In-Depth Investigation of the Validity of the Archie Equation in Carbonate Rocks

Abstract

Abstract Archie found an empirical equation for consolidated sandstones relating several formation parameters, such as, porosity and water saturation. Despite its common use by petroleum engineers, Archie equation is not easy to apply to carbonate rocks because formation parameters (a, m, n) are functions of changes in the pore geometry, clay content, tortuosity of the pores, as well as formation pressure. The other important issue that Archie equation fails to address is the fluid critical point for the multi-component state in which different phases co-exist. This being the case for light oil and condensate reservoirs, the straightforward application of the Archie equation in carbonate rocks has severe limitations. The Archie equation is valid only when the rock is strongly water wet and clay free, which is not the case in carbonate rocks. There is no linear or direct correlation between resistivity index (IR) and formation water saturation in the carbonate rocks. Therefore, the Archie equation cannot be generalized over the entire carbonate reservoir. In this paper, a series of experiments is performed in order to derive the correct form of the Archie Equation that can be applied to carbonate rocks. The parameter a is further split to account for the composition, pore geometry and formation pressure. By separating these parameters, it is possible to find more precise correlation with formation resistivity and formation water saturation for carbonate reservoirs. Also derived are the correlations between resistivity and the composition of the carbonate rock as well as formation pressure. Finally, an equation is proposed for taking into account changes due to the presence of critical fluids. The generalized equation can then be applied to any fluid in a carbonate formation with varied geometry and clay content.