Simple holistic solution to Archie's-law puzzle in porous media

Random networks are investigated as models of heterogeneous media. A general approximate structure is used where the networks are described as a system of embedded networks, and the critical behavior and averaging behavior of such networks are developed. These results are applied to a study of the electrical conductivity of porous media, with special attention to an Archie's law behavior. It appears that the wide range of crack and pore widths in rocks makes the resulting conductivity relatively insensitive to the topology of their interconnections and allows one to make reasonable predictions of rock conductivities, given the distribution of crack and pore widths. It also appears that with low porosity rocks the conductivity is controlled by the microcrack population which only accounts for a fraction of the total porosity. It would seem, therefore, that Archie's law is a feature of some general trend between porosity and crack and pore width distributions rather than a fundamental property of porous media. The law of the geometric mean is an accurate predictor of the physical properties of a mixture of different materials. This mixing law can result from an equal balance of series and parallel arrangements which can be produced by an appropriate distribution of shapes. A brief look is given to problems of anisotropic distributions for the conductivity problem and it is shown how the averaging process greatly dilutes the microscopic anisotropy in producing the macroscopic properties.

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Fractal analyses on saturation exponent in Archie's law for electrical properties of hydrate-bearing porous media

Journal of Petroleum Science and Engineering ◽

10.1016/j.petrol.2020.107642 ◽

2021 ◽

Vol 196 ◽

pp. 107642

Author(s):

Zhun Zhang ◽

Lele Liu ◽

Chengfeng Li ◽

Jianchao Cai ◽

Fulong Ning ◽

...

Keyword(s):

Porous Media ◽

Electrical Properties ◽

Archie’S Law ◽

Fractal Analyses ◽

Saturation Exponent

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Resistivity‐porosity‐particle shape relationships for marine sands

Geophysics ◽

10.1190/1.1440891 ◽

1978 ◽

Vol 43 (6) ◽

pp. 1250-1268 ◽

Cited By ~ 261

Author(s):

P. D. Jackson ◽

D. Taylor Smith ◽

P. N. Stanford

Keyword(s):

Porous Medium ◽

Porous Media ◽

Marine Sediments ◽

Particle Shape ◽

Published Data ◽

Formation Factor ◽

Archie’S Law ◽

Shaped Particle ◽

Marine Clays ◽

Error Envelope

A laboratory investigation has been made of formation factor‐porosity relationships (formation factor being the ratio of the resistivity of a porous medium to the resistivity of the pore‐fluid), using natural and artificial sand samples whose grains varied widely in both size and shape. All samples obeyed Archie’s law, [Formula: see text] (where FF is the formation factor and n is the porosity) including mixtures of two differently shaped particle types. The exponent m was dependent on the shape of the particles, increasing as they became less spherical, while variations in size and spread of sizes appeared to have little effect. The results have been combined to produce an FF/n relationship, with an error “envelope”, which may be applicable to marine sediments in general, being in agreement with published data for marine clays. It is also suggested that the exponent m may be a better measure of the “tortuosity” of porous media than the formulas quoted in the literature.

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