Modelling and validation of dry and saturated velocities in carbonates from Saudi Arabia – Part II

Abstract

Ultrasonic compressional (P-wave) and shear (S-wave) velocity data, obtained from a set of 35 dry and water-saturated (carbonate) core samples, were presented as a first part to this study, in a separate paper by Bakhorji and Schmitt (2022). These carbonate samples were obtained from a prominent reservoir in Saudi Arabia.In this follow-up paper, the velocity measurements, obtained from these 35 core samples, were utilized to, firstly, predict and validate four appropriate rock physics models and to, secondly, derive empirical relationships relating the P- and S-wave velocities to the porosity and calcite content of the samples (over the effective pressure range from 5 MPa to 25 MPa). The derived empirical relationships were validated against the wireline P- and S-wave velocities assuming insitu reservoir pressure conditions. The empirical models predicted the P- and S-wave velocities accurately over the reservoir interval of interest. The shear strengthening / weakening effect, or the saturation effect on the shear moduli, was also modelled and is discussed further.The comparisons of the Biot, Gassmann, Mavko-Jizba-Biot (MJ-Biot) and Mavko-Jizba-Gassmann (MJ-Gassmann) model predictions, with the measured water-saturated P- and S-wave velocities, show that the squirt mechanism was not applicable for our samples. The Gassmann model consistently over-predicts the water-saturated S-wave velocities at low pressure, but closely fits the measured velocities at high pressures, whereas Biot over-predicts the water-saturated velocities in most of the studied samples. We conclude that Biot global-flow is most likely to be the principle dispersion mechanism in these samples.