Inferring soils' heterogeneous structure via hydro-electrical measurements at altering spatial scales

Understanding and predicting water flow and solute transport at the subsurface are important for agronomical, hydrological, and environmental applications. Nevertheless, due to the heterogeneous nature of soils, those predictions are subject to significant uncertainties. Although stochastic approaches have been proposed to cope with soil heterogeneity, uncertainties in model predictions remain high due to data scarcity and lack of spatially continuous measurements. Geo-electrical methods have the potential to significantly reduce models' uncertainties due to their ability to provide continuous, extensive, and non-invasive information of the subsurface. At the core of these methods, the obtained subsurface's electrical conductivity can be translated to hydrological state-variables via site-specific hydro-electrical relations calibrated with lab or field data. However, due to soil's heterogeneity, the hydro-electrical relations can be scale-dependent.

This work studied the impact of soil's heterogeneity at the sub-core level on the effective hydro-electrical relations scale dependency. For that purpose, synthetic soil samples with various geostatistical parameters were generated. Constant capillary pressure was applied, and water saturation maps were obtained using a van-Genuchten model and the Leverett J-function for retention and retention scaling. The water saturation maps were transformed to soil's electrical conductivity by adopting Archie's law with assumed "intrinsic" parameters. An electrical current was injected, and the corresponding electric potential was calculated. The soil's effective electrical conductivities at different spatial scales were estimated, and new effective hydro-electrical relations were calibrated for each measurement scale.

This forward approach had shown that each soil structure has a unique signature on the effective hydro-electrical relations calibrated at different measurement scales. Following those observations, a novel stochastic inversion technique, based on an iterative Bayesian approach and Markov Chain Monte Carlo sampling, was used to confine the soil's geostatistical properties. The proposed inversion technique was tested on three different scenarios: two synthetic cases with a known structure, and one real data case based on CT images of a two-phase CO₂ and brine injection at altering fractional flows. Results have shown that the proposed approach was capable of confining the soil's geostatistical parameters with high accuracy and a narrow distribution around the actual values that were tested, by calibrating the effective hydro-electrical properties at only three different measurements scales.