WELLOG BOREHOLE RESISTIVITY
Revised:
© 2007-2008 WELLOG
All Rights Reserved
WHAT IS RESISTIVITY?
Resistivity is a measurement of the resistance of a bulk volume of material.
In the case of measurement of the resistivity of materials the
earth is made of, the geometry of the electrodes used to make the measurement
is incorporated into an equation. The equation is based on ohms law.
OHMS LAW:
Ohms law: E = I x R
Where: E = Voltage in volts
I = Current in amperes
R = Resistance in ohms
GEOMETRIC FACTOR:
As stated previously, when a bulk measurement of earth material is made, the resistance varies according to the dimensions of the material. A constant is derived based on the geometry of the material included within the measurement. Obviously, when voltage is applied to a material, current will flow through the material according to the voltage applied, the resistance to the flow imposed by the material, area (volume), and the distance (length between or spacing) of the electrodes.
The geometry of Area/Length = meters2/meter = meters
or…
Area/Length = feet2/feet = feet
Calculation of the geometric constant when a “whole earth” surrounds the electrodes, as in a borehole, the calculation is performed as follows:
G = 4 x pi x D
Where:
G = geometric constant (no units)
D = distance between measuring electrodes in the normal electrode configuration.
Pi = 3.14 (approximately)
Illustration: Resistivity model.
Rearranging ohms law, R = E/I
Where:
R = resistance (ohms)
E = voltage
I = current
Including a geometric constant (G) to calculate resistivity,
R = E/I x G
Where:
R = resistivity (ohm-meters or ohm-feet)
E = voltage
I = current
G = geometric constant (no units)
Examples of G when resistivity is measured in ohm-meters:
A normal logging sonde uses an 8 inch (.2 meter) electrode spacing.
G = 4 x pi x .2 = 2.55
A normal logging sonde uses a 16 inch (.4 meter) electrode spacing.
G = 4 x pi x .4 = 5.10
A normal logging sonde uses a 32 inch (.8 meter) electrode spacing.
G = 4 x pi x .8 = 10.20
A normal logging sonde uses a 64 inch (1.6 meter) electrode spacing.
G = 4 x pi x 1.6 = 20.40
In some systems, the results are expressed in ohm-feet. G is calculated;
A normal logging sonde uses an 8 inch (.66 feet) electrode spacing.
G = 4 x pi x .66 = 2.64
A normal logging sonde uses a 16 inch (1.33 feet) electrode spacing.
G = 4 x pi x 1.33 = 6.28
A normal logging sonde uses a 32 inch (2.66 feet) electrode spacing.
G = 4 x pi x 2.66 = 12.56
A normal logging sonde uses a 64 inch (5.33 feet) electrode spacing.
G = 4 x pi x 5.33 = 25.12
HOW CURRENT IS APPLIED TO THE FORMATION:
Illustration: AMN
tool configuration
The resistivity logging system is designed to provide a constant
current to the formation. The current is constant over the selected range of
measurement. The method used to create a constant current is based on the use
of a large series resistance that is greater than 10 times the range of
formation resistivity. In a typical resistivity tool, formation current leaves
the current electrode (A) and returns to cable armor or a bridle electrode (B)
at least 50 feet up-hole.
HOW VOLTAGE IS MEASURED:
Measurement of voltage is performed at the measurement electrode (M) at a given distance from the current electrode (A), for example, 16 inches in the case of the 16 inch normal configuration. The reference for the voltage is obtained from a distant surface electrode (N).
HOW RESISTIVITY BECOMES A MEASURED VALUE: (values rounded within 1 percent for simplicity)
10 ohm-meter measurement:
In the example of a 16 inch normal measurement, using a scale of 10 ohm-meters; calculation of resistance measured by the electrodes;
10 ohm-meters/5.0 = formation resistance = 2.00 ohms
A typical resistivity tool applies 150 volts alternating DC to the formation through a large 300 ohm resistance.
150 volts/300 ohms = .50 amperes. A current of .50 amperes x 2.00 ohms generates 1.0 volt at the M electrode.
A measurement of 1.0 volts is obtained when the resistivity is 10 ohm-meters.
A
measurement of 0.5 volts is obtained when the resistivity is 5
ohm-meters.
100 ohm-meter measurement:
In the example of a 16 inch normal measurement, using a scale of 100 ohm-meters; calculation of resistance measured by the electrodes;
100 ohm-meters/5.0 = formation resistance = 20.0 ohms
A typical resistivity tool applies 150 volts alternating DC to the formation through a large 3000 ohm resistance.
150 volts/3000 ohms = .05 amperes. A current of .05 amperes x 20.0 ohms generates 1.0 volts at the M electrode.
A measurement of 1.0 volts is obtained when the resistivity is 100 ohm-meters.
1000 ohm-meter measurement:
In the example of a 16 inch normal measurement, using a scale of 1000 ohm-meters; calculation of resistance measured by the electrodes;
1000 ohm-meters/5.0 = formation resistance = 200 ohms
A typical resistivity tool applies 150 volts alternating DC to the formation through a large 30000 ohm resistance.
150 volts/30000 ohms = .005 amperes. .005 amperes x 200 ohms generates 1.0 volts at the M electrode.
A measurement of 1.0 volts is obtained when the resistivity is 1000 ohm-meters.
TOOL CALIBRATION:
Using the information given above, it is possible to use precision resistors to perform borehole logging tool system calibration.
When a logging tool is connected for calibration, it is necessary to simulate the borehole environment electrically. Resistors are connected in series beginning at the current electrode (A) and connecting to electrode (M) and then to the cable armor (B and N).
10 ohm-meter calibration:
Precision 2 ohm resistors are connected as stated above. When the tool is energized with a current of 0.5 amperes, a voltage of 1.00 volts will be measured between electrodes M and N.
100 ohm-meter calibration:
Precision 20 ohm resistors are connected as stated above. When the tool is energized with a current of 0.05 amperes, a voltage of 1.00 volts will be measured between electrodes M and N.
1000 ohm-meter calibration:
Precision 200 ohm resistors are connected as stated above. When the tool is energized with a current of 0.005 amperes, a voltage of 1.00 volts will be measured between electrodes M and N.
APPLICATIONS:
Borehole resistivity is used in application that range from water
well logging, mineral logging and petroleum well logging.