WELLOG                                 BOREHOLE RESISTIVITY

WHAT IS RESISTIVITY?

Resistivity is a measurement of the resistance of a “bulk volume” of material.

To measure the resistivity of materials, the geometry of the electrodes used to make the measurement is incorporated into an equation. The fundamental equation for resistance 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:

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 (volume)

of the material included within the measurement. When voltage is applied to a material, current will flow through the material proportional to the voltage applied and inversely

proportional to the resistance to the flow imposed by the material having area (A), and the length (L) 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 L

Where:

G = geometric constant (no units)

L = 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,

Resistivity (p) = G x E/I

Where:

p = resistivity (ohm-meters or ohm-feet)

E = voltage

I = current

G = geometric constant (includes dimension i.e. meters, feet, inches)

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 M =  2.55

A normal logging sonde uses a 16 inch (.4 meter) electrode spacing.

G = 4 x pi x .4 M =  5.10

A normal logging sonde uses a 32 inch (.8 meter) electrode spacing.

G = 4 x pi x .8 M =  10.20

A normal logging sonde uses a 64 inch (1.6 meter) electrode spacing.

G = 4 x pi x 1.6 M =  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 Ft =  2.64

A normal logging sonde uses a 16 inch (1.33 feet) electrode spacing.

G = 4 x pi x 1.33 Ft =  6.28

A normal logging sonde uses a 32 inch (2.66 feet) electrode spacing.

G = 4 x pi x 2.66 Ft = 12.56

A normal logging sonde uses a 64 inch (5.33 feet) electrode spacing.

G = 4 x pi x 5.33 Ft = 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 bridle or 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.

Current = 150 volts/300 ohms = .50 amperes.   A current of .50 amperes x 2.00 ohms = 1.0 volt at the M electrode with reference to the bridle or surface 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.

Current = 150 volts/3000 ohms = .05 amperes.  A current of .05 amperes x 20.0 ohms = 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.

Current = 150 volts/30000 ohms = .005 amperes.   A current of .005 amperes x 200 ohms = 1.0 volts at the M electrode.

A measurement of 1.0 volts is obtained when the resistivity is 1000 ohm-meters.

Summary: Resistivity scales (ranges) are changed by controlling current.

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).

Circuit:   (A)---Resistor---(M)---Resistor---(N)------(B)

10 ohm-meter calibration:

Two 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:

Two 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:

Two 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 applications that range from water well logging to mineral logging and petroleum well logging.

Resistivity is important! Resistivity can:

Identify mineralization in water wells that may cause poor water quality.

Identify mineralization in mineralized areas to show areas of possible economic interest.

Identify zones containing water or oil to show thickness of potential oil producing zones.

Borehole requirements:

Borehole resistivity is performed in wells that contain NO casing. Formation resistivity measurement using normal and lateral electrodes requires conductive Fluid, i.e. water must fill the borehole.

Tools using electromagnetic induction can measure resistivity without fluid in the borehole.