Page 184 - Percolation Models for Transport in Porous Media With

182 CHAPTER 11 GAS COLMATATION IN ELECTRIC ACTION

11.1 Temperature Effects in Capillaries Caused

by Electric Current

We shall begin with the description for the distribution of the electric current
flowing in a micro heterogeneous medium. Using the notation (3.1) already intro-
duced, write the expression for the amplitude Io of the current flowing through an
arbitrary r 1-chain
Io(rt) = Eocr'r~¢(rt) (11.1)
where the so-called heterogeneity factor of the medium is

, a >
A.( ) [ 2 -2 * ]-1
'I' r1 = r 1 < r1, r
It is clear from (11.1) that the amplitude of the current flowing through an
r1-chain depends only on the amplitude of the field intensity Eo, the electric con-
ductivity u' ofthe fluid that fills the pore space, and the heterogeneity factor ¢(rt)
of the medium.
According to the results of §1.2, the total current flowing in the medium is
determined by the expression
r.
Jo = J Io(rl) dn(rl)

Hydraulic conductivity of the r1-chain (for Poiseuille flow in capillaries) can be
found from an expression similar to (11.1)

Permeability of the medium in this case is
rc
K = J k(rt) dn(rt)
a.
It can be shown that the functions ¢(rt) and '1/J(rt) increase as the degree of
heterogeneity of the medium (the variance of f(r)) decreases.
The energy release density in an r-capillary (r1 $ r $a*) of an r1-chain is

It follows that q0 ( r, rt) goes up as r decreases and is maximal in the r 1 -capillary.
For exponential distribution functions of the form
f(r) = afri (11.3)