An equation for estimating water saturation in clean formations utilizing resistivity and sonic logs: theory and application

An equation estimating water saturation values from resistivity and sonic logs, which are the common available logs in most of the wells and formations, was investigated for different lithologies. It is essentially based on the combination of Archieʹs and Raigaʹs relationships, with their respective coefficients a, m, n, and x. Application of this equation to real field data in the USA and Egypt show particularly good agreement in a variety of cases, in particular, if the formation true resistivity (Rt) is greater than 5 Ω m. In the case where Rt is less than 5 Ω m, multiplication of this equation by a certain correction factor is recommended. This factor, which can be empirically estimated, was found to be ranging numerically from 1 to 1.8 depending on the shale transit time (Δtsh) and cementation exponent (m). With the exception of core measurements, and where no porosity tools other than sonic logs are available, this equation can be considered as a good predictor for estimating water saturation in clean formations (non-shaly). In case of clay content, the application of the equation should include the same correction procedures of the sonic log reading those applied in usual interpretation. Worthy of remarks is that this equation gives reasonable and reliable values for rocks having transit time ranging between 40 and 150 μs/ft; above this range, the usefulness of this equation must remain in doubt. Knowledge of porosity is not necessary in such evaluation, which reflects the general usefulness of this equation. More data are needed to test the existing relation in numerous conditions.