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:**

**WHAT ARE ARCHIE’S BASIC RELATIONSHIPS**

Most water saturation equations used in resistivity well-log interpretation are based in some way on Archie’s relationships. Resolve those equations to clean rocks, and Archie’s basic water-saturation equation emerges. Archie’s basic relationships (1942) most often are misunderstood and misused, as can be seen in many variations and usages in literature; and often are modified by location-specific empirical coefficients and exponents that are not compatible with basic electricity or rock properties. Whether or not any of these modifications provide solutions to local problems is of no interest in these discussions. The purpose of this paper is to dispel misunderstandings, prevent misuse, and promote better interpretations through better understanding. Archie’s basic relationships follow:

*S*_{w}^{n}* = R*_{0}_{ }* / R*_{t measured}

*F *= 1.0 /* *(* ϕ *)* *^{m}

*R*_{0} = * FR*_{w}

where, at the present time, the formation factor equation in many log analysis applications has been modified to

*F*_{t}* _{ }* =

where the *a* coefficient most often is given a value lower than 1.0. Each parameter in these equations will be developed graphically or mathematically, and through this development a conception of what each represents will emerge.

**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.*