Hydraulic conductivity estimate via tracer test and ensemble Kalman filter data assimilation: theoretical and numerical fundamentals

Hydraulic properties of natural aquifers, such as porosity, hydraulic conductivity, and storativity, exhibit an erratic spatial variability at different scales that is difficult to recognize without expensive in situ sampling campaigns, laboratory analyses, and, when available, spatially distributed pumping tests. Nevertheless, the importance of the heterogeneous structure of natural formations on solute transport is well recognized, being the non-Fickian evolution of contaminant plumes and the relevant dispersive phenomena controlled by the variability of the hydraulic conductivity K at the local scale. Tracer test analyses have been widely adopted to identify the complex distribution of in situ hydraulic properties. In particular, the use of geophysical methods like the borehole Electrical Resistivity Tomography (ERT) have been in rapid increase, due to their potential to accurately describe the spatio-temporal evolution of the injected solute. Under the assumptions that the solute spreads as a passive tracer and with high values of the Peclet number, the plume evolution is controlled by the porosity and the spatial distribution of hydraulic conductivity. Combining the Lagrangian formulation of transport and the ensemble Kalman filter (EnKF) data assimilation technique, the purpose of this study is to infer the spatial distribution of K at the local scale from a sequence of time-lapse concentration imaging. The capabilities of the proposed approach are investigated simulating various assimilation experiments via synthetic tracer tests in a three-dimensional finite domain reproducing a heterogeneous aquifer. In a first scenario, all the available concentration measurements are assimilated and the entire hydraulic conductivity field is updated, while in the remaining scenarios the K values are updated only in a limited number of nodes by assimilating the concentrations in these same nodes, the hydraulic conductivity in the rest of the domain being the result of a subsequent conditional generation. The performance of the method is carefully analyzed in terms of root mean square error of the reconstructed hydraulic log-conductivity field. Besides to highlight its weakness and strength, the results show that the proposed approach can represent an effective tool for describing the hydraulic conductivity distribution at the locale scale.