Hydraulic conductivity of variably saturated porous media: Film and corner flow in angular pore space

SUMMARY While the frequency-dependence of permeability under fully saturated conditions has been studied for decades, the corresponding characteristics of partially saturated porous media remain unexplored. Notably, it is not clear whether the use of effective pore fluid approaches under such conditions is valid. To address this issue, we propose a method that allows us to obtain dynamic permeability functions for partially saturated porous media. To this end, we conceptualize the considered pore space as a bundle of capillary tubes of different radii saturated by two immiscible fluid phases. We then solve the Navier–Stokes equations within the pore space and define a capillary pressure–saturation relationship, which permits to obtain saturation- and frequency-dependent effective permeability estimates. The application of this method to a realistic model of an unconsolidated granular sediment demonstrates that dynamic effective permeability functions for wetting and non-wetting fluid phases exhibit distinct characteristics, thus rendering effective pore fluid approaches inadequate. Finally, we explore the capability of the seminal dynamic permeability model developed by Johnson et al.[J. Fluid Mech. 176, 379 (1987)] to account for the effects of partial saturation. We find that the frequency scaling proposed by Johnson et al. prevails in partially saturated scenarios. However, the parameters associated with this model need to be redefined to account for saturation-dependent effects.

Download Full-text

Numerical estimation of electrical conductivity in saturated porous media with a 2-D lattice gas

Geophysics ◽

10.1190/1.1444775 ◽

2000 ◽

Vol 65 (3) ◽

pp. 766-772 ◽

Cited By ~ 28

Author(s):

Michel Küntz ◽

Jean Claude Mareschal ◽

Paul Lavallée

Keyword(s):

Electrical Conductivity ◽

Porous Media ◽

Power Law ◽

Lattice Gas ◽

Effective Conductivity ◽

Pore Space ◽

Solid Matrix ◽

Conductivity Ratio ◽

Saturated Porous Media ◽

Formation Factor

A 2-D lattice gas is used to calculate the effective electrical conductivity of saturated porous media as a function of porosity and conductivity ratio [Formula: see text] between the pore‐filling fluid and the solid matrix for various microscopic structures of the pore space. The way the solid phase is introduced allows the porosity ϕ to take any value between 0 and 1 and the geometry of the pore structure to be as complex as desired. The results are presented in terms of the formation factor [Formula: see text], with [Formula: see text] the effective conductivity of the saturated rock and [Formula: see text] the conductivity of the fluid. It is shown that the formation factor F as a function of the porosity ϕ follows a power law [Formula: see text], equivalent to the empirical Archie’s law. The exponent m varies with the microgeometry of the pore space and could therefore reflect the microstructure at the macroscopic scale. The prefactor a of the power law, however, is close to 1 regardless of the microstructure. For a given microgeometry of the pore space, the variation of the residual electrical conductivity of the solid matrix induced by a finite conductivity ratio [Formula: see text] does not significantly influence the variation of the effective conductivity of the fluid‐solid binary mixture unless the porosity is low.

Download Full-text

Experimental study of the effect of nanoscale zero-valent iron injected on the permeability of saturated porous media

Water Science & Technology Water Supply ◽

10.2166/ws.2021.384 ◽

2021 ◽

Author(s):

Jie Tang ◽

Fei Liu ◽

Chong Zhang ◽

Qiang Xue

Keyword(s):

Porous Media ◽

Hydraulic Conductivity ◽

Zero Valent Iron ◽

Source Zone ◽

Distribution Area ◽

Saturated Porous Media ◽

Loss Mechanism ◽

Injection Point ◽

Nanoscale Zero Valent Iron ◽

Constant Head

Abstract In comparison of modified nanoscale zero-valent iron (NZVI), bare NZVI used to remediate deep contaminated groundwater source areas has more advantages. However, the influences of injected bare NZVI deposition on the permeability of aquifer remain unclear, which are still the key factors of engineering cost and contamination removal. Hence, this study sought to assess method of measuring hydraulic conductivity with constant head device and examine the permeability loss mechanism of NZVI injected into different saturated porous media, using column tests. The results showed that it was feasible to determine hydraulic conductivity by the constant head device. The permeability loss caused by NZVI injection increased with a decrease in grain size of porous media, and was determined by the amount and distribution of NZVI deposition. NZVI distribution area had a good linear correlation with dispersivity of the porous media. Additionally, although surface clogging occurred in all porous media, the amount of NZVI deposition at the injection point in fine sand was largest, so that its permeability loss was the most, which was more likely to cause hydraulic fracturing and then expand the area of contaminant source zone. These results have implications for NZVI field injection to successful groundwater remediation.

Download Full-text