Page 197 - Well Logging and Formation Evaluation

Homing-in Techniques 187

1. An electrode that injects a low-frequency current into the formation,
separated by an insulated bridle (typically 100–300ft long) from the
sensor package
2. A sensor package consisting of orthogonal direct current (DC) and
alternating current (AC) magnetometers. DC magnetometers are used
to establish the tool orientation with respect to HS, and AC magne-
tometers are used to measure the magnetic fields caused by current on
the target well.

The AC magnetic field measured in the sensor plane is the vector sum
of the magnetic fields from each element of current. In the case of an infi-
nite line source of current, the field measured at a sensor is given by Biot-
Savart’s law:

Ÿ
H = I [2* *p dist] [ * dist Ÿ Ÿ Tvec ] (12.2.1)
where:
H = vector of magnetic field strength, in T
I = current flowing, in amperes
dist = vector linking the sensor to the line source by shortest distance,
in m
distŸ= unit vector along dist
TvecŸ= unit vector along the line source direction.

These components are illustrated in Figure 12.2.1.
If the current on the target well were everywhere constant, modeling
would be relatively simple, and similar algorithms to those applied in the
magnetostatic methodology could be applied. Unfortunately, this is not
the case, since the current is influenced by the following factors:

1. Even in a theoretical case of isotropic media, and infinite target casing
of uniform thickness, predicting the current as a function of depth in
the target well is a complicated mathematical process involving the use
of Bessel functions and numerical integration. The field measured in
the survey well is affected not only by the sensor’s proximity to the
target, but by the injecting electrode’s proximity to the target casing,
which both vary with depth.
2. In reality the target casing is not infinite, and often one is homing in
near the shoe of a casing string, where the target current will fall to
zero (yielding no magnetic field).