3D hydrogeological parametrization using scarce piezometric data

A reliable description of aquifer heterogeneities is crucial for solute transport modelling. Inverse methods, a field of research that has been developing greatly in recent decades, can provide the horizontal structure of heterogeneities, with the collection of piezometric data as a cornerstone. But the latter are very little sensitive to the vertical structure of the aquifer, leaving its estimation dependent on complex and expensive field methods (electrical resistivity and radar tomography, self-potential methods, cross-hole testing, hydraulic tomography) or lab analysis (grain-size analysis from core sample, secondary permeability tests).

In order to take advantage of the possibilities offered by the inversion techniques, while sidestepping the inconvenience of geophysical and field approach, a method is proposed using 2D inversion of flow (solely reliant on piezometric series) as parameterization constraints for a 3D hydrogeological model (see Figure 1).

The methodology is tested via a synthetic example, ensuring full knowledge and control of the aquifer's structure. It is composed of 5 lithofacies, distributed according to a sedimentary pattern, the level of heterogeneity for hydraulic conductivity spans 3 orders of magnitude and groundwater is unconfined. This synthetic example provides both the piezometric chronicles used to inverse 2D flow parameter fields and the lithological logs used to interpolate the 3D lithological model. Finally, the parameters of each facies are obtained through an optimization loop, minimizing the difference between the 2D and the 3D transmissivity (and specific yield).

The method results in the estimation of parameters very close to the known parameters, even with a scarce piezometric and lithological data sampling. The maximal discrepancy is 61% of the initial value for the permeability and 16% for the specific yield (mean error being respectively 18 and 4%). Although the methodology does not prevent interpolation error, it succeeds in reconstructing flow and transport dynamics very close to the synthetic control data. Due to the inherent limitations of the 2D inversion approach, the method only applies to the saturated zone at this point.