Longitudinal dispersion in heterogeneous layered porous media during stable and unstable pore-scale miscible displacements

Dispersion and mixing of fluids during miscible displacement in porous media are known to be strongly affected by heterogeneity and viscous fingering. In this study, direct pore-level numerical simulations are employed to model flow and solute transport during both stable and unstable miscible displacements in two-dimensional packings of circular grains. Longitudinal dispersion coefficients are then computed by fitting the numerically obtained concentration profiles to the analytical solution of the convection-dispersion equation. We observed that diffusive, mixed diffusive-advective, and mechanical dispersion regimes are present during stable displacements whereas the middle diffusive-advective regime is absent in unstable displacements due to the evolution of viscous fingers. Viscous fingering also increases the longitudinal dispersion coefficient several orders of magnitude compared to the stable displacement. The results reveal that the scale-dependency of longitudinal dispersion is a function of layering direction and viscosity contrast. During stable displacement in porous domains with no layering or with the layering perpendicular to the displacement direction, the longitudinal dispersion coefficient increases along the length of flow until it reaches an asymptotic value. When layering is in the direction of displacement, however, the scale-dependency behavior is a function of the layering pattern. In unstable displacements, however, longitudinal dispersion always exhibits an asymptotic behavior. Finally, it is observed that the effect of heterogeneity and layering on the magnitude of the longitudinal dispersion coefficient diminishes as viscosity ratio increases to higher adverse values.