Temporal Moments for Kinetically Sorbing Solute Transport in Radial Flow

We will apply a method of determining the temporal moments of kinetically sorbing solute transport to radial flow situations. The temporal moments for kinetically sorbing solute are determined from the travel time cumulative distribution function (CDF) of a non-reactive solute and the geochemical model describing the sorption and desorption of the reactive solute. The method is a stochastic approach based on a Lagrangian description of solute transport in heterogeneous porous media. The equations of this approach are general and can be specialized for use with any kinetic geochemical model that employs linear sorption isotherms. The dependence of the reactive temporal moments on only the geochemical model and the travel time CDF of a non-reactive tracer can reduce computational effort, because after the CDF of the non-reactive tracer is calculated, it can be used repeatedly with different geochemical models as needed. Conditioning on measurements of hydraulic conductivity or transmissivity, which reduces uncertainty, can easily be incorporated when conditional non-reactive travel time CDFs are available. The method can be applied to problems of various flow configurations and dimensionalities. We will use published experimental and numerical results for radial flow to determine the mean and variance of the travel time of a contaminant to a pumping well. We will show how these results can be used to quantify the risk posed by a source of groundwater contamination near a well.