Abstract
Abstract. When scientists apply Archie's first law they often include an extra parameter a, which was introduced about 10 years after the equation's first publication by Winsauer et al. (1952), and which is sometimes called the “tortuosity” or “lithology” parameter. This parameter is not, however, theoretically justified. Paradoxically, the Winsauer et al. (1952) form of Archie's law often performs better than the original, more theoretically correct version. The difference in the cementation exponent calculated from these two forms of Archie's law is important, and can lead to a misestimation of reserves by at least 20 % for typical reservoir parameter values. We have examined the apparent paradox, and conclude that while the theoretical form of the law is correct, the data that we have been analysing with Archie's law have been in error. There are at least three types of systematic error that are present in most measurements: (i) a porosity error, (ii) a pore fluid salinity error, and (iii) a temperature error. Each of these systematic errors is sufficient to ensure that a non-unity value of the parameter a is required in order to fit the electrical data well. Fortunately, the inclusion of this parameter in the fit has compensated for the presence of the systematic errors in the electrical and porosity data, leading to a value of cementation exponent that is correct. The exceptions are those cementation exponents that have been calculated for individual core plugs. We make a number of recommendations for reducing the systematic errors that contribute to the problem and suggest that the value of the parameter a may now be used as an indication of data quality.
Highlights
In petroleum engineering, Archie’s first law (Archie, 1942) is used as a tool to obtain the cementation exponent of rock units
Where ρo is the resistivity of the fully water-saturated rock sample, ρf is the resistivity of the water saturating the pores, φ is the porosity of the rock, m is the cementation exponent (Glover, 2009), and the ratio ρo / ρf is called the formation factor
While the original Archie’s law is the most correct physical description of electrical flow in a clean porous rock that is fully saturated with a single brine, the Winsauer et al (1952) variant is the most practical to apply because it compensates to some extent for systematic errors that are present in the experimental data
Summary
Archie’s first law (Archie, 1942) is used as a tool to obtain the cementation exponent of rock units. While most scientists fit Eq (2) to measurements made on a group of data from core plugs from the same geological unit or facies type on a log formation factor vs log porosity plot, some petrophysicists prefer to calculate cementation exponents for individual core plugs than calculate a mean and standard deviation for a given group of measurements.
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