Page 45 - Percolation Models for Transport in Porous Media With

36 CHAPTER2. ONE-PHASE FLOW IN ROCKS

If stress is relatively small (u; < 10 Pa) formula {2.35) can be simplified
8

In this case the expression (2.36) becomes

3
£i = (Ifg ) L Bij log(l + g u;/C), g = AB. (2.37)
0
0
0
j=l
In the case of uniform comprehensive contraction, u; = u 0 and
(2.38)

Thus, using formulas (2.33) and (2.38), one can find the distribution function
of conducting channels in a medium subject to uniform contraction

0 0
f(r) = f[r + 0.5(lfg )(l- 2~tp) log{ I+ g u fC)J. (2.39)
0
By substituting this function into formulas (2.1) and (2.4), one can find the
change of the permeability and the electric conductivity of the medium. For-
mula (2.39) implies that within the framework of the model of the linear correla-
tion between r and t:n, uniform comprehensive contraction of the medium does not
change the shape of the distribution function but only causes its shift by 0.5lt:n.
The variation of the distribution function may change the parameter rc as well as
the average conductivity of the chains in the skeleton of the IC. We shall present
here the resultant expression which determines how the coefficient of permeability
of the medium depends on pressure P = u 0 (through the dependence (2.38))

1
K = 2~vr'{ -/ t<r>drr J ~ t<r>drj" ~(;1~" (2.40)

where I(rl) = {8/7r) j f(r)(r- ~}- 4dr (i f(r) dr) -l, ~ = 0.5lt:n.

r1 1
The specific electric conductivity of the medium in this case is also found from
formula (2.40}, but with

I(rt) = l- 1 l f(r)[Po(r - .l.) + Ilili(w)] dr (] f(r) dr) - 1

When contraction of the medium under the stress tensor O'i is not monoaxial,
the components of the strain tensor £i are found from the formula (2.36).