Tracer Tests in Stratified Alluvial Aquifers: Predictions of Effective Porosity and Longitudinal Dispersivity versus Field Values

Abstract

Tracer tests in aquifers are key tests to delineate protection perimeters around drinking water wells. They help to determine field values of effective porosity, ne, and longitudinal dispersivity, αL, from curve fitting to a breakthrough curve (BTC). It is difficult to predict ne, but correlations obtained with field or numerical tracer tests may be used to predict αL. The BTCs of field tracer tests differ from those predicted by the advection-dispersion theory in three ways: (1) early arrival with smaller than expected ne, (2) scale-dependent αL, and (3) a long thick tail. In this article, physical principles are used to obtain new closed-form predictive equations for ne and αL in stratified alluvial aquifers. The new equations give ne and αL for the hydraulically equivalent homogeneous aquifer. The predicted values for ne are shown to fit the field values of seven well-documented field tracer tests. The new equations explain the ne field values and can explain field values of αL for stratified aquifers, their variation with distance, and the variance of the ln(K) distribution. If the tracer is injected for a limited time, the predicted BTC also displays the three usual features of field data, which simply result from a lognormal K-distribution. The new equations and their experimental verification correctly elucidate some difficulties due to aquifer heterogeneity and improve our ability to predict groundwater movements in the subsurface.