Comparison of nonlocal Eulerian to Lagrangian moments for transport in an anisotropic heterogeneous aquifer with deterministic linear nonequilibrium sorption

An Eulerian perturbation scheme is applied to study transport of a reactive chemical experiencing linear nonequilibrium sorption with deterministic rate constants in a heterogeneous porous medium. Exact solutions for the mean concentrations are used to obtain mean values of spatial moments through the third moments. Comparisons are made with results obtained for the identical problem in a Lagrangian frame [Dagan and Cvetkovic, 1993]. If local-scale dispersion is neglected in the Eulerian analysis and the fully nonlocal flux is retained, then the Eulerian and Lagrangian moments agree. However, if either the Eulerian model is localized or the local-scale dispersion is retained, then the moments disagree. This disagreement is especially acute in the asymptotic limits. If local-scale dispersion is included in the first-order Lagrangian analysis, then one anticipates agreement through the third moments between the two approaches.