Semi-analytical solution for residence time distribution in trapezoidal aquifers receiving a linearly-variable recharge
Résumé
The residence time distribution (RTD) is an important feature in many problems related to water quality, risk assessment, interpretation of tracer data… Its relevance and interest arise from being a lumped characteristic encompassing the dynamics of hydrologic systems. Accordingly, part of the research on RTDs has been dedicated to the development of close-formed expressions, that can be used as interpretation frameworks and prediction tools.
We propose here to complement the current analytical RTDs with the development of a semi-analytical solution for trapezoidal aquifers receiving a linearly-variable recharge. The solution is developed for a homogeneous system in steady-state conditions under the Dupuit assumption i.e. negligible vertical head gradient. Along with the development of the solution, we carry out an analysis of the role of system properties – typically recharge rate, thickness, porosity - over the generation of the RTD. We evidence the interplay of the magnitude of the pore velocity and the flow pattern giving rise to the shape of the RTD.
We besides assess the validity of the solution by testing it against numerical simulations in confined and unconfined conditions. We specifically focus on the limiting cases of highly converging (or diverging) flow patterns arising from triangular aquifers. We discuss the range of applicability of the solution in natural systems and highlight its interest in pre-mountainous areas.
The analytical solution provided here presents all the distinguishing features of analytical solutions: formulated with a few parameters only, explicit and straightforward to use. It stands out from existing solutions (e.g. exponential model) by its generality and flexibility. It can be used in a variety of configurations for direct or inverse problem analyses.