Lattice boltzmann method applied to multiphase flows and preferential paths in porous media

Abstract

The Lattice Boltzmann Method (LBM) has been increasingly adopted in Chemical Engineering. Although popular and easy to implement, the Shan-Chen pseudopotential model suffers from many limitations regarding thermodynamic consistency, the formation of spurious currents, and others. Several alternative models that mitigate these effects are found in the literature. Through algebraic manipulations, we propose a unified model from which these multiphase interaction forces can be recovered. Isothermal phase transition simulations of single-component stationary and oscillating droplets validate the model numerically and reinforce that the multiphase forces are essentially interchangeable. The multiphase parameters are selected based on the vapor densities at low temperatures in the Maxwell coexistence curve, where there is a narrow range of optimal values. Writing them as functions of the reduced temperature enhances the thermodynamic consistency without losing stability or increasing spurious velocities. The validity of a preferential path predictor in a non-Darcy regime is also verified, and the results are confronted with the simulated preferred paths. LBM successfully recovers the Forchheimer equation. Although the model reasonably predicts the preferred paths, the inertial contributions in the Forchheimer regime make the porous pattern, grain shape, and path deflections disturb those predictions.