ABSTRACT

The basic relationship for interpreting the electrical resistivity log is Archie's law. Since its formulation in 1941, it has been modified and expanded to explain a wide range of rock formations. In 1957, de Witte expanded Archie's relationship to include shaly sands. In 1968, Waxman and Smits explained shaly sand conductivity in terms of cation exchange in clay. All of this work is, to a great extent, of an empirical nature. Consequently, all of these relationships contain parameters which have no direct physical interpretation. Recently, however, Sen has derived Archie's law from basic principles using the Hanai-Bruggeman equation, where it is assumed that water is the continuous component and that the matrix is a pure insulator. In this paper, the Hanai-Bruggeman approach is expanded to include a conducting matrix. The result is in agreement with de Witte for low matrix conductivity, but suggests that the equation of Waxman and Smits should be modified. It is also found that a wide range of formation factor studies can be understood in terms of a conducting matrix. Even for the case of so called"clean sands," matrix conductivity plays a significant role. Since the derived equation contains no arbitrary parameters, it should provide a framework for classifying rock formations and should prove useful in resistivity log interpretation. A more extensive version of this paper has been submitted to Geophysics.

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