Effect of Hysteresis on the Archie Saturation Exponent
Authors: Al-Kaabi A.U. , Mimoune K. , Al-Yousef H.Y. 
Published: December 2007

Abstract
It is common practice in the oil industry to use a single value of the Archie saturation exponent (n) in reserves evaluation based upon well log data. This practice ignores, in essence, the development (or depletion) stage of the reservoir. This study investigates the effect of saturation hysteresis on the saturation exponent using a double membrane (oil-wet membrane and water-wet porous plate) arrangement. An electrocapillarometer was used for this purpose. With the electrocapillarometer, it is possible to perform measurements while the displacing phase is injected continuously at predetermined rate, as opposed to waiting for equilibrium. This facilitates rapid data acquisition. The influence of the experimental procedure on the saturation exponent, vis-a-vis, static (constant pressure) and dynamic (constant rate) desaturation methods was also investigated. Using this same membrane arrangement, it was possible to determine the wettability of the reservoir rock at reservoir conditions of pressure and temperature.
In this study, the Archie saturation exponent was determined to reveal a saturation history dependent (hysteresis) behavior. The hysteresis aspect of the study identified a region of a) oil-displacing water (primary drainage) where the saturation exponent was found to be 1.8; b) spontaneous water imbibition followed by forced imbibition. The saturation exponent in this region was 2.72. Another region is the spontaneous secondary drainage, followed by forced secondary drainage. The saturation exponent in this region was 2.14. Results from the electrocapillarometer (in the case of oil-displacing water) were compared with those from a conventional constant pressure, single membrane system. There was very good agreement. The wettability index obtained with the electrocapillarometer was also compared with an independent determination of USBM wettability index using the centrifuge at reservoir temperature. Both showed the samples to be water wet and the numerical value of wettability indices agree very well.
A one dimensional two-phase numerical simulator was developed and used to perform a sensitivity analysis for the following situations:desaturation at constant capillary pressure,desaturation using constant injection rate followed by a waiting period to achieve equilibrium,desaturation using continuous injection at constant rate without a waiting period to achieve equilibrium.
In this paper we discuss guidelines to interpret and use results obtained from the above three methods.

Introduction
In order to estimate reserves based on resistivity logs, it is essential that some rock electrical parameters are measured in the laboratory at simulated reservoir conditions of temperature and pressure. The rock electrical parameters, namely, saturation exponent (n) and cementation factor (m) are used in Archie equation to estimate water saturation: (1)
where Ro is the resistivity of 100% brine saturated rock and Rt is the resistivity of a partially saturated rock. Ro is also defined by Archie as:
(2)
where F is the formation resistivity factor and Rw is the brine resistivity. The formation resistivity factor can be calculated from the following equation:
(3)
where is the porosity and m is the cementation factor.
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