STANDARD HANDBOOK OF PETROLEUM & NATURAL GAS ...

906 Drilling and Well Completions
If the acceleration is variable, as in sinusoidal movement, piezoelectric systems
are ideal. In case of a constant acceleration, and hence a force that is also
constant, strain gages may be employed. For petroleum applications in boreholes,
however, it is better to use servo-controlled accelerometers. Reverse pendular
accelerometers and “single-axis” accelerometers are available.
Figure 4-2 19 shows the schematic diagram of a servo-controlled inverted pendular
dual-axis accelerometer. A pendulum mounted on a flexible suspension can oscillate
in the direction of the arrows. Its position is identified by two detectors acting
on feedback windings used to keep the pendulum in the median position. The
current required to achieve this is proportional to the force max, and hence to ax.
This system can operate simultaneously along two axes, such as x and y, if
another set of detectors and feedback windings is mounted in the plane perpendicular
to xOp, such as yoz. The corresponding accelerometer is called a twoaxis
accelerometer.
Figure 4-220 shows the schematic diagram of a servo-controlled single-axis
accelerometer. The pendulum is a disk kept in position as in the case of the reverse
pendulum. Extremely efficient accelerometers can be built according to this principle
in a very limited space. The Sunstrand accelerometer is seen in Figure 4-221.
Every accelerometer has a response curve of the type shown schematically in
Figure 4-222. Instead of having an ideal linear response, a nonlinear response
is generally obtained with a “skewed” acceleration for zero current, a scale factor
error and a nonlinearity error. In addition, the skew and the errors vary with
temperature. If the skew and all the errors are small or compensated in the
accelerometer’s electronic circuits, the signal read is an ideal response and can
be used directly to calculate the borehole inclination. If not, “modeling” must
be resorted to, i.e., making a correction with a computer, generally placed at
the surface, to find the ideal response. This correction takes account of the skew,
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Figure 4-219. Sketch of principle of a servo-controlled inverted pendular
dual-axis accelerometer.