Pore-Scale Study of the Non-Linear Mixing of Fluids with Viscous Fingering in Anisotropic Porous Media

Mixing processes of miscible viscous fluids in anisotropic porous media are studied through a lattice Boltzmann method in this paper. The results show that fluid mixing can be enhanced by the disorder and interfaces induced by viscous fingers. Meanwhile, the permeability anisotropy affects the developments of viscous fingers and the subsequent mixing behaviors significantly. Specifically, as the streamwise (longitudinal) permeability is larger than the spanwise (transverse) one, the mixing process is faster and stronger than that in the contrary case. Furthermore, the anisotropy can lead to different behaviors of the dissipation rates in streamwise and spanwise directions. Generally, the dissipation rate is dominated by the transverse concentration gradients when the longitudinal permeability is higher than the transverse one; on the contrary, as the transverse permeability is higher than the longitudinal one, the contributions to the dissipation rate from longitudinal and transverse concentration gradients are both significant.