Page 197 - Percolation Models for Transport in Porous Media With

11.3 MODIFICATION OF PERMEABILITY 195

resumes to conduct current. Consequently the fluid gets heated again, then the
bubbles grow, and the capillary is shut off. Thus, as electric current passes through
the medium, colmatation effects are cyclic. This is also confirmed by experimental
studies of cores saturated with a conducting leaching solution. The results of these
studies will be discussed in detail below.
According to the upper expression in {11.54), when the losses due to the heating
of the skeleton of the medium are not too intensive (for instance, in micro grained
media) and the liquid contains a good deal of gas (i.e., when the density of the
bubble germs n. is large), merging of the vapor bubbles in the thin capillaries
dominates in the colmatation of the medium. Furthermore colmatation will take
place almost at the same time in all r 1-chains of the rock. This must have a
visual impression of abrupt termination of the fluid flow in the rock. As for the
time dependencies ofthe permeability and the electric current flowing through
the medium, they must have a typical form of the percolation relations near the
percolation threshold

K(t) ~ K{O){l- tftp)a',
I(t) ~ J{O){l - t/tp)P•,
tp =<a*, t(rl), Tc >

where the exponents at and f3t must be of the order of unity {less than one).
If the density of the bubble germs is relatively small, then the merging of the
bubbles and their independent growth may rival in some chains. When the heat
exchange between the liquid and the skeleton takes place (this happens when the
specific heat of the rock is large, as in fractured media), colmatation can be long-
lasting. It is also possible in this case that a complete colmatation of the medium
is not achieved.
We shall now compare the obtained results to those of an experimental study
of electric treatment of a sandy-argillaceous medium saturated with a leaching
solution. The parameters of the medium, the liquid, and the electric treatment are
to be set to equal those in the experiment, i.e., the specific electric conductivity of
the fluid, 0' = 1.7 n- 1 m- 1 ; the characteristic size of a pore and a grain, I= 2·10- 4
1
m; the cross-section of the experimental tubes (see §9.2), S 0 = 9 · 10- 4 m 2 ; the
number of conducting channels, in order of magnitude, No ~ S 0 /1 2 = 2.3 ·10 4 ; the
average capillary radius, r ~ 8 · to- 5 m; the amplitude of the alternating electric
field intensity, Eo = 180 V Jm; the energy input density, qp !:'::! 5.5 · 10 watt per
4
m 3 • Typical values of bubble radii and densities at NTP (p = 0.1 MPa, To = 293
K {20° C), T& = 373 K {100° C)) are a0 =10- 6 m, n. ~ 10 13 m- 3 •
It follows from {11.15) and {11.17) for the parameters specified and for the vis-
cosity J.t = 10- 3 Pa· s, that the time for establishing of a steady state movement,
Ty "' 10- 7 seconds, is much less than the characteristic time of movement for a