Saturation exponent at various wetting condition: fractal modeling of thin-sections

Saturation exponents, along with resistivity log data, are usually needed for evaluating the initial saturation of a hydrocarbon reservoir. A number of experimental investigations have shown that reservoir wettability affects the exponent value. A remarkable divergence of conclusions, however, still appears in the literature. This paper presents the results of a study based on the application of fractal concepts. The concepts have been used to derive parameters such as clay content and electrical tortuosity of thin-sections at a given wetting condition and for various water saturations. A general equation of electrical resistivity was then developed, incorporating these parameters. The advantage of this approach is that, it is independent of rock–fluid equilibrium problems that commonly influence laboratory measurements. The present work employed 20 thin-sections of limestone and sandstone. It was found that the lowest exponent of 1.8 was obtained for strongly water-wet shaley sandstone and the highest value of 5.3 was for strongly oil-wet conditions. The exponent consistently increases as the wetting condition is shifted from strongly water-wet toward oil-wet. It is close to 2.0 for clean sandstone at strongly water-wet conditions; this supports Archieʹs empirical formula.