WELLOG THE POWER of TWO

Revised 04-20-2005

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 2⁰

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For example, the 12 bit binary number 1111 1011 0110 is composed of

1 x 2¹¹ = 2048

1 x 2¹⁰ = 1024

1 x 2⁹ = 512

1 x 2⁸ = 256

1 x 2⁷ = 128

0 x 2⁶ = 0

1 x 2⁵ = 32

1 x 2⁴ = 16

0 x 2³ = 0

1 x 2² = 4

1 x 2¹ = 2

0 x 2⁰ = 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 micro-volts. Using the 10 inch caliper measurement above, this equates to 150 micro-inches! 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 ohm-meters. 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.