**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 = meters^{2}/meter = meters

or…

Area/Length = feet^{2}/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.

Revised: 11-24-2018 ©
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