Historical Use of m and a in Well Log Interpretation: Is Conventional Wisdom Backwards?

Abstract

Abstract Archie's laboratory experiments established a relationship between theformation resistivity factor and porosity, which set forth the use of twoconstants: m and a. From Archie's work these constants wereregression constants representing the slope and intercept, respectively.Subsequent researchers used the general form of Archie's relation, but theyfound differing values for m and a. The terms cementation factorand tortuosity factor have been used to describe each of these terms.Conventional wisdom believes that a higher m relates to vuggy porosity and alower m suggests fracture porosity. This is generally true if thetortuosity factor is assumed (typically 0.81 or 1.0) and the cementation factoris calculated. However, if m and a are found simultaneously, theory and manylaboratory observations suggest the opposite may be more likely. This studyshows that the tortuosity factor, a, is a function of the average angleof electrical movement with respect to the bulk fluid flow, and cementationfactor m is related to the flow area contrast between pore throat and porebody. Historical Background In 1942, Archie published the results of his investigations on therelationship of true formation resistivity and certain characteristic physicalproperties of a reservoir rock. The impetus for his work was the challenge todevelop methods and relationships that could be used in the quantitativeapplication of electrical resistivity log information in the detection andevaluation of a subsurface hydrocarbon accumulation. He reasoned that in orderto be able to recognize a reservoir formation containing hydrocarbons andconnate water, it is first necessary to be able to recognize the resistivity ofa formation when all its pores are filled with connate water (Sw=100%). Without this understanding, it would not be possible toappreciate the resistivity added to a formation when some connate water in thepore system of a reservoir rock is replaced by hydrocarbons. Archie's work established the following simple relationship: F = Ro/Rw where:F =Formation resistivity factorRo =Resistivity of rock/formation with pores filled withbrineRw =Resistivity of the brine The concept of the formation resistivity factor was straightforward. If theresistivity of a brine is measured, then the resistivity of a reservoir rockwhose pores are 100% saturated with that brine is also measured, therock-saturated measurement will be larger than the first. The difference inthese resistivity values is the result of the effects of the formation on thepath of the electrical current travelling through the electrolytic brine in therock pore system.