Lattice Boltzmann Study Of Miscible Viscous Fingering In Porous Media

As a kind of fundamental interfacial instability problem, miscible viscous fingering in porous media is relevant to a number of industrial and engineering processes such as oil recovery, groundwater contamination, polymer synthesis and micro-electromechanical. It is found that miscible viscous fingering involves multiple research scales and various flow processes such as convection and diffusion. Besides, the interfacial instability behaviors can be observed. Based on the above reasons, current studies about miscible viscous fingering are still very limited. In order to overcome the defects of huge computation and complex boundary treatment in the traditional methods, the lattice Boltzmann method is used to simulate the evolution of miscible viscous fingering. The present work mainly focuses on the following aspects:A coupled lattice Boltzmann model for flows in porous media is proposed. Two independent distribution functions are adopted to solve the Darcy equation and the convection-diffusion equation, respectively. The stable displacement between two fluids with the same viscosity is simulated, and the result shows that the coupled model can precisely simulate fluid flow in porous media.Two-dimensional and three-dimensional isothermal miscible viscous fingering processes are investigated. The two-dimensional results indicate that the increase in viscosity contrast and Peclet number will promote the formation of viscous fingering and reduce the displacement efficiency. It is also concluded that the growth of the mixing length can be divided into two stages, and in the second stage, the length grows faster. The three-dimensional results are qualitatively consistent with the two-dimensional ones, but different in quantity due to the shape of the fingers.With the effects of temperature on the viscosity considered, the non-isothermal miscible viscous fingering is studied. The numerical results show that decrease in thermal lag coefficient and increase in Lewis number will weaken the effects of temperature gradients on the interfacial instability. Therefore, the evolutionary trend of solutal front acts against the direction which the temperature gradients promote.