Paul F. Worthington
The British Petroleum Company Ltd
London
ABSTRACT
Empirical relationships between electrical resistivity and porosity f are influenced by formation anisotropy because they are derived from correlations between a vector quantity on the one hand and a scalar quantity on the other. In particular, the derived form of the Archie relationship F=a/fm shows a directional dependence because the formation factor F is a function of tortuosity.
By collating data relating to horizontally and vertically orientated sandstone specimens it has been demonstrated that computed values of the coefficient a and the exponent m can be influenced by the direction of the underlying resistivity measurements. Furthermore this directional dependence can be much greater if the values of the ratio of formation resistivity to electrolyte resistivity used to obtain a and m do not approximate the corresponding intrinsic formation factors but show significant departures as a result of shale effects. Observed variations in a and m with orientation have not conformed to the established relationship between these two parameters. This is shown to be a consequence of both the distribution of the average values of
F and f and the mode of computation of trends through the mean points.
Procedures are outlined for reducing the influence of formation anisotropy upon the Archie coefficient and exponent. These adjustments must be effected before m can be meaningfully correlated with, for example, the degree of shaliness or the degree of cementation. An appropriate directional dependence must be retained, however, if m is to be correlated with a parameter such as permeability.