Volume 113, Issue 4, April 2003
Index of content:
- GENERAL LINEAR ACOUSTICS 
Acoustic and mechanical response of reservoir rocks under variable saturation and effective pressure113(2003); http://dx.doi.org/10.1121/1.1554696View Description Hide Description
We investigate the acoustic and mechanical properties of a reservoir sandstone saturated by two immiscible hydrocarbon fluids, under different saturations and pressure conditions. The modeling of static and dynamic deformation processes in porous rocks saturated by immiscible fluids depends on many parameters such as, for instance, porosity, permeability, pore fluid, fluid saturation, fluid pressures, capillary pressure, and effective stress. We use a formulation based on an extension of Biot’s theory, which allows us to compute the coefficients of the stress–strain relations and the equations of motion in terms of the properties of the single phases at the in situ conditions. The dry-rock moduli are obtained from laboratory measurements for variable confining pressures. We obtain the bulk compressibilities, the effective pressure, and the ultrasonic phase velocities and quality factors for different saturations and pore-fluid pressures ranging from normal to abnormally high values. The objective is to relate the seismic and ultrasonic velocity and attenuation to the microstructural properties and pressure conditions of the reservoir. The problem has an application in the field of seismic exploration for predicting pore-fluid pressures and saturation regimes.
113(2003); http://dx.doi.org/10.1121/1.1548159View Description Hide Description
The unrestrained, traction-free vibrations of finite elastic cylinders with trigonal material symmetry are studied using two approaches, based on the Ritz method, which formulate the weak form of the equations of motion in cylindrical and rectangular coordinates. Elements of group theory are used to divide approximation functions into orthogonal subsets, thus reducing the size of the computational problem and classifying the general symmetries of the vibrational modes. Results for the special case of an isotropic cylinder are presented and compared with values published by other researchers. For the isotropic case, the relative accuracy of the formulations in cylindrical and rectangular coordinates can be evaluated, because exact analytical solutions are known for the torsional modes. The calculation in cylindrical coordinates is found to be more accurate for a given number of terms in the series approximation functions. For a representative trigonal material, langatate, calculations of the resonant frequencies and the sensitivity of the frequencies on each of the elastic constants are presented. The dependence on geometry (ratio of length to diameter) is briefly explored. The special case of a transversely isotropic cylinder (with the elastic stiffness equal to zero) is also considered.
113(2003); http://dx.doi.org/10.1121/1.1558372View Description Hide Description
In the Ritz method of calculating vibrational normal modes, a set of finite series approximation functions provides a matrix eigenvalueequation for the coefficients in the series and the resonant frequency. The matrix problem usually can be block-diagonalized by grouping the functions into subsets according to their properties under the symmetry operations that are common to the specimen geometry and crystal class. This task is addressed, in this study, for the case of cylindrical specimens of crystals belonging to one of the higher trigonal crystal classes. The existence of doubly degenerate resonant modes significantly complicates the analysis. Group-theoretical projection operators are employed to extract, from series approximation functions in cylindrical coordinates, the terms that transform according to each irreducible representation of the point group. This provides a complete symmetry-based block diagonalization and categorization of the modal symmetries. Off-diagonal projection operators are used to provide relations between the displacement patterns of degenerate modes. The method of analysis is presented in detail to assist in its application to other geometries, crystal structures, and/or forms of Ritz approximation functions.
Investigation of the vibrational modes of edge-constrained fibrous samples placed in a standing wave tube113(2003); http://dx.doi.org/10.1121/1.1548155View Description Hide Description
In earlier work it was suggested that the frictional constraint of a porous sample around its circumference in a standing wave tube resulted in shearing resonances of the sample. In the present work that effect has been confirmed by direct measurement of the spatial distribution of the velocity of the solid phase of a fibrous sample placed in a rigidly terminated standing wave tube and driven into motion by a plane, incident sound field. The measurements were performed using a standing wave tube to which a transparent downstream section was attached. A laser Doppler velocimeter was then used to measure the velocity of the solid phase of acoustically driven samples. The materials considered here were two types of aviation-grade glass fiber. A poroelastic finite element model was used to simulate the response of the constrained fibrous samples. Good agreement between measured and predicted mode shapes was found both when the samples were constrained only around their edges, and when an additional constraint plane was inserted axially through the samples. The present results confirm that glass fiber samples placed in a standing wave tube exhibit shearing modes and that those modes are associated with previously observed transmission loss minima.
Experimental validation of two elastodynamic models for the wave field generated by ultrasonic transducers113(2003); http://dx.doi.org/10.1121/1.1557213View Description Hide Description
Two different three-dimensional elastodynamic models are introduced to simulate the wave field generated in steel by two types of surface mounted ultrasonic transducers. By replacing the actual transducer by an equivalent surface source distribution, the models become amenable to an exact analytical analysis. The first model simulates the action of a contact transducer through a distribution of nonmoving line segment sources. The second model simulates the action of an angle beam transducer through a single moving line segment source. Almost any transducer aperture shape may be modeled, while the source may apply a nonuniform traction. To speed up the numerical space–time domain calculations, the Cagniard–De Hoop method is employed to analytically evaluate the wave field produced by a single nonmoving line segment source. This solution provides the integrand for both single-integral models. The models are experimentally validated for a contact transducer and three different angle beam transducers. The validation involves a comparison of the wave-field patterns, the directivity curves and some time-domain signals from the wave field. It is shown that the models reliably identify the wide variety of waves generated by ultrasonic transducers, such as focused waves, edge waves,Rayleigh waves and head waves.