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.
Introduction
Archie's Equation
Archie1 introduced an equation, which relates resistivity index (IR) and formation resistivity factor (FR) in order to calculate water saturation. Using this equation, water saturation is commonly computed.
Archie's equation requires the values of cementation exponent, m, saturation exponent, n and the rock consolidation factor, a. He derived two empirical relationships, namely, the formation resistivity factor, FR, which is related to porosity, and the resistivity index, IR, which is related to the water saturation. The equation was not a precise one, as he pointed out, and was only an approximate relationship. The conventional procedure to determine m and n parameters is by the crossplot techniques. Plotting formation resistivity factor, FR, versus core or log porosity on the log-log paper is used to find a and m values. The value of m is the slope and a is the intercept. However, in carbonate rocks, most of the points are scattered and one slope cannot be drawn. The same situation occurs when water saturation, Sw, is plotted against resistivity index, IR, to find the value of n.
In his paper, Archie mentioned that the measurement of the formation resistivity, Rt, is often inaccurate as a result of the effect of borehole size, mud and its filtrate, bed thickness, wellbore deviation and connate water salinity. The logging industry has made great strides in obtaining accurate information on porosity and resistivity but has failed to narrow the uncertainty for a, m, and n parameters.