Page 173 - Percolation Models for Transport in Porous Media With

170 CHAPTER 10 PRODUCTION CHANGE: ELECTRIC ACTION

it can be easily shown that its growth with respect to the initial production is
determined by the relationship
Raq IRaq
dr dr
Q(t)/Qo = I K 0 (r)S0 (r) I K(r, t)S0 (r) (10.15)
rw rw
The absolute value of well production is determined by the expression

R,.o
Po- Pw / dr {10.16)
Q(t) = J.L I K(r, t)S0(r)
rw
which also allows to establish the production rate of an initially non-conducting
well (K(rw, 0} = K(rw} = 0, Qo(O) = 0).
To determine the threshold voltage on the power electrodes during the electric
treatment with impulse current (with duration of impulse r), it is necessary to set
t = 0, r = rw E = E'(r} in (10.8), {10.9}.
Thus we obtain

In the special case of
E(r, 0} =Eo= const

we have
(10.17)

Since Ht » Hw » rw, the expression (10.17) can be simplified some more:

U'(r) ~ E'(r)rw ln(Hw/rw) (10.18)

In the case of electric treatment with alternating current the starting point
t'(Eo) for the irreversible changes of permeability in the critical zone of the well
can be found by substituting the value of field intensity E(rw) in the well into
(8.26} and by using the calculated curve depicted in fig. 56.
According to the results of chapter 8, the field intensity distribution (10.9}
allows to find the change in the electric conductivity as a function of the distance
from the well at any instant that follows (see fig. 56}. The latter, in its turn,
permits to calculate the new resistance of the medium using {10.8} and the change
of the well production using (10.15}. Then the procedure is to be repeated. The
outlined algorithm for the determination of the field intensity distribution as a
function of time and the corresponding changes of the electric conductivity and
the permeability distributions, as well as the time dependencies of the current and
the production rate, was realized on a computer.