Departure Curves for the Self-Potential Log

Abstract

Published in Petroleum Transactions, AIME, Volume 213, 1958, pages 11–16. Abstract An analog computer study was made of the reduction of the magnitude of the SP by formation geometry and resistivity effects. Practical field situations were studied. The analog data were converted to the form of departure charts. These charts may be used to determine the reduction in the SP due to the above effects with good precision. Introduction Quantitative interpretation of the SP log in terms of formation water resistivity is presently based on the premise that the observed SP is equal to the electrochemical potential developed across a shale between the mud filtrate and the formation water. This procedure inherently assumes that, first, no electrokinetic (streaming) potential is present, and, second, that the SP is not reduced by resistivity or geometry effects in the formation. The Analog Model The analog model used for this study was the Guyod Analog Computer which originally was designed and built for resistivity log departure curve studies. It consists of a two-dimensional mesh of resistors, with the vertical mesh corresponding linearly to vertical distance along the borehole, and the horizontal mesh corresponding to radial distance from the borehole axis. By proper choice of horizontal resistor values, a three-dimensional, axially symmetric, borehole-formation problem can be modeled with this two-dimensional array. These and other details of the model are contained in a paper by H. Guyod. The geometry used for the SP studies with the analog is depicted in Fig. 1. This configuration has a horizontal plane of symmetry, and, hence, the model, and the following discussion, need only to be concerned with one quadrant such as shown in Fig. 2. A further simplification arises by considering that both the natural potential sources and those used in the model have fixed internal impedance. Therefore, the current flows produced by these sources can be separated and studied independently (i.e., the superposition theorem can be applied).