Mathematical Modeling of the Counter-Current Imbibition Phenomenon in a Water-Wet Fractured Medium
摘要
The imbibition phenomenon is prevalent in both natural settings and applied industries. Studying the mechanism of imbibition and comprehending the laws that govern the influence of related factors holds tremendous significance. This study employs the classical Darcy’s equation to examine the imbibition process in a heterogeneous hydrocarbon reservoir. Due to the highly nonlinear nature of the governing equations, analytical solutions are rare. In this study, we introduce the Homotopy Analysis Method (HAM) to solve the Counter-current spontaneous imbibition problem, providing an explicit series solution with adjustable convergence. HAM is particularly advantageous as it does not depend on small parameters and offers greater flexibility compared to traditional analytical methods. The method proposed in this study offers a more direct, accurate, and user-friendly approach for computing spontaneous imbibition performance compared to previously available methods. We assert its generality concerning functional forms for relative permeability and capillary pressure, making it applicable across the entire range of wettability, provided that these effects are appropriately considered in the parameterization of capillary pressure and saturation normalization. This study analyzes counter-current spontaneous imbibition in fractured heterogeneous porous media, primarily characterized by spatial variations in porosity and absolute permeability. Effects of the viscosity ratio, wettability of the medium, and inclined planes on the normalized water saturation are analyzed.