Improved Data-Analysis Method Determines Archie Parameters From Core Data (includes associated paper 24964 )

Abstract

Summary. We present a data analysis approach to determine Archie parameters m and n from standard resistivity measurements on core samples. The analysis method, core Archie-parameter estimation (CAPE), results in computed water saturations that agree well with core-measured saturations. CAPE determines m and n by minimizing the error between computed and measured water saturations. The conventional method minimizes the error in nonphysical quantities. Also, CAPE provides a natural, physically meaningful method of "averaging" Archie parameters, and with an error statistic, aids in zonation of a well or reservoir into different sets of Archie parameters. Finally, we show that the Archie constant a is a weak-fitting parameter, with no physical significance, that can generally be set to unity. Introduction The conventional data-analysis method for determining the Archie parameters m and n was first presented by Archie when he introduced the Archie equation. The conventional method has remained largely unchanged, except that sometimes a constant a is added to the formation factor equation. The constant a is conventionally determined with Archie's original procedure for determining m, the only difference being that the line is not constrained to go through F = 1 when = 1. Conventional Determination of n. The conventional determination of n is based on rearranging Archie's equation. The clinical Archie equation is Sw = ...................(1) Archie did not use the constant a in his expression, but others have since added it. a is commonly used and is often referred to as part of Archie's equation, though strictly speaking it is not. In the conventional determination of n, Eq. 1 is rearranged as log(Rt)= -n log(Sw) +log(aRw/m). ...................(2) The laboratory-measured Rt and Sw points for a single core sample are plotted on loglog graph paper (Fig. 1), and a least-squares fit of log(Rt) vs. log(Sw) is made, n is obtained from the negative of the slope of the least-squares fit. Terms on both sides of the equal sign in Eq. 2 can be combined to yield log(I R) = -n log(Sw),.............(3) where I R = resistivity index (Rt/Ro), and Ro - aRw/m......................(4) Sometimes data are plotted as log(I R) vs. log(Sw). This form is mathematically equivalent to a plot of log(Rt) vs. log(Sw) and yields the same value for n. Data for several core samples are sometimes plotted as log(I R)vs. log(Sw) and a single least-squares fit is obtained. Conventional Determination of m and a. The equation assumed is the form of the formation factor traditionally associated with Archie's equation: F = a/m = Ro/Rw,................(5) where F = formation factor found from Ro/Rw, Ro = resistivity when the sample is fully water saturated (Sw = 100%), and Rw = water resistivity. Eq. 5 is rewritten as log(F) = -m log () + log(a)......(6) All core samples are used simultaneously in the plot. A least-squares fit is made of log(F) vs. log() (Fig. 2). a is sometimes fixed to unity and sometimes used as a variable to be determined. m is determined from the least-squares fit, as is a if it is not fixed at unity. Note that only points for which Sw = 1 are used, and all other points are ignored. Thus, Sw = 1 points are required for the conventional method. If Sw = 1 points are not measured directly, they are sometimes approximated by extrapolating plots of Sw vs. Rt for individual core samples. Comments on Conventional Determination of m, n, and a. The conventional method treated the determination of n as a problem independent from the determination of m and a. Thus it ignored a great deal of data in the determination of m and a namely, all points for which Sw less than 100%. We have developed a data-analysis method to determine Archie's parameters m, n, and optionally a, using standard resistivity measurements on core samples. CAPE is a mathematical procedure that does not address the physics of Archie's equation or attempt to discriminate between valid and invalid input data. Thus, poor input data will result in suspect output. Additionally, CAPE does not address the question as to whether Archie's equation is valid for the data. What CAPE does is determine the set of Archie parameters that minimizes the error in computed water saturation. Benefits from the new CAPE method are listed below. 1. CAPE-computed water saturations agree better with core-measured saturations than those conventionally computed. JPT P. 103⁁