Pressure effects in Nur's critical porosity model estimates for carbonate rocks

Abstract

The forecasting of fluid saturation changes within the reservoirs is one of the main issues of rock physics, which is often done using Biot-Gassmann theory. However, this theory demands the knowledge of the dry rock elastic moduli. Nur's (critical porosity) model is one of the theories to evaluate those dry rock properties from porosity and the mineral elastic properties of rock constituents. Therefore, that model is appropriate for estimating the dry rock bulk and shear moduli in well log analysis, especially in situations where there are no sonic logs available. In this paper, we analyzed four carbonate rock datasets reported in the literature, which consisted of measurements of porosity, mineral content and elastic velocities. Our approach focused on investigating how the misfits between the model and the experimental data varied according to porosity and pressure, through best-fitting regressions. Those observations allowed the setting of a modification on the Nur's model that can account for the pressure influence in porosity. This modified Nur's model significantly improved the accuracy of the results, exhibiting average relative errors 50% smaller than the original model estimates. The performance of that model varied for the different carbonate textures and pointed out that the siliciclastic content influences the predictability error of that modified critical porosity model. Rocks exhibiting the highest siliciclastic content showed an error reduction trend as pressure increases, while the other samples with minor siliciclastic content did not show significative accuracy variation.