Page 33 - Percolation Models for Transport in Porous Media With

24 CHAPTER2. ONE-PHASE FLOW IN ROCKS

forms a cubic network. The coefficient of permeability for such a system, which
simulates the pore space structure of grained media, can be calculated using the
approach discussed in §1.2. This coefficient is determined from (1.11) for the case
4
of hydraulic conductivity u = (rr/8)r :

where I(rl) = 8/rr fro;' f(r)(drfr 4 ) (fro;' f(r) dr) -l, rc is the critical radius de-
fined by an expression similar to (1.7)

00
J f(r)dr = P:. (2.1')

Note that in deducing the relationship (2.1), the tortuousity of the elements
forming the skeleton of the IC is already taken into account, since this deduction
was carried out for a space network.
Now consider electric conductivity of a grained medium when a conducting fluid
with specific electric conductivity u' is contained in the medium. We assume that
neither the grains nor the cementing substance conducts electric current. Note
that polarization effects can make significant contributions to the current flow
through a two-phase medium. Therefore the electric conductivity of the medium
is determined not only by u', but also by >..', a parameter which characterizes
"surface" electric conductivity induced by the diffuse layer of ions near the phase
interface. Detailed research on the effect of polarization on electric conductivity
of media was made by S.M. Scheinmann {1969). We shall present here only the
final results obtained using the two-phase model.
When the low-frequency current passes through two successive conducting
channels, the resistance can be described by the following formula [43],

p = II~(w) +Po, ~(w) = tanh(JiWTi)/JiWTi. (2.2)

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6K

Figure 5: Model of the pore space structure for a grained medium