Page 172 - Percolation Models for Transport in Porous Media With

10.1 CALCULATION 169

In this case the apparent resistance of the medium is
00
Ro(t) e:! j[E(r,t)S (r)t dr (10.8)
1
0
Having divided (10.2) by E(r, t) and after integrating with respect to r from
rw to oo, with regard to (10.8), we obtain

J(t) = U / Ro(t), E(r, t) = J(t)[E(r, t)S (r)t 1 {10.9)
0
After adding the initial condition

E(r, 0) =Eo {10.10)

we obtain the following from {10.9) - {10.10)
R{O) = Ro, /(0) = Io = U/Ro, (10.11)

0
E(r,O) = Io(EoS (r)t 1
The expressions {10.7)- {10.11) represent a closed system of equations for the
determination of the field intensity distribution E(r, t), if the dependence of the
specific electric conductivity on r and t is known.
To determine the change in the well production after electric treatment, we
will use the equations of steady state flow of an incompressible fluid in a porous
medium

divv = 0, {10.12)
v = -KJL-hilp {10.13)

where v is the flow velocity vector.
Under the assumption the fluid flows at a constant depth, the initial and bound-
ary conditions, have the following form

p(r, 0) =Po, p(rw, t) = Pw, p(Raq, t) =Po, {10.14)
K(r, 0) = Ko(r) e:! K(Raq, t)

Here, as in (10.1) - {10.3), the quasi-stationary nature of the process is pro-
posed, and therefore time tin (10.12) - (10.14) can be treated as a parameter. In
{10.14) Pw is the pressure of the fluid in the well, Po is the pressure at the supply
line Raq ~> rw, where the permeability K 0 does not change and is equal to its
initial value. The initial layer pressure is also equal to Po·
Since the well production