CONCLUSIONS

The most important thing to be drawn from this paper is the model in Figure 1. From that model, two versions of Archie’s saturation equation are derived for dual-water dual-porosity conditions: the common two-exponent version and an equivalent single-exponent version. Also, each of Archie’s parameters have been derived, identified, and explained. These fundamental relationships and parameters have been derived from trigonometrics of the graphic model and corroborating algebraics, and have shown that Archie’s relationships developed herein are a dual-water methodology.

Second is the definitive exploration of the exponent n illustrating its behavior in both water-wet and oil-wet rocks. This exhaustive exploration reveals information about the saturation exponent n that never before has been revealed in literature.

The concept described herein is based on the very fundamental electrical law relative to the conversion of resistance to resistivity, and on the efficiency of the network of pores and pathways in the rock through which the electrical-survey current must flow. The basic electrical resistance equation is the key to understanding the Formation Resistivity Factor. The true formation factor equation alone contains all terms necessary for the calculation of Dual Water Archie.

Archie’s relationships, as the parameters have been defined in this model, have been shown to apply in dual-water dual-porosity conditions and in shaly sands and other rocks of limited heterogeneity. The methodology developed herein can serve as the spine to which numerous correctional and mineral-specific subroutines can be attached to add analytical refinements. The model and the foregoing developments in this paper have shown that Archie’s relationships have a straightforward, physical and mathematical basis, and, in this concept, have been shown to apply to heterogeneous rocks with uniform distributions of porosity, saturations, and electrically-conductive constituents.

Archie’s relationships are fundamental and the foregoing developments are deemed necessary for the relationships to be understood, used in literature, and employed in saturation calculations. An understanding of what influences these parameters and what they represent will provide the user with a place to start and a recognition of what is required from other disciplines for the solution of interpretation problems, and will complement the user’s inventory of tools for describing rocks as they reside in nature.

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