THE INFLUENCE OF AQUITARD PROPERTIES ON LATE-TIME BREAKTHROUGH CURVES

Any aquitard material that is embedded within an aquifer can change the late-time breakthrough curve (BTC) by trapping solutes in a relatively immobile phase. We conceptualize the effect of aquitard layers as a series of first-order mass transfer processes that are controlled primarily by the thickness of aquitard units. The shape of the late-time BTC depends on the thickness and the associated volume fractions of immobile water in “blocks” of fine-grained material. We explore the implication that the late-time BTCs can be predicted accurately given even very limited knowledge of subsurface heterogeneity, such as drillers' logs. Monte Carlo simulations confirm that the ensemble solute concentration at later time can be approximated by a summation of exponential functions with rates dictated by aquitard thicknesses. Specifically, if the volume fraction of immobile blocks has a power-law histogram or probability distribution function (pdf), then a power-law BTC late tail will be guaranteed. When the volume fraction of immobile blocks has an exponential pdf, the late-time BTC will have a transition from power-law to exponential decay, where the transition time is a function of the thickest immobile block. The aquitard material also causes a discrepancy between the resident and the flux concentrations of conservative solutes in either the mobile or the total (mobile and immobile) phases. The flux versus resident late-time BTCs may differ by many orders-of-magnitude, forcing us to distinguish between the two when making either measurements in the field or predictions of clean-up levels. Transformations between the resident and the flux concentrations for solutes in every phase are derived analytically and confirmed numerically for different aquitard pdfs.