Localized lattice Boltzmann equation model for simulating miscible viscous displacement in porous media

Abstract

A localized lattice Boltzmann equation (LBE) model for simulating the miscible viscous displacement in porous media is proposed. The Darcy’s law for flow and the convection–diffusion equation (CDE) describing the transport of solute are solved numerically by the present model. To ensure the local implementation of the collision process in this model, the pressure and concentration gradients are computed from the moments of the nonequilibrium distribution functions, which are of second-order accuracy. Consequently, the advantages of the lattice Boltzmann method (LBM) are retained. The model is validated with a stable displacement problem, and is employed to study the viscous fingering instability that occurs in the process of the miscible viscous displacement. The results agree well with previous studies. Furthermore, although the present model is an explicit scheme, it is interesting to find that it is capable of simulating the viscous displacement over a wide range of Péclet (Pe) numbers, indicating the superior stability of this model.