A stochastic model of solute transport in groundwater: Application to the Borden, Ontario, Tracer Test

Results from the Borden tracer test are used to evaluate the performance of the stochastic model developed by Graham and McLaughlin (1989a, b). The model assumes that spatial variations in hydraulic conductivity induce variations in a steady state velocity field which, in turn, induce variations in solute concentration. Analytical expressions for the unconditional ensemble moments of velocity are derived from the unconditional ensemble moments of log hydraulic conductivity. The velocity moments are related to the ensemble moments of concentration by a set of coupled partial differential equations. The dependent variables in these equations are the concentration mean and covariance and the velocity-concentration covariance (or macrodispersive flux). Macrodispersion is not assumed to be Fickian. The moment equations are solved with a dual-grid finite element algorithm. The nonstationary concentration covariances obtained from the finite element solution provide the information needed to condition estimates of velocity and concentration on a small set of concentration measurements. In the Borden application considered here conditioning is performed sequentially, at 85 days and at 260 days after the injection of a pulse of conservative tracer (chloride). The conditional mean concentration provides a better estimate of the true chloride concentration than the unconditional mean. The concentration variance and macrodispersive flux both decrease at conditioning times but gradually increase after the solute plume moves out of the sampling grid. The performance of the stochastic model, as indicated by an analysis of measurement residuals, is generally consistent with the model's own estimates of concentration uncertainty.