Effect of viscosity and heterogeneity on dispersion in porous media during miscible flooding processes

In this paper, a mathematical model has been developed to quantitatively examine the effect of viscosity and heterogeneity on dispersion in porous media at the pore scale during miscible flooding processes. More specifically, the Navier-Stokes equation and advection-diffusion equation are coupled with supplementary equations to describe the solvent transport behaviour. Two-dimensional heterogeneous models are numerically developed as a function of porosity and permeability, assuming that the grain sizes satisfy normal distribution. In addition, the performance of miscible hydrocarbon gas injection in heterogeneous porous media is comprehensively evaluated. It is found that a larger aspect ratio (ratio of pore throat size) in the single non-flowing pore model results in a greater asymmetry of the concentration curve. As for single non-flowing pore models and heterogeneous models, the dispersion coefficients increase with the expansion of the non-flowing domain. Both the heterogeneity of porous media and the variable viscosity of the fluid mixture contribute to the asymmetry of the concentration curve in the heterogeneous model. A negative correlation is established between the sorting coefficients of pore throat size and the power-law coefficients. As for slug injection, the injected solvent slug size along the longitudinal direction does not effectively influence the longitudinal length of the mixing zone for a given porous medium and fluids, though the Peclet number and the porosity greatly affect the length and concentration distribution of the mixing zone.