Page 159 - Percolation Models for Transport in Porous Media With

8.4 CONDUCTIVITY AND PERMEABILITY CHANGE II 155

Calculations show that fori = 1, j = 2 (heterogeneous medium) and fori =
5, j = 10 (homogeneous medium) and for the chosen characteristic values of the
parameters of the medium, only the "temperature mechanism" is possible.
Presented in fig. 56 are the curves calculated for the following sets of charac-
teristics of the process and the medium, 1- E0 , V /m, i = 5, j = 10; 2- E0 , V Jm,
i = 1, j = 2; 1' - Eo/2, V Jm, i = 5, j = 10; Z - Eo/2, V /m, i = 1, j = 2. It can
be seen from the presented results that the more homogeneous the medium (for
fixed< r >and K ) and the greater Eo, the more the relative changes of K(t) and
1
I:(t) and the steeper the initial piece of the relation K(t).
The quantities t' and t" depend most significantly on E 0 , the values of thresh-
olds Tc and T:, the average radius< r >of capillaries, through F2(r1,R,t)- on
the variance of f(r) and the fraction K of non-conducting capillaries. Usually
1
these quantities lie in the following ranges, t' from several seconds to several hours
and t" from several minutes to many years. This fact implies that for some me-
dia the maximal values of I: and K cannot be achieved during electric treatment
with small current. According to the calculations, the optimal duration of electric
treatment (when the most significant changes of I: and K occur) is a quantity
of the order (10 2 - 10 5 )t'. Here the more homogeneous the medium (for a fixed
< r > ), the greater t' and the smaller the interval between t' and t".