Hydraulic conductivity identification by EnKF and travel time modeling of transport

Borehole ERT monitoring of saline tracer tests allows to collect time-lapse geophysical data as changes occur in an aquifer as a result of dynamical variations in the hydrological state of the subsurface, and it seems to be a promising tool for the hydrological characterization of natural aquifers. Nevertheless, ERT measurements are not directly related to the hydraulic parameters needed to predict flow and transport in porous media. The electrical conductivity field must be reconstructed by means of a geophysical inversion on the basis of current and voltage measurements, and the use of a petrophysical law (e.g., Archie’s law) is required to deduce the solute concentration and the plume evolution closely linked to the distribution of the hydraulic properties. To retrieve the hydraulic properties of aquifers, e.g., the hydraulic conductivity distribution K(x), from an ERT monitored saline tracer test, and to overcome the need for the knowledge of the concentration spatio-temporal evolution, we propose a novel approach that couples travel time modeling of transport with the ensemble Kalman filter (EnKF) used as an inversion tool. The definition of the solute transport in terms of travel (or residence) times allows to analyze the sequence of changes in electrical resistivity deduced from a ERT survey without converting the electrical data into concentrations. Moreover, in the case of a multiple well saline tracer test, only two dimensional images of electrical conductivity defining the control planes (CP) need to be reconstructed by the geophysical inversion from current and voltage measurements, with a noticeable saving of computer resources with respect to the fully 3D case. To demonstrate the ability of the proposed approach, we consider a synthetic 3D case, where multiple control planes, each of these defined by a pair of ERT monitored boreholes, are located downstream from an injection well perpendicular to the mean flow direction. The CPs are properly subdivided in subareas, each of them characterized by a travel time distribution. The assimilation of the travel times in a Lagrangian model of transport whose K distribution represents the system state of the EnKF allows to update the average hydraulic conductivity for each subarea and hence to determine the K spatial variability with a resolution related to the one of the control plane discretization. We report on the capability of the inversion procedure as a function of the number of control planes available and their discretization in subareas.