Prediction of seismic-wave velocities in rock at various confining pressures based on unconfined data

Laboratory measurement of P- and S-wave velocities ([Formula: see text] and [Formula: see text], respectively) under confining pressure indicates that with an increase in confining pressure, [Formula: see text] and [Formula: see text] will increase. The trend is exponential at low pressures, transitioning to linear above a critical pressure. However, the trend of the velocity-pressure curve for each rock specimen may be determined knowing the coefficients of this curve. We first studied how the coefficients of the velocity-pressure curve were expected to be functions of elastic moduli. Then, four empirical equations were used to estimate four coefficients of the velocity-pressure curve, using the rock density and [Formula: see text] and [Formula: see text] at atmospheric pressure (unconfined conditions). This analysis was carried out based on laboratory experiments on 285 rock specimens of different lithology from around the world, namely the United States, China, Germany, Iran, and deep-sea-drilling projects. For each rock specimen, [Formula: see text] and [Formula: see text] were measured at different confining stress levels, rendering more than 4000 data points. The accuracy of the estimated wave velocities was on the order of 2%–3% of the measured values on average. This methodology is especially valuable for prediction and analysis of the rock behavior at deep well conditions. This is applicable for predicting geophysical properties of the earth’s crust at depth, geomechanical study of hydrocarbon and geothermal reservoirs, wellbore stability analysis, and in situ stress determination.

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Effects of fluids and dual-pore systems on pressure-dependent velocities and attenuations in carbonates

Geophysics ◽

10.1190/1.2969774 ◽

2008 ◽

Vol 73 (5) ◽

pp. N35-N47 ◽

Cited By ~ 29

Author(s):

Remy Agersborg ◽

Tor Arne Johansen ◽

Morten Jakobsen ◽

Jeremy Sothcott ◽

Angus Best

Keyword(s):

Fluid Flow ◽

Confining Pressure ◽

Substitution Effects ◽

Fluid Substitution ◽

Pore System ◽

S Wave ◽

Low Velocity ◽

Wave Velocities ◽

Three Samples ◽

Local Fluid Flow

The effects of fluid substitution on P- and S-wave velocities in carbonates of complex texture are still not understood fully. The often-used Gassmann equation gives ambiguous results when compared with ultrasonic velocity data. We present theoretical modeling of velocity and attenuation measurements obtained at a frequency of [Formula: see text] for six carbonate samples composed of calcite and saturated with air, brine, and kerosene. Although porosities (2%–14%) and permeabilities [Formula: see text] are relatively low, velocity variations are large. Differences between the highest and lowest P- and S-wave velocities are about 18% and 27% for brine-saturated samples at 60 and [Formula: see text] effective pressure, respectively. S-wave velocities are measured for two orthogonal polarizations; for four of six samples, anisotropy is revealed. TheGassmann model underpredicts fluid-substitution effects by [Formula: see text] for three samples and by as much as 5% for the rest of the six samples. Moreover, when dried, they also show decreasing attenuation with increasing confining pressure. To model this behavior, we examine a pore model made of two pore systems: one constitutes the main and drainable porosity, and the other is made of undrained cracklike pores that can be associated with grain-to-grain contacts. In addition, these dried rock samples are modeled to contain a fluid-filled-pore system of grain-to-grain contacts, potentially causing local fluid flow and attenuation. For the theoretical model, we use an inclusion model based on the [Formula: see text]-matrix approach, which also considers effects of pore texture and geometry, and pore fluid, global- and local-fluid flow. By using a dual-pore system, we establish a realistic physical model consistently describing the measured data.

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Evaluation of P and S Wave Velocities and Their Return Energy of Rock Specimen at Various Lateral and Axial Stresses

Geotechnical and Geological Engineering ◽

10.1007/s10706-020-01221-9 ◽

2020 ◽

Vol 38 (3) ◽

pp. 3253-3270 ◽

Cited By ~ 1

Author(s):

Mojtaba Heidari ◽

Rassoul Ajalloeian ◽

Akbar Ghazifard ◽

Mahmoud Hashemi Isfahanian

Keyword(s):

Rock Specimen ◽

S Wave ◽

Wave Velocities

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An experimental study to investigate the physical and dynamic elastic properties of Eagle Ford shale rock samples

Journal of Petroleum Exploration and Production Technology ◽

10.1007/s13202-021-01243-w ◽

2021 ◽

Author(s):

Faisal Altawati ◽

Hossein Emadi ◽

Rayan Khalil

Keyword(s):

Elastic Properties ◽

Injection Pressure ◽

Confining Pressure ◽

Xrd Analysis ◽

Low Permeability ◽

S Wave ◽

Eagle Ford ◽

Core Samples ◽

Wave Velocities ◽

Dynamic Elastic Properties

AbstractUnconventional resources, such as Eagle Ford formation, are commonly classified for their ultra-low permeability, where pore sizes are in nano-scale and pore-conductivity is low, causing several challenges in evaluating unconventional-rock properties. Several experimental parameters (e.g., diffusion time of gas, gas injection pressure, method of permeability measurement, and confining pressure cycling) must be considered when evaluating the ultra-low permeability rock's physical and dynamic elastic properties measurements, where erroneous evaluations could be avoided. Characterizing ultra-low permeability samples' physical and elastic properties helps researchers obtain more reliable information leading to successful evaluations. In this study, 24 Eagle Ford core samples' physical and dynamic elastic properties were evaluated. Utilizing longer diffusion time and higher helium injection pressure, applying complex transient method, and cycling confining pressure were considered for porosity, permeability, and velocities measurements. Computerized tomography (CT) scan, porosity, permeability, and ultrasonic wave velocities were conducted on the core samples. Additionally, X-ray Diffraction (XRD) analysis was conducted to determine the mineralogical compositions. Porosity was measured at 2.07 MPa injection pressure for 24 h, and the permeability was measured using a complex transient method. P- and S-wave velocities were measured at two cycles of five confining pressures (up to 68.95 MPa). The XRD analysis results showed that the tested core samples had an average of 81.44% and 11.68% calcite and quartz, respectively, with a minor amount of clay minerals. The high content of calcite and quartz in shale yields higher velocities, higher Young's modulus, and lower Poisson's ratio, which enhances the brittleness that is an important parameter for well stimulation design (e.g., hydraulic fracturing). The results of porosity and permeability showed that porosity and permeability vary between 5.3–9.79% and 0.006–12 µD, respectively. The Permeability–porosity relation of samples shows a very weak correlation. P- and S-wave velocities results display a range of velocity up to 6206 m/s and 3285 m/s at 68.95 MPa confining pressure, respectively. Additionally, S-wave velocity is approximately 55% of P-wave velocity. A correlation between both velocities is established at each confining pressure, indicating a strong correlation. Results illustrated that applying two cycles of confining pressure impacts both velocities and dynamic elastic moduli. Ramping up the confining pressure increases both velocities owing to compaction of the samples and, in turn, increases dynamic Young's modulus and Poisson's ratio while decreasing bulk compressibility. Moreover, the results demonstrated that the above-mentioned parameters' values (after decreasing the confining pressure to 13.79 MPa) differ from the initial values due to the hysteresis loop, where the loop is slightly opened, indicating that the alteration is non-elastic. The findings of this study provide detailed information about the rock physical and dynamic elastic properties of one of the largest unconventional resources in the U.S.A, the Eagle Ford formation, where direct measurements may not be cost-effective or feasible.

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Subsonic near-surface P-velocity and low S-velocity observations using propagator inversion

Geophysics ◽

10.1190/1.1990220 ◽

2005 ◽

Vol 70 (4) ◽

pp. R15-R23 ◽

Cited By ~ 5

Author(s):

Robbert van Vossen ◽

Andrew Curtis ◽

Jeannot Trampert

Keyword(s):

Shear Velocity ◽

Confining Pressure ◽

Compressional Wave ◽

P Wave ◽

Soil Conditions ◽

Detailed Knowledge ◽

S Wave ◽

Near Surface ◽

Unconsolidated Sands ◽

Wave Velocities

Detailed knowledge of near-surface P- and S-wave velocities is important for processing and interpreting multicomponent land seismic data because (1) the entire wavefield passes through and is influenced by the near-surface soil conditions, (2) both source repeatability and receiver coupling also depend on these conditions, and (3) near-surface P- and S-wave velocities are required for wavefield decomposition and demultiple methods. However, it is often difficult to measure these velocities with conventional techniques because sensitivity to shallow-wave velocities is low and because of the presence of sharp velocity contrasts or gradients close to the earth's free surface. We demonstrate that these near-surface P- and S-wave velocities can be obtained using a propagator inversion. This approach requires data recorded by at least one multicomponent geophone at the surface and an additional multicomponent geophone at depth. The propagator between them then contains all information on the medium parameters governing wave propagation between the geophones at the surface and at depth. Hence, inverting the propagator gives local estimates for these parameters. This technique has been applied to data acquired in Zeist, the Netherlands. The near-surface sediments at this site are unconsolidated sands with a thin vegetation soil on top, and the sediments considered are located above the groundwater table. A buried geophone was positioned 1.05 m beneath receivers on the surface. Propagator inversion yielded low near-surface velocities, namely, 270 ± 15 m/s for the compressional-wave velocity, which is well below the sound velocity in air, and 150 ± 9 m/s for the shear velocity. Existing methods designed for imaging deeper structures cannot resolve these shallow material properties. Furthermore, velocities usually increase rapidly with depth close to the earth's surface because of increasing confining pressure. We suspect that for this reason, subsonic near-surface P-wave velocities are not commonly observed.

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Coupled Effects of Stress, Moisture Content and Gas Pressure on the Permeability Evolution of Coal Samples: A Case Study of the Coking Coal Resourced from Tunlan Coalmine

Water ◽

10.3390/w13121653 ◽

2021 ◽

Vol 13 (12) ◽

pp. 1653

Author(s):

Guofu Li ◽

Yi Wang ◽

Junhui Wang ◽

Hongwei Zhang ◽

Wenbin Shen ◽

...

Keyword(s):

Moisture Content ◽

Coalbed Methane ◽

Gas Permeability ◽

Axial Stress ◽

Gas Pressure ◽

Pressure Curve ◽

Permeability Evolution ◽

Confining Stress ◽

Qinshui Basin ◽

Gas Seepage

Deep coalbed methane (CBM) is widely distributed in China and is mainly commercially exploited in the Qinshui basin. The in situ stress and moisture content are key factors affecting the permeability of CH4-containing coal samples. Therefore, considering the coupled effects of compressing and infiltrating on the gas permeability of coal could be more accurate to reveal the CH4 gas seepage characteristics in CBM reservoirs. In this study, coal samples sourced from Tunlan coalmine were employed to conduct the triaxial loading and gas seepage tests. Several findings were concluded: (1) In this triaxial test, the effect of confining stress on the permeability of gas-containing coal samples is greater than that of axial stress. (2) The permeability versus gas pressure curve of coal presents a ‘V’ shape evolution trend, in which the minimum gas permeability was obtained at a gas pressure of 1.1MPa. (3) The gas permeability of coal samples decreased exponentially with increasing moisture content. Specifically, as the moisture content increasing from 0.18% to 3.15%, the gas permeability decreased by about 70%. These results are expected to provide a foundation for the efficient exploitation of CBM in Qinshui basin.

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The relation between seismic P‐ and S‐wave velocity dispersion in saturated rocks

Geophysics ◽

10.1190/1.1443537 ◽

1994 ◽

Vol 59 (1) ◽

pp. 87-92 ◽

Cited By ~ 35

Author(s):

Gary Mavko ◽

Diane Jizba

Keyword(s):

Wave Velocity ◽

Large Scale ◽

Velocity Dispersion ◽

Seismic Velocity ◽

Ultrasonic Velocities ◽

S Wave ◽

Local Flow ◽

Wave Velocities ◽

Shear Compliance

Seismic velocity dispersionin fluid-saturated rocks appears to be dominated by tow mecahnisms: the large scale mechanism modeled by Biot, and the local flow or squirt mecahnism. The tow mechanisms can be distuinguished by the ratio of P-to S-wave dispersions, or more conbeniently, by the ratio of dynamic bulk to shear compliance dispersions derived from the wave velocities. Our formulation suggests that when local flow denominates, the dispersion of the shear compliance will be approximately 4/15 the dispersion of the compressibility. When the Biot mechanism dominates, the constant of proportionality is much smaller. Our examination of ultrasonic velocities from 40 sandstones and granites shows that most, but not all, of the samples were dominated by local flow dispersion, particularly at effective pressures below 40 MPa.

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Application of machine learning algorithms to predict permeability in tight sandstone formations

Nafta-Gaz ◽

10.18668/ng.2021.05.01 ◽

2021 ◽

Vol 77 (5) ◽

pp. 283-292

Author(s):

Tomasz Topór ◽

Keyword(s):

Machine Learning ◽

Oil And Gas ◽

Learning Algorithms ◽

Confining Pressure ◽

Machine Learning Algorithms ◽

Core Material ◽

Confining Stress ◽

Tight Sandstone ◽

Oil And Gas Exploration ◽

Better Than

The application of machine learning algorithms in petroleum geology has opened a new chapter in oil and gas exploration. Machine learning algorithms have been successfully used to predict crucial petrophysical properties when characterizing reservoirs. This study utilizes the concept of machine learning to predict permeability under confining stress conditions for samples from tight sandstone formations. The models were constructed using two machine learning algorithms of varying complexity (multiple linear regression [MLR] and random forests [RF]) and trained on a dataset that combined basic well information, basic petrophysical data, and rock type from a visual inspection of the core material. The RF algorithm underwent feature engineering to increase the number of predictors in the models. In order to check the training models’ robustness, 10-fold cross-validation was performed. The MLR and RF applications demonstrated that both algorithms can accurately predict permeability under constant confining pressure (R2 0.800 vs. 0.834). The RF accuracy was about 3% better than that of the MLR and about 6% better than the linear reference regression (LR) that utilized only porosity. Porosity was the most influential feature of the models’ performance. In the case of RF, the depth was also significant in the permeability predictions, which could be evidence of hidden interactions between the variables of porosity and depth. The local interpretation revealed the common features among outliers. Both the training and testing sets had moderate-low porosity (3–10%) and a lack of fractures. In the test set, calcite or quartz cementation also led to poor permeability predictions. The workflow that utilizes the tidymodels concept will be further applied in more complex examples to predict spatial petrophysical features from seismic attributes using various machine learning algorithms.

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Nonlinear behavior of soil sediments identified by using borehole records observed at the Ashigra Valley, Japan

Bulletin of the Seismological Society of America ◽

10.1785/bssa0850061821 ◽

1995 ◽

Vol 85 (6) ◽

pp. 1821-1834

Author(s):

Toshimi Satoh ◽

Toshiaki Sato ◽

Hiroshi Kawase

Keyword(s):

Shear Strain ◽

Main Part ◽

Nonlinear Behavior ◽

Strong Motion ◽

S Wave ◽

Ground Shaking ◽

Wave Velocities ◽

The One ◽

Soil Sediments ◽

Strong Ground

Abstract We evaluate the nonlinear behavior of soil sediments during strong ground shaking based on the identification of their S-wave velocities and damping factors for both the weak and strong motions observed on the surface and in a borehole at Kuno in the Ashigara Valley, Japan. First we calculate spectral ratios between the surface station KS2 and the borehole station KD2 at 97.6 m below the surface for the main part of weak and strong motions. The predominant period for the strong motion is apparently longer than those for the weak motions. This fact suggests the nonlinearity of soil during the strong ground shaking. To quantify the nonlinear behavior of soil sediments, we identify their S-wave velocities and damping factors by minimizing the residual between the observed spectral ratio and the theoretical amplification factor calculated from the one-dimensional wave propagation theory. The S-wave velocity and the damping factor h (≈(2Q)−1) of the surface alluvial layer identified from the main part of the strong motion are about 10% smaller and 50% greater, respectively, than those identified from weak motions. The relationships between the effective shear strain (=65% of the maximum shear strain) calculated from the one-dimensional wave propagation theory and the shear modulus reduction ratios or the damping factors estimated by the identification method agree well with the laboratory test results. We also confirm that the soil model identified from a weak motion overestimates the observed strong motion at KS2, while that identified from the strong motion reproduces the observed. Thus, we conclude that the main part of the strong motion, whose maximum acceleration at KS2 is 220 cm/sec2 and whose duration is 3 sec, has the potential of making the surface soil nonlinear at an effective shear strain on the order of 0.1%. The S-wave velocity in the surface alluvial layer identified from the part just after the main part of the strong motion is close to that identified from weak motions. This result suggests that the shear modulus recovers quickly as the shear strain level decreases.

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