Probing porous media with first and second sound. II. Acoustic properties of water-saturated porous media

Abstract

The ultrasonic properties (reflection/transmission and bulk attenuation/speed) of porous and permeable media saturated with a Newtonian fluid, namely water, are considered. The frequency dependence of the transmission amplitudes of pulses is measured through a slab of thickness d1, repeated for another slab of thickness d2 for a given material. With these two measurements on two different thicknesses, it is possible in principle to separate bulk losses from reflection/transmission losses for compressional waves in these materials. The bulk properties are calculated from the Biot theory for which all of the input parameters have been measured separately; the attenuations are particularly sensitive to the values of Λ, determined from second-sound attenuation measurements reported in the companion article. There is excellent quantitative agreement between the theoretical and experimental values in the cases considered; there are no adjustable parameters involved. The reflection and transmission coefficients are reported for some of the multiply reflected pulses and their amplitudes are compared with those calculated from the Deresiewicz–Skalak and Rosenbaum boundary conditions appropriate to either the open-pore or sealed-pore surfaces, as the case may be. Again, there is excellent quantitative agreement between theory and experiment. Compared with the open-pore boundary conditions, it is noted that there is a large reduction, both theoretically and experimentally, in the efficiency with which the slow compressional wave is generated when the sealed-pore boundary conditions apply, but this efficiency is not reduced to zero.

Multi-Component Acoustic Characterization of Porous Media

“…Berryman (1980) has found that the predicted body-wave velocities are in very good agreement with the experimentally observed values for all three body wavemodes. For the frequency-dependent attenuation of the P 2 -mode Johnson et al (1994) have found excellent agreement between theory and experiment. In addition, for the reflection coefficients as predicted by Biot's theory they have observed reasonably good agreement between the predicted and measured frequency-dependent coefficients at ultrasonic frequencies, for all three body wavemodes.…”

“…For the estimation of E and ν we use f = 820 Hz, corresponding with the (frequency-independent) results in Figure 7.2, because the pSt-wave does Table 7.1: Material parameters as used for water-saturated QF20 porous material. We have measured the magnitudes of ρs, φ and k 0 ourselves; the other values are taken from (Johnson et al, 1994). The values of E and ν have been calculated from those of K b and G. give unique minima in the (E, ν)-domain, exactly at the E-and ν-values of the QF20 (Table 7.1).…”

“…Next, we investigate the feasibility of the extraction of the interface-wave impedances from a simultaneous particle displacement and fluid pressure measurement using the same experimental set-up as described in Section 6.4. In this case, we use water-saturated QF20, which is an artificial porous material (Johnson et al, 1994). Finally, we compare the experimental results with the theoretical predictions using the computational model developed in Chapters 4 and 5.…”

Experimental Study of Sound Waves in Sandy Sediment

“…This assumption may not be correct for unconsolidated sand. The generalized moduli formulas appear correct when the grains are bonded [22], but the "bonding" of sand grains may include sliding friction and/or a fluid-reinforced frame [7,11]. Finding good formulas for intermediate moduli of sandy sediments is a task for future work.…”

“…Johnson et al [22] observed slow compression waves in consolidated fluidsaturated porous media, e.g., fused glass beads (called "Ridgefield Sandstone" even though it was man-made) and ceramic water filters (QF-20), and calculated for the first time all of the input parameters necessary for a complete description of the acoustic properties of all the modes over the entire frequency spectrum.…”