Conductivity Anisotropy in Shale-Free Sandstone

The existence of conductivity anisotropy has implications for formation evaluations using Archie's model for relating formation water saturation to formation resistivity. Bulk anisotropy of sedimentary rocks can arise from the interleaving of rock units having differing electrical properties. For special core analysis, whole core is often selectively plugged in attempting to obtain homogeneous samples in the supposition that measurements taken on homogeneous samples will yield values representing typical reservoir properties. It is an article of faith that heterogeneous rocks composited from components similar to the homogeneous samples will exhibit physical properties predictably intermediate between the properties of the homogeneous samples. This is a reasonable belief that is demonstrably true for certain scalar parameters of the formation, for example porosity. Unfortunately, the direction-dependent properties of the formation do not behave in this intuitive manner. For example, we examine a two-component layered model sandstone for which the values of Archie's porosity exponent m and saturation exponent n for the composite rock have values that are very different from those of the individual components. The exact values of m and n for composite rocks depend not only upon their values of the constituent components but also upon the relative volume fractions of the components, and the orientation at which the conductivity measurements are made. Estimates of m and n in layered rocks based on simple averaging are incorrect. The theoretical results are supported by the general variability in the resistivities of samples having similar porosities in the experiment that determines m, manifest as the commonly observed scatter in the formation resistivity factor-porosity plots, and as anomalously low values of saturation exponents (n 1) often observed in aeolian sand-stones. Neglecting the existence of these effects (as has been, and is still, done) must result in a false sense of the accuracy of formation evaluations, as well as an unwarranted lack of confidence in results from the laboratory when they are in conflict with naive preconceptions of how formation properties should behave in the aggregate. A theoretical understanding of this issue must, at a minimum, improve estimates of uncertainty in formation evaluations. There is a definite (but as yet unrealized) promise that these effects can be accounted for and properly weighted in formation evaluations based upon triaxial induction logging instrument responses.