Accurate modeling of water flow and solute transport in unsaturated soils is of significant importance for precision agriculture, environmental protection and aquifer management. Traditional modeling approaches are considerably challenging since they require well‐defined boundaries and initial conditions. Physics‐informed neural networks (PINNs) have recently been developed to learn and solve forward and inverse problems also constrained to a set of partial differential equations and are more flexible than traditional modeling approaches. However, hydrological applications of PINNs used so far spatial measurements of hydraulic head, water content and/or solute concentrations, which were well distributed in the subsurface for training the system. Such measurements are hard to obtain in real‐world applications. Here, we propose to train PINNs with non‐invasive geoelectrical tools for simulating two‐dimensional water flow and solute transport during infiltration and redistribution processes with unknown initial conditions. Two‐dimensional flow and transport numerical simulations were used as benchmarks to examine the suitability of the described approach. Results have shown that the trained PINNs system was able to reproduce the spatiotemporal distribution of both water content and pore‐water salinity during both processes with high accuracy, using five time‐lapse geoelectrical measurements and matric head measurements at a single location. The trained PINNs system reconstructed the initial conditions of both state parameters at both processes. It was also able to separate the measured electrical signal into its two components, that is, water content and pore‐water salinity. The subsurface geoelectrical tomograms were significantly improved compared to those obtained from a classical inversion of the raw geoelectrical data.

Studies of CO₂‐brine two‐phase flow are predominantly carried out on core samples or reservoir‐scale domains. In this work we investigate intermediate‐scale flow considering a cubic rock with 1 m³ volume incorporating sub‐core (mm)‐scale heterogeneity. First, a coreflooding experiment is analyzed to estimate subcore permeability spatial distribution and the results are used as input into the meter‐scale model without any upscaling required. High‐resolution numerical simulations are conducted to model CO₂ injection into a brine saturated rock. We find significant differences between the meter‐scale rock simulation and core experiment saturation distributions resulting from highly influential boundary effects on the core scale and pronounced gravity impact on the meter scale. A detailed analysis of flow and brine trapping in rock simulations is presented considering different flow models and permeability structures. It is shown that gravity and capillary heterogeneity have substantial impact on the saturation in the deeper regions, which exhibit sufficiently low capillary pressure, and these regions also show increased trapping of brine. Two trapping mechanisms are discussed: Type I which is a result of entry pressure considerations and Type II, which occurs due to lack of CO₂ connectivity. The two types of trapping are found to be correlated to the permeability structure. A formula is presented relating between trapping and permeability statistical parameters, that is, variance of log‐permeability and correlation length scale, as well as to the Bond number characterizing the ratio between gravity and capillary effects.

Determining soil hydraulic properties is complex, posing ongoing challenges in managing subsurface and agricultural practices. Electrical resistivity tomography (ERT) is an appealing geophysical method to monitor the subsurface due to its non‐invasive, easy‐to‐apply and cost‐effective nature. However, obtaining geoelectrical tomograms from raw measurements requires the inversion of an ill‐posed problem, which causes smoothing of the actual structure. Furthermore, the spatial resolution is determined from the distances in the electrode placement, thus inherently upscaling the obtained structure. This study explores the applicability of physics‐informed neural networks (PINNs) for upscaling permeability and petrophysical relations and monitoring water dynamics at heterogeneous soils using time‐lapse geoelectrical data. High‐resolution numerical simulations mimicking water infiltration were used as benchmarks. Synthetic ERT surveys with electrode spacing 10 times larger than the numerical model resolution were conducted to provide 2D electrical tomograms. The tomograms were fed to a PINNs system to obtain the permeability, petrophysical relations, and water content maps. An additional PINNs system incorporating water content measurements was trained to examine measurement sensitivity. Results have shown that the PINNs system could produce reliable results regarding the upscaled permeability and petrophysical relations fields. Water dynamics at the subsurface was accurately predicted with an average error of ∼3%. Adding water content measurements to PINNs training improved the system outcomes, mainly at the ERT low sensitivity zones. The PINNs system reduced water saturation errors by more than 30% compared to the common practice of directly translating the geoelectrical tomograms to water saturations using known, homogeneous petrophysical relations.

Relative permeability (k_r) is an important property characterizing multi‐phase flow in porous media, in particular considering applications of oil and gas production or CO₂ storage in subsurface formations. Coreflooding experiments are the most common method of determining k_r, usually conducted at a given total injection rate. However, k_r is known to be a rate dependent effective property due to capillary heterogeneity effects and therefore full characterization requires conducting experiments at different flow rates, a complex and time consuming process. This work presents a new approach for calculating rate dependent effective k_r curves based on a 1D semi‐analytical solution for steady state flow. The method entails calibrating a 1D permeability structure to represent the 3D flow of coreflooding experiments. Then, the calibrated 1D model is used to estimate k_r curves at varying rates. We apply the method to three cases, two synthetic and one based on experimental data. Results show applicability for a wide range of flow rates.