Length scales relating the fluid permeability and electrical conductivity in random two-dimensional model porous media
- 1 September 1992
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 46 (10), 6080-6090
- https://doi.org/10.1103/physrevb.46.6080
Abstract
We present results of a study testing proposed length scales l relating the bulk electrical conductivity σ of a fluid-saturated porous medium to its permeability k, via the relation k∝σ/, where is the fluid conductivity. For a class of two-dimensional model random porous media, we compute σ, k, and the following three length scales: h, the ratio of pore volume to pore surface area; Λ, as defined by electrical-conductivity measurements; and , as defined by a nonwetting-fluid-injection experiment. Over a range of two and half decades in k, we find that both Λ and are reasonably good predictors of k, whereas h clearly fails. We also examine differences between the electric fields and the fluid-flow fields for a given pore structure by comparing their respective two-point correlation functions. The length scale Λ is analytically related to an electric-field correlation length, and is found, to a good approximation, to be proportional to a fluid-velocity correlation length. The results of this paper demonstrate the important effect that spatial randomness in the pore space has on flow problems. In a random pore structure, with a distribution of pore sizes, the flow will tend to go more through the largest pore necks, decreasing the importance of the narrowest necks that tend to dominate the behavior of periodic models.
Keywords
This publication has 20 references indexed in Scilit:
- Fluid permeability in porous media: Comparison of electrical estimates with hydrodynamical calculationsPhysical Review B, 1992
- Rigorous link between fluid permeability, electrical conductivity, and relaxation times for transport in porous mediaPhysics of Fluids A: Fluid Dynamics, 1991
- Flow, conduction, and a characteristic length in periodic bicontinuous porous mediaPhysical Review A, 1991
- Relationship between permeability and diffusion-controlled trapping constant of porous mediaPhysical Review Letters, 1990
- Permeability versus conductivity for porous media with wide distribution of pore sizesPhysical Review B, 1989
- Characteristic pore sizes and transport in porous mediaPhysical Review B, 1987
- Prediction of rock electrical conductivity from mercury injection measurementsJournal of Geophysical Research, 1987
- The microgeometry and transport properties of sedimentary rockAdvances in Physics, 1987
- Quantitative prediction of permeability in porous rockPhysical Review B, 1986
- New Pore-Size Parameter Characterizing Transport in Porous MediaPhysical Review Letters, 1986