A Pseudopotential Lattice Boltzmann Method for Simulation of Two-Phase Flow Transport in Porous Medium at High-Density and High–Viscosity Ratios

Abstract

In this work, the capability of a multiphase lattice Boltzmann method (LBM) based on the pseudopotential Shan-Chen (S-C) model is investigated for simulation of two-phase flows through porous media at high-density and high–viscosity ratios. The accuracy and robustness of the S-C LBM are examined by the implementation of the single relaxation time (SRT) and multiple relaxation time (MRT) collision operators with integrating the forcing schemes of the shifted velocity method (SVM) and the exact difference method (EDM). Herein, two equations of state (EoS), namely, the standard Shan-Chen (SC) EoS and Carnahan-Starling (CS) EoS, are implemented to assay the performance of the numerical technique employed for simulation of two-phase flows at high-density ratios. An appropriate modification in the forcing schemes is also used to remove the thermodynamic inconsistency in the simulation of two-phase flow problems studied at low reduced temperatures. The comparative study of these improvements of the S-C LBM is performed by considering an equilibrium state of a droplet suspended in the vapor phase. The solver is validated against the analytical coexistence curve for the liquid-vapor system and the surface tension estimation from the Laplace Law. Then, according to the results obtained, a conclusion has been made to choose an efficient numerical algorithm, including an appropriate collision operator, a realistic EoS, and an accurate forcing scheme, for simulation of multiphase flow transport through a porous medium. The patterns of two-phase flow transport through the porous medium are predicted using the present numerical scheme in different flow conditions defined by the capillary number and the dynamic viscosity ratio. The results obtained for the nonwetting phase saturation, penetration structure of the invading fluid, and the displacement patterns of two-phase flow in the porous medium are comparable with those reported in the literature. The present study demonstrates that the S-C LBM with employing the MRT-EDM scheme, CS EoS, and the modified forcing scheme is efficient and accurate for estimation of the two-phase flow characteristics through the porous medium.