A Nondimensional Evaluation of Tracer Sensitivity to Density Effects

Abstract

The purpose of this paper is to assess the importance of the density difference between a tracer solution and ground water on the determination of aquifer properties by inversion of tracer signals. To estimate the effect of this density difference, we developed a nondimensional, approximate solution to a Boundary Value Problem (BVP) based on a partial differential equation first presented by Bear and Dagan (1964). The BVP models the displacement of water by another aqueous solution with a different density in a rectangular, vertical cross section of a homogeneous porous medium. A rectangular sandbox analog model was used to verify the validity of the nondimensional solution for the case of a moving interface during the displacement of water by a heavier-than-water aqueous solution. A constant flow rate was maintained by applying constant heads at a fully penetrating vertical inflow and outflow chamber. The theory, which can be applied as a prediction tool for laboratory experiments, permits us to explore the implications of using denser-than-water tracers for determining aquifer hydraulic conductivity and dispersion coefficient values. According to our assessments, density effects should not be ignored, as small density differences can lead to serious uncertainties in permeability and dispersivity determinations.