A Method of Analyzing Electrical Logs Recorded on a Logarithmic Scale
Authors: Blakeman Edmund R. 
Published: December 2007

Abstract
A minimum of three resistivity measurements are necessary to estimate the influence of invasion and thereby assure an adequate determination of Rt. This requirement is fulfilled by the Dual Induction-Laterolog, the first modern logging tool to combine three focused resistivity devices. The three resistivity curves are recorded simultaneously on a logarithmic resistivity scale. Proportional dividers can be used to obtain ratios and products of the resistivity measurements by treating the logarithmic scale in a manner similar to the principle of the slide rule. This leads to a very quick, easy and mechanical method of determining Di, Rt, Rxo. and estimates of Sw. These values are obtained as plots directly on the log, thus providing a permanent record that is an integral part of the log itself. The method significantly reduces interpretation time by eliminating the necessities of making calculations and reading scales. Also, the accuracy of the log is more nearly maintained, particularly since interpolation is mechanical rather than interpretive. Thin-bed corrections and borehole-enlargement corrections are also greatly simplified. It is believed that the use of the proportional divider techniques with logarithmic resistivity scales will significantly improve the otherwise time-consuming task of log analysis.

Introduction
To determine true formation resistivity has always been a fundamental problem in quantitative log analysis. Modern induction logs have simplified this problem for cases of moderate invasion so that a value adequately close to R is often recorded directly. However, the problem remains that one cannot be sure that the recorded resistivity is adequately close to Rt, and too often the analyst fails to recognize when it is not. The Dual Induction-Laterolog is an important step forward in obtaining adequate values of Rt for invaded formations. This logging sonde includes three focused resistivity devices:a Laterolog (LLs) which has a comparatively shallow depth of investigation (resistivity designated RLLs);an induction log (ILm) which has a moderate depth of investigation (resistivity designated RILm); andan induction log (ILd) which has a depth of investigation about twice as large as ILm (resistivity designated RILd).
Resistivities from these three devices are recorded simultaneously on a logarithmic scale. In effect, the Dual Induction-Laterolog provides three "equations", each containing the three variables Di, Rxo and Rt. This assumes a simple frontal invasion pattern; that is, a permeable formation with a homogeneous invaded zone of resistivity Rxo extending to a diameter Di, beyond which lies a homogeneous zone of true formation resistivity Rt. A simultaneous solution of the three "equations" to obtain Di, Rxo and R is shown as Fig 1. A fullscale reproduction of Fig. 1 is shown in the Appendix. The purpose of the paper is to introduce a simple, quick and accurate method of mechanically determining Di, Rxo, and Rt, and of estimating water saturation. With this method, the time-consuming necessities of mathematical manipulation and the reading and interpolation of numerical values are essentially eliminated. A systematic procedure of log analysis develops from this method. The proposed method utilizes the logarithmic resistivity scale from which ratios of resistivity values can be extracted in a manner similar to the principle of the slide rule. That is, the distance between two resistivity curves represents the logarithm of the ratio of the two resistivities, inasmuch as the logarithm of a ratio is expressed by subtracting the logarithm of the denominator from the logarithm of the numerator. This distance can be extracted with a pair of proportional dividers. Similarly, the proportional dividers can be used to enter this ratio into the logarithmic scale of an interpretation chart. With this idea as a beginning, the technique can be expanded into a systematic method of determining Di, Rxo, Rt and Rxo/Rt. Continuous plots of Rt and Rxo/Rt can be quickly made on the log. Estimates of water saturation Sw can be made directly from the Rxo/Rt plot and, in this manner, possible oil-bearing zones can be isolated. With the Rt plot and a porosity log, the value of Sw can be verified.
JPT
P. 844^