A unified model for the permeability, electrical conductivity and streaming potential coupling coefficient in variably saturated fractured media

Abstract

We present a new unified model for the permeability, electrical conductivity, and streaming potential coupling coefficient in variably saturated fractured media. For those, we conceptualize the fractured medium as a partially saturated bundle of parallel capillary slits with varying sizes. We assume that the fracture size distribution of the corresponding medium follows a fractal scaling law, which allows us establish a pressure head-saturation relationship based on the Laplace equation. We first describe the flow rate, the conduction current, and the electrokinetic streaming current within a single fracture. Then, we upscale these properties at the scale of an equivalent fractured media partially saturated in order to obtain the relative permeability, the electrical conductivity and the streaming potential coupling coefficient. The newly proposed model explicitly depends on pore water chemistry, interface properties, microstructural parameters of fractured media, and water saturation. Model predictions are in good agreement with both experimental and simulated data and with another model from the literature. The results of this work constitute a useful framework to estimate hydraulic properties and monitor water flow in fractured media.

Modeling the Drying Process of Porous Catalysts: Impact of the Pore Size Distribution

“…Originally developed and verified against macroporous materials, i.e., soil or wood, the volume averaged formulation has also been successfully applied for the prediction of postdrying catalyst profiles in micro- and mesoporous materials. ,, In all those cases, the transport is highly dependent on averaged properties of the porous media, e.g., saturation, permeability, and capillary pressure to name a few. Often, those are determined experimentally for a support, yet research into analytical derivations of those parameters from routinely measured bulk properties is quite active. − Those models often rely on dedicated configurations of the pore size distributions and therefore allow the derivation of the relevant parameters from the porosity and the knowledge of minimum and maximum pore size. One interesting exception to this approach is given by the derivation of the averaged properties from an available pore size distribution, which offers a variety of potential insights in the impact of local pore morphology onto the drying process …”

“…Often, those are determined experimentally for a support, yet research into analytical derivations of those parameters from routinely measured bulk properties is quite active. 18 − 22 Those models often rely on dedicated configurations of the pore size distributions and therefore allow the derivation of the relevant parameters from the porosity and the knowledge of minimum and maximum pore size. One interesting exception to this approach is given by the derivation of the averaged properties from an available pore size distribution, which offers a variety of potential insights in the impact of local pore morphology onto the drying process.…”