A parameter identifiability study of two chalk tracer tests

Abstract. 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 (RCTT). Arguably, an appropriate model should consider radially convergent dispersion (RCD) and Fickian matrix diffusion. Such a model requires the estimation of at least four parameters. A question arises as to whether or not this level of model complexity is supported by the information contained within the calibration data. Generally modellers have not answered this question due to the calibration techniques employed. A dual-porosity model with RCD was calibrated to two tracer test datasets from different UK Chalk aquifers. A multivariate sensitivity analysis, which assumed only a priori upper and lower bounds for each model parameter, was undertaken. Rather than looking at measures of uncertainty, the shape of the multivariate objective function surface was used to determine whether a parameter was identifiable. Non-identifiable parameters were then removed and the procedure was repeated until all remaining parameters were identifiable.

It was found that the single fracture model (SFM) (which ignores mechanical dispersion) obtained the best mass recovery, excellent model performance and best parameter identifiability in both the tests studied. However, there was no objective evidence suggesting that mechanical dispersion was negligible. Moreover, the SFM (with just two parameters) was found to be good at approximating the Single Fracture Dispersion Model SFDM (with three parameters) when different, and potentially erroneous parameters, were used. Overall, this study emphasises the importance of adequate temporal sampling of breakthrough curve data prior to peak concentrations, to ensure adequate characterisation of mechanical dispersion processes, and continued monitoring afterwards, to ensure adequate characterisation of fracture spacing (where possible), when parameterising dual-porosity solute transport models.