Modeling Fluid Dynamics in Porous Media: A Pore-Scale Flow Analysis

This study investigates single-phase fluid flow in porous media using advanced numerical methods, with a focus on pore-scale dynamics, to address the limitations of traditional models, such as Darcy's law. The research utilizes the Creeping Flow interface and the Brinkman equation to analyze velocity and pressure distributions in heterogeneous porous media. Qualitative results indicate the presence of distinct flow patterns characterized by high-velocity areas (up to 8 × 10⁻⁵ m/s) localized in narrow, interconnected channels. At the same time, stationary zones have very little flow, which shows how pore shape affects the paths that fluids take. The Brinkman equation accounts for viscous shear effects and exhibits smoother changes in velocity (0–1.8 × 10⁻⁵ m/s) compared to the Creeping Flow model, which predicts sharper gradients. Pressure distributions reveal significant decreases (0.39–6.91 Pa) in constricted areas, demonstrating the impact of tortuosity and connectedness on flow resistance. A quantitative study shows that the Creeping Flow model is most effective for systems with low permeability, whereas the Brinkman equation performs better for systems with intermediate flow rates. These results help us better understand how fluids move across porous networks, which is beneficial for applications such as increasing oil production and removing contaminants. The study bridges theoretical modeling and practical scenarios, providing a foundation for optimizing resource management and sustainable extraction techniques.