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

摘要

Archie found an empirical equation for consolidatedsandstones relating several formation parameters, such as,porosity and water saturation. Despite its common use bypetroleum engineers, Archie equation is not easy to apply tocarbonate rocks because formation parameters (a, m, n) arefunctions of changes in the pore geometry, clay content,tortuosity of the pores, as well as formation pressure. Theother important issue that Archie equation fails to address isthe fluid critical point for the multi-component state in whichdifferent phases co-exist. This being the case for light oil andcondensate reservoirs, the straightforward application of theArchie equation in carbonate rocks has severe limitations.The Archie equation is valid only when the rock is stronglywater wet and clay free, which is not the case in carbonaterocks. There is no linear or direct correlation betweenresistivity index (IR) and formation water saturation in thecarbonate rocks. Therefore, the Archie equation cannot begeneralized over the entire carbonate reservoir.In this paper, a series of experiments is performed inorder to derive the correct form of the Archie Equation thatcan be applied to carbonate rocks. The parameter a is furthersplit to account for the composition, pore geometry andformation pressure. By separating these parameters, it ispossible to find more precise correlation with formationresistivity and formation water saturation for carbonatereservoirs. Also derived are the correlations betweenresistivity and the composition of the carbonate rock as well asformation pressure. Finally, an equation is proposed fortaking into account changes due to the presence of criticalfluids. The generalized equation can then be applied to anyfluid in a carbonate formation with varied geometry and claycontent.