Convection-Diffusion with the Colour Gradient Lattice Boltzmann Method for Three-Component, Two-Phase Flow

The Rothman-Keller colour gradient Lattice Boltzmann Method (LBM) provides a means to simulate two phase flow of immiscible fluids by modelling number densities of two fluids, plus a “recoloring” step that ensures separation of the two fluids. Here, we model an additional number density representing the concentration of an additive to fluid 1 which affects the viscosity of this fluid. The Peclet number – rate of advection to diffusion – is used to set the diffusion coefficient of the concentration. We present tests to demonstrate the method including flow and merging of two adjacent droplets with different additive concentrations, and two-phase flow tests in a 2D porous matrix involving injection of fluid with an additive that increases the viscosity and thus decreases viscous fingering (e.g. a polymer additive). We demonstrate that use of polymers from the start of waterflooding leads to a high saturation of 90% much sooner than when polymers are applied after breakthrough. This work demonstrates that the RK color gradient multiphase LBM can be used to study viscous fingering behavior in porous media in which the injected low viscosity fluid can have its viscosity varied with time by use of an additive. This is both of scientific interest and has economic implications to Enhanced Oil Recovery, in which water–potentially with a polymer additive to increase viscosity– is injected from an injection well into a rock layer saturated with a high viscosity fluid (oil) to help push out the oil into a production well.