A new discrete model to better consider tracer distribution along boreholes during the Finite Volume Point Dilution Method

The Finite Volume Point Dilution Method (FVPDM) is a single-well tracer experiment which has been successfully used in many hydrogeological contexts to quantify groundwater fluxes. During continuous injection of tracer into a well, the tracer concentration evolution measured within the tested well directly depends on the groundwater flow crossing the well screens. Up to now, the FVPDM mathematical formulation used to simulate the tracer concentration evolution measured in the tested well assumed perfect homogenization of the tracer along the tested interval, which is a reasonable assumption in many cases. However, when FVPDM are performed in long-screened boreholes or in very permeable aquifer materials, the recirculation flow rate imposed to ensure mixing is suspected to be too low to perfectly homogenize the tracer. In order to assess the effect of non-perfect mixing on FVPDM results, we introduce here a new discrete model that explicitly considers the recirculation flow rate. The mathematical developments are validated using field measurements, and a sensitivity analysis is proposed to assess the effect of the mixing flow rate on tracer concentration homogenization within the well. Results confirm that, when the recirculation flow rate applied is not high enough compared to the groundwater flow rate, the tracer distribution is not uniform in the tested interval. In this case, the use of the classical analytical solution, commonly used to interpret the concentration evolution leads to highly overestimated groundwater fluxes. The discrete model introduced here can be used instead to properly estimate groundwater fluxes and assess the tracer distribution within the tested interval. The discrete model offers the possibility of interpreting field measurements conducted under non-perfect mixing conditions and increases the range of fluxes that can be investigated through FVPDM.