Page 38 - Percolation Models for Transport in Porous Media With

2.3 CONDUCTIVITY OF CAVERNOUS MEDIA 29

~ = 1. In this case, we find that z ~ 6 + 7. The probability of a channel of radius
r ~ r 1 forming between two pores is

{2.13)

By comparing (2.13) and {1.1) fort= 0, one can find the threshold value ~c of
the porosity of the medium at which percolation begins. The corresponding value
of the parameter tc can be found from the following condition

(2.14)

Using the relation (2.13), in the general approach, it is possible to find the
correlation radius of the IC formed from the channels satisfying the condition
€ ~ !t,

Consequently the concentration of parallel conducting chains, which equals
Rl-D), is defined by the following relationship

The quantity e1 characterizes the minimal size of a channel from the chain. The
distribution function of the parallel conducting chains--With respect to the param-
eter e1 is F{et) = - dn/dt 1 • Permeability of a caveroous medium is determined
from a relationship similar to (1.10)
Eo
K =I k{ti)F{ti)dtl· (2.16)
0
Here k( e1 ) is the average partial conductivity of the chain which contains chan-
nels of the minimal radius characterized by €1. Find f(et), the probability density

,,..--............ ,

/ ' '
I /
I
I

Figure 7: Intersection geometry for spherical pores