Robert C. Ransom

What are Archie’s Basic Relationships

What is Meant by the Plot of *R*_{t} versus *S*_{wt}*ϕ*_{t}

Parallel Resistivity Equations Used in Resistivity Interpretation

What is the Formation Resistivity Factor

How is Exponent *n* Related to Exponent *m*

Observations and Conclusions from Figure 10 about Exponent *n*

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

**Table of Retrievable Contents:**

**SYMBOLS DEFINED**

*a *Historically, the coefficient of the Formation Resistivity Factor. In this paper, the coefficient of *R*_{w }. 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 *R*_{we} 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 *m*_{1} ) for the two-exponent version of Archie's equation, and the other is *m*_{2} 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.

*ϕ*_{t} Total porosity fraction consisting of the sum of effective and noneffective porosity fractions.

*ϕ*_{e} That part of the total porosity fraction that is hydrodynamically effective and can be occupied by hydrocarbon.

*ϕ*_{ne} 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 *R*_{wb }.

*F*_{t} The Formation Resistivity Factor of the rock, where the conductive water volume fraction always is *S*_{wt}*ϕ*_{t }, where *S*_{wt } ≤ 1.0. In this paper, the numerator always is equal to 1.0.

*R*_{w} Formation water resistivity. Interstitial-water resistivity.

*R*_{wa} The apparent resistivity of formation water found by dividing *R*_{t} by *F*_{t }, where *S*_{wt } = 1.0.

*R*_{wb} The apparent resistivity of water bound in clay shales.

*R*_{we} Same as *R*_{we} 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 *R*_{w} as it is incorporated in Equation (1b) for the calculation of *R*_{we} . Water with resistivity *R*_{w }is interstitial water. Water with resistivity *R*_{we} (or *R*_{weq} ) 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.

*R*_{wz} Is the *R*_{wa} 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. *R*_{wz} is a graphical approximation of *R*_{we} and a special condition of *R*_{wa }.

*R*_{0} The true resistivity of the uninvaded rock when water saturation is 1.0. The water or pseudo water can have the resistivity value *R*_{we }. Sometimes calculated, sometimes read directly from the deep resistivity curve, sometimes derived from the deep resistivity curve. *R*_{0} is a special condition of *R*_{t }.

*R*_{t} 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. *R*_{0}_{ } is a special condition of *R*_{t }.

*S*_{we} Water saturation as a fraction of the effective porosity *ϕ*_{e }.

*S*_{wt} Water saturation as a fraction of the total porosity *ϕ*_{t }.

*S*_{wt}*ϕ*_{t} The total conductive water volume fraction where* S*_{wt } ≤ 1.0. A fraction of one unit of formation volume. Sometimes referred to as the bulk volume of water.

**A CLARIFYING CONCEPT OF ARCHIE'S RESISTIVITY RELATIONSHIPS AND PARAMETERS.**

**A MODEL AND DISCUSSION**

*Within the text, clicking on the bold terms **FIGURE (*)** and **APPENDIX (*)** will take you to the specific page of interest. Use your browser's back button to return to your previous page.*