Hezhu Yin

Compressional velocity and porosity in sand‐clay mixtures

Laboratory measurements of porosity and compressional velocity were conducted on unconsolidated brine saturated clean Ottawa sand, pure kaolinite, and their mixtures at various confining pressures. A peak in P velocity versus clay content in unconsolidated sand‐clay mixtures at 40 percent clay by weight was found. The peak in velocity is 20–30 percent higher than for either pure clay or clean sand. A minimum in porosity versus clay content at 20–40 percent clay by weight is also observed. Such behavior is explained using a micro‐geometrical model for mixtures of sand and clay in which two classes of sediments are considered: (1) sands and shaley sands, in which clay is dispersed in the pore space of load bearing sand and thus reduces porosity and increases the elastic moduli of the pore‐filling material and (2) shales and sandy shales, in which sand grains are dispersed in a clay matrix. For these sediments, the model reproduces the extrema in velocity and porosity and accounts for much of the scatter in ...

Effective properties of cemented granular materials

Abstract An analytical model is developed to describe the effective elastic properties of a cemented granular material that is modeled as a random packing of identical spheres. The elastic moduli of grains may differ from those of cement. The effective bulk and shear moduli of the packing are calculated from geometrical parameters (the average number of contacts per sphere and porosity), and from the normal and tangential stiffnesses of a two-grain combination. The latter are found by solving the problems of normal and tangential deformation of two elastic spherical grains cemented at their contact. A thin cement layer is approximated by an elastic foundation, and the grain-cement interaction problems are reduced to linear integral equations. The solution reveals a peculiar distribution pattern of normal and shear stresses at the cemented grain contacts: the stresses are maximum at the center of the contact region when the cement is soft relative to the grain, and are maximum at the periphery of the contact region when the cement is stiff. Stress distribution shape gradually varies between these two extremes as the cements stiffness increases. The solution shows that it is mainly the amount of cement that influences the effective elastic properties of cemented granular materials. The radius of the cement layer affects the stiffness of a granular assembly much more strongly than the stiffness of the cement does. This theoretical model is supported by experimental results.

Wave Velocities in Sediments

Systematic relations between porosity and compressional and shear velocitiesV p andV S in the three component sand, grains, clay and brine systems of (1) porous sandstone, (2) sands, and (3) suspensions, were obtained using experimental data and models. In cemented shaley sandstonesVp and Vswere found to correlate linearly with porosity and clay content. The velocities in clean sandstones are about 7% higher than those predicted by the linear fit, indicating that a small amount of clay significantly reduces the elastic moduli of sandstones.

Strength of cemented grains

We conducted compaction tests (isotropic drained loading) on randomly packed glass beads that were a) uncemented and b) cemented by epoxy at their contacts. In the latter case, the volume of the epoxy accounted for 10 percent of the pore space. Intensive crushing of grains was observed in the first case at about 50 MPa. In the second case, the cemented grains stayed intact, the failure being localized within the epoxy. Therefore, even small amounts of cement at contacts prevent the failure of grains. Theoretically, this effect follows from our theory of cemented granular materials: stress concentration is high at the contacts of uncemented grains, whereas even small amounts of relatively soft cement result in a more uniform stress distribution over a larger contact area.

Contact laws for cemented grains: Implications for grain and cement failure

Analytical solutions are presented to predict the intergranular contact load transfer in cemented granular media where both grain material and cement are elastic. The grains can be separated, have a direct point contact, or be compacted prior to cement deposition. For all these cases contact stress distributions are obtained for normal, tangential and torsional deformation of two cemented deformable grains. An important result is that intergranular cement, even if very soft, is load-bearing. Thus cementation reduces contact stress concentration (as compared with direct Hertzian interaction). Contact stresses are maximum near the center of the contact region when the cement is soft relative to the grains, and are maximum at the periphery of the contact region when the cement is stiff. These results allow us to predict the following modes of static and dynamic failure of the grains and intergranular bonds in a particulate material. (1) Uncemented grains will tend to shatter whereas cemented grains will stay intact, and the cement will fail. (This conclusion is supported by hydrostatic loading experiments where intensive crushing of uncemented glass beads was observed at about 50 MPa, whereas grains cemented at their contacts with small amounts of epoxy stayed intact.) (2) Where intergranular cementation is present, grain failure may still be expected if the cement is strong and stiff. In this case, grain damage will be initiated at the periphery of the cement layer. (3) Yielding of a cement material that is soft (as compared with the grain material) will initiate at the center of the contact region, whereas stiff cement will yield at the periphery.

Stress‐induced ultrasonic velocity and attenuation anisotropy of rocks

Intrinsic and stress-induced ultrasonic velocity and attenuation anisotropic properties of rocks have been investigated in this experiment. Three pairs of three-components transducers (one compressional wave, and two orthogonally polarized shear waves) were attached to the six faces of the tested cubic rock sample under “general triaxial loading”. ’ Eight rock samples (granite, limestone, sandstones, shales, and Ottawa sand) have been tested. Distinct velocity anisotropy, S-wave splitting, and attenuation anisotropic patterns -were observed. Stress-induced velocity and attenuation are significant in “soft rock”. A physical model-orthorhombic anisotropy of both velocity and attenuation were observed through the analysis of the results.

Scale effects on dynamic wave propagation in heterogeneous media

To study scale-effects on wave propagation in 3-D heterogeneous media, we conducted dynamic and static laboratory experiments on seven samples of glass beads cast with epoxy. We measured P and S wave velocities and frequency dispersion by the pulse-transmission method, and static elastic Youngs modulus by a uniaxial stress test. We changed the scale of the heterogeneity by varying the diameter of the glass beads in each sample, and obtained wavelength to scale ratios varying from 0.2 to 20. We observed about 22% P-wave velocity dispsersion and 15% S-wave velocity dispersion within this range of wavelength to scale ratios. We observed no scale effects on the static Youngs modulus of the same seven samples. It is clear that strong wave velocity dispersion in the experiment is due to the dynamic wavelength-scale effects caused by scattering.

Porosity, permeability, and acoustic velocity in granular materials

The effects clay-content, grain-size on porosity, permeability, and seismic velocities of granular materials was studied through a series of laboratory experiments. Porosity, permeability, and ultrasonic P-wave and S-wave velocities were measured among unconsolidated clean Ottawa sand, pure kaolinite, and ten of mixtures varied by kaolinite weight percent at both dry and brine saturated conditions, and at various confining pressures up to 50 MPa. With clay-content as a variable, porosity is minimized at 20% 40% clay by weight depending on confining pressure. Permeability is most affected when clay-content is less than the above minimums, called here the critical clay-content, and fairly independent of clay when clay-content is greater than the critical claycontent. A peak in P-wave velocity versus clay-content was found at about 40% clay by weight.

Seismic detection of residual contaminants

The key to effective characterization and treatment of contaminated sites is their ability to delineate the spread of contaminants in the shallow subsurface. A promising non-invasive technique that allows one to identify contaminants is the geophysical three-dimensional mapping of seismic velocities, reflections, and attenuation. The physical principle of this technique is that the same rock, if filled with different fluids, transmits sound waves differently. There are tow main reason for this effect: (a) pore-fluid compressibility and (b) pore-fluid viscosity. While the effect of pore-fluid compressibility has been extensively used for hydrocarbon detection (bright spots), the latter, pore-fluid viscosity, effect has been neglected, mainly because it is noticeable at high frequencies only. The authors present theoretical models which show that at relatively high, but practically important, frequencies (1--10 kHz) the effect of pore-fluid viscosity becomes seismically visible and thus allows one to locate residual viscous contaminants left in thin pores and/or between sand grains. This conclusion is supported by a laboratory ultrasonic-experiment where adding small amounts of viscous epoxy to a glass-bead pack resulted in increasing compressional-wave velocity.