Enhancing Color Gradient Lattice Boltzmann Models for Immiscible Displacement in Porous Media

Resumo

Porous structures are essential in nature and particularly relevant in petroleum reservoirs, as they allow for the storage and migration of fluids such as oil, water, and gas. Understanding these properties is crucial for optimizing exploration and reducing operational costs. Computational simulation methods, such as the Lattice Boltzmann Method (LBM), provide an efficient way to model these phenomena and are especially effective in porous media with complex geometries, supporting studies of multiphase flows.The color gradient method based on LBM is an efficient tool for simulating two-phase flows, allowing independent control of surface tension and interface thickness. It stands out for its ability to accurately represent stationary bubbles and phase coalescence, making it ideal for studying bubble stability and dynamics in porous or confined media.The article proposes two improvements to the color gradient model in the Lattice Boltzmann Method, aiming for greater stability and accuracy in simulations of immiscible displacement in narrow porous media. The first is the introduction of a volume exclusion term, which reduces compressibility and prevents numerical instabilities. The second is the adoption of the TRT (Two-Relaxation-Time) model, which eliminates second-order Knudsen number effects and improves physical consistency. Modifications to the segregation rules and surface force formulations are also suggested, making the model more robust and suitable for complex geometries.