Robert C. Ransom

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What are Archie’s Basic Relationships

The Graphical Model

What is Meant by the Plot of Rt versus Swtϕt

Summary of Equations

Parallel Resistivity Equations Used in Resistivity Interpretation

What is the Formation Resistivity Factor

The m Exponents

How is Exponent n Related to Exponent m

The a Coefficient

The Saturation Evaluation

Challenging Well-Log Examples

Observations and Conclusions from Figure 10 about Exponent n

Are There Limitations to Archie's Relationships Developed in this Model?




Symbols Defined



All Figures

About the Author

Table of Retrievable Contents:


a           Historically, the coefficient of the Formation Resistivity Factor. In this paper, the coefficient of Rw . Usually equal to 1.0 in clean rocks, and different from 1.0 in the presence of any conductive influence other than formation water. Often lower than 1.0. When incorporated in comprehensive Rwe relationships, the numerator in the Formation Resistivity Factor must always be 1.0.

m          The porosity exponent in the Formation Resistivity Factor. Related to the shape and dimensions of electrolyte-filled paths. There are two versions of exponent m. One is the usual m (or m1 ) for the two-exponent version of Archie's equation, and the other is m2 for the equivalent single-exponent version.

n           The saturation exponent found in Archie's water saturation equation. Related to the electrical interference caused by the presence of hydrocarbon in electrolyte-filled paths. What exponent m becomes after hydrocarbon has migrated into the rock and has displaced the water.

ϕt         Total porosity fraction consisting of the sum of effective and noneffective porosity fractions.

ϕe         That part of the total porosity fraction that is hydrodynamically effective and can be occupied by hydrocarbon.

ϕne       Is the noneffective porosity in clay shale related to water attracted to the clay crystal and water held osmotically, and is directly related to the fraction of clay shale present. It is a porosity volume that has not been penetrated by hydrocarbon. Water saturation in the noneffective pore space is 1.0 and resistivity is represented by Rwb .

Ft          The Formation Resistivity Factor of the rock, where the conductive water volume fraction always is Swtϕt , where Swt 1.0. In this paper, the numerator always is equal to 1.0.

Rw        Formation water resistivity. Interstitial-water resistivity.

Rwa      The apparent resistivity of formation water found by dividing Rt by Ft , where Swt = 1.0.

Rwb      The apparent resistivity of water bound in clay shales.

Rwe      Same as Rwe in other work. A calculated value for the equivalent water resistivity when secondary conductive influences are present. In this paper, the product of coefficient a and Rw as it is incorporated in Equation (1b) for the calculation of Rwe . Water with resistivity Rw is interstitial water. Water with resistivity Rwe (or Rweq ) is not interstitial water and does not exist in nature at 100% water saturation. It is a hypothetical water mixture of dual waters, influenced by the presence of oil, that exists at 100% water saturation only in a dual-water concept. Electrically the dual waters can be mixed, physically they cannot. This dual-water mixture cannot be recovered in a production test.

Rwz      Is the Rwa value determined from a zone known to be or believed to be completely filled with water or nearly saturated with water. Hydrocarbon saturation is zero or near zero. Rwz is a graphical approximation of Rwe and a special condition of Rwa .

R0        The true resistivity of the uninvaded rock when water saturation is 1.0. The water or pseudo water can have the resistivity value Rwe . Sometimes calculated, sometimes read directly from the deep resistivity curve, sometimes derived from the deep resistivity curve. R0 is a special condition of Rt .

Rt         The true resistivity of the uninvaded rock, whether or not it contains hydrocarbon. Sometimes read directly from the deep resistivity curve, sometimes derived from the deep resistivity curve, sometimes calculated. R0 is a special condition of Rt .

Swe      Water saturation as a fraction of the effective porosity ϕe .

Swt       Water saturation as a fraction of the total porosity ϕt .

Swtϕt   The total conductive water volume fraction where Swt 1.0. A fraction of one unit of formation volume. Sometimes referred to as the bulk volume of water.



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