Attenuation In Sandstone Research Articles

Amplitude-initiated open hysteresis loop of <i>P</i>-wave attenuation in sandstone: experimental study

In the area of solid state physics and materials science, new knowledge has been attained in recent years about micro-nano-plasticity using high-precision measurements at low stresses and strain. Rock microplasticity is currently poorly understood, but in the future it may prove useful in resolving problems of a fundamental and applied nature. This study examines the effect of cyclically varying pulse amplitude and wave velocity on the attenuation parameters of longitudinal wave (P-wave) in sandstone. Laboratory measurements were performed on rock specimens using the reflected wave method in the frequency range of 0.5–1.4 MHz at five values of strain amplitude ~ (0.5-2.0)10 –6 . Trial simulations were performed, in order to establish the effect of amplitude-dependent wave velocity on the parameters of wave attenuation in the sandstone. Wave attenuation behavior under combined action of the amplitude-dependent factor and wave velocity deviation is complex. The change in strain amplitude shifts the attenuation peak 1/ Q p ( f ) in the attenuation-frequency coordinates. The maximum change in peak attenuation value due to the amplitude factor and wave velocity deviation reaches 3–4 %. An open wave attenuation hysteresis loop was identified as a consequence of the closed amplitude cycle A1(+) --- A1(+) --- A1(–), where A1(+) = A1(–). Open attenuation hysteresis occurs both in the cases of constant and variable wave velocities. The length of the open part of the attenuation hysteresis loop relative to the peak value of the attenuation is as follows: for constant wave speed, 62.63 %, in the mode of increasing wave speed, 91.58 %; and, in the mode of decreasing wave speed, 47.01 %. The effect of open hysteresis of wave attenuation in sandstone can be explained by the action of microplastic deformation detected in the experiments.

Sorption‐Induced Deformation and Elastic Weakening of Bentheim Sandstone

AbstractA number of studies show that adsorption of small amount of water causes significant reduction of elastic moduli and increase of elastic wave attenuation in sandstones. This effect is of practical importance for near‐surface seismic studies and for applications of conventional rock physics theories, which require measurements of elastic properties of dry rock. Additionally, adsorption of water causes deformation of porous materials and rocks, which can be explained by the concept of varying surface stress, or change in the pressure of fluid adsorbed in pores. In this work we suggest that the adsorption‐induced elastic weakening of sandstones is caused by changing fluid pressure in compliant pores on grain contacts. In order to validate this concept, we conduct simultaneous measurements of the elastic moduli and deformation of the Bentheim sandstone with adsorption and desorption of water and observe ~20% change in the bulk and shear moduli accompanied with the strain of the order of 10−4. Then, we estimate that the fluid pressure change should be of the order of several megapascals to cause such deformation. Comparison of the measured variations in the elastic moduli related to the estimated change in the fluid pressure with the stress dependency of the bulk and shear moduli in Bentheim sandstone shows a broad agreement of the two sets of measurements. A reasonable magnitude of the estimated fluid pressure change is consistent with the suggested hypothesis.

Seismic wave attenuation and modulus dispersion in sandstones

We have conducted laboratory experiments over the 1–200 Hz band to examine the effects of viscosity and permeability on modulus dispersion and attenuation in sandstones and also to examine the effects of partial gas or oil saturation on velocities and attenuations. Our results have indicated that bulk modulus values with low-viscosity fluids are close to the values predicted using Gassmann’s first equation, but, with increasing frequency and viscosity, the bulk and shear moduli progressively deviate from the values predicted by Gassmann’s equations. The shear moduli increase up to 1 GPa (or approximately 10%) with high-viscosity fluids. The P- and S-wave attenuations ([Formula: see text] and [Formula: see text]) and modulus dispersion with different fluids are indicative of stress relaxations that to the first order are scaling with frequency times viscosity. By fitting Cole-Cole distributions to the scaled modulus and attenuation data, we have found that there are similar P-wave, shear and bulk relaxations, and attenuation peaks in each of the five sandstones studied. The modulus defects range from 11% to 15% in Berea sandstone to 16% to 26% in the other sandstones, but these would be reduced at higher confining pressures. The relaxations shift to lower frequencies as the viscosity increased, but they do not show the dependence on permeability predicted by mesoscopic wave-induced fluid flow (WIFF) theories. Results from other experiments having patchy saturation with liquid [Formula: see text] and high-modulus fluids are consistent with mesoscopic WIFF theories. We have concluded that the modulus dispersion and attenuations ([Formula: see text] and [Formula: see text]) in saturated sandstones are caused by a pore-scale, local-flow mechanism operating near grain contacts.

Saturation-path dependency of P-wave velocity and attenuation in sandstone saturated with CO2 and brine revealed by simultaneous measurements of waveforms and X-ray computed tomography images

We performed a laboratory experiment to measure compressional (P)-wave velocity and its attenuation in low-permeability striped sandstone at ultrasonic frequency during drainage ([Formula: see text] injection) and imbibition (brine injection). X-ray computed tomography (CT) images of the rock sample were simultaneously recorded during the injections. On the basis of the CT images, we calculated the [Formula: see text] saturation inside a prolate-spheroid-shaped volume (the first Fresnel zone) that enclosed the wave-propagation path. The relationship of P-wave velocity and that of attenuation to the [Formula: see text] fraction were then obtained. Both relationships showed nonuniqueness with remarkable hysteresis in a drainage-imbibition cycle. To explain the nonunique relationship of P-wave velocity to the [Formula: see text] fraction, we investigated the continuous random patchy saturation model by using exponent-type autocorrelation. The nonunique relationship of velocity to the [Formula: see text] fraction was explained by the model with a correlation length from an order of tens of millimeters in drainage to an order of hundreds of microns in imbibition. We also examined the potential influence of the fractal dimension of [Formula: see text] distribution by using the fractal patchy saturation model and a von-Kármán-type autocorrelation function. The fractal dimension of pore-space modulus as related to [Formula: see text] distribution was estimated on the basis of the CT images. The fractal dimension during imbibition found a larger value than that during drainage. The change in fractal dimension had a limited effect on velocity and attenuation changes. These nonunique relationships might have a significant impact on the use of seismic methods for estimation of [Formula: see text] volume in an inhomogeneous storage reservoir.

Bulk modulus dispersion and attenuation in sandstones

We report experimental data on the frequency dependence of bulk elastic modulus in porous sandstones. A new methodology was developed to investigate the dispersion/attenuation phenomena on a rock’s bulk modulus [Formula: see text] for varying confining pressures in the range of 1–50 MPa and fluids of varying viscosities (i.e., air, glycerin, and water). This methodology combined (1) ultrasonic (i.e., [Formula: see text]) P- and S-wave velocity measurements, leading to the high-frequency (HF) [Formula: see text], (2) stress-strain measurements from forced periodic oscillations of confining pressure at low-frequency (LF) ranges (i.e., [Formula: see text]), leading to [Formula: see text] and [Formula: see text], and (3) pore-pressure measurement to document the induced fluid-flow in the LF range (i.e., [Formula: see text]). The stress-strain method was first checked using three standard samples: glass, gypsum, and Plexiglas samples. Over the frequency and pressure range of the apparatus [Formula: see text] was stable and accurate and the lowest measurable LF attenuation was [Formula: see text]. The methodology was applied to investigate Fontainebleau sandstone samples of 7% and 9% porosity. The [Formula: see text] and [Formula: see text] exhibited correlated variations, which also correlated with an experimental evidence of frequency-dependent fluid-flow out of the sample. Attenuation peaks as high as [Formula: see text] and [Formula: see text] are measured. The attenuation/dispersion measured under glycerin saturation was compared to Biot-Gassmann predictions. The overall behavior of one sample was consistent with a dispersion/attenuation characteristic of the drained/undrained transition. On the reverse, the other sample exhibited exotic behaviors as the measurements were underestimated by the drained/undrained transition and indicated a direct transition from drained to unrelaxed domain. These different behaviors were consistent with the values of the critical frequencies expected for the drained/undrained (i.e., [Formula: see text]) and relaxed/unrelaxed (i.e., [Formula: see text]) transitions.

Laboratory measurements of seismic attenuation in sandstone: Strain versus fluid saturation effects

In the past few decades, great attention has been focused on uncovering the physics of seismic wave attenuation in fluid-saturated rocks. However, the relationship among many variables affecting attenuation is still not completely clear. For instance, although the role of strain in enhancing friction dissipation is relatively well known for dry rocks, it remains unclear how and how much it affects attenuation in fluid-saturated rocks. We experimentally measured attenuation in the extensional mode in Berea sandstone at strains between [Formula: see text] and [Formula: see text], and at frequencies in the seismic bandwidth (1–100 Hz). These strains were similar to those typically observed in seismic exploration ([Formula: see text]). We also measured the transient fluid pressure caused when a stepwise stress was applied resulting in such strains. For the studied strain range, our results indicated that: (1) the overall attenuation in dry Berea sandstone increased linearly with strain, (2) the frequency-dependent component of attenuation, which was associated with fluid saturation, was approximately insensitive to strain, and (3) the overall attenuation can be considered as a sum of a frequency-independent and a frequency-dependent components.

An experimental study of modulus dispersion and attenuation in sandstones at seismic frequencies

A study of the low frequency dispersion and attenuation in sedimentary rocks is important for interpreting seismic data obtained during fluid extraction in producing fields or during injection of carbon dioxide for storage purposes. We present the results of the laboratory measurements of elastic and anelastic parameters of dry and distilled water/brine saturated sandstones with low (~7.8 and 9.6 mD) and high (~590 mD) permeability conducted at seismic (1-100 Hz) and teleseismic (0.1-1 Hz) frequencies. The experiments were performed with a laboratory apparatus utilizing stress-strain relationship which was developed to measure the complex Young’s moduli of rocks at seismic frequencies. The measurements carried out in saturated sandstones with low permeability at effective pressures from 2.5 to 23 MPa revealed prominent peaks of attenuation in the seismic and teleseismic bands. A significant dispersion of the Young’s moduli was also observed. The change in the salinity of the fluid from 0 to 45,000 ppm NaCl did not affect any of the measured parameters. The dispersion of the elastic moduli of the dry sandstones was within the accuracy of our measurements.

Application of the BISQ model to clay squirt flow in reservoir sandstones

An understanding of the variations of compressional wave velocity and attenuation in sandstones as a function of pore‐fluid properties is important for the identification and monitoring of hydrocarbon reservoirs. In order for seismic inversion to be well constrained a rock physics model that describes accurately the observed behavior is required; a number of such models have been proposed but have not been extensively tested against laboratory data. The unified Biot and squirt flow model was applied to data obtained from ultrasonic experiments conducted on a wide range of sandstone types when saturated with different pore fluids with viscosities ranging from 0.3 to 1000 cP. This model was seen to match well all the observed velocity and attenuation values as opposed to the Biot model, which was only successful for clean sandstones saturated with low viscosity fluids. This has led to the conclusion that a squirt flow mechanism is important at the grain scale. In addition, an increase in the dynamic uniaxial strain modulus of the dry frame with increasing pore‐fluid viscosity was observed. In the absence of free gas or grain contact microcracks (the laboratory data were collected at 60 MPa effective pressure), this can be linked to decreasing local flow and decreasing relaxation in the soft pore space of the sandstone, the extent of which is in turn connected to the clay content and pore structure of the sandstone. These results imply that at ultrasonic frequencies the squirt‐flow is due to the presence of clay.

Theory of compressional and transverse wave propagation in consolidated porous media

A theory of compressional and shear wave propagation in consolidated porous media (rocks) is developed by extending ideas already introduced in connection with unconsolidated marine sediments. The consolidated material is treated as an elastic medium which exhibits a specific form of stress relaxation associated with grain boundaries and microcracks. The stress relaxation, which is linear in the sense that it obeys superposition, shows hysteresis, as characterized by a material response function. Two linear wave equations are derived, one for compressional and the second for shear waves, from which expressions for the wave speeds and attenuations are established. In both cases, the attenuation is found to scale with the first power of frequency, consistent with many observations of attenuation in sandstones, limestones, and shales; the wave speeds show weak logarithmic dispersion. These expressions for the wave speeds and attenuations satisfy the Kronig–Kramers dispersion relationships, as they must if the response of the medium to disturbances is to be causal. Some comments are offered on the nature of the material response, notably that it appears to be primarily associated with grain-boundary interactions occurring at a molecular level, rather than being related to the macroscopic properties of the material, such as density or porosity.

The effects of pore‐fluid salinity on ultrasonic wave propagation in sandstones

Petrophysical interpretation of increasingly refined seismic data from subsurface formations requires a more fundamental understanding of seismic wave propagation in sedimentary rocks. We consider the variation of ultrasonic wave velocity and attenuation in sandstones with pore‐fluid salinity and show that wave propagation is modified in proportion to the clay content of the rock and the salinity of the pore fluid. Using an ultrasonic pulse reflection technique (590–890 kHz), we have measured the P-wave and S-wave velocities and attenuations of 15 saturated sandstones with variable effective pressure (5–60 MPa) and pore‐fluid salinity (0.0–3.4 M). In clean sandstones, there was close agreement between experimental and Biot model values of [Formula: see text], but they diverged progressively in rocks containing more than 5% clay. However, this effect is small: [Formula: see text] changed by only 0.6% per molar change in salinity for a rock with a clay content of 29%. The variation of [Formula: see text] with brine molarity exhibited Biot behavior in some samples but not in others; there was no obvious relationship with clay content. P-wave attenuation was independent of pore‐fluid salinity, while S-wave attenuation was weakly dependent. The velocity data suggest the frame bulk and shear moduli of sandstones are altered by changes in the pore‐fluid salinity. One possible mechanism is the formation damage caused by clay swelling and migration of fines in low‐molarity electrolytes. The absence of variation between the attenuation in water‐saturated and brine‐saturated samples indicates the attenuation mechanism is relatively unaffected by changes in the frame moduli.

Fluid effects on velocity and attenuation in sandstones

Ultrasonic velocity and attenuation measurements in sandstones with a variety of saturating fluids are compared with the predictions of Biot’s theory of porous media acoustics. Velocity data show systematic deviations from Biot theory as a function of pore fluid viscosity. Ultrasonic attenuation is much larger than the Biot prediction and for several sandstones is nearly constant for a three decade variation in viscosity. This behavior contrasts with synthetic porous media such as sintered glass beads, where Biot theory provides accurate predictions of velocity and attenuation. A sandstone was modified by curing a residual saturation of epoxy in the pore space, filling small pores and microcracks. This altered rock has a significantly reduced attenuation, demonstrating the dominance of small pores in controlling ultrasonic attenuation. Discrepancies between Biot theory and ultrasonic measurements are due to complex pore shapes in sandstones that are not present in simpler synthetic porous media such as sintered glass beads. Two non-Biot viscous attenuation mechanisms are needed: local flow in microcracks along grain contacts, and attenuation from pore-wall surface roughness. The combination of these mechanisms with Biot theory can explain ultrasonic measurements on sandstones. A model calculation of attenuation for a pore wall with surface roughness shows a significant increase in attenuation compared to the smooth wall calculation of Biot theory. This attenuation enhancement explains the absence of a Biot slow wave in fluid saturated rocks, and the observed correlation between ultrasonic attenuation and clay content in sandstones. When extended to the lower frequencies of geophysical field measurements, attenuation from all viscous dissipation mechanisms is negligible. This implies that ultrasonic attenuation measurements of sandstones provide no useful information about seismic attenuation in fluid-filled rocks in the earth, and mechanisms other than viscous dissipation must be invoked to describe the attenuation in geophysical field measurements.

Shear wave velocity and attenuation from pulse‐echo studies of Berea sandstone

The pulse‐echo spectral‐ratio technique has been adapted to the determination of ultrasonic shear wave attenuation in sandstone at variable states of saturation and pressure. The method can measure shear attenuation coefficients in the range 0.5 dB/cm to 8 dB/cm to within ±0.5 dB/cm. For the Berea sandstone, this range corresponds to values of the shear quality factor (Qs) between 10 and 100. Spectra of Qs show that between 600 and 1100 kHz, Qs decreases with frequency, particularly at high pressures (up to 70 MPa). Ultrasonic shear wave attenuation in a 90% water‐saturated sample was intermediate between that for dry samples and the relatively high attenuation in fully saturated rock. Strong pressure dependence is seen in the shear attenuation for all saturation states, indicating a dominant role of dissipation mechanisms operating within open and compliant cracks. Substantial shear attenuation remains at the highest effective pressure applied to the saturated sample, which may be due to a more “global” fluid‐flow loss mechanism. Scattering losses, as described by weak scattering theories for compressional waves, do not appear to be dominant at these frequencies.

Fluid effects on velocity and attenuation in sandstones.

Measurements of ultrasonic velocity and attenuation in sandstones with a variety of saturating fluids are compared with the predictions of Biot’s theory of porous media acoustics. The data show systematic deviations from Biot theory as a function of pore fluid viscosity. Two non-Biot attenuation mechanisms are needed to explain the data: local flow in microcracks and enhanced attenuation from pore-wall roughness. A model calculation of attenuation with pore-wall roughness shows that attenuation in rocks can be many times larger than Biot predictions. This attenuation enhancement explains the inability to detect a Biot slow wave in fluid-saturated rocks and the observed correlation between ultrasonic attenuation and clay content in sandstones. The non-Biot attenuation mechanisms are negligible when extrapolated to the lower frequencies of geophysical field measurements, so ultrasonic attenuation in rocks provides no information about attenuation at the field scale.

Sonic properties of rocks under confining pressure using the resonant bar technique

This paper presents in detail the resonant bar technique used to measure acoustic properties of materials in the sonic frequency range (≃5–20 kHz). Measurements are corrected for the effects of added mass and jacketing; extrinsic effects such as the sample diameter or the dispersion at higher frequencies can mask intrinsic properties of material and are analyzed here. When this technique is used on porous saturated media such as rocks, it is important to avoid the “Biot–Gardner–White” effect; this intrinsic effect can lead to erroneous high attenuations in unjacketed saturated samples. Experimental evidence of its occurrence on water-saturated rods is presented. Experimental results of velocity and attenuation obtained on various rock types such as limestones and sandstones show the drastic sensitivity of these measurements to effective pressure. Hertz’s theory can be applied to describe the behavior of under-consolidated sandstones. Under high confining pressure, sonic attenuation in water-saturated limestone samples is found to be very low (Q⩾100); attenuation in sandstones is always low (Q⩾50), except for some shaly sandstones.

Velocity and attenuation in sandstone at elevated temperatures and pressures

New measurements of seismic velocity and attenuation have been made in the kiloHertz frequency range to temperatures of 120°C, confining and pore pressure to 200 bars in Berea sandstone. With increasing temperature, shear velocity and attenuation decrease at all pressures in a fully saturated rock. The data suggest that thermal relaxation is not a significant loss mechanism under these conditions. We propose that dissipation is controlled by a viscous fluid flow mechanism, in which a sharp frequency peak in attenuation is shifted from 2kHz at room temperature to 8 kHz at 120°C as the pore fluid viscosity is decreased with increasing temperature. However, the velocity decrease is too great to be accounted for by a change of relaxation times. A non‐dispersive temperature softening in shear may control the velocities.