Page 175 - Percolation Models for Transport in Porous Media With

172 CHAPTER 10 PRODUCTION CHANGE: ELECTRIC ACTION

cylindrically (flow at the depth H) or spherically symmetric.
For steady state flow, the temperatures of the fluid and the skeleton are locally
equal. Estimates show that in the critical zone, the effect of heat conductance is
negligible compared to the convective heat transfer for actual wells and actual con-
ditions of the recovery. In this case the stationary heat equation has the following
form
(10.19)
Here Cf, p 1, and Pe are the specific heat and the density of the fluid and the specific
electric resistance of the medium, respectively. Furthermore

Q r I
v(r) =- SO(r) ;• j(r) = SO(r) (10.20)

where
So(r) = { 2trrH, ~ = 1, (10.21)
4trr 2 , t = 2
In this section, the case of cylindrical symmetry is denoted by index i = 1 and
the case of spherical symmetry, by index i = 2.
After substituting (10.20), (10.21) into (10.19), taking into account the fact
that VT = oTfor(rfr), and integrating with respect to r from r to Raq, we
obtain the radius distribution of temperature
ln(Ra!Lir) i = 1,
PeT2 { 21TB '
T(r) -T(Raq) = --Q ( ) (10.22)
PfCf 1 1 1 i=2
41r r - R;;;; '

The rate of the joule heat release in the medium is

i = 1,
(10.23)
i=2
If the temperature dependence of the permeability of a micro volume

K = K(T) (10.24)

is known, then using (10.22), we obtain
K = K(r)

The well production rate before the electric treatment is determined from
(10.16), if we set K = Ko = const, r = Raq

2trH/ ln(Raq/rw), i = 1,
_Po- Pw R'
Q o- o { (10.25}
f..t 4tr/(r;;/-R;;q 1 ), i=2