Page 156 - Percolation Models for Transport in Porous Media With

152 CHAPTER 8. CONDUCTIVITY AND ELECTRIC CURRENT

l 2r- 2 > 1), then the superimposition of the thermal fields of adjacent capillaries
and the increase of the average temperature in the medium with respect to the
increase of the temperature in the capillaries can be neglected.
Under exactly the same assumptions as those made in §8.1, expressions similar
to {8.4), {8.6) can be obtained. Taking into account that t > Tk(r), we use the
asymptotic expressions for the function A(y') and B(y') for y' > 1 again. Thus
we obtain

(8.20)

The relationship (8.20) shows that T and T' are monotone increasing functions
oft. However the temperature gradient T'(t,r) is upper bounded fort> Tk(r),
and therefore for currents with

the "gradient mechanism" of cement destruction cannot be realized. It is evident
from (8.7) and (8.20) that for
t > 9" = ')'oe- r(r)exp(p'Tc/(lT:)J, p' = C~Bo/(CoAo)
1
and 1 0 >I' the "temperature mechanism" of cement destruction prevails.
For T: Rj Tcr- 1 (strong cement), form (8.20) we find that 9" is small. But
forT: Rj Tcl- 1 (weak cement), 9'' Rj Tk exp(p'lr- 1 ) > Tk(r), and the "gradient
mechanism" of cement destruction remains the principal one.

8.4 Permeability and Electric Conductivity after
Electric Treatment

Consider the flow of the electric current through an element of the medium. Since
the expressions (8.20) are monotone increasing functions oft and monotone de-
creasing functions of r, it follows that initially the threshold values of temperature
Tc or the temperature gradient T: are assumed in the thinnest r1-capillaries of r 1-
chains at a certain instant r0(r1). This instant can be called the minimal starting
time of the irreversible changes to the permeability and the electric conductivity
of the rt-chain.
H we assume that
{8.21)