Despite the fact that Carbonate reservoirs contain more than half of the world’s oil and gas reserves, their physical properties have not received enough attention. Carbonate rocks are formed from a combination of biological and chemical processes that add complexity and heterogeneity to its structure and petrophysical properties. Fluid saturation is one of the important factors that influences the elastic properties of rocks. Most studies on determining the applicability of using the Gassmann fluid substitution model in carbonates concluded that the Gassmann model, most of the time, is not suitable for predicting the observed saturated velocities in carbonates. This paper will compare alternative techniques for modeling these velocities using data from the Arab-D reservoir in Saudi Arabia. Here, water-saturated P- and S-wave velocities were measured in thirty seven carbonate samples from the Arab- D reservoir, and only a subset of fifteen of these were selected for the fluid model prediction study. The measured velocities were compared to model predictions from dispersion-free Gassmann, Biot, squirt-Gassmann and squirt-Biot models. Only eight of the selected samples were used in the squirt models, since these required the use of quasi-static data in order to calculate the compliant porosity as a function of confining pressure. We found that the squirt mechanism was not active on all the studied samples. For P-wave the Biot mechanism is likely to be the principle dispersion mechanism in these samples. For S-wave velocities, Gassmann’s model consistently over-predictes the saturated velocities at low confining pressures, but closely fits those measured at high pressure, whereas the Biot model over-predicted the saturated velocities in most of the studied samples.
Fluid saturation is one of the more important factors that influencing the elastic properties of rocks. It is well documented that the seismic velocities of saturated rocks vary significantly with the wave frequency (e.g. Schmitt, 1999; Batzle et al., 2006; Winkler, 1983). Velocities of dry rock are usually assumed to be independent of frequency. Seismic velocities are measured over a wide spectrum of frequencies ranging from seismic (10-100 Hz) through sonic (~10 kHz to 20 kHz) up to ultrasonic (0.1-1 MHz); therefore corrections for the frequency dependence, socalled socalled dispersion, are important for an accurate comparison of the velocities derived using different modeling techniques. Regardless of the frequency, the P-wave velocities generally increase and the S-wave velocities decrease upon complete saturation. This increase in P-wave velocity is due to the changes of pore fluid bulk modulus as the pore fluid changes from gas in the case of the dry measurements, to water in the case of the water saturation measurements. The shear modulus of both water and gas are equal to zero, so the decrease of S-wave velocity is due to the increase of the overall bulk density of the porous rock upon saturation. The Biot mechanism (global flow) generates by the participation of the fluid in the solid motion through viscous friction and inertial coupling generally between the fluid and solid in the porous material.
