Archie (1941) found an empirical equation for consolidate sandstone relating some formation parameters, porosity and water saturation. Archie equation is not easy to apply to rocks because formation parameters (a, m and n) are functions of electrical tortuosity. Electrical tortuosity is determined by pore geometry, tortuousity of the pore system and wettability which, affects oil - water distribution in the pores. Carbonate rocks with their complex pore systems and intermediate to oil wettability are difficult to describe petrophysically with a single a, m and n over a reservoir interval. Formation Resistivity Factor (FR) is highly variable. There is often no linear and direct relation between the resistivity index (IR) and formation water saturation (Sw) as the variably sized pores desaturate at different rates. These cases are labeled as non-Archie rocks. Archie is strictly valid only when the rock is strongly water wet, clay free and has a more or less uniform pore size distribution. An important issue that Archie equation misses is the fluid critical point for multi - component state in which different phases co-exist. It is not clear how at reservoir conditions oil and water coexist in the pore system. Introduction Archie (1941)(1) introduced an equation, which combines resistivity index (IR) and Formation Resistivity Factor (FR) in order to calculate water saturation. Using this equation, water saturation is commonly computed. Archie equation requires the values of cementation exponent ‘m’, saturation exponent ‘n’, and the rock consolidation factor ‘a’. He derived two empirical relationships; 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 mentioned and was only an approximate relationship. The conventional procedure to determine ‘m’ and ‘n’ parameters is by 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 driven. The same situation occurs when water saturation is plotted against resistivity index (IR) to find the value of ‘n’. In his paper, Archie mentioned that formation resistivity (Rt), as a quantitative value is not accurate 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. In clean, clastic quartz reservoirs, the industry has been able to apply a constant ‘a’, ‘m’ and ‘n’ with some success. Carbonates present a much more difficult situation. Their pore geometry is often complex and infinitely variable foot by foot in the reservoir. The application of constant Archie parameters in carbonates results in inaccurate and occasionally "just plain wrong" water saturation. The industry has for several decades sought a down-hole cementation exponent predictor through various mathematical and empirical models. One method determined ‘m’ in the flushed zone and then applied the results to the virgin zone(2). This method assumed the saturation exponent was equal to the cementation exponent. The effect of the mud cake, the borehole conditions and incomplete invasion complicated the results. The presumption of ‘n’ equal to ‘m’ has proved false(3). Table 1 presents a failed attempt to relate visual examinations of the core pore systems to the cementation exponent in lieu of special core analysis (SCAL) data. There is currently no reliable way to determine in-situ what the continuing varying values of this cementation exponent are. Some researcher(4) found that the values of ‘m’ and ‘n’ only represent two numbers that minimize the error function of the equation. In fact Archie(5) emphasized that rocks are heterogeneous and their characteristics cannot be expressed as a real mathematical equation. The effect of pore structure(6), rock wettability(7), hysteresis, type of oil(8), dispersion(9), pressure, temperature, and effective stress(10) on ‘m’ and ‘n’ parameters were variably addressed by other researchers.
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