Elastic properties of carbonates from laboratory measurements at seismic and ultrasonic frequencies

the reservoir’s diff erential pressure. Most samples are initially humidifi ed to avoid the softening matrix eff ect of initial introduction of moisture in the pore space. Small amounts of water (less than 1% of the pore volume) can reduce the bulk and shear moduli of the rock signifi cantly. Th e data in this paper are the estimated mean properties (markers in the plots) and one standard deviation of the random error (error bars in the plots). Th ese values are obtained from a statistical analysis between the measured experimental data and an assumed true model. Th roughout the paper, the comparisons in modulus and velocity are between the mean values. Figure 2 shows the P-wave velocity for two samples over a broad frequency band. Th ree representative points are presented for the low-frequency data (3, 100, and 1000 Hz). Th e ultrasonic data are collected simultaneously with the lowfrequency data at 800 KHz. Th e data at 104 Hz are obtained from the P-wave sonic log at the same wells and depths from where the rock samples were cored. Th is velocity is an averR saturated with a fl uid can be described as viscoelastic materials. Th e velocity and elastic moduli of viscoelastic materials increase with frequency. Th erefore, the elastic rock properties that we measure at high frequencies might not resemble the observations at lower frequencies. Laboratory measurements of velocity and elastic moduli are mostly performed at frequencies higher than those of surface seismic data, but with the stress-strain experimental procedure the moduli and velocity of laboratory samples can be measured at seismic frequencies. In this study, we compare measurements at 10 Hz and 0.8 MHz, at reservoir diff erential pressures, on 11 carbonate samples from the Middle East. We compare how the measurements at these two frequencies probe the sample. We make observations on the dispersion of the diff erent rock properties and eff ect when performing fl uid substitution with Gassmann’s relation. And, fi nally, we will show that for these samples the variation of elastic properties from low to high frequencies is signifi cant. However, if the ratio or difference between dispersive parameters is analyzed, this diff erence between measurements at diff erent frequencies can be reduced. Th e carbonate samples are measured dry and fully saturated with either a light hydrocarbon (liquid butane) or brine (180 000 ppm NaCl) at reservoir diff erential pressures. Diff erential pressure is the diff erence between confi ning and pore pressure. Th e samples have a range of porosity, permeability, and textures (labeled A through L in Figure 1). Th e moduli and velocities at seismic frequencies (10 Hz) are measured by applying a sinusoidal stress to the rock and measuring the resulting strain in diff erent directions on the rock sample and on the reference material (aluminum). Th e measured strain amplitudes are at the same scale as for seismic waves (~10-7). At ultrasonic frequencies (0.8 MHz), we measure the time of fl ight of a wave transmitted through the rock sample. From this time, we estimate the Pand S-wave velocities and from these the rock moduli. Th e core samples belong to two diff erent reservoirs with a diff erential pressure of about 35 MPa. Velocity and elastic modulus are measured at a diff erential pressure (Pd) of 31 MPa for all samples except for sample L, which is measured at a Pd of 24 MPa. For all rocks, pore pressure was constant at 3.5 MPa. Th e stress-strain system in the laboratory is pressurized with nitrogen gas, but for safety reasons the system is not able to reach the confi ning pressure of the reservoir. However, the pressures in the experimental setup are close to Figure 1. Crossplot of porosity and permeability for the measured carbonate samples.