TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractArchie's laboratory experiments established a relationship between the formation resistivity factor and porosity, which set forth the use of two constants: m and a. From Archie's work these constants were regression constants representing the slope and intercept, respectively. Subsequent researchers used the general form of Archie's relation, but they found differing values for m and a. The terms cementation factor and tortuosity factor have been used to describe each of these terms. Conventional wisdom believes that a higher m relates to vuggy porosity and a lower m suggests fracture porosity. This is generally true if the tortuosity factor is assumed (typically 0.81 or 1.0) and the cementation factor is calculated.However, if m and a are found simultaneously, theory and many laboratory observations suggest the opposite may be more likely. This study shows that the tortuosity factor, a, is a function of the average angle of electrical movement with respect to the bulk fluid flow, and cementation factor m is related to the flow area contrast between pore throat and pore body.
Saturation exponent n in Archie's water saturation equation is theexponent value in water saturation that establishes the relationship betweenwater saturation of the rock to the ratio of fluid filled rock resistivity tothe actual rock resistivity. Most theoretical derivations show that thereis no exponent or that n is equal to one. However, decades of resultsfrom core analyses and openhole log analyses show n greater than one andmost often assumed to be two. Most of the literature is in agreement that the saturation exponent isaffected by wettability and saturation history (drainage or imbibition). Furthermore, the saturation exponent depends on rock type, primarily the mannerin which the conductive water is connected and configured. Severalauthors quote values of n ranging from as low as 1 to over 20 forstrongly oil wet rocks. Too often an assumed value is accepted ascorrect. This paper reevaluates the relationship between water saturation and rockresistivities in order to determine the significance of n and makerecommendations on improving an assumed value for n. Introduction The quest to determine and understand n began shortly after Archie's earliest work correlating water saturation to resistivity (or resistivityindex). Surprisingly theoretically based derivations show that ndoes not exist (or arguably is one). This paper identifies some of thefeatures that are influence n and core and logging methods of estimatingn. Measurement Methods Several methods to determine the value of n are as follows: coremeasurement, combination of core measurement and log data, and log dataonly. Core measurement. This method can resolve the value of n byvarying core water saturation and correlate it against the rockresistivity. The slope of a log-log plot yields n. It isimportant to note that for water-wet core samples, the various saturations mustbe derived during the drainage process not the imbibition process. Thecore starts out 100% saturated with water and oil is used to displace thewater. At various water saturations resistivity measurements aretaken. Combination of core and log. This method combines core derivesSw with Rt values from log. One technique in thismethod is to log-log crossplot Rt versus Swirr and theslope of the line is saturation exponent n. Another technique is to determine Swirr, porosity, cementation exponent m and tortuosity factor a from a coresample, and solve for n using Rt values from log. TheSwirr is from capillary pressure data. A variation of thistechnique is to use Swirr from relative permeability data [Asquithet al., 1997]. Log data only. Dielectric logs can independently solve forSxo. Using the values of Rxo from resistivitytools, a log-log plot of Rxo versus Sxo yields a slope ofthe line equal to the saturation exponent n.
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