Identification of the release history of a groundwater contaminant in non-uniform flow field through the minimum relative entropy method

Abstract:

The interest in approaches that allow the estimation of pollutant source release in groundwater has increased exponentially over the last decades. This is due to the large number of groundwater reclamation procedures that have been carried out: the remediation is expensive and the costs can be easily shared among the different actors if the release history is known. Moreover, a reliable release history can be a useful tool for predicting the plume evolution and for minimizing the harmful effects of the contamination. In this framework, Woodbury and Ulrych (1993, 1996) adopted and improved the minimum relative entropy (MRE) method to solve linear inverse problems for the recovery of the pollutant release history in an aquifer. In this work, the MRE method has been improved to detect the source release history in 2-D aquifer characterized by a non-uniform flow-field. The approach has been tested on two cases: a 2-D homogeneous conductivity field and a strong heterogeneous one (the hydraulic conductivity presents three orders of magnitude in terms of variability). In the latter case the transfer function could not be described with an analytical formulation, thus, the transfer functions were estimated by means of the method developed by Butera et al. (2006). In order to demonstrate its scope, this method was applied with two different datasets: observations collected at the same time at 20 different monitoring points, and observations collected at 2 monitoring points at different times (15-25 monitoring points). The data observed were considered affected by a random error. These study cases have been carried out considering a Boxcar and a Gaussian function as expected value of the prior distribution of the release history. The agreement between the true and the estimated release history has been evaluated through the calculation of the normalized Root Mean Square (nRMSE) error: this has shown the ability of the method of recovering the release history even in the most severe cases. Finally, the forward simulation has been carried out by using the estimated release history in order to compare the true data with the estimated one: the best agreement has been obtained in the homogeneous case, even if also in the heterogenous one the nRMSE is acceptable.