The Kozeny-Carman equation with a percolation threshold.

Area of Science:

• Geosciences
• Hydrogeology
• Sedimentology

Background:

• The Kozeny-Carman equation is a standard for estimating permeability (k) in porous media.
• Previous work by Koltermann and Gorelick (1995) and Esselburn et al. (2011) explored sediment properties and pore structure.
• Understanding pore occupancy is crucial for accurate permeability estimations.

Purpose of the Study:

• To develop a novel procedure for calculating permeability (k) from the Kozeny-Carman equation.
• To integrate concepts from percolation theory with existing sediment transport models.
• To assess the robustness of the Kozeny-Carman equation under varying pore occupancy conditions.

Main Methods:

• Developed a procedure linking percolation theory to the Kozeny-Carman equation.
• Focused on the proportion of coarser pores occupied by finer sediments relative to a percolation threshold (ω(c)).
• Calculated the effective grain-size term using geometric or harmonic means based on pore percolation, referencing Koltermann and Gorelick (1995) and Esselburn et al. (2011).

Main Results:

• A percolation threshold (ω(c)) was identified in physical sediment models.
• The Kozeny-Carman equation was found to be robust, providing representative permeability values.
• The method's accuracy is maintained even when the percolation threshold is not precisely known.

Conclusions:

• The developed procedure successfully calculates permeability by incorporating percolation theory.
• The Kozeny-Carman equation remains a reliable tool for permeability estimation in diverse sedimentological contexts.
• This approach enhances the understanding of pore-scale processes influencing bulk hydraulic properties.