Inferring Geostatistical Properties of Hydraulic Conductivity Fields from Saline Tracer Tests and Equivalent Electrical Conductivity Time-series

Abstract:

Reliable quantitative analysis of a solute plume's fate using the time-lapse Direct Current (DC) geophysical method is hindered by the absence of accurate upscaling frameworks translating small-scale salinity heterogeneity into upscaled equivalent electrical conductivities under typically non-ergodic conditions. We use Approximate Bayesian Computation and the Kullback-Leibler divergence measure to quantify to what extent horizontal and vertical equivalent electrical conductivity time-series constrain the variance and integral scales of 2-D multivariate Gaussian log-hydraulic conductivity fields. To achieve this, we create a database of 10⁵ hydraulic conductivity field realizations on which we simulate equivalent electrical conductivity and mass breakthrough time-series arising from tracer tests with imposed horizontal flow. Considering a perfect and known relationship between salinity and electrical conductivity at the point scale, we find that horizontal equivalent electrical conductivity time-series best constrain the geostatistical properties, followed by the corresponding vertical component and the mass breakthrough. Also, the added value of combining time-series is comparatively low. We find that the variance, controlling the spreading rate of the solute, is the best constrained parameter, followed by the integral scale in the vertical direction and lastly the integral scale in the horizontal direction. Among the test cases considered, we find that horizontally layered models with moderate to high variance are the best resolved. The sensitivity of the equivalent electrical conductivity to the solute spreading suggests that the former could constrain the mixing potential of the solute. Our work demonstrates that electrical data are not only impacted by sub-resolution heterogeneity, but also that the statistics of the underlying material heterogeneity can be partially inferred. Since the salinity field at the averaging scale (e.g., the model resolution in tomograms) is typically non-ergodic, our results also serve as a starting point for quantifying uncertainty due to small-scale heterogeneity in laboratory-experiments, tomographic results and fully-coupled hydrogeophysical inversions involving DC data.