The uses and abuses of the Archie equations, 1: The formation factor-porosity relationship

• Published in: Journal of applied geophysics Vol. 30; no. 3; pp. 215 - 228
• Main Author: Worthington, Paul F.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.05.1993
• ISSN: 0926-9851; 1879-1859
• DOI: 10.1016/0926-9851(93)90028-W

Model studies of the first Archie equation, which relates the formation resistivity factor and porosity specifically for effectively clean (shale-free) porous media, have quantified the changes to this relationship caused by latent shale effects. The scales of these departures correspond to the ranges reported by experimental investigators on the basis of empirical studies of supposedly clean formations, for which some of the experimental data would actually be physically untenable. Thus, many of the published versions of this equation do not, as is claimed, definitively relate porosity to an intrinsic formation factor but merely to an apparent formation factor, which shows an incidental relationship to porosity that is salinity-dependent and can even become inverted. The primary implication of departures from clean conditions, illustrated using field data from reservoirs with varying degrees of shaliness, is that the relationship between (apparent) formation factor and porosity can remain well defined even though the numerical form changes significantly with variations in salinity. The inadvertent use of such an arbitrary relationship to estimate formation factor from porosity can transmit errors of over 30 saturation units to be subsequent determination of water (and thence hydrocarbon) saturation. On this basis, the “standard” practice of determining the form of the first Archie equation from measurements of “formation factor” that use simulated formation water must be viewed with extreme caution. There is no guarantee that a well-defined linear trend on a bilogarithmic scale actually reflects effectively clean conditions. This is contrary to conventional thinking, which predicts a curvilinear trend where shale effects are manifest. Apart from the demonstrable effect on the determination of hydrocarbon saturation, these observations also have a direct bearing on the concept of reservoir zonation and on evaluation approaches that use the Archie exponent as an indicator of lithology, pore geometry, degree of induration, or permeability.