Differences in the scale-dependence of dispersivity estimated from temporal and spatial moments in chemically and physically heterogeneous porous media

Abstract

Tracer tests designed to estimate field-scale dispersivities are commonly based upon the interpretation of breakthrough curves. Implicitly, no distinction is made between these dispersivity values and those inferred by analyzing the evolution of tracer plumes. Although this assumption is reasonable in ideal homogeneous media, its applicability to complex geologic formations is unclear. Recent laboratory tracer tests in a heterogeneous test aquifer have suggested that some differences may exist. This work provides computational investigations aimed to study the meaning and differences of these two types of dispersivity estimates in three-dimensional chemically and physically heterogeneous porous media. Specifically, the scale-dependence of longitudinal dispersivities for conservative and linearly sorbing tracers estimated from temporal moments of breakthrough curves are compared with those obtained from spatial moments of tracer plumes in uniform flow systems. The scale-dependence of dispersivity from spatial and temporal moments was found to be identical for small σ ln K 2 and σ R 2 . For larger values of σ ln K 2 and σ R 2 ( σ ln K 2 > 0.5 , σ R 2 > 0.5 ) , however, the dispersivities estimated from temporal moments approach a constant value at smaller distances than estimates obtained from spatial moments. Yet, both dispersivities asymptotically approach the same constant value at large travel distances. From a practical standpoint, it is also shown that accurate field dispersivity coefficients can be obtained from uniform flow tracer test by simply using few fully-penetrating observation wells, bypassing the need for more expensive tracer techniques based upon the spatial description of concentrations.