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_wⁿ = R₀ / R_{t  measured}

F = 1.0 / ( ϕ ) ^m

R₀ = FR_w

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

F_t = a / ( ϕ_t ) ^m

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.

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