WELLOG                               Resistivity Logging


REVISED 05-02-2011             

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Part 1, Page 6





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” Normal; 16” = .4 meters; G = 12.56 x .4 = 5.02.


Where:            MN = distance between MN electrodes in meters for ohm-meters




                        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.




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:


            F = 1 / f2


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.





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.





The Electric Logging tool was originally introduced by Conrad and Marcel Schlumberger in 1927 in Pechelbronn France.


[First Log]  [E-log page]


Mono-electrode configuration.


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.





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.




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 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.




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.




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.




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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