Page 39 - Percolation Models for Transport in Porous Media With

30 CHAPTER2. ONE-PHASE FLOW IN ROCKS

for conducting channels as a function of parameter ft. The number of channels
formed by those pores whose centers are 2Rp(1 - t:l} apart is found from for-
mula (2.12). Consequently the probability density /(t:l) = - dN0 /dt: 1 can be
found (up to a normalizing factor) from the relationship
(2.17}

Given /(t:l), it is possible to find (up to a factor of the order unity) k(t:l}, a
parameter which characterizes the conductivity of a chain composed of successive
channels
<t 1 -1
....., 7r ( /(t:) dt: )
k(t:t) = 8 j /(t:}dt: j rt{t:) (2.18}
1 <t
From (2.18), using (2.17), we can find the dependence k(t:t}. After substituting
it in (2.16) together with (2.15), we obtain the resultant expression

Here 'Y is a numerical factor of the order unity. In evaluating the integral
in (2.16), v was set to equal!. Taking account of the relationship fc = 1-(~c/~)t,
we can use (2.19) to find the dependence near the percolation threshold

2.4 Conductivity of Fractured Media

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/
/
I
I
I
I
/
/V

Figure 8: Intersection geometry for circular fractures