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When a natural porous formation is viewed from an Eulerian perspective, incomplete characterization of the hydraulic conductivity leads to nonlocality in the constitutive theory, irrespective of whether the medium has evolving heterogeneity with velocity fluctuations over all scales. Within this framework two nonlocal constitutive models are developed for natural systems, one for conservative tracers and the other for reactive chemicals undergoing linear nonequilibrium sorption with deterministic rate constants. Exact solutions for the mean concentrations are obtained and used to determine the mean values of the spatial moments up to the third. A Lagrangian model (Dagan and Cvetkovic, 1993) for a similar problem is reviewed and comparisons are made between the expected Lagrangian and Eulerian moments. If the local-scale dispersive process is neglected in the Eulerian analysis, then the Lagrangian moments obtain. However, if the local-scale dispersive process is included in the Eulerian model, then the second transverse moment disagrees with that obtained through the Lagrangian analysis. It is shown that this disagreement is especially acute in the asymptotic limits.
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Cushman et al. (1996) studied this question.
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