A Multi-Scale Numerical Simulation Method Considering Anisotropic Relative Permeability

Most of the oil reservoirs in China are fluvial deposits with firm reservoir heterogeneity, where differences in fluid flow capacity in individual directions should not be ignored; however, the available commercial reservoir simulation software cannot consider the anisotropy of the relative permeability. To handle this challenge, this paper takes full advantage of the parallelism of the multi-scale finite volume (MsFV) method and establishes a multi-scale numerical simulation approach that incorporates the effects of reservoir anisotropy. The methodology is initiated by constructing an oil–water black-oil model considering the anisotropic relative permeability. Subsequently, the base model undergoes decoupling through a sequential solution, formulating the pressure and transport equations. Following this, a multi-scale grid system is configured, within which the pressure and transport equations are progressively developed in the fine-scale grid domain. Ultimately, the improved multi-scale finite volume (IMsFV) method is applied to mitigate low-frequency error in the coarse-scale grid, thereby enhancing computational efficiency. This paper introduces two primary innovations. The first is the development of a multi-scale solution method for the pressure equation incorporating anisotropic relative permeability. Validated using the Egg model, a comparative analysis with traditional numerical simulations demonstrates a significant improvement in computational speed without sacrificing accuracy. The second innovation involves applying the multi-scale framework to investigate the impact of anisotropy relative permeability on waterflooding performance, uncovering distinct mechanisms by which absolute and relative permeability anisotropy influence waterflooding outcomes. Therefore, the IMsFV method can be used as an effective tool for high-resolution simulation and precise residual oil prediction in anisotropic reservoirs.