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Studies of electrical properties in rocks have been performed as functions of frequency, temperature, applied field, pressure, oxygen fugacity, water content, and other variables. In the context of this Handbook, we are concerned only with those properties that affect the water saturation calculation as proposed by Archie and others, and their shale corrected derivatives.

Most water saturation models rely on work originally done by Gus Archie in 1940-41. He found from laboratory studies that, in a shale free, water filled rock, the Formation Factor (F) was a constant defined by:
       1: F = R0 / Rw

He also found that F varied with porosity:
       2: F = A / (PHIt ^ M)


For a tank of water, R0 = Rw. Therefore F = 1. Since PHIt = 1, then A must also be 1.0 and M can have any value. If porosity is zero, F is infinite and both A and M can have any value. However, for real rocks, both A and M vary with grain size, sorting, and rock texture. The normal range for A is 0.5 to 1.5 and for M is 1.7 to about 3.2. Archie used A = 1 and M = 2. In fine vuggy rock, M can be as high as 7.0 with a correspondingly low value for A. In fractures, M can be as low as 1.1. Note that R0 is also spelled Ro in the literature. In some carbonates, M seems to vary with porosity.


For rocks with both hydrocarbon and water in the pores, he also defined the term Formation Resistivity Index ( I ) as:
       3: I = Rt / R0
       4: Sw = ( 1 /
I ) ^ (1 / N)


The value for R0 is measured in the laboratory using either a two or four electrode resistivity apparatus, with the sample 100% saturated with water of resistivity Rw. The porosity is also measured.


The core sample is then partially saturated by extraction of water with a centrifuge. The water extracted is measured to determine water saturation and resistivity Rt is measured. This step is repeated for several saturations.


Results of these tests are shown in the next twp Sections.


Electrical properties can be measured at the same time on the same core plugs as used for capillary pressure measurements. Since both measurements strongly affect the results of reservoir assessment and reservoir simulation projects, it would seem prudent to evaluate both properties in the lab before spending a lot of money on reservoir development.


<==Combined resistivity index and cap pressure report.


Most modern rock laboratories can perform these so-called "special core analysis" procedures. Unfortunately, many operators fail to have this work done, which is a great shame, as the data can change the calculated water saturation values quite dramatically compared to using "world-average" numbers. 


Values of A, M, or N that are lower than the world-average values will increase calculated oil or gas in place.


An outline of the laboratory procedure is listed below.



  1. Obtain 1-1/2 inch diameter by maximum length cylinders from core material.

  2. Perform BaCl Cation Exchange Capacity measurement on sample end pieces.

  3. Package with Teflon tape and stainless steel end screens if unconsolidated.

  4. Extract core fluids using low temperature solvent extraction.

  5. Dry samples in humidity controlled oven.

  6. Determine Boyles’ Law porosity, grain density and nitrogen permeability at reservoir stress.

  7. Vacuum saturate with synthetic reservoir brine.

  8. Mount samples at reservoir stress and temperature (optional) in electrical conductivity/porous plate capillary pressure apparatus with water wet porous plate end piece.

  9. Flush with synthetic brine at backpressure and monitor for 100% brine saturation and electrical stability.

 10. Determine Formation and Cementation factor.  FRw= Ro/Rw   m=log FRw/log porosity

 11. De-saturate using humidified nitrogen or oil in appropriate pressure steps to describe a full capillary pressure curve.

 12. Monitor resistance and production volume on a daily basis at each pressure step.

 13. Dean Stark extract for final water saturation verification


Cementation Exponent (M) from Special Core Data
Measure R0 and PHI on several core samples, preferably samples with a range of porosity values, and calculate formation factor F. Plot porosity vs lab measured formation factor on log-log axes. Fit regression or eyeball line to data. Slope of line is M. Intercept at PHIe = 1 is A. The line force-fitted through F = PHIe = 1.0 is called a "pinned" line. Some people prefer the pinned line but most data sets do not support this approach. Strictly speaking, the line must pass through F = 1 = PHIe, so the line must be non-linear approaching this point on the graph. An example is shown below.

Find A and M from special core data (electrical properties data) - M is slope of best fit line
(pinned or free regression - your choice), A is intercept at PHIe = 1.0. Multiple samples with a range of porosity are best for regression, but a single sample with the line pinned at PHIe = 1.0 can also be used.


saturation exponent (N) from Special Core Data
Measure Rt and calculate water saturation and resistivity index  of a core plug at various water saturations. Plot saturation  versus formation resistivity index on log-log axes. Draw line through the data to intercept at SW = 1.0. The slope of this line is N. Data from several wells may have to be combined to get a reasonable fit, although the values from a single core plug may suffice.

Find N from special core data (electrical properties data). Slope is N and line must pass
through Sw = 1.0 at RI = 1.0..


CEC is the quantity of positively charged ions (cations) that a clay mineral or similar material can accommodate on its negatively charged surface, expressed as milli-ion equivalent per 100 g, or more commonly as milliequivalent (meq) per 100 g. Clays are aluminosilicates in which some of the aluminum and silicon ions have been replaced by elements with different valence, or charge. For example, aluminum (Al+++) may be replaced by iron (Fe++) or magnesium (Mg++), leading to a net negative charge. This charge attracts cations when the clay is immersed in an electrolyte such as salty water and causes an electrical double layer. The cation-exchange capacity (CEC) is often expressed in terms of its contribution per unit pore volume, Qv.

In formation evaluation, it is the contribution of cation-exchange sites to the formation electrical properties that is important. Various techniques are used to measure CEC in the laboratory, such as wet chemistry, multiple salinity, and membrane potential. Wet chemistry methods, such as conductometric titration, usually involve destruction or alteration of a portion of the core sample.

The multiple salinity and membrane potential methods are more direct measurements of the effect of CEC on formation resistivity and spontaneous potential.

Conductometric titration is a  technique for estimating the cation-exchange capacity of a sample by measuring the conductivity of the sample during titration. The technique includes crushing the end pieces of a core sample and mixing it for some time in a solution like barium acetate, during which all the cation-exchange sites are replaced by barium (Ba++) ions. The solution is then titrated with another solution, such as MgSO4, while observing the change in conductivity as the magnesium (Mg++) ions replace the Ba++ ions.


For several reasons, but mainly because the sample must be crushed, the measured cation-exchange capacity may differ from that which affects the in situ electrical properties of the rock.


The C0/Cw, or multiple salinity, is another technique used for the determination of the electrical properties of a shaly core sample. The sample is flushed with brines of different salinities, and the conductivity determined after each flush. A plot of the conductivity of the sample (C0) versus the conductivity of the brine (Cw) gives the excess conductivity caused by clays and other surface conductors. Then, using a suitable model (Waxman-Smits, dual water) it is possible to determine the intrinsic formation factor F* and porosity exponent M*, and the cation-exchange capacity.


The excess conductivity is termed BQv. Qv is a function of CEC and B is related to the mobility of the clay cations.
B = 4.6 * (1 - 0.6 * exp (-0.77 / RW@77F))
      6: Qv = CEC * DENS / PHIe / 100
      7: Co = (1 / F*) * (B * Qv + Cw)
OR rearranging eqn 7
      8: F* = (B * Qv + Cw) / C0
      9: M* = -log(F*) / log(PHIe)
      10; RI* =
      11: N* =

In contrast to the above, remember that, for clean rocks, the Archie model gave:
      12: F = Cw / C0 = R0 / Rw
      13: M = -log(F) / log(PHIe)
      14: RI = Rt / R0
      15: N = -log(RI) / log(Sw)

  C0: Conductivity of rock fully saturated with brine solution (mho/m)
  F* =  formation factor for shaly sandstone
  Qv = cation exchange capacity per unit pore volume (meq/cc)
  Cw = conductivity of the brine (mho/m)
  B = equivalent conductance of clay exchange cations at room temperature (mho cm2/meq)
  RW@77F = formation water resistivity converted to 77 degrees F


In some literature, equation 5 is modified to use RW@FT and formation temperature instead of RW@77F.

The formation factors (F*) of the shaly sand is calculated as the reciprocal of the slope of the linearly fitted Co-Cw curve, and the shaliness term BQv is equal to the value of Cw when C0 is zero.


Examples of multiple salinity tests showing variations in resistivity index (left) and Ct/Cw (right) for four common clay types. Only the 100% Sw line (open diamonds) is a C0/Cw line.


With a micro CT scan image of pore size distribution, software is employed  uses the finite element method (FEM) to solve the Laplace equation for the electric potential field inside a digital sample for a specified potential difference at the boundaries. The electrical current field in the pores is computed and then summed-up to obtain the total current through the sample. The effective conductivity of the sample is simply the ratio of this current to the potential drop per unit length. Formation factor is then calculated as the ratio of brine conductivity to the calculated conductivity of the rock sample. Source:

"META/FRF" -- Electrical Properties Spreadsheet
This spreadsheet provides a tool for summarizing Electrical Properties dara and includes crossplots to find
A, M, and N.

 Electrical Properties Analysis, includes crossplots to find A, M, and N. English and Metric Units

Sample output from "META/FRF" spreadsheet for summarizing electrical properties data.


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