Formation Evaluation Through Casing - Cased-Hole Log Analysis and Reservoir Performance Monitoring - page 144

Time Constants

All radioactive processes are subject to statistical variations. For example, if a
source of gamma rays emits an average of 100 gamma rays each second over a
period of hours, the source will emit 360,000 gamma rays per hour
(100/s × 60 s × 60 min). However, if the count is measured for 1 s, the actual count
might be less than 100 or more than 100. Thus, a choice must be made. Gamma rays
can be counted for a very short interval of time, resulting in a poor estimate of the
real count rate; or the gamma rays can be counted for a long time, resulting in a
more accurate estimate of the count rate at the expense of an inordinately long time
period. In order to average out the statistical variations, various time constants may
be selected according to the radioactivity level measured. The lower the count rate,
the longer the time constant required for adequate averaging of the variations.
In the logging environment, gamma rays can be counted for a short period of
time (e.g., 1 s) with the recognition that during that time period, the detector will
have moved past the formation whose activity is being measured. Thus, the logging
speed and the time interval used to average count rates are interrelated. The follow-
ing rules of thumb are generally recognized:

Logging speed (ft/h) Time constant (s)

3,600 1

1,800 2

1,200 3

900 4

At very slow logging speeds (900 ft/h = 1.5 ft/s) and long time constants, a more
accurate measurement of absolute activity is obtained at the expense of good bed reso-
lution. At high logging speeds and short time constants, somewhat better bed resolu-
tion is obtained at the expense of absolute accuracy. At some future time, when the
efficiency of gamma ray detectors and their associated electronics improve by one or
two orders of magnitude, the use of a time constant will be obsolete except in the cases
of very very inactive formations with intrinsically low gamma ray count rates.
To illustrate this interdependence of logging speed and time constant, Fig. 11.7
shows the same formation logged at two different speeds. On the first run, the log-
ging speed was 80 ft/min and the time constant 1 s. On the second run, the speed
was 30 ft/min and the time constant was 2 s. Note the differences in both statistics
and bed resolution between the two runs.