On the influence of local dispersion in solute transport through formations with evolving scales of heterogeneity RID A-2321-2010

The aim of the present study is to determine the longitudinal dispersion coefficient D-L for transport in formations of long-range permeability fields by considering both large-scale advection and local-scale dispersion; the nonergodicity of the plume will be considered throughout the work. The scope is twofold: (1) to analyze the mutual role played by both the "macroscale" and the local scales of heterogeneity in determining the overall transport properties and (2) to check the validity of the results obtained in the past, in particular concerning the occurrence of anomalous transport. The results are obtained through the Lagrangean formulation of transport, by the means of a few simplifying assumptions. Two models of permeability K variations are considered: (1) a stationary Y = In K with unbounded integral scale and (2) a formation of Y of stationary increments. For both cases, the longitudinal macrodispersion coefficient D-L always grows with time when local-scale dispersion is present, indicating that transport is always anomalous for the random fields examined. The results are in variance with those obtained in the past by considering nonergodic transport but neglecting the local-scale dispersion [e.g., Dagan, 1994; Bellin et al., 1996] and in qualitative agreement to those obtained by adopting the ergodic assumption [e.g., Neuman, 1990; Glimm and Sharp, 1991], which, however, predicted higher rates of growth of D, with time. We conclude that the interplay between large-scale, advective displacement and local-scale dispersion has a fundamental impact on the occurrence of anomalous transport in long-range correlated permeability random fields.