Lattice Boltzmann Method Simulation Of A Multiphase Flow In A 2D Homogeneous Porous Media For Predict The Reservoir Characterizations And Flooding Process In Hydrocarbon Fields

Abstract

In this paper, a liquid-vapor lattice-Boltzmann program with an external force has been developed and used for the study of Stokes equations for a low Reynolds number multiphase flow in a periodic homogeneous two-dimensional porous media. The underlying theoretical model makes it possible to couple the state equation of a non-ideal fluid with the pressure tensor at the interface and uses the excess free-energy density formalism. The fluid properties can be prescribed in a thermodynamically consistent manner, which remains accurate at states close to the critical point. We have simulated some known two-phase flow configurations, like displacement of vapor by its liquid in homogeneous twodimensional porous media reconstructed by image treatment under the action of an external flow field. We present also results for the averaged velocity as a function of time iteration and the permeability of two dimensional porous media as a function of kinematic viscosity and mesh resolution. Our results confirm that the LBM scheme reproduces Darcy’s law through the analysis of the dependency of the permeability on the kinematic viscosity