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

Küntz, Michel; Mareschal, Jean‐Claude; Lavallée, Paul

doi:10.1190/1.1444775

Cited by 42 publications

(28 citation statements)

References 29 publications

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“…De La Rue and Tobias [44] measured the conductivity for glass spheres and sand in a zinc bromide suspension and found that Archie's law gave a good fit with (correlation coefficient squared ), while Archie [42] found for clean sands. Similar results were found in additional numerical and experimental studies [45], [46]. Jackson et al [47] found that depends on the grain shape, with for spheres, for shell fragments, and for marine sands.…”

Section: Sensor Calibration and Measurement Characteristicssupporting

confidence: 80%

A Conductivity Concentration Profiler for Sheet Flow Sediment Transport

Lanckriet

Puleo

Waite

2013

IEEE J. Oceanic Eng.

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A new sensor for measuring sediment concentration under sheet flow conditions is presented. Electrical conductivity, measured using a four-electrode method, is used as a proxy for sediment concentration. The relationship between conductivity and sediment concentration was calibrated using known masses of neutrally suspended sediment in a heavy liquid and agrees well with existing linear and power-law relationships . A 29-point conductivity profile at 1-mm resolution is generated by multiplexing through a vertical array of 32 plate electrodes. Numerical simulations of the voltage field around the sensor indicate that the horizontal extent of measurement volume is 1.5 times the sensor width. The finite extent of the measurement volume leads to smoothing of the vertical concentration profile. The sensor resolves sheet flow layers with a thickness greater than 3.5 mm, and a correction formula is introduced to correct the measured sheet thickness for the smoothing effect. Initial field results in the swash zone of a natural beach quantify sheet flow processes with unprecedented detail. Short-lived sheet flow with a maximum thickness of 19 mm was observed during the uprush, and a longer duration sheet flow with a maximum thickness of 8 mm was observed during the backwash.

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Section: Sensor Calibration and Measurement Characteristicssupporting

confidence: 80%

A Conductivity Concentration Profiler for Sheet Flow Sediment Transport

Lanckriet

Puleo

Waite

2013

IEEE J. Oceanic Eng.

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“…While this dependence is opposite prediction, it may be possible to reconcile prediction and simulations. In Figure 5 in Kuentz et al [2000] the porosity dependences of the various systems all appear parallel at low porosities. The ordinate covers more than an order of magnitude of porosity.…”

Section: Approximate Derivation Of Archie's Lawmentioning

confidence: 89%

Continuum percolation theory and Archie's law

Hunt¹

2004

Geophysical Research Letters

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[1] Results for the unsaturated hydraulic conductivity, K, are adapted to generate the electrical conductivity, s, as a function of moisture content, q. The result for s, evaluated q = f, (f the porosity), yields s / f m , known as Archie's Law. This result is based on the fact that s must vanish as the critical moisture content for percolation, q t , is approached, and on the apparent proportionality of q t to f, at least in coarser porous media (with insignificant clay content). In three dimensions the power is expected to be 1.88, but in two dimensions, approximately 1.35. The former result is compatible with data summarized in Thompson et al., giving m = 1.86 ± 0.19, while the latter appears compatible with two-dimensional simulations by Kuentz et al., who found m = 1.28 ± 0.07. The same analysis demonstrates that K cannot be written as a power of the porosity.

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“…Consider, first, computer simulations of Kuentz et al (). They obtained, for six distinct 2‐D porous media, m = 1.28±.07 for the Archie exponent, consistent with the 2‐D value, μ = 1.3, for the percolation conductivity exponent.…”

Section: Porosity‐dependent Scalingmentioning

confidence: 99%

Flow, Transport, and Reaction in Porous Media: Percolation Scaling, Critical‐Path Analysis, and Effective Medium Approximation

Hunt

Sahimi

2017

Reviews of Geophysics

132

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We describe the most important developments in the application of three theoretical tools to modeling of the morphology of porous media and flow and transport processes in them. One tool is percolation theory. Although it was over 40 years ago that the possibility of using percolation theory to describe flow and transport processes in porous media was first raised, new models and concepts, as well as new variants of the original percolation model are still being developed for various applications to flow phenomena in porous media. The other two approaches, closely related to percolation theory, are the critical‐path analysis, which is applicable when porous media are highly heterogeneous, and the effective medium approximation—poor man's percolation—that provide a simple and, under certain conditions, quantitatively correct description of transport in porous media in which percolation‐type disorder is relevant. Applications to topics in geosciences include predictions of the hydraulic conductivity and air permeability, solute and gas diffusion that are particularly important in ecohydrological applications and land‐surface interactions, and multiphase flow in porous media, as well as non‐Gaussian solute transport, and flow morphologies associated with imbibition into unsaturated fractures. We describe new applications of percolation theory of solute transport to chemical weathering and soil formation, geomorphology, and elemental cycling through the terrestrial Earth surface. Wherever quantitatively accurate predictions of such quantities are relevant, so are the techniques presented here. Whenever possible, the theoretical predictions are compared with the relevant experimental data. In practically all the cases, the agreement between the theoretical predictions and the data is excellent. Also discussed are possible future directions in the application of such concepts to many other phenomena in geosciences.

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

Cited by 42 publications

References 29 publications

A Conductivity Concentration Profiler for Sheet Flow Sediment Transport

A Conductivity Concentration Profiler for Sheet Flow Sediment Transport

Continuum percolation theory and Archie's law

Flow, Transport, and Reaction in Porous Media: Percolation Scaling, Critical‐Path Analysis, and Effective Medium Approximation

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