Electrical conductivity model for reactive porous media under partially saturated conditions with hysteresis effects

The electrical conductivity of a porous medium is strongly controlled by the structure of the medium at the microscale as the pore configuration governs the distribution of the conductive fluid. The pore structure thus plays a key role since different geometries translate in variations of the fluid distribution, causing different behaviors measurable at the macroscale. In this study, we present a new physically-based analytical model derived under the assumption that the pore structure can be represented by a bundle of tortuous capillary tubes with periodic variations of their radius and a fractal distribution of pore sizes. By upscaling the microscale properties of the porous medium, we obtain expressions to estimate the total and relative electrical conductivity. The proposed pore geometry allows us to include the hysteresis phenomenon in the electrical conductivity estimates. The variations on these estimates caused by pore structure changes due to reactive processes are accounted by assuming a uniform dissolution of the pores. Under this hypothesis, we describe the evolution of the electrical conductivity during reactive processes. The expressions of the proposed model have been tested with published data from different soil textures, showing a satisfactory agreement with the experimental data. Hysteretic behavior and mineral dissolution are also successfully addressed. By including hysteresis and mineral dissolution/precipitation in the estimates of the electrical conductivity, this new analytical model presents an improvement as it relates those macroscopic physical phenomena to its origins at the microscale. This opens up exciting possibilities for studies involving electrical conductivity measurements to monitor water movement, and hysteretic and reactive processes in porous media.