Tutorial: Introduction to Resistivity Principles for Formation Evaluation: A Tutorial Primer

Kennedy, David (Texas A&M University) | Garcia, Fredy (Ecopetrol S.A.)



The standard model for relating bulk formation resistivity to porosity and water saturation was introduced to the petroleum industry in 1941; it remains the industry standard to this day. The model was discovered empirically by means of graphical analysis. Basically, G.E. Archie discovered that when the logarithm of formation resistivity factor was plotted against the logarithm of porosity the resulting trend could be fitted by a straight line. A similar relationship was discovered connecting the logarithms of resistivity index and water saturation. When these two power laws are combined into a single equation, it can be solved for water saturation (which is not observable from a borehole) in terms of bulk formation resistivity, interstitial brine resistivity, and porosity (all of which can be estimated from observations made in boreholes). This revolutionized log interpretation. There has always been a problem with the model in terms of its “explainability”. That is, it cannot be derived in any straightforward way from accepted first principles of physics. It does not contradict any first principle, but neither does it seem to follow ineluctably from them. However, since the model works, most formation evaluators have memorized the relationships that follow from the model and simply “get used to them”. That remains the situation to this day. However, there is a path around this obstacle to understanding formation resistivity at a fundamental level, and that way forward is to abandon the resistivity formulation in favor of its reciprocal, conductivity. It is surprising that such a seemingly trivial change could open a new vista into the relationships among formation electrical properties. A conductivity formulation permits the asking of questions about how a formation’s conductivity should respond to changes not only in brine conductivity, but also in the fractional amount of brine in a formation, and its geometrical configuration. By answering these questions in an obvious way, and with some analysis of data taken in the laboratory, an intuitively obvious model explaining bulk formation conductivity emerges. The model is not the same as the Archie model. However, when certain parameters are taken to their limiting values, and the model is converted into resistivity space, Archie’s power law model is revealed as an approximation to the limiting cases. Thus, from the conductivity formulation, an intuitive understanding of the Archie model emerges. Moreover, the conductivity model can be derived in at least three different ways, each yielding different insights into formation conductivity.