase for the two-phase fluid. In this paper, based on several types of novel IMPES semi-implicit schemes for solving two-phase flow in porous media that we have published in recent years, we propose a new framework for deriving the pressure equation in IMPES. That is, we first discretize the volume conservation equation of each phase using a spatial discretization method with local conservation, and then add up the discretized volume conservation equations of each phase. In this way, a complete match in spatial discretization between the pressure equation and the saturation equation is achieved. Essentially, it overcomes the difficulty in previous literatures that the IMPES semi-implicit method cannot simultaneously ensure that both phases of the fluid satisfy local mass conservation. The novel IMPES method ensures that each phase of the fluid satisfies local mass conservation, the saturation is bounded, the computational scheme is an unbiased solution, and it is suitable for solving two-phase flow problem with different capillary pressure distributions in heterogeneous porous media. The novel phase-wise conservation IMPES framework proposed in this paper also has an advantage that the traditional IMPES does not have. That is, in the novel phase-by-phase conservation IMPES framework, it is only necessary to define the spatial discretization method of the volume conservation or mass conservation equation, and there is no need to separately define the spatial discretization method of the pressure equation. The solutions of several types of novel IMPES semi-implicit schemes that we have published in recent years can be regarded as special cases of the novel phase-by-phase conservation IMPES framework proposed in this paper. The IMPES framework in this paper can also be applied for more complex multi-component and multi-phase flow in porous media to construct more novel schemes. At the same time, through numerical examples of heterogeneous porous media, this paper verifies the effectiveness and superiority of the novel IMPES method in dealing with two-phase flow problems under complex geological conditions. Compared with the traditional method, it is more adaptable, more stable, and more efficient.
|
