The impact of local diffusion on longitudinal macrodispersivity and its major effect upon anomalous transport in highly heterogeneous aquifers

Flow and transport are solved for a heterogeneous medium modeled as an ensemble of spherical inclusions of uniform radius R and of conductivities K, drawn from a pdf f (K) (Fig. 1). This can be regarded as a particular discretization scheme, allowing for accurate numerical and semi-analytical solutions, for any given univariate f (Y) (Y = ln K) and integral scale I_Y. The transport is quantified by the longitudinal equivalent macrodispersivity α_Leq, for uniform mean flow of velocity U and for a large (ergodic) plume of a conservative solute injected in a vertical plane (x = 0) and moving past a control plane at x ≫ I_Y. In the past we have solved transport for advection solely for highly heterogeneous media of σ_Y² ≤ 8. We have found that α_Leq increases in a strong nonlinear fashion with σ_Y² and transport becomes anomalous for the subordinate model. This effect is explained by the large residence time of solute particles in inclusions of low K. In the present work we examine the impact of local diffusion as quantified by the Peclet number Pe = UI_Y / D₀, where D₀ is the coefficient of molecular diffusion. Transport with diffusion is solved by accurate numerical simulations for flow past spheres of low K and for high Pe = O (10² - 10⁴). It was found that finite Pe reduces significantly α_Leq as compared to advection, for σ_Y² ≳ 3 (Pe = 1000) and for σ_Y² ≳ 1.4 (Pe = 100), justifying neglection of the effect of diffusion for weak to moderately heterogeneous aquifers (e.g. σ_Y² ≤ 1). In contrast, diffusion impacts considerably α_Leq for large σ_Y² due to the removal of solute from low K inclusions. Furthermore, anomalous behavior is eliminated, though α_Leq may be still large for Pe ≫ 1.