The Kozeny-Carman equation with a percolation threshold

A procedure has been developed for calculating permeability (k) from the Kozeny-Carman equation, a procedure that links ideas from percolation theory with the ideas of Koltermann and Gorelick (1995) and Esselburn et al. (2011). The approach focuses on the proportion of coarser pores that are occupied by finer sediments relative to a percolation threshold proportion (ω(c)). If the proportion occupied is below ω(c), then the unoccupied coarser pores percolate. Otherwise they do not percolate. Following the ideas of Koltermann and Gorelick (1995), the effective grain-size term in the Kozeny-Carman equation is calculated using the geometric mean if the unoccupied coarse pores percolate, and using the harmonic mean if otherwise. Following ideas of Esselburn et al. (2011), this approach is implemented by evaluating the potential for grains in each size category to occupy pores among sediment of each larger-size category. Application of these ideas to physical sediment models for sands and gravels, which have known k, indicates that a threshold does indeed exist. Results also suggest that the Kozeny-Carman equation is robust and gives representative values for k, even though ω(c) is not precisely known.