Sedimentary rocks display nonlinear elastic behavior. This nonlinearity is a strong function of frequency, strain amplitude, and the properties of the saturating fluid. Experimental observations and potential mechanisms that cause these nonlinearities are presented in this and a companion paper. Young’s moduli and Poisson’s ratios obtained from ultrasonic laboratory measurements (50 kHz, 100 kHz, 180kHz and 1 MHz), low‐frequency measurements (1–2000 Hz) and static measurements (0.001–0.05 Hz) show significant differences under identical stress conditions. A comparison of the laboratory‐measured quantities with log‐derived moduli measured at 20 kHz indicates that [Formula: see text]. This shows clearly that a wide variety of sandstones demonstrate frequency‐dependent elastic behavior (viscoelastic behavior) over a range of frequencies. Differences between static (low‐frequency, high‐strain amplitude) velocities and ultrasonic velocities can be explained partially by differences in frequency as predicted by grain contact models. Such models, however, do not explain the strain amplitude dependence observed in our data. A series of uniaxial stress cycling measurements were carried out to investigate the influence of strain amplitude on elastic moduli. These low‐frequency measurements (0.01 Hz) clearly show that the Young’s modulus decreases with strain amplitude for a wide variety of sandstones. Attenuation increases with strain amplitude. The strain amplitude dependence does not change when the rocks are saturated with brine although the rocks soften measureably.

Dynamic elastic properties o/ dry and water--saturated Green River shale samples were computed from compressional-and shear-wave velocity measurements, P-and S-wave velocity measurements were made in three mutually p er-perdicu!ar directions wilb respect to the bedding nlanes. Measurements were also made in several )i//ererrt directions by varyivg the angle between THE U. OF TEXAS AUSTIN, TEX, GULF RESEARCH & DEVELOPMENT CO. PITTSBURGH, SOCIETY OFPETROLEUM ES GlNEEn5 JOURNAL .

Uniaxial stress cycling experiments were conducted on dry, brine saturated and hexadecane saturated Berea sandstone samples to observe in detail the hysteresis in stress‐strain diagrams and to understand the influence of different fluids on the strain amplitude dependence of elastic moduli and attenuation. Cycling experiments were also conducted with sandstone samples saturated with CTAB, a cationic surfactant that renders the mineral surfaces hydrophobic. Hexadecane and CTAB were selected so as to investigate the relative contributions of adhesion hysteresis and stick‐slip sliding on attenuation in sedimentary granular rocks. Young’s moduli and Poisson’s ratios obtained from the cycling tests show a significant dependence on strain amplitude on dry as well as water and hexadecane saturated samples. Bow‐tie‐shaped diagrams are obtained when loading and unloading tangent moduli are plotted against strain. The type of fluid in the pore space and at the grain contacts has a large influence on the hysteresis observed in the stress‐strain diagrams.

This paper discusses the acoustic determination of producing bottornhole pressure (BHP). Two different techniques are presented for wells that have liquid above the formation and gas flowing upward through the gaseous liquid column. One technique involves the acoustic measurement of the liquid level and the casing-pressure buildup rate when the casinghead valve is closed. When these data are used along with an empirically derived correlation given here, the gradient of the gaseous liquid column in the annulus can be obtained. This technique offers a reasonably accurate procedure for determining the producing BHP of a well by acoustic means. The second method involves two acoustic measurements. A backpressure valve is used in the casing head to depress and to stabilize the liquid level at two positions while the well is produced at a constant rate. The gradient of the gaseous liquid column is then calculated and extrapolated to the formation depth.This paper discusses results from the field testing of numerous wells where the actual gradients of gaseous liquid columns were measured in a variety of casing/tubing sizes, oil gravities, gas flow rates, and pressures.

Results are presented for compressional and shear velocities and attenuations in fully brine-saturated tight gas cores with porosities from 3 to 11.9 percent and clay contents from 1 to 38 percent. The influence of porosity, clay content, frequency, and stress on velocities and attenuations were examined using the amplitude spectra of P-and S-waves in the frequency domain. Attenuations of samples were obtained using the spectral ratio method. For a few selected samples the attenuations were also measured using the length correlation method and these results were compared with the spectral ratio results.In tight gas sandstones, the attenuations obtained were 2 to 5 times greater than the attenuation obtained for Berea sandstone. In general, the presence of clay softens the rock grain contacts causing smaller values of compressional (Vp) and shear (Vs) velocities as the clay content increases. However, the VplVs ratio was found to increase with clay content. Compressionaland shear-wave amplitude spectra exhibited a shift in peak frequency toward lower frequencies for samples with higher clay content when compared to clean samples. Velocities and attenuations were found to be frequency dependent, but the positive slope of both compressional and shear attenuations indicate that scattering starts to dominate at the lower frequency end of the ultrasonic measurements. Both V p and Vs increased while both compressional and shear attenuations decreased when stress was increased.