WELLOG Resistivity
Logging
©
2003 - 2008 WELLOG
All Rights Reserved
Part
1, Page 6
RESISTIVITY CONCEPTS:
Resistivity can be defined as the degree to which a substance resists the flow of electric current.
Resistance from Ohms Law relates to current and
voltage as follows:
R
= V/I
Where: R
= Resistance
V
= Voltage
I
= Current
The most simple
galvanic measurement is Resistance. A
Resistance log is performed by connecting one electrode to the surface (ground)
and another electrode to a downhole
tool that is immersed in borehole fluid.
Applying a constant current and measuring voltage allows calculation of
resistance. This type of log is called a single-point resistance log. If both electrodes are placed on the tool
then a differential resistance log is produced.
Multiple-electrode arrays extend the depth of
investigation. A better representation of True Formation resistivity (Rt) is obtained. Formation Resistivity can be measured when
four electrodes are used. Two electrodes – one on the surface and one down-hole
on the tool are used to generate an electrical current in the formations in and
around the electrodes. The surface electrode is referred to as B and the
down-hole electrode as A. The voltage measured between two points referred to
and M and N is then calculated as follows:
VMN
= R x I/4p x ((1/rAM-1/rAN)-(1/rBM-1/rBN))
View of
resistivity model.
The Resistivity (R) (in a homogenous medium) is
determined by:
R
= V / I x G
The apparent Resistivity (ra) (in a heterogeneous medium) is
determined by:
ra = V / I x G
Where: G
= Geometric array factor
V
= Voltage
I
= Current
Note about symbology:
The greek
symbol (r) is commonly used in geophysics and (R) is used in the well
logging industry for Resistivity.
The meaning is the same in both cases.
Calculation of Geometric Factor (G):
Normal array:
G
= 4 x p x
(1/rAM – 1/rAN – 1/rBM + 1/rBN) -1
Simplified: G
= 4 x p x MN
For example: 16”
Where: MN
= distance between MN electrodes in meters for ohm-meters
Or…
MN
= distance between MN electrodes in feet for ohm-feet
Lateral array:
G
= 4 p x (1/rAM – 1/rAN) -1
Resistivity is a “physical property” and is
independent of size and shape.
Resistivity, (R) is expressed in units of
ohm-meter2 / meter – abbreviated ohm-meters or ohms.
Conductivity is the reciprocal of resistivity.
Conductivity = 1 / R
Conductivity is frequently expressed in units
of micro-mhos/cm.
Conductivity
in micro-mhos/cm = 10000/R
Where Resistivity (R) is in units of ohms –
meter2 / meter (also ohm-meters).
Also, conductivity is expressed in units of milli-mhos per meter or simply milli-mhos. Another unit is milli-siemens.
Visit this web page for more information on the units of siemens and mhos.
Conduction in liquids is controlled by ion
flow. Ions are created when sodium chloride
(or NaCl equivalent i.e. Potassium) are present in
drilling and formation waters. The
higher the sodium chloride concentration the higher the conductivity and lower
the resistivity. Ion flow is controlled
by fluid viscosity and therefore temperature affects the flow of ions and
conductivity. Resistivity is affected by
temperature. As temperature increases,
conductivity increases and resistivity decreases.
Determination of Rw:
This step is often overlooked! Here’s a couple of rules…
Before any interpretation of resistivity data
can take place, Rw must be known.
As mentioned previously, the value of Rw is affected by temperature. If a water sample is taken
and Rw is measured, it is equally important to…
Note the temperature of the water sample!
Determination of Rw from SP:
Resistivity of formation water is related to
the SP curve.
Rw may be obtained from a chart.
Geothermal gradient:
Geothermal gradient is a measure of temperature
increase with depth. Geothermal gradients are normally 1.0
to 1.7 degrees per 100 feet. For
example: If a well has a surface temperature of 75 degrees F and bottom hole
temperature is 175 degrees F at a depth of 10,000 feet, the geothermal gradient
is 1.0 degrees per 100 feet.
Evaluation of a formation using Rw should always be performed using a corrected Rw at formation temperature.
Rw @ temperature should be documented on the log heading.
A FREE CALCULATOR:
When interpretation is performed on resistivity IT MUST BE AT
IN-SITU TEMPERATURE. For example: given Rw at 70
degrees F. What is Rw in the well at 200 degrees
F? Here’s a Resistivity at T2 calculator.
Resistivity related to porosity:
The amount of water contained in a formation is
directly related to porosity. Porosity therefore affects formation resistivity.
As the volume of water increases, the capacity for ions increases. More ions
mean more conductivity. Conductivity and Resistivity are inversely related as
previously mentioned.
Resistivity of a formation 100 percent water
saturated (Ro) = Formation resistivity factor (F) times Resistivity of the
water (Rw).
Formation resistivity is affected by three
factors: Salt Concentration, Temperature, Pore volume (porosity).
Formation Resistivity Factor is a proportionality constant based on the ratio of Ro to Rw.
The equation is: F = Ro/Rw Known as the Archie equation.
Ro is resistivity of a 100 percent water filled
formation and Rw is resistivity of the water.
Given Rw = .05,
If Ro = 5.0 then F = 100
If Ro = 1.25 then F = 25
If Ro = .55 then F = 11
Formation resistivity
Factor (F) is related to Porosity (f) as follows:
F
= a / fm
The variables (a) and (m) are related to
lithology. Cementation factor (m) in a cemented
sandstone or a porous limestone is 2.0 and (a) is equal to 1.0.
Resulting in the equation:
Calculation of Formation factor from porosity:
Porosity of 10 percent results in a Formation
resistivity Factor of 100
Porosity of 20 percent results in a Formation
resistivity Factor of 25
Porosity of 30 percent results in a Formation
resistivity Factor of 11
Notice these three Formation Resistivity
factors are the same as calculated with F = Ro/Rw
above.
RESISTIVITY TOOLS:
Water saturation and hydrocarbon saturation
affect formation resistivity. The measurement
of resistivity is therefore one of the most important measurements to be made
in logging a well. A resistivity tool is most useful if it measures two or more
characteristics of formation resistivity. Resistivity measurements combined
with porosity measurements and estimations of permeability allow a complete
analysis of a well to be performed.
ELECTRIC LOG (E-LOG):
The Electric Logging tool was originally
introduced by Conrad and Marcel Schlumberger in 1927 in Pechelbronn
The concept of operation of the electric
logging tool is as follows:
When two electrodes are placed in a oil or water filled well and voltage is applied to them, a
current will flow through the well fluid and formation fluids. If additional electrodes are placed in the
vicinity of the current producing electrodes, a voltage can be measured. The voltage measured is directly related to
the resistivity of the surrounding formation fluids. Electric logging tools generate an
alternating current and measure the resulting alternating voltage at
measurement electrodes. The depth of
measurement is directly related to the spacing or separation between
electrodes. The depth is approximately
equal to ˝ of the distance from the measure electrode and the midpoint between
the two current electrodes.
Different electrode configurations yield
different depths of investigation.
The “normal” electrode
configuration is as follows:
One current electrode (A) on the tool down-hole
and the other current electrode (B) located at the surface. Measurement
electrodes (M) are spaced from the down-hole current electrode at 8 inches, 16
inches, 32 inches or 64 inches above the “A” electrode
depending on tool design. The reference electrode (N) is on the surface. The
most common configuration is 16 inch (short normal) and 64 inch (long normal)
spacing. This configuration results in a
shallow resistivity and deep resistivity measurement.
The “lateral”
configuration uses a current electrode (A) down-hole on the upper part of
the tool or on an electrode “bridle” and the other current electrode (B) on the
surface. Two lower electrodes (M) (N)
measure the lateral voltage which is representative of a much deeper formation
resistivity. Lateral measurements can be from 72 inches to 18 feet or more
depending on electrode spacing and tool design. See AMN Lateral
configuration. Also a configuration referred to as MAB electrode configuration.
The advantage of short spacing is better thin
bed definition. The advantage of longer
spacing is a deeper measurement of true formation resistivity. Comparison of deep and
shallow resistivity give information about invasion. If shallow and deep resistivity
are the same, no invasion has occurred.
If there is separation, the most probable reason is that invasion has
occurred causing the shallow (invaded) and deep water resistivities to differ.
The electric logging tool requires a fluid
filled borehole in order to have a complete electrical path.
CONSIDERATIONS:
All logging methods have
limitations to consider.
Bed thickness effect:
The curves produced by the normal devices are affected by bed thickness and
resistivity (Lynch 1962).
View a chart for bed
thickness correction for 16” normal.
View a chart for bed
thickness correction for 64” normal.
Formation transitions:
Where the resistive bed
is more than
Although the radius of
investigation increases as the electrode spacing increases, the use of AM
spacing greater than 64 inches is not practical because thinner beds are not
only shown at less than true resistivity but may be recorded as conductive beds
if their thickness is less than or equal to the AM spacing. Focused
resistivity tools overcome this limitation.
INVERSION METHODS:
Recently, software
has been developed for improving resistivity log interpretation. Old logs and
new are being subjected to inversion processing that removes the effect of
surrounding formations. These techniques will make electrical resistivity a
more accurate viable logging method well into the future.
INDUCTION LOG:
Induction
tools operate on the concept of electromagnetic induction. A transmitter coil is energized at a
frequency of 20,000 cycles per second (20 KHz).
The electromagnetic field is coupled through the surrounding formations.
Variation in formation fluid resistivity causes phase shifting of the
transmitted signal. The formation produces a secondary electromagnetic
field. A receiver coil having a fixed
spacing receives the transmitter signal and the phase shifted secondary signal
related to conductivity is converted into resistivity. Depth of investigation is directly related to
coil spacing. The induction resistivity tool does not require conductive fluid
in the borehole because it uses electromagnetism.
The induction tool will not operate in steel
casing.
DUAL INDUCTION LOG:
Because depth of investigation is related to
coil spacing, the Dual Induction tool was developed in order to get two depths
of investigation. The Dual Induction
tool has one or more transmitter coils and two receiver coils at two fixed
positions from the transmitter. Focusing is performed thru the addition of
other coils. Focusing of the electromagnetic field reduces the effect of
borehole signal.
Invasion profiles are obtained from charts available from the
logging service company.
GUARD LOG:
In wells containing highly conductive drilling
fluids, guard tools are used. A focused guard tool offers the
function of having a focused current path into the formation. Electrodes surrounding the current electrode
are used to focus the tool current outward into the surrounding formation and
not allow the current to travel through the conductive borehole fluid.
Proper interpretation of
focused logging tool measurements involve use of correction charts.
OTHER RESISTIVITY TOOLS:
Many specialized varieties of resistivity tools
are available. Micro-resistivity [Wall] devices, for example, micro-log,
mini-log, FoRxo, Contact and others that measure
resistivity of the borehole mud cake and flushed zone. One such tool has a depth
of investigation of 2 inches for example.
Micro-resistivity provides a measurement of Rxo
and Rmf. This information is valuable for the purpose
of determination of permeability. Permeability is established by calculation of
the saturation of the flushed zone (Sxo).
Sxo = (Rmf/Rxo)1/2
Determine porosity from micro resistivity using
this chart.
Recently added Electric and Induction tools can
perform a synthetic aperture – measuring at a great many different depths into
the surrounding formation. Such tools give a more precise profile of
resistivities surrounding the borehole.
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