Effects of pore-scale dispersion, degree of heterogeneity, sampling size, and source volume on the concentration moments of conservative solutes in heterogeneous formations

Pore-scale dispersion (PSD), aquifer heterogeneity, sampling volume, and source size influence solute concentrations of conservative tracers transported in heterogeneous porous formations. In this work, we developed a new set of analytical solutions for the concentration ensemble mean, variance, and coefficient of variation (CV), which consider the effects of all these factors. We developed these models as generalizations of the first-order Solutions in the log-conductivity variance of point concentration proposed by [Fiori A, Dagan G. Concentration fluctuations in aquifer transport: a rigorous first-order solution and applications. J Contain Hydrol 2000;45(1-2):139163]. Our first-order solutions compare well with numerical simulations for small and moderate formation heterogeneity and from small to large sampling and source volumes. However, their performance deteriorates for highly heterogeneous formations. Successively, we used our models to study the interplay among sampler size, source volume, and PSD. Our analysis shows a complex and important interaction among these factors. Additionally, we show that the relative importance of these factors is also a function of plume age, of aquifer heterogeneity, and of the measurement location with respect to the mean plume center of gravity. We found that the concentration moments are chiefly controlled by the sampling volume with pore-scale dispersion playing a minor role at short times and for small Source Volumes. However, the effect of the source volume cannot be neglected when it is larger than the sampling volume. A different behavior occurs for long periods, which may be relevant for old contaminations, or for small injection volumes. In these cases, PSD causes a significant dilution, which is reflected in the concentration statistics. Additionally, at the center of the mean plume, where high concentrations are most likely to occur, we found that sampling volume and PSD are attenuating mechanisms for both concentration ensemble mean and coefficient of variation, except at very large source and sampler sizes, where the coefficient of variation increases with sampler size and PSD. Formation heterogeneity causes a faster reduction of the ensemble mean concentrations and a larger uncertainty at the center of the mean plume. Therefore, our results highlight the importance of considering the combined effect of formation heterogeneity, exposure volume, PSD, source size, and measurement location in performing risk assessment. (C) 2007 Elsevier Ltd. All rights reserved.