Effect of sorption heterogeneity on moments of solute residence time in convergent flows

Abstract

In this paper, we analyze the impact of physical and chemical heterogeneity on solute travel time to a pumping well. We consider a solute undergoing reversible linear instantaneous equilibrium sorption. Both the distribution coefficient, $K_{d}$, and the transmissivity field, $T$, are considered spatially variable, and are modeled as partially correlated spatial random functions. Groundwater flow and solute transport are then solved within the context of a numerical Monte Carlo framework. The results are analyzed on the basis of dimensional analysis techniques. Simple and compact expressions characterizing the dependence of the target travel time moments on relevant dimensionless groups are proposed. The functional form of these expressions is inspired by, and is consistent with, the previous works of Sanchez-Vila and Rubin (Water Resour. Res. 39(4):1086, 2003) and Riva et al. (J. Contam. Hydrol. 82:23–43, 2006) A key result is that the effects of the chemical and physical heterogeneities on the mean travel time can be decoupled consistently with existing analytical results. The relative role of physical and geochemical heterogeneities in travel time variance is more complex, and such a decoupling is not observed. Potential uses of this work include the assessment of aquifer reclamation time by means of a single pumping well.