Velocity compressional

Whalley (1980) presented a theoretical argument to suggest that both the thermal expansivity and Poisson s ratio should be similar to that of ice. With the above two estimates, Whalley calculated the compressional velocity of sound in hydrates with a value of 3.8 km/s, a value later confirmed by Whiffen et al. (1982) via Brillouin spectroscopy. Kiefte et al. (1985) performed similar measurements on simple hydrates to obtain values for methane, propane, and hydrogen sulfide of 3.3, 3.7, and 3.35 km/s, respectively, in substantial agreement with calculations by Pearson et al. (1984). 

Pandit and King (1982) and Bathe et al. (1984) presented measurements using transducer techniques, which are somewhat different from the accepted values of Kiefte et al. (1985). The reason for the discrepancy of the sonic velocity values from those in Table 2.8 and above is not fully understood. It should be noted that compressional velocity values can vary significantly depending on the hydrate composition and occupancy. This has been demonstrated by lattice-dynamics calculations, which showed that the adiabatic elastic moduli of methane hydrate is larger than that of a hypothetical empty hydrate lattice (Shpakov et al., 1998). 

Shimizu et al. (2002) extended the previous Brillouin spectroscopy measurements by performing in situ measurements on a single crystal methane hydrate. They examined the effect of pressure on shear (TA) and compressional (LA) velocities, and compared these results to that for ice. The shear velocities of methane hydrate and ice were very similar, showing a slight decrease (about 2 to 1.85 km/s) with increasing pressure (0.02-0.6 GPa). Conversely, the compressional velocities of ice and methane hydrate were different. The... 

Lee and Collett (2001) measured the compressional (P-wave) and shear (S-wave) velocities of natural hydrates in sediments (33% average total porosity) at the Mallik 2L-38 well. The P-wave velocity of nongas-hydrate-bearing sediment with 33% porosity was found to be about 2.2 km/s. The compressional velocity of gas-hydrate-bearing sediments with 30% gas hydrate concentration (water-filled porosity of 23%) was found to be about 2.7 km/s, and 3.3 km/s at 60% concentration (water-filled porosity of 13%), that is, about a 20% or 50% increase to nongas-hydrate-bearing sediment. The shear velocity was found to increase from 0.81 to 1.23 km/s. 

For hydrates in ocean sediments, the technology for detecting the BSR was determined in 1953 with the development of a precision ocean depth recorder (Hamblin, 1985, p. 11). In this technique a sonic wave penetrates (and is reflected from) the ocean floor, with the time recorded for the return of the reflected wave to the source. Velocity contrasts beneath the ocean floor mark a change in material density, such as would be obtained by hydrate-filled sediments overlying a gas. BSRs related to hydrates are normally taken as indications of velocity contrasts between velocity in hydrated sediments and a gas, marked by a sharp decrease in sonic compressional velocity (Vp) and a sharp increase in shear velocity (Vs) (Ecker et al., 1996). 

There are certain aspects of performance that make the Apm oscillators potentially attractive as chemical sensors. First of all, the fact that both surfaces contribute to the signal means that the sensitivity is higher than for the corresponding SAW device. The most important advantage follows from the fact that velocity of the lowest order of the antisymmetric mode is much slower than the compressional velocity of sound in most liquids (900-1,500 m s-1), which means that the energy... 

Solution Using values of C 1, C44, and p hYxn Table 2.2 in the equations given above for the compressional velocity (V ) and shear velocity (va) yields the following ... 

Vi is the compressional velocity layer 1. V2 is the compressional velocity layer 2. 

These dynamic moduli correspond to the initial tangent moduli of the stress-strain curve for an instantaneously applied load and are usually higher than those obtained in static tests. The frequency and nature of discontinuities within a rock mass affect its deformability. In other words, a highly discontinuous rock mass exhibits a iower compressional wave velocity than a massive rock mass of the same type. The influence of discontinuities on the deformability of a rock mass can be estimated from a comparison of its in situ compressional velocity, /pf, and the laboratory sonic velocity, /p, determined from an intact specimen taken from the rock mass. The velocity ratio, /pf/t/pi, reflects the deformability and so can be used as a quality index. A comparison of the velocity ratio with other rock quality indices is given in Table 2.7. 

Figure 5.5 The influence of calcium carbonate filler loading on ultrasonic compressional velocity through polypropylene injection mouldings...

The elastic properties of hydrates are important to understanding the sonic and seismic velocity field data obtained from the natural hydrates-bearing sediments. Data on the mechanical properties of CO2 hydrates are hmited. Table 10.3 shows the elastic properties of ice, CH4 hydrates, and CO2 hydrates. It should be noted that these properties may vary for different guests and occupancies. For example, Kiefte et al. [21] measured the compressional velocity of methane, propane, and hydrogen sulfide hydrates as 3.3, 3.7, and 3.35 km/s, respectively. 

FIGURE 6.32 Compressional velocity as a fimctirai of porosity for inclusions filled with gas (left figure) and water (right figure), calculated fra- different aspect ratios (0.10, 0.15, 0.20, and 0.05). Input parameters are (limestone matrix) ts=73GPa, /Js=32GPa, = 0.01 GPa,... 

Figure 6.34 shows a comparison of calculated compressional velocities with experimental data from measurements on granite of different grain sizes (Lebedev et al., 1974a,b). Forward-calculated curves cover the experimental data and indicate also for this model that textural properties are connected with the aspect ratio as model input. 

---