Introduction to Electrokinetics - Electrokinetics for Petroleum and Environmental Engineers - page 21

The total amount of current transmitted (I) for various electrode arrange-
ment can be estimated (Rudenberg, 1945; Casagrande, 1949) by using equa-
tions such as those presented below:

a. For two cylindrical electrodes of equal length and cross-sec-
tional area, the required electrical current is equal to:

LE
d
r

2 p

(1.13) I =

r ln

where ρ is the formation resistivity in ohm-meters; L and r are
the length and radius of the electrode in meters, E is the imposed
electrical potential in volts; and d is the distance between the
anode and the cathode in meters.
b. For two cylindrical electrodes with different radii:

⎛ ⎞

⎜
⎜
⎜

⎟
⎟
⎟

p
r

LE 1 1

(1.14)

I = +

d
r

d
r

ln ln

⎝ ⎠

1

2

c. For a row of alternate anodes and cathodes, the amount of
electrical current can be given approximately by:

⎛ ⎞

⎜
⎜
⎜

⎟
⎟
⎟

NLE p

r

1 1

(1.15) I = +

d
r

d
r

ln ln

⎝ ⎠ 1 2

where N is the number of electrodes in each group.
Before one can proceed with estimating the consumption of power,
some assumptions have to be made. The following estimation of the benefit
of current application is very difficult because of the decrease in the cur-
rent flow as a result of increasing overall resistance. On assuming that (1)
the electrical current is available at the electrode; (2) the formation resis-
tivity is constant and is equal to 10 ohm-meters; (3) the electrode length
and radius are equal to three and 0.1 meters, respectively; (4) the applied
potential is equal to 100 volts, and (5) the distance between electrodes is