Time-scale-dependent analysis of multiple-peaked breakthrough curves obtained in weakly stratified aquifers

Abstract:

A method is developed for the analysis of the results of radially-converging tracer tests conducted in stratified aquifers. The method is based on a semi-analytical solution of the classical advection-dispersion equation and assumes (i) perfectly horizontal saturated flow towards the pumping well, (ii) vertical stratification of flow according to lithology, and (iii) independent migration of solutes in each a soil strata. The semi-analytical solution allows the modeling of multiple-peaked breakthrough curves (BTC), as can be observed in short-distance tracer tests conducted in sedimentary formations characterized by a relatively small longitudinal dispersivity.

A two-step methodology is proposed for the back-analysis of tracer test results using that solution. First, Gaussian decomposition is applied to the experimental BTC in order to provide its space-scale image. The latter provides a time-scale-dependent interpretation of the BTC with respect to the number of soil layers in which transport is taking place. For large time scales, a single layer of soil characterized by a large longitudinal dispersivity can be identified. As time scale decreases, more layers and a reduced value of dispersivity can be used to model solute transport.

In the second step of the methodology, the series of Gaussian distributions obtained as outcome of the Gaussian decomposition step is interpreted as a series of probability density functions (PDFs) for solute mean travel times in each layer. These PDFs are used as priori estimations of the unknown transport parameters in a Markov Chains Monte Carlo optimization method.

The method is applied to the results of a tracer test conducted in a sedimentary aquifer in Belgium. Two injections were performed, at distances of 4.8 m and about 25 m from the pumping well. Fluorescent tracers were used in combination with a field fluorometer recording data on an hourly basis, validated against classical samples analyzed in the laboratory. Both breakthrough curves measured at the pumping well exhibited clearly-distinguishable multiple peaks. A near-perfect fit of the analytical solution onto experimental data was reached for 5 layers.