COMPARISON OF EULERIAN TO LAGRANGIAN EXPECTED SPATIAL MOMENTS FOR TRANSPORT IN A HETEROGENEOUS POROUS-MEDIUM WITH DETERMINISTIC LINEAR NONEQUILIBRIUM SORPTION

When a natural porous formation is viewed from an Eulerian perspective , incomplete characterization of the hydraulic conductivity leads to n onlocality in the constitutive theory, irrespective of whether the med ium has evolving heterogeneity with velocity fluctuations over all sca les. Within this framework two nonlocal constitutive models are develo ped for natural systems, one for conservative tracers and the other fo r reactive chemicals undergoing linear nonequilibrium sorption with de terministic rate constants. Exact solutions for the mean concentration s are obtained and used to determine the mean values of the spatial mo ments 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 dispersi ve process is neglected in the Eulerian analysis, then the Lagrangian moments obtain. However, if the local-scale dispersive process is incl uded in the Eulerian model, then the second transverse moment disagree s with that obtained through the Lagrangian analysis. It is shown that this disagreement is especially acute in the asymptotic limits.