Petrophysical models are applied to wireline dielectric dispersion measurement to estimate water saturation, water salinity, and the water phase tortuosity mn. The parameter mn (which is also referred to as "MN" in other sources) combines the effects of pore-space tortuosity (cementation exponent m in Archie's equation) and distribution of water and hydrocarbons in the pore system (saturation exponent n). We present a new method to separate these effects and obtain Archie's m and n exponents from this water phase tortuosity mn. The method described in this paper makes it possible to fully utilize dielectric dispersion log data to estimate key petrophysical parameters in situ, whereas these parameters were previously only available through expensive and time-consuming core analysis. Together, m and n may be used to infer wettability and estimate water saturation more accurately and reliably in the uninvaded zone.
When m can be estimated by nuclear magnetic resonance (NMR), borehole images, or core resistivity measurements, the dielectric parameter mn can be used to estimate n, which can be used to infer wettability. In the absence of capillary pressure hysteresis, mn obtained in the invaded zone by downhole dielectric tools may be used to estimate water saturation in the uninvaded zone by using deep resistivity tools and Archie's law. Practically, these applications are very limited in their scope. The new method assumes that the parameters m and n from the Archie equation are constant for depths with similar rock types. For each rock type, the parameter mn is plotted against a variable combining porosity and water saturation. The data are then fit with a linear function that yields Archie's m and n when the variable takes the values of 1 and 0, respectively. The fit is more heavily weighted towards data points with lower uncertainty.
We demonstrate via simulations that Archie's m and n exponents can be accurately and reliably estimated by the new method. This is supported by our study of several limestone cores in various stages of brine/oil saturation in the laboratory where we find that the predicted linear model fits the data reasonably well and can be used to estimate both m and n. We have also applied this method to several wells of a carbonate field. Rock types in each well are determined based on factor analysis of NMR data. The dielectric data for each rock type across all the wells are then analyzed with the method described here to yield values of m and n for each rock type, together with an evaluation of the uncertainty on these parameters. The results are then compared with m and n data from special core analysis (available in two wells of the field). We find that the new method's results fall within the uncertainty of the core analysis results.