Mechanical compaction and ultrasonic velocity of sands with different texture and mineralogical composition

This study presents the results of experimental compaction while measuring ultrasonic velocities of sands with different grain size, shape, sorting and mineralogy. Uniaxial mechanical compaction tests up to a maximum of 50 MPa effective stress were performed on 29 dry sand aggregates derived from eight different sands to measure the rock properties. A good agreement was found between the Gassmann saturated bulk moduli of dry and brine saturated tests of selected sands. Sand samples with poor sorting showed low initial porosity while sands with high grain angularity had high initial porosity. The sand compaction tests showed that at a given stress well‐sorted, coarse‐grained sands were more compressible and had higher velocities (Vp and Vs) than fine‐grained sands when the mineralogy was similar. This can be attributed to grain crushing, where coarser grains lead to high compressibility and large grain‐to‐grain contact areas result in high velocities. At medium to high stresses the angular coarse to medium grained sands (both sorted sands and un‐sorted whole sands) showed high compaction and velocities (Vp and Vs). The small grain‐to‐grain contact areas promote higher deformation at grain contacts, more crushing and increased porosity loss resulting in high velocities. Compaction and velocities (Vp and Vs) increased with decreasing sorting in sands. However, at the same porosity, the velocities in whole sands were slightly lower than in the well‐sorted sands indicating the presence of loose smaller grains in‐between the framework grains. Quartz‐poor sands (containing less than 55% quartz) showed higher velocities (Vp and Vs) compared to that of quartz‐rich sands. This could be the result of sintering and enlargement of grain contacts of ductile mineral grains in the quartz‐poor sands increasing the effective bulk and shear stiffness. Tests both from wet measurements and Gassmann brine substitution showed a decreasing Vp/Vs ratio with increasing effective stress. The quartz‐rich sands separated out towards the higher side of the Vp/Vs range. The Gassmann brine substituted Vp and Vs plotted against effective stress provide a measure of the expected velocity range to be found in these and similar sands during mechanical compaction. Deviations of actual well log data from experimental data may indicate uplift, the presence of hydrocarbon, overpressure and/or cementation. Data from this study may help to model velocity‐depth trends and to improve the characterization of reservoir sands from well log data in a low temperature (<80–100^o C) zone where compaction of sands is mostly mechanical.     

Effect of sub‐core scale heterogeneities on acoustic and electrical properties of a reservoir rock: a CO2 flooding experiment of brine saturated sandstone in a computed tomography scanner

The effect of sub‐core scale heterogeneity on fluid distribution pattern, and the electrical and acoustic properties of a typical reservoir rock was studied by performing drainage and imbibition flooding tests with CO₂ and brine in a laboratory. Moderately layered Rothbach sandstone was used as a test specimen. Two core samples were drilled; one perpendicular and the other parallel to the layering to allow injection of fluids along and normal to the bedding plane. During the test 3D images of fluid distribution and saturation levels were mapped by an industrial X‐ray CT‐scanner together with simultaneous measurement of electrical resistivity, ultrasonic velocities as well as amplitudes. The results showed how the layering and the flooding direction influenced the fluid distribution pattern and the saturation level of the fluids. For a given fluid saturation level, the measured changes in the acoustic and electrical parameters were affected by both the fluid distribution pattern and the layering orientation relative to the measurement direction. The P‐wave amplitude and the electrical resistivity were more sensitive to small changes in the fluid distribution patterns than the P‐wave velocity. The change in amplitude was the most affected by the orientation of the layering and the resulting fluid distribution patterns. In some instances the change due to the fluid distribution pattern was higher than the variation caused by the change in CO₂ saturation. As a result the Gassmann relation based on ‘uniform' or ‘patchy' saturation pattern was not suitable to predict the P‐wave velocity variation. Overall, the results demonstrate the importance of core‐imaging to improve our understanding of fluid distribution patterns and the associated effects on measured rock‐physics properties.     

Laboratory measurements of seismic attenuation and Young's modulus dispersion in a partially and fully water‐saturated porous sample made of sintered borosilicate glass

We measured the extensional‐mode attenuation and Young's modulus in a porous sample made of sintered borosilicate glass at microseismic to seismic frequencies (0.05–50 Hz) using the forced oscillation method. Partial saturation was achieved by water imbibition, varying the water saturation from an initial dry state up to ～99%, and by gas exsolution from an initially fully water‐saturated state down to ～99%. During forced oscillations of the sample effective stresses up to 10 MPa were applied. We observe frequency‐dependent attenuation, with a peak at 1–5 Hz, for ～99% water saturation achieved both by imbibition and by gas exsolution. The magnitude of this attenuation peak is consistently reduced with increasing fluid pressure and is largely insensitive to changes in effective stress. Similar observations have recently been attributed to wave‐induced gas exsolution–dissolution. At full water saturation, the left‐hand side of an attenuation curve, with a peak beyond the highest measured frequency, is observed at 3 MPa effective stress, while at 10 MPa effective stress the measured attenuation is negligible. This observation is consistent with wave‐induced fluid flow associated with mesoscopic compressibility contrasts in the sample's frame. These variations in compressibility could be due to fractures and/or compaction bands that formed between separate sets of forced‐oscillation experiments in response to the applied stresses. The agreement of the measured frequency‐dependent attenuation and Young's modulus with the Kramers–Kronig relations and additional data analyses indicate the good quality of the measurements. Our observations point to the complex interplay between structural and fluid heterogeneities on the measured seismic attenuation and they illustrate how these heterogeneities can facilitate the dominance of one attenuation mechanism over another.     

P‐ and S‐wave anisotropy to characterise and quantify damage in media: laboratory experiment using synthetic sample with aligned microcracks

Damage characterisation in solid media is studied in this work through ultrasonic measurements. A synthetic three‐dimensional printed sample including a system of horizontally aligned microcracks is used. In contrast to other manual fabrication methods presented in the literature, the construction process considered here ensures a better control and accuracy of size, shape, and spatial distribution of the microcrack network in the synthetic sample. The acoustic measurements were conducted through a specific device using triple acoustic sensors, which allows capturing at each incident direction three wave modes. The evolution of the ultrasonic velocities with respect to incident angle accounted for the damage‐induced anisotropy. The experimental results are then compared with some well‐known effective media theories in order to discuss their potential use for the following studies. Finally, we highlighted and compared the accuracy of these theories used for inversion procedure to quantify damage in the medium.     

Influence of subsurface injection on time‐lapse seismic: laboratory studies at seismic and ultrasonic frequencies

Seismic monitoring of reservoir and overburden performance during subsurface CO₂ storage plays a key role in ensuring efficiency and safety. Proper interpretation of monitoring data requires knowledge about the rock physical phenomena occurring in the subsurface formations. This work focuses on rock stiffness and elastic velocity changes of a shale overburden formation caused by both reservoir inflation induced stress changes and leakage of CO₂ into the overburden. In laboratory experiments, Pierre shale I core plugs were loaded along the stress path representative for the in situ stress changes experienced by caprock during reservoir inflation. Tests were carried out in a triaxial compaction cell combining three measurement techniques and permitting for determination of (i) ultrasonic velocities, (ii) quasistatic rock deformations, and (iii) dynamic elastic stiffness at seismic frequencies within a single test, which allowed to quantify effects of seismic dispersion. In addition, fluid substitution effects connected with possible CO₂ leakage into the caprock formation were modelled by the modified anisotropic Gassmann model. Results of this work indicate that (i) stress sensitivity of Pierre shale I is frequency dependent; (ii) reservoir inflation leads to the increase of the overburden Young's modulus and Poisson's ratio; (iii) in situ stress changes mostly affect the P‐wave velocities; (iv) small leakage of the CO₂ into the overburden may lead to the velocity changes, which are comparable with one associated with geomechanical influence; (v) non‐elastic effects increase stress sensitivity of an acoustic waves; (iv) and both geomechanical and fluid substitution effects would create significant time shifts, which should be detectable by time‐lapse seismic.     

Estimating gas saturation in a thin layer by using frequency‐dependent amplitude versus offset modelling

Various models have been proposed to link partial gas saturation to seismic attenuation and dispersion, suggesting that the reflection coefficient should be frequency‐dependent in many cases of practical importance. Previous approaches to studying this phenomenon typically have been limited to single‐interface models. Here, we propose a modelling technique that allows us to incorporate frequency‐dependent reflectivity into convolutional modelling. With this modelling framework, seismic data can be synthesised from well logs of velocity, density, porosity, and water saturation. This forward modelling could act as a basis for inversion schemes aimed at recovering gas saturation variations with depth. We present a Bayesian inversion scheme for a simple thin‐layer case and a particular rock physics model and show that, although the method is very sensitive to prior information and constraints, both gas saturation and layer thickness theoretically can be estimated in the case of interfering reflections.     

Effects of petrophysical parameters on attenuation and dispersion of seismic waves in the simplified poroelastic theory: Comparison between the Biot's theory and viscosity‐extended theory

The simplified macro‐equations of porous elastic media are presented based on Hickey's theory upon ignoring effects of thermomechanical coupling and fluctuations of porosity and density induced by passing waves. The macro‐equations with definite physical parameters predict two types of compressional waves (P wave) and two types of shear waves (S wave). The first types of P and S waves, similar to the fast P wave and S wave in Biot's theory, propagate with fast velocity and have relatively weak dispersion and attenuation, while the second types of waves behave as diffusive modes due to their distinct dispersion and strong attenuation. The second S wave resulting from the bulk and shear viscous loss within pore fluid is slower than the second P wave but with strong attenuation at lower frequencies. Based on the simplified porous elastic equations, the effects of petrophysical parameters (permeability, porosity, coupling density and fluid viscosity) on the velocity dispersion and attenuation of P and S waves are studied in brine‐saturated sandstone compared with the results of Biot's theory. The results show that the dispersion and attenuation of P waves in simplified theory are stronger than those of Biot's theory and appear at slightly lower frequencies because of the existence of bulk and shear viscous loss within pore fluid. The properties of the first S wave are almost consistent with the S wave in Biot's theory, while the second S wave not included in Biot's theory even dies off around its source due to its extremely strong attenuation. The permeability and porosity have an obvious impact on the velocity dispersion and attenuation of both P and S waves. Higher permeabilities make the peaks of attenuation shift towards lower frequencies. Higher porosities correspond to higher dispersion and attenuation. Moreover, the inertial coupling between fluid and solid induces weak velocity dispersion and attenuation of both P and S waves at higher frequencies, whereas the fluid viscosity dominates the dispersion and attenuation in a macroscopic porous medium. Besides, the heavy oil sand is used to investigate the influence of high viscous fluid on the dispersion and attenuation of both P and S waves. The dispersion and attenuation in heavy oil sand are stronger than those in brine‐saturated sandstone due to the considerable shear viscosity of heavy oil. Seismic properties are strongly influenced by the fluid viscosity; thus, viscosity should be included in fluid properties to explain solid–fluid combination behaviour properly.     

Range imaging: a new method for high‐resolution topographic measurements in small‐ and medium‐scale field sites

Topographic measurements are essential for the study of earth surface processes. Three‐dimensional data have been conventionally obtained through terrestrial laser scanning or photogrammetric methods. However, particularly in steep and rough terrain, high‐resolution field measurements remain challenging and often require new creative approaches. In this paper, range imaging is evaluated as an alternative method for obtaining surface data in such complex environments. Range imaging is an emerging time‐of‐flight technology, using phase shift measurements on a multi‐pixel sensor to generate a distance image of a surface. Its suitability for field measurements has yet not been tested. We found ambient light and surface reflectivity to be the main factors affecting error in distance measurements. Low‐reflectivity surfaces and strong illumination contrasts under direct exposure to sunlight lead to noisy distance measurements. However, regardless of lighting conditions, the accuracy of range imaging was markedly improved by averaging multiple images of the same scene. For medium ambient lighting (shade) and a light‐coloured surface the measurement uncertainty was approximately 9 mm. To further test the suitability of range imaging for field applications we measured a reach of a steep mountain stream with a horizontal resolution of approximately 1 cm (in the focal plane of the camera), allowing for the interpolation of a digital elevation model on a 2 cm grid. Comparison with an elevation model obtained from terrestrial laser scanning for the same site revealed that both models show similar degrees of topographic detail. Despite limitations in measurement range and accuracy, particularly at bright ambient lighting, range imaging offers three‐dimensional data in real time and video mode without the need of post‐processing. Therefore, range imaging is a useful complement or alternative to existing methods for high‐resolution measurements in small‐ to medium‐scale field sites. Copyright © 2012 John Wiley & Sons, Ltd.