NEW RESULTS IN RESISTIVITY WELL LOGGING*

Two independent theoretical analyses show that, spacing for spacing, the two-electrode normal device investigates deeper than the seven-electrode focused Laterolog 7. The first analysis, published earlier, compares the radii of investigation of the different sondes from the portion of the ground that contributes maximum to, or fifty percent of, the measured signal. The second relates to the nature of the departure curves for the two sondes for an infinitely thick resistive formation pierced by a bore hole. With increasing spacing, the apparent resistivity for the normal device rises much faster and asymptotically approaches the true resistivity much earlier than that for Laterolog 7. These two analyses also prove that, in a Laterolog 7, the radius of investigation increases as O₁O₂ decreases relatively to A₁A₂. Since any complex point electrode system is equivalent to a superposition of elementary dipoles or two-electrode devices, it follows that no resistivity sonde of discrete point electrodes can have a radius of investigation larger than that for the normal device of the same spacing. Laboratory measurements in a model tank confirm these theoretical results. For thin highly resistive formations we find from theoretical and model studies that the normal device is markedly superior to Laterolog 7 as it gives apparent resistivity values much closer to the true. It has other advantages as well. Thus, our results on the comparative performances of the normal and Laterolog 7 devices are at variance with those published so far since the introduction of Laterolog 7 in 1951. For reasons given in the text, the chief characteristic of Laterolog 7—namely, focusing the current from the central electrode in a thin horizontal sheet into the target formation—does not endow it with any special advantage. The main reason is that the measured potential in a Laterolog 7 is caused not only by the current focused into the target formation but also by the currents from the outer two electrodes which flow, due to the same focusing process, entirely through the adjacent formations and the mud column. Indeed, the contribution to the measured signal by the outer two power electrodes is considerably larger than that from the central.