Groundwater travel time uncertainty analysis using sensitivity derivatives

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Abstract
The evaluation of a Hydrogeologic system requires the definition of a system performance measure. Groundwater travel time is a key performance measure used in the performance assessment of a potential site for the storage of high‐level radioactive waste. Two approaches commonly used to quantify the uncertainty in a given prediction of a performance measure are the first‐order second‐moment (FOSM) approach and the stochastic approach. The FOSM approach predicts the mean and variance of the performance measure based on the mean and variance of the system parameters (e.g., permeability, porosity) and the sensitivity of the performance measure with respect to the system parameters. The sensitivity of the performance measure is directly determined by calculating its first derivative with respect to selected system parameters. The uncertainty of the performance measure is then calculated by multiplying the performance measure sensitivity to the uncertainty of the system parameters. The FOSM approach has been employed to determine the uncertainty of the predicted groundwater travel time performance measure at the proposed high‐level waste (HLW) repository site that had been undergoing detailed investigation in Deaf Smith County, Texas. The results are compared to a similar study using the stochastic approach. In the stochastic technique, the uncertainty is determined by sampling the probability distribution function (PDF) of the uncertain, independent parameters and directly calculating the PDF of the dependent parameter (or performance measure) by conducting multiple simulations. Although the approaches use different techniques to evaluate groundwater travel time uncertainty, the results from both are remarkably similar in this application. The FOSM approach is also used to predict changes in the mean groundwater travel time for selected changes in permeability values within the model. It is demonstrated that for changes in permeability of one half standard deviations or less, additional simulations are not required in order to reasonably predict the change in the groundwater travel time using FOSM. However, for perturbations of approximately 1 standard deviation, FOSM does not provide a reasonable prediction of the change in groundwater travel time. These results indicate the stochastic approach should be used when the variance or uncertainty of the Hydrogeologic parameters is high because of the limitations on the perturbation of these parameters in the FOSM approach.