Page 151 - Percolation Models for Transport in Porous Media With

8.2 CONDUCTIVITY AND PERMEABILITY CHANGE I 147

Here Co and Cb depend on the form of u(t) and are of the order unity each;

"Yo R:l 1.780 is the Euler- Masceroni constant. It can be seen from (8.9} that as T
grows, T' decreases quicker than T.
Compare the energy density Wt and amplitude It of a short impulse (r < Tk},
when T'(rt) = T~ and (8.8} holds, to the energy density w2 and amplitude I2 of a
very long impulse (r2 ~ Tk}, when T(r} = Tc and (8.9} holds,

For example, for Tt = 10- 5 s, T2 = 2 s, Tk = 2.5 · 10- 4 s (for r = 10- 5 m,
Kt = 10- 7 m 2 /s and T~ R:l Tcr-t} we obtain w2/Wt R:l 5 · 10 3 , I2/ It R:l 0.16, i.e., if
the "temperature mechanism" is realized, it is possible to decrease the amplitude of
the impulse a little (by a factor of 5 to 10}. At the same time, energy consumption
grows by thousands of times, and the duration of impulse has to be increased by
hundreds of thousands of times. Thus impulse current with short impulses and
a large amplitude, for which the "gradient" mechanism of cement destruction is
realized, is the most effective one.
The dependence of the threshold value of the current amplitude Ic on the
capillary radius r for a fixed duration T of impulse can be determined from formulas
(8.4} - (8.6}

(8.10}

8.2 Permeability and Electric Conductivity un-
der Impulse Current

Consider impulse current passing through an element of the medium. Current
flows both along "parallel" rt-chains of the "skeleton of the infinite cluster" and
along bridges that connect the rt-chains. However the current flowing along rt-
chains can be calculated as though there are no bridges, since the allowances to
the presence of these bridges, and consequently, the possible rearrangement of the
current flow in rt-chains, are insignificant according to the results of §1.2.
Let the fraction of capillaries filled with cement be equal to K = 1 - K. Fur-
1
thermore let all these capillaries be thin, i.e., K =< a*, 1, rz >, where rz is the
1
radius of the thickest capillary filled with cement.
All chains with a*$ r $ rz do not conduct. We will further mark the quantities
relating to the fluid with index 1, and those relating to the cement, with index
2. Using the expressions (3.1}, (8.1} for amplitude I 0(rt) of the current flowing