Azra N. Tutuncu

Nonlinear viscoelastic behavior of sedimentary rocks, Part I: Effect of frequency and strain amplitude

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 Eultrasonic>Elog>Elowfreq>Estatic. 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 a...

An experimental investigation of factors influencing compressional‐ and shear‐wave velocities and attenuations in tight gas sandstones

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 VP/VS ratio was found to increase with clay content. Compressional‐and shear‐wave amplitude spectra ...

The influence of fluids on grain contact stiffness and frame moduli in sedimentary rocks

The frame moduli of sedimentary rocks are strongly influenced by the properties of the grain contacts. A modified Hertz contact theory is presented for the self consistent calculation of deformation, equilibrium separation distance (film thickness), and contact area of deformation for two spherical asperities in contact and subjected to an external load. We show that surface forces, i.e., electrostatic repulsion, Born, structural, and Van der Waals forces can be incorporated into the contact deformation problem. From the results presented, it is evident that surface forces play an important role in determining seismic wave velocities and attenuations at low confining stresses. The velocities and attenuations computed from the model are compared with measured values for glass beads, Navajo, Berea, Obernkirchner, and Fort Union sandstones. The velocities and attenuations calculated as functions of stress, frequency, fluid type, and saturation are in good agreement with reported experimental data.

Grain contact adhesion hysteresis: A mechanism for attenuation of seismic waves

We propose a new mechanism for attenuation of seismic waves in rocks. It is shown that grain contact adhesion hysteresis leads to energy dissipation without having to invoke frictional sliding at grain contacts. Adhesion hysteresis gives rise to frequency independent attenuation that increases with strain amplitude for large strains and decreases with overburden stress. We can obtain qualitatively correct trends that show the effect of fluid saturation, pore structure and grain size through simple models for granular sedimentary rocks.

An experimental investigation of the role of pore fluids on the nonlinear hysteretic behavior of Berea sandstone

Uniaxial stress cycling experiments were conducted on dry, brine saturated and hexadecane saturated Berea sandstone samples to observe 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 was selected 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 rock stiffness and hysteresis observed in the stress-strain diagrams but very little effect on the magnitude of attenuation.

Grain Contact Adhesion Hysteresis: A Mechanism For Attenuation of Seismic Waves In Sedimentary Granular Media

Attenuation is observed experimentally in dry sedimentary rock samples at low frequency and high overburden stress. Currently well established attenuation mechanisms such as frictional sliding, squirt flow and viscous dissipation can not adequately explain the observed attenuation. We propose a new mechanism for attenuation of seismic waves in sedimentary granular rocks. The origin of this mechanism lies in grain contact adhesion hysteresis. The propagation of seismic waves causes the gap width at grain contacts to vary. At high frequencies Hz), in liquid saturated rocks this leads to attenuation due to squirt flow. However in dry rocks at low frequency Hz) this periodic oscillation in gap width (h) leads to energy dissipation due to hysteresis on a surface force vs. separation distance (h) diagram. The path taken when h is decreasing is different than when h is increasing (grains are being pulled apart). Surface forces and applied load play an important role in the magnitude of the calculated attenuation. The trends obtained from the proposed grain contact adhesion hysteresis mechanism are consistent with experimental observations. We show here that grain contact adhesion hysteresis causes energy dissipation without frictional sliding at grain contacts and gives rise to frequency independent attenuation that increases with strain amplitude and decreases with overburden stress. The conclusions obtained from the calculations are qualitative since they do not account for the complex distribution of asperity sizes and separations that would exist in a rock. However, they provide a qualitative explanation for some hitherto unexplained experimental observations.

Effect of Strain Amplitude And Frequency On Compressional And Shear Wave Velocities And Amplitudes In Sandstones

A series of experiments have been carried out on sandstone samples with wide range of porosities and permeabilities in order to investigate the influence of strain amplitude and frequency on compressional and shear velocities and attenuation of sedimentary granular rocks. Low frequency velocity data was obtained from uniaxial stress cycling measurements that were conducted at a frequency of Hz at different levels of strain amplitude from 1 to Attenuation information was obtained at Hz from the stressstrain hysteresis observed in the cycling measurements. Compressional velocity data was collected at various stresses using four different transducer/receiver sets with frequencies 50 KHz, 100 KHz, 180 KHz and 1 MHz. The strain amplitudes for all four types of ultrasonic measurements are in the range of Shear velocities were simultaneously recorded at 1 MHz. Compressional wave amplitude data were collected at a few selected stresses in order to obtain attenuation at ultrasonic frequencies. Velocities calculated from the static moduli increase as average stress is increased. The dry velocities are very sensitive to strain amplitude. As strain amplitude increases, both compressional and shear velocities decrease. When the velocities calculated from the static moduli (102 Hz) are plotted together with the velocities measured using the 50 KHz, 100 KHz, 180 KHz and 1 MHz transducers, velocity dispersion is clearly observed. However, differences between static velocities and velocities measured from 50 KHz to 1 MHz can not be explained on the basis of the frequency dependence alone. Differences between the strain amplitudes of the measurement techniques is believed to be one of the major causes of dispersion observed in the dry rocks used in this study.

A Discussion On Possible Mechanisms of Nonlinear Hysteretic Behavior In Sedimentary Granular Rocks: Grain Contact Adhesion Versus Stick-slip Sliding

The stress-strain behavior of dry and saturated Berea sandstones has been studied in detail in order to investigate the relative contributions of grain contact adhesion hysteresis and stick-slip sliding on energy loss in granular sedimentary rocks. The information gathered from the uniaxial stress cycling experiments show evidence of frictional stick-slip sliding when the samples were saturated with hexadecane and CTAB solutions. Dry and brine saturated cases did not show any stick-slip effects. The pore fluids at the grain contacts were found to play an important role in the observed hysteresis in the stress-strain diagrams and in determining the stick-slip effects.