**WELLOG **** ****Resistivity Logging**

**© 2003 - 2011 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:**

** V _{MN}
= R x I/4**

**View of
resistivity model.**

**The Resistivity (R) (in a
homogenous medium) is determined by:**

** R
= V / I x G**

**The apparent Resistivity (****r****a) (in a heterogeneous
medium) is determined by:**

** ****r****a = 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/r _{AM} – 1/r_{AN} – 1/r_{BM} + 1/r_{BN}) ^{-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/r _{AM} – 1/r_{AN})^{ -1}**

**Resistivity is a “physical
property” and is independent of size and shape.**

**Resistivity, (R) is expressed in
units of ohm-meter ^{2} / 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 – meter ^{2} / 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 / ****f**^{m}^{}

**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 6 AM
spacings thick, logging up hole, there is a gradual increase in resistivity
until the M electrode on the sonde enters the bottom of the bed. This level of
resistivity is maintained until the A electrode enters the bed. As the sonde
continues there is a gradual increase in resistivity until the midpoint of the
bed is reached. Thereafter a gradual reduction occurs in resistivity, which is
symmetrical with the curve below the midpoint of the bed, until the sonde passes
out of the bed. The recorded resistivity approaches but does not fully equal
the true resistivity of the bed. The bed also appears to be 1 AM spacing thinner than it actually is, the
major resistivity deflections occurring ˝ AM above the bed bottom and ˝ AM
spacing below the bed top. As the bed thickness decreases, the resistivity peak
at the center decreases in amplitude. Further thinning to AM or less than AM
causes the resistivity deflection to disappear entirely, and the curve actually
reverses. The resistive bed now appears to be more conductive than the
surrounding formations. **

**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}**

**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.**