An Approach to Determining Water Saturation in Shaly Sands
Authors: Patchett J.G. , Rausch R.W. 
Published: December 2007

Abstract
Fresh waters and the presence of clay in many Rocky Mountain and West Coast sands require special methods of log analysis. Archie's saturation equation requires addition of a shale correction term, and the SP equation must also be modified to account for clays. Suitable equations were developed several years ago, but have not been widely used due to the algebraic complexity. A computer-oriented method has now been developed to overcome this problem. The basic shaly sand equations are rearranged in four different ways to permit solution for various sets of available input data. Essential to application of the method is the correction of observed SP values to those that would be observed if the resistivity of the formation waters were exactly interchangeable with the activity. A graphic method for doing this is given. Where conditions require consideration of the erect of clay in the sandy, the method presented hay been found to improve the accuracy of water-saturation determinations.

Introduction
Log interpretation in many Rocky Mountain and West Coast basins is complicated by rapid vertical and lateral changes in water resistivity. Calculation of formation water resistivity from the SP curve becomes difficult in zones that contain clay, since changes in SP deflection may be due to changes in either clay content or water salinity. In hydrocarbon-producing reservoirs, the problem is further complicated because hydrocarbon saturation also reduces the SP. A log interpretation system using computers has been developed to provide a solution to this problem, based on equations proposed by de Witte. Four different simultaneous solutions of de Witte's equation have been made. Each solution method uses a different set of input data as independent variables. Thus, a choice of solution method is possible, depending upon the logs run and the availability of other data, Two of the solutions do not require a knowledge of water resistivity.
This system is intended to be used primarily in multiple sandstone-shale sequences of low and moderate resistivities where the principal contaminant in the sandstones is clay. However, where sufficient regional data are available, interpretation in single-zone sandstone reservoirs can also be improved by using the method.

THEORY AND HISTORY OF SHALY SAND ANALYSIS
The log interpretation formula originally proposed by Archie in 1941 is applicable only to rock-fluid systems wherein the rock has negligible electrical conductivity. In 1949, Patnode and Wyllie showed that if the rock itself can be considered conductive due to the presence of clay, a different calculation approach is necessary. During the following years, this problem was investigated at great length, as was the related problem of the effect of rock conductivity on the SP. These investigations established functional relationships between SP, resistivity, water saturation and water resistivity for such a formation. Refs. 2 and 12 provide summaries of these studies.
Unfortunately, practical use of these relationships required that water resistivity be known independently from the SP. Although log interpretation methods for rock systems containing clay were proposed at that time, they were not generally accepted for routine use. There are three principal reasons for this. First, in many field situations involving high-salinity water, rock conductivity may be neglected (even if present) without introducing appreciable error. This may be seen by considering the following expression for water-saturated rock.
(1)
where 1/Rs is conductivity due to clay. As Rw becomes small, 1/FRw becomes much greater than 1/Rs which may be neglected.
Where 1/Rs may be neglected, the sandstone is called clean. If the term may not be neglected, the sandstone is termed dirty or shaly. For resistivity purposes, the classification between clean and shaly sands then depends not only upon the conductivity due to shale in the sand, but also upon the resistivity of the associated water (shale is used here to mean surface condition due to disseminated clay). A sand of given conductivity might safely be treated as clean in association with high-salinity water, but would require shaly sand methods if associated with fresher waters. Shaly sand methods are not required in many areas having saline waters; but in Rocky Mountain and West Coast sands having relatively fresh waters (often more than 0.3 ohm-m resistivity at formation conditions), the shaly sand methods are needed.
Errors in Rw calculations from the SP due to the presence of shale are likewise related to water salinity. In saline water formations drilled with fresh mud, the ratio of mud filtrate resistivity to water resistivity is high, the SP is large and the presence of shale can introduce large errors in water resistivity calculated by the conventional method. When the resistivity ratio is low, the errors are smaller. At zero SP, no error would result from shale. Thus, from the SP viewpoint, a given rock could be shaly if associated with a saline water, and clean in association with a fresh water, which is the opposite of the resistivity-oriented definition above.