Page 155 - Percolation Models for Transport in Porous Media With

8.3 THRESHOLD VALUES. ELECTRIC ACTION 151

typical value of the destruction strength for the cementing substance, u is the
electric conductivity of the fluid, k is the coefficient characterizing the pore space
structure of the medium.
In both cases the permeability and the electric conductivity reach saturation
values for large t (we shall denote the limiting values by K' and E', respectively).
These values are less than the permeability K" and the electric conductivity E" of
the corresponding media without cement in thin capillaries (~t' = 0). The greater
the quantity E~r, which is proportional to the energy of a single impulse, and
the less r, the closer K' and E' to K" and E". If ~t' < 0.15, then K and E
stop changing soon and no significant growth of these quantities is observed. If
~t' > 0.15, then the permeability can grow by ten and more times and the electric
conductivity, by several dozens per cent.
In fig.55, b, the In Eo dependencies (for ~t' = 0.6) are presented for a fixed value
of the energy in the impulse w0 = 10 5 V 2 s/m 2 (curves 1, 2) and for w0 = 1.2 ·10' 4
V 2 s/m 2 (curves 1', 2'). The presented plots show that the most significant changes
of K and K' occur for small T and large Eo. As the medium becomes more
homogeneous these changes become more apparent. The more homogeneous the
medium, the less E. ( T) and the wider the range

E.(r) + E*(r)

8.3 Determination of Threshold Values for Elec-
tric Treatment

It was shown in §8.1 that impulse electric treatment, i.e., electric treatment by
currents with large amplitudes (and consequently with large Eo) is most effective.
However its realization requires special equipment, and therefore the case of electric
treatment by currents with small amplitudes (and consequently with small Eo) is
more interesting for common practice. This case, however, causes substantial
increase to the duration of electric treatment.
Take periodic current. To be able to disregard electro-kinetic phenomena,
suppose that the average field intensity for a period vanishes, and the period is no
greater than 0.1 second.
If the contribution made by the high-frequency harmonics (those with fre-
quencies greater than 100 kHz) to u(t) is small, then the effects of the reactive
components of the electric conductivity of the medium can be neglected. In this
case the current in any capillary can be given in the form I(r) = Iou(t).
Since, as it was mentioned above, the characteristic heat exchange periods for
a capillary are much less than those for the grains, and the heat capacity of a grain
is much greater than the beat capacity of a capillary (their ratio is of the order