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)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=lnK) and integral scale IYIY. The transport is quantified by the longitudinal equivalent macrodispersivity αLeqαLeq, for uniform mean flow of velocity U   and for a large (ergodic) plume of a conservative solute injected in a vertical plane (x=0x=0) and moving past a control plane at x≫IYx≫IY. In the past we have solved transport for advection solely for highly heterogeneous media of σY2⩽8. We have found that αLeqαLeq increases in a strong nonlinear fashion with σY2 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=UIY/D0Pe=UIY/D0, where D0D0 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)Pe=O(102-104). It was found that finite Pe   reduces significantly αLeqαLeq as compared to advection, for σY2≳3(Pe=1000) and for σY2≳1.4(Pe=100), justifying neglection of the effect of diffusion for weak to moderately heterogeneous aquifers (e.g. σY2⩽1). In contrast, diffusion impacts considerably αLeqαLeq for large σY2 due to the removal of solute from low K   inclusions. Furthermore, anomalous behavior is eliminated, though αLeqαLeq may be still large for Pe≫1Pe≫1.