WELLOG THE POWER of TWO
Computers use
a binary number system. Binary numbers are based on powers of two.
BINARY NUMBER
SYSTEM:
Each digit
from right to left represents an increasing value based on increasing powers of
two.
1
= 2 to the zero power = 1
10
= 2 to the first power = 2
100 = 2 to the second power = 4
1000 = 2 to
the third power = 8
1001 = 8 + 1
= 9
View a
listing of 8
bit binary numbers and their related voltages from 0 to 5.0 volts.
2 ^{11}
2^{0}


For example,
the 12 bit binary number 1111 1011 0110 is composed of
1 x 2^{11} =
2048
1 x 2^{10} =
1024
1 x 2^{9}
= 512
1 x 2^{8}
= 256
1 x 2^{7}
= 128
0 x 2^{6}
=
0
1 x 2^{5}
= 32
1 x 2^{4}
= 16
0 x 2^{3}
=
0
1 x 2^{2}
=
4
1 x 2^{1}
=
2
0 x 2^{0}
=
0
total
= 4022 in the
decimal number system.
12 BIT BINARY
NUMBERS:
A binary
number having 12 bits has the ability to represent any decimal value from 0 to
4095.
In a computer
using a 12 bit data acquisition system, a voltage of 5.0 volts is divided into
4096 parts.
The value of
each binary increase (step) from 0 to 4095 represents 5v/4096 = .00122 volts or
1.22 millivolts.
View a
listing of 12
bit binary numbers and their related voltages from 0 to 5.0 volts.
WELL LOGGING
TOOL EXAMPLE:
A common tool
used in Well Logging is a caliper tool. A caliper tool may be used to measure
the diameter of a well and be calibrated to measure 6 to 10 inches. If 10
inches is represented by 10 volts, and each binary step from 0 to 10 inches is
represented by a binary step from 0 to 4095, then each step represents .0024
inches.
Again, using
the example above, 4022, 9.819335 volts = 9.819335 inches.
RESOLUTION
versus ACCURACY:
What if the
caliper tool above is calibrated to 1 percent accuracy? One percent accuracy
represents .1 volts or .1 inches. The 12 bit acquisition system having 4095
steps divided into one percent, represents 40.95 steps
per one percent!
ENOUGH
RESOLUTION?
A 12 bit
acquisition system can provide more than 40 times better resolution than the 1
percent accuracy of the caliper tool used in our example! If the resolution of
the tool exceeds the accuracy it is good enough!
A 10 bit
acquisition system provides 1024 steps. That means a 10 bit acquisition system
can resolve logging measurements to one part in 1024 or .0097 inches or volts
in the caliper example. That’s more than 10 times better resolution than the 1
percent accuracy of the tool! In this case, 10 bit resolution is good enough.
ADDITIONAL
BITS:
A 16 bit
acquisition system defines a measurement using 16 binary bits. This
system has the ability to divide a given measurement into 65,536 parts.
One part in 65,536 equals .000015 of the total. A 10 volt signal would have its
least significant bit representing 150 microvolts. Using the 10 inch caliper
measurement above, this equates to 150 microinches! Most caliper tools
have mechanical “play” or backlash in gears and pivot points that cause .25
inches of inaccuracy in the system. If, in fact one wishes to measure to a
reasonable accuracy of .1 inches then an 8 bit acquisition system is
satisfactory. It will resolve the caliper measurement to less than .05 inches.
OTHER
CONSIDERATIONS:
Noise floor:
Logging
systems have something called a noise floor. The noise floor is a low voltage
noise level below which the logging signal is embedded in noise. Noise
can originate from mechanical, thermal and other sources found in circuit
design. Noise is inherent in any logging system no matter how well it has
been designed. A given measurement having a span of 0 to 10 volts may have a
noise floor at 2 millivolts. This means that measurements below 2 millivolts
are below the noise floor and represent system noise. Acquisition of “data”
below the noise floor has no value. A 12 bit system will resolve signals down
to the noise floor. A 16 bit system resolves signals embedded in noise. The
additional four bits would offer no data of any value and are usually truncated
or cut off.
Presentation:
Typical
presentation of log data in API log format uses a maximum 5 inch span (two
tracks). Most presentation of log data is done in 150 dot
per inch (DPI) print format. If we calculate the number of possible dot
positions – it crunches out to 150 x 5 = 750 dot
positions. A 10 bit acquisition system gives 1024 possible levels and is
actually better than the limits of presentation. In summary, a 10 bit or 12 bit
acquisition system will suffice for presentation purposes. The extreme plotting
format of 2400 DPI (photo) when plotted over 5 inches allows 12000 dot
positions. This format will present the 1024 steps of 10 bit and 4096 steps of
12 bit data. Systems having 16 bits exceed these presentation limits.
Effect on interpretation:
The ultimate
use of the data acquired by these systems is interpretation by professionals
referred to as Log Analysts. Log Analysts perform calculations on log data in
order to determine the potential for production of water, oil or other
commodities from a given well. The largest numbers used are, for example,
formation resistivity which may have a value as high as 20,000
ohmmeters. A variation of .1 percent, 20 ohms,
is not critical in determining the economic worth or potential for
production in a given well. A 10 bit system provides sufficient resolution to
define a change of resistivity on the order of 20 ohms in this measurement. A
12 bit system does better at around 5 ohms. Fractional ohm definition (i.e.
19432.4 ohms) using 16 bits is of no practical benefit to Log Interpretation.
SUMMARY:
In summary,
10 bit or 12 bit acquisition systems offer resolution that meets or exceeds
logging system capabilities, presentation limitations, and interpretation
requirements.
If you have
questions on acquisition systems contact sales@wellog.com.
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WELLOG Revised 11072016 All Rights Reserved