Page 35 - Percolation Models for Transport in Porous Media With
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26 CHAPTER2. ONE-PHASE FLOW IN ROCKS
complexity of the electric current flow problem in a two-phase media, no solution
for other geometries of channels is available at present. Therefore it is suggested
in determining the electric conductivity of a grained medium that parameters of
cylindrical channels be chosen correspondingly. Any channel connecting pores in
a grained medium can be represented as two cylindrical channels of equal lengths
h = l2 = l/2 but of different effective radii. After setting the radius of the thin
channel to equal r and the radius of the thick one to be of the same order of
magnitude as the radius l/2 of the grain and using (2.3), we find the expression
for Po in the explicit form
(2.6)
In (2.6), the relationship 4A' /((T'l) ~ 1 was taken into account. When radii
of channels are large enough (2A' /(u'r) ~ 1), the surface conductivity may be
neglected and the formula (2.6) reduces to
1
2
Po= -,l[1 + (l/r) ].
1fU
2.2 "Permeability- Porosity" Correlation
Since the distribution function of conducting channels with respect to intrinsic
conductivities is not always known, finding the correlation between the coefficient
of permeability and the porosity of a medium is of a certain practical interest. In
this approach, it is certainly impossible to take account of the effects caused by
differences in intrinsic conductivities of the channels in a grained medium. However
for those grained media, whose permeability is determined primarily by a group
of capillaries with approximately equal intrinsic conductivities, such a method is
justified. Therefore we shall draw our attention to the model of a grained medium
discussed in §2.1 (see fig. 5).
Let !l>o be the porosity of the model structure in question (further called struc-
tural porosity of the medium). Structural porosity is related to the coefficient of
charge as follows, f = 1 - !l>0 • Suppose that some of the sites are trapped with
impermeable substance, and thus the porosity of the medium is 
