Relative impacts of permeability heterogeneity and viscosity contrast on solute transport and mixing in porous media

Solute transport in porous media is affected by several factors. The heterogeneous structure of the permeability field is a key factor controlling the spreading and mixing behaviors of a solute cloud. On the other hand, other factors such as the viscosity contrast between the dissolved solute and the ambient fluid can also play an important role. This work aims to explore the impact of field heterogeneity and viscosity contrast on the transport behavior of an inert solute in a two-dimensional flow field. We performed high-resolution numerical simulations based on the spectral method to solve coupled flow and transport equations for a given range of viscosity contrast and log-permeability variance. We analyze the degree and rate of mixing, contour length of the solute cloud, spatial statistics of the concentration field and arrival times at a control plane to characterize spreading and mixing in the domain. We provide a quantitative separation of the impacts of fingering and heterogeneity and we parameterize the concentration probability distribution function. We find that the interplay between viscous fingering, high-permeability channeling, and low-permeability stagnation at small scales create important features in the spreading and mixing characteristics.