The moments of the breakthrough curves of instantaneously and kinetically sorbing solutes in heterogeneous geologic media: Prediction and parameter inference from field measurements

Abstract

This paper presents a concise methodology for estimating the moments of the breakthrough curves for tracers and reactive solutes in heterogeneous aquifers. Under some conditions these are also the temporal or travel time moments between a source and a given destination downstream. The temporal moments of tracers as well as instantaneously or kinetically sorbing solutes, characterized by linear isotherms, are expressed in terms of a few parameters which characterize the chemical reactions and the spatial distribution and correlation structure of the hydraulic conductivity. The chemical reaction parameters are assumed to be homogeneous. The estimated moments can also be made conditional to field measurements. Applications for the case of uniform mean flow are presented, but the general approach can be applied for other flow regimes such as injection‐pumping well doublets. Physical and chemical nonequilibrium processes are represented by mobile‐immobile domains and two‐site models, respectively. The estimated temporal moments can be used for both predictive purposes as well as for interpretation of field experiments. These two objectives are pursued in this paper. A significant advantage of the solution is that it does not require the assumptions of Gaussianity or log Gaussianity of the travel times. Throughout the discussion the combined and relative effects of the mass transfer and kinetic parameters and the spatial variability of the conductivity on the travel time moments are evaluated.