**ABSTRACT**

A dual-water Archie model for the interpretation of resistivity well logs is developed. From that development, a philosophy for Archie's parameters emerges that is quite different from some literature in our industry. In this paper, a model of electrical current behavior in the water in rock is presented. This model is based on the very fundamental electrical law relative to the conversion of resistance to resistivity, and the efficiency of the network of pores and pathways in the rock through which the electrical-survey current must flow. Electrical law, mathematical proofs and derivations are employed in order to promote a better understanding and a better use of Archie’s relationships.

The geometry of water occupying void space in rock is shown to be the most important factor in controlling efficiency of the flow of electrical-survey current through interstitial-water paths in rock, thus giving value to Archie’s parameters.

The classic Archie saturation equation (1942) emerges from the model presented herein, and in doing so is shown to be a dual-water dual-porosity relationship, and is extended to address shaly sands and additional levels of heterogeneity and practical reservoir complexity.

In addition, the development illustrates how heterogeneities such as clay shale and semi-conductive minerals influence resistivity relationships. The model further illustrates both the resistivity behavior in the presence of hydrocarbon and the problems of interpretation in partially oil-wet and oil-wet rock.

The Archie parameters *m* and *n* serve special functions in electrical-current flow in both water-wet- and oil-wet rocks. An exhaustive exploration of saturation exponent *n* reveals behavior that has never before been explained in literature.

The two most important developments arising from this paper are the presentation of the model for the dual-water Archie method and the demonstration of the behavior of the saturation exponent *n* under in situ conditions. The demonstrated behavior of the water-saturation exponent *n* is considerably different from that behavior propounded by conventional wisdom.

Concurrently with the development of the Archie dual-water relationship from the model is the emergence of a second equation that employs a single exponent *m*_{2} that replaces the two commonly used exponents *m* and *n* in the Archie saturation equation. The second equation opens an avenue to calculate water saturations without the knowledge of any part of *m* or *n* and precludes any requirements for their evaluation.

The reality that many oil- and gas- formations are complex in terms of mineralogy, lithology, wettability and saturation distributions makes a better understanding of the analytical process imperative.

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:**

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

**A MODEL AND DISCUSSION**

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AUTHOR’S **NOTE TO THE READER**: This is the latest version of the paper (05-10-2018) that has a much broadened presentation of the model and includes a very comprehensive study of the behavior of the saturation exponent *n* relative to both oil-wet and water-wet rocks.