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Updated: Jul 4, 2026
08:23
Finite Element Modelling of a Cellular Electric Microenvironment
Published on: May 18, 2021
Nonuniversal conductivity exponents in continuum percolating Gaussian fractures.
F Flukiger1, F Plouraboué, M Prat
1Institut de Mécanique des Fluides de Toulouse, U.M.R. C.N.R.S.-INP/UPS, N5502 Avenue du Professeur Camille Soula 31400 Toulouse, France.
Summary
This study investigates electrical and hydraulic conductivity in Gaussian fractures, revealing nonuniversal percolation exponents that deviate from theoretical predictions for infinite systems. Finite size corrections are crucial for understanding these conductivity behaviors.
Area of Science:
- Physics
- Geophysics
- Complex Systems
Background:
- Percolation theory is essential for understanding fluid flow and conductivity in fractured media.
- Gaussian fractures present complex geometries that challenge standard theoretical models.
- Previous studies often assume infinite systems, neglecting finite size effects.
Purpose of the Study:
- To determine the electrical and hydraulic conductivity percolation exponents in a Gaussian fracture.
- To investigate the influence of finite size corrections on these exponents.
- To analyze the conductivity distribution near the percolation threshold.
Main Methods:
- Utilized the method proposed by Plouraboué [Phys. Rev. E 73, 036305 (2006)].
- Analyzed conductivity percolation in a simulated Gaussian fracture model.
- Examined probability density functions of local conductivities.
Main Results:
- Observed nonuniversal conductivity percolation exponents, differing from infinite system predictions.
- Demonstrated the significant impact of finite size corrections on conductivity exponents.
- Found that conductivity probability density functions follow a power-law distribution near the percolation threshold in the hydraulic case.
Conclusions:
- Standard theoretical predictions for infinite systems are insufficient for Gaussian fractures.
- Finite size effects are critical for accurate modeling of conductivity in such systems.
- Power-law distributions characterize conductivity near the percolation threshold, particularly for hydraulic flow.
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