Articles | Volume 7, issue 4
Research article
29 Jul 2016
Research article |  | 29 Jul 2016

Archie's law – a reappraisal

Paul W. J. Glover

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.

Short summary
In 1942 Archie discovered equations which have been used ever since to calculate reserves of oil and gas around the world. Two equations exist, one which is theoretically justified, and one which is not. Unfortunately it is the one which is not justified that often gives the best results. This research examines the extent to which the two approaches give differing results, concluding that the Winsauer et al. form of Archie's equations is better for use with data containing systematic errors.