A parameter sensitivity analysis of two chalk tracer tests

As with most fractured rock formations, Chalk is highly heterogeneous. Therefore, meaningful estimates of model parameters must be obtained at a scale comparable with the process of concern. These are frequently obtained by calibrating an appropriate model to observed concentration - time data from radially convergent tracer tests. Arguably, an appropriate model should consider radially convergent dispersion and Fickian matrix diffusion. Such a model requires the estimation of at least four parameters. A question arises as to whether this level of model complexity is supported by the information contained within the calibration data. A four-parameter model was developed for the analysis of two Chalk aquifer radially convergent tracer tests. The parameters included an advective travel time, ta, a characteristic fracture diffusion time, Tcf, a characteristic matrix block diffusion time, tcb and a Peclet number, P. Because the tracer test duration was less than 500 h, tcb was impossible to identify. Further analysis showed that a large set of correlated values of P, ta and tcf would lead to equally good model fits. To resolve this ambiguity, more and better quality data are needed at the very start of the breakthrough curve, to constrain the mechanical dispersion parameter, P.