A comparison study of multi-component Lattice Boltzmann models for flow in porous media applications

Abstract

A comparison study of three different multi-component Lattice Boltzmann models is carried out to explore their capability of describing binary immiscible fluid systems. The Shan–Chen pseudo potential model, the Oxford free energy model and the colour gradient model are investigated using the multi-relaxation time scheme (MRT) algorithm to study the flow of binary immiscible fluids. We investigate Poiseuille flow of layered immiscible binary fluids and capillary fingering phenomena and evaluate the results against analytical solutions. In addition, we examine the capability of the various models to simulate fluids with significant viscosity and density contrast and suitable interface thickness. This is of great importance for large scale flow in porous media applications, where it is important to minimise the interfacial thickness from a computational point of view. We find that the Shan–Chen model can simulate high density ratios up to 800 for binary fluids with the same viscosity. Imposing a viscosity contrast will lead to highly diffusive interfaces in the Shan–Chen model and therefore this will affect significantly the numerical stability. The Free Energy model and the colour gradient model have similar capabilities on this point: they can simulate binary fluids having the same density but with significant viscosity contrast. This is of great importance to study the flow of water, supercritical CO2 and oil in porous media, for CO2 storage and Enhanced Oil Recovery (EOR) operations.