Page 194 - Percolation Models for Transport in Porous Media With

192 CHAPTER 11 GAS COLMATATION IN ELECTRIC ACTION

When
(11.42)

we have
(11.43)

Using the solution of the problem (11.41) under the condition (11.33}, it is
possible to show that after integrating in (11.41), the relationship (11.43) gets the
following form

1
1
w~ = H8.>.o(8*)A - x0 , (11.44)
>.0(8*) = 1- exp( -1/8*)- (1/8*) Ei(1/8*), 8* = t/To
Using the asymptotics for the functions (11.12), the given relation can be rep-
resented in the form of the following approximate ones

H • { 1 - (1/8*) exp( -1/8*), 8* «: 1'
8
(11.45}
w~ = Axo (1/8*)[1 + ln(8* frp) + 8* /2], 8* ~ 1
or
HXt t «: To,
wa = { AXil' (11.46)
* X
kl/} To ln[(e/rp)(t/To)], t ~To

However when t ~ a 2 (4Kt), intensive heat transfer to the skeleton of the
medium decreases, and the whole medium begins to get heat. In this case it
is possible to take
H8.
e(8.) ~ e<o) +-A (11.47)
Xo
It is evident that the upper expression in (11.46} coincides with the condition
(11.42), since both of the expressions reflect the case when the volume of the
bubbles is small compared to the volume of the surrounding water.

11.3 Permeability Change under Electric Field

It was shown in §§11.1, 11.2 that as electric current passes through a micro het-
erogeneous medium, bubbles of liquid migrate towards thin "hot" capillaries of
the medium. This is caused by the temperature gradients and the temperature
dependence of the surface tension in the liquid. In the thin capillaries, the bubbles
grow due to the inflow of the heat released by the electric current. The grow-
ing bubbles shut the capillary cross-sections; this causes the permeability and the
electric conductivity of the medium to drop.