The Impact Of Resistivity Uncertainty On Water Saturation Available to Purchase

Suitable technical and economical strategies for reservoir development can be defined only on the basis of an accurate determination of the volume of hydrocarbons originally in place, i.e. on a reliable estimation of the petrophysical properties of the reservoir rocks. However, since the formation evaluation process relies on mathematical algorithms applied to data acquired under reservoir conditions that can severely affect the precision of the measurements, a need is felt to estimate the accuracy associated to the calculated porosity and water saturation profiles. In particular, the uncertainty affecting water saturation strongly depends on the reliability of the true resistivity profile estimation. The measured apparent resistivity is usually quite different from the true formation resistivity due to the presence of a number of environmental effects; therefore a new methodology, based on direct modeling and inversion techniques, has been recently developed in order to compute more accurate true formation resistivity profiles. In this paper it is shown how the error affecting the measured and/or modeled resistivity and its propagation to water saturation can be estimated by resorting to a probabilistic approach. Results indicated that the uncertainty associated to the true resistivity is essentially related to the accuracy of the acquisition tool, to the geological and petrophysical characteristics of the formation (presence of thin layers, invasion, high resistivity contrasts) and, above all, to the lack of knowledge of the formation more complex characteristics. In particular, the latter aspect represents one of the most relevant sources of potentially large errors, which can be controlled only if a field domain of physically acceptable resistivity values can be defined. Such values can be either derived from a priori petrophysical information or estimated with the aid of statistical analysis or both. It has been verified that the uncertainty affecting the modeled formation resistivity can exceed the accuracy of the acquisition tools, and that it can be properly estimated only by application of a suitable procedure accounting for all sources of errors. In this study the uncertainty related to water saturation was estimated by two different approaches: the analytical method, and a numerical approach based on Monte Carlo simulations. Although results appeared to be quite similar, it was shown that only the numerical method provides representative probabilistic distributions for input and output data. Finally, the error affecting water saturation was calculated when using the deepest resistivity log, usually assumed to be unaltered by mud invasion effects, as an estimation of the true resistivity instead of the modeled resistivity. Several tests, run on both real and synthetic formation models, showed that the difference is not negligible, as errors can be as high as 50% of the calculated water saturation.