The Influence of pore pressure and confining pressure on dynamic elastic properties of Berea sandstone

Geophysics ◽  
1985 ◽  
Vol 50 (2) ◽  
pp. 207-213 ◽  
Author(s):  
N. I. Christensen ◽  
H. F. Wang
Keyword(s):  
Pore Pressure ◽  
Shear Wave ◽  
Confining Pressure ◽  
Compressional Wave ◽  
Berea Sandstone ◽  
Incremental Change ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Pulse Transmission ◽  
Pressure Increment

Compressional‐ and shear‐wave velocities of watersaturated Berea sandstone have been measured as functions of confining and pore pressures to 2 kbar. The velocities, measured by the pulse transmission technique, were obtained at selected pressures for the purpose of evaluating the relative importance of confining pressure and pore pressure on elastic wave velocities and derived dynamic elastic constants. Changes in Berea sandstone velocities resulting from changes in confining pressure are not exactly canceled by equivalent changes in pore pressure. For properties that involve significant bulk compression (compressional‐wave velocities and bulk modulus) an incremental change in pore pressure does not entirely cancel a similar change in confining pressure. On the other hand, it is shown that a pore pressure increment more than cancels an equivalent change in confining pressure for properties that depend significantly on rigidity (shear‐wave velocity and Poisson’s ratio). This behavior (as well as observed wave amplitudes) is related to the presence of high‐compressibility clay that lines grains and pores within the quartz framework of the Berea sandstone.

Sonic logging of compressional‐wave velocities in a very slow formation

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1627-1633 ◽  
Author(s):  
Bart W. Tichelaar ◽  
Klaas W. van Luik
Keyword(s):  
Shear Wave ◽  
Wave Velocity ◽  
Compressional Wave ◽  
P Wave ◽  
Dipole Source ◽  
Frequency Spectra ◽  
Unconsolidated Sands ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Sonic Logging

Borehole sonic waveforms are commonly acquired to produce logs of subsurface compressional and shear wave velocities. To this purpose, modern borehole sonic tools are usually equipped with various types of acoustic sources, i.e., monopole and dipole sources. While the dipole source has been specifically developed for measuring shear wave velocities, we found that the dipole source has an advantage over the monopole source when determining compressional wave velocities in a very slow formation consisting of unconsolidated sands with a porosity of about 35% and a shear wave velocity of about 465 m/s. In this formation, the recorded compressional refracted waves suffer from interference with another wavefield component identified as a leaky P‐wave, which hampers the determination of compressional wave velocities in the sands. For the dipole source, separation of the compressional refracted wave from the recorded waveforms is accomplished through bandpass filtering since the wavefield components appear as two distinctly separate contributions to the frequency spectrum: a compressional refracted wave centered at a frequency of 6.5 kHz and a leaky P‐wave centered at 1.3 kHz. For the monopole source, the frequency spectra of the various waveform components have considerable overlap. It is therefore not obvious what passband to choose to separate the compressional refracted wave from the monopole waveforms. The compressional wave velocity obtained for the sands from the dipole compressional refracted wave is about 2150 m/s. Phase velocities obtained for the dispersive leaky P‐wave excited by the dipole source range from 1800 m/s at 1.0 kHz to 1630 m/s at 1.6 kHz. It appears that the dipole source has an advantage over the monopole source for the data recorded in this very slow formation when separating the compressional refracted wave from the recorded waveforms to determine formation compressional wave velocities.

FLUID SATURATION EFFECTS ON DYNAMIC ELASTIC PROPERTIES OF SEDIMENTARY ROCKS

Geophysics ◽  
1976 ◽  
Vol 41 (5) ◽  
pp. 895-921 ◽  
Author(s):  
A. R. Gregory
Keyword(s):  
Shear Wave ◽  
Elastic Moduli ◽  
Sedimentary Rocks ◽  
Compressional Wave ◽  
Reflection Coefficients ◽  
High Porosity ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Fluid Saturation ◽  
Saturation Effects

The influence of saturation by water, oil, gas, and mixtures of these fluids on the densities, velocities, reflection coefficients, and elastic moduli of consolidated sedimentary rocks was determined in the laboratory by ultrasonic wave propagation methods. Twenty rock samples varying in age from Pliocene to early Devonian and in porosity from 4 to 41 percent were tested under uniform pressures equivalent to subsurface depths of 0 to 18,690 ft. Fluid saturation effects on compressional‐wave velocity are much larger in low‐porosity than in high‐porosity rocks; this correlation is strengthened by elevated pressures but is absent at atmospheric pressure. At a frequency of 1 MHz, the shear‐wave velocities do not always decrease when liquid pore saturants are added to rocks as theorized by Biot; agreement with theory is dependent upon pressure, porosity, fluid‐mineral chemical interactions, and the presence of microcracks in the cementing material. Experimental results support the belief that lower compressional‐wave velocities and higher reflection coefficients are obtained in sedimentary rocks that contain gas. Replacing pore liquids with gas markedly reduces the elastic moduli of rocks, and the effect is enhanced by decreasing pressure. As a rule, the moduli decrease as the porosity increases; Poisson’s ratio is an exception to the rule. Liquid and gas saturation in consolidated rocks can also be distinguished by the ratio of compressional and shear wave velocities [Formula: see text]. The potential diagnostic value of elastic moduli in seismic exploration may stimulate interest in the use of shear‐wave reflection methods in the field.

scholarly journals Modified Fixed Wall Oedometer When Considering Stress Dependence of Elastic Wave Velocities

Sensors ◽  
2020 ◽  
Vol 20 (21) ◽  
pp. 6291
Author(s):  
Jong-Sub Lee ◽  
Geunwoo Park ◽  
Yong-Hoon Byun ◽  
Changho Lee
Keyword(s):  
Elastic Wave ◽  
Shear Wave ◽  
Compressional Wave ◽  
Stress Dependence ◽  
Bender Elements ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Vertical Effective Stress ◽  
Side Friction ◽  
Applied Stresses

A modified oedometer cell for measuring the applied stresses and elastic waves at the top and bottom of the specimen is developed to evaluate the effect of the side friction on the stress dependence of the elastic wave velocities. In the modified cell, two load cells are installed at the top and bottom plates, respectively. To generate and detect the compressional and shear waves, a pair of piezo disk elements and a pair of bender elements are mounted at both the top and bottom plates. Experimental results show that the stresses measured at the bottom are smaller than those measured at the top during the loading and vice versa during unloading, regardless of the densities and heights of the specimens. Under nearly saturated conditions, the compressional wave velocities remain almost constant for the entire stress state. With plotting stresses measured at top, the shear wave velocities during unloading are greater than those during loading, whereas with plotting stresses measured at bottom, the shear wave velocities during unloading are smaller than those during loading owing to the side friction. The vertical effective stress may be simply determined from the average values of the stresses measured at the top and bottom of the specimens.

Estimation of Dry-Rock Elastic Moduli Based on the Simulation of Mud-Filtrate Invasion Effects on Borehole Acoustic Logs

2009 ◽  
Vol 12 (06) ◽  
pp. 898-911 ◽  
Author(s):  
Tobiloluwa B. Odumosu ◽  
Carlos Torres-Verdín ◽  
Jesús M. Salazar ◽  
Jun Ma ◽  
Benjamin Voss ◽  
...  
Keyword(s):  
Bulk Modulus ◽  
Shear Wave ◽  
Elastic Properties ◽  
Elastic Moduli ◽  
Compressional Wave ◽  
Shear Rigidity ◽  
Spatial Distributions ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Mud Filtrate

Summary Reliable estimates of dry-rock elastic properties are critical to the accurate interpretation of the seismic response of hydrocarbon reservoirs. We describe a new method for estimating elastic moduli of rocks in-situ based on the simulation of mud-filtrate invasion effects on resistivity and acoustic logs. Simulations of mud-filtrate invasion account for the dynamic process of fluid displacement and mixing between mud-filtrate and hydrocarbons. The calculated spatial distributions of electrical resistivity are matched against resistivity logs by adjusting the underlying petrophysical properties. We then perform Biot-Gassmann fluid substitution on the 2D spatial distributions of fluid saturation with initial estimates of dry-bulk (kdry) modulus and shear rigidity (µdry) and a constraint of Poisson's ratio (?d) typical of the formation. This process generates 2D spatial distributions of compressional and shear-wave velocities and density. Subsequently, sonic waveforms are simulated to calculate shear-wave slowness. Initial estimates of the dry-bulk modulus are progressively adjusted using a modified Gregory-Pickett (1963) solution of Biot's (1956) equation to estimate a shear rigidity that converges to the well-log value of shear-wave slowness. The constraint on dynamic Poisson's ratio is then removed and a refined estimate of the dry-bulk modulus is obtained by both simulating the acoustic log (monopole) and matching the log-derived compressional-wave slowness. This technique leads to reliable estimates of dry-bulk moduli and shear rigidity that compare well to laboratory core measurements. Resulting dry-rock elastic properties can be used to calculate seismic compressional-wave and shear-wave velocities devoid of mud-filtrate invasion effects for further seismic-driven reservoir-characterization studies.

Seismic velocities of unconsolidated sands: Part 1 — Pressure trends from 0.1 to 20 MPa

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. E1-E13 ◽  
Author(s):  
Michael A. Zimmer ◽  
Manika Prasad ◽  
Gary Mavko ◽  
Amos Nur
Keyword(s):  
Shear Wave ◽  
Pressure Dependence ◽  
Glass Bead ◽  
Theoretical Models ◽  
Compressional Wave ◽  
P Wave ◽  
Seismic Velocities ◽  
Unconsolidated Sands ◽  
Wave Velocities ◽  
Shear Wave Velocities

Knowledge of the pressure dependences of seismic velocities in unconsolidated sands is necessary for the remote prediction of effective pressures and for the projection of velocities to unsampled locations within shallow sand layers. We have measured the compressional- and shear-wave velocities and bulk, shear, and P-wave moduli at pressures from [Formula: see text] in a series of unconsolidated granular samples including dry and water-saturated natural sands and dry synthetic sand and glass-bead samples. The shear-wave velocities in these samples demonstrate an average pressure dependence approximately proportional to the fourth root of the effective pressure [Formula: see text], as commonly observed at lower pressures. For the compressional-wave velocities, theexponent in the pressure dependence of individual dry samples is consistently less than the exponent for the shear-wave velocity of the same sample, averaging 0.23 for the dry sands and 0.20 for the glass-bead samples. These pressure dependences are generally consistent over the entire pressure range measured. A comparison of the empirical results to theoretical predictions based on Hertz-Mindlin effective-medium models demonstrates that the theoretical models vastly overpredict the shear moduli of the dry granular frame unless the contacts are assumed to have no tangential stiffness. The models also predict a lower pressure exponent for the moduli and velocities [Formula: see text] than is generally observed in the data. We attribute this discrepancy in part to the inability of the models to account for decreases in the amount of slip or grain rotation occurring at grain-to-grain contacts with increasing pressure.

scholarly journals Seismic Short-Refraction Studies on the Ross Ice Shelf, Antarctica

1979 ◽  
Vol 24 (90) ◽  
pp. 313-319
Author(s):  
Joseph F. Kirchner ◽  
Charles R. Bentley
Keyword(s):  
Shear Wave ◽  
Transverse Isotropy ◽  
Compressional Wave ◽  
Least Squares Regression ◽  
Horizontal Shear ◽  
Ice Shelf ◽  
Compressional Waves ◽  
Ross Ice Shelf ◽  
Wave Velocities ◽  
Shear Wave Velocities

AbstractSeismic short-refraction studies were carried out at five stations on the Ross Ice Shelf during the 1976–77 summer season as part of the comprehensive Ross Ice Shelf Geophysical and Glaciological Survey. Measurements of the velocities of compressional waves were made at each location. Compressional wave velocities were measured along more than one azimuth at three sites, and shear wave velocities (both components) at two. Travel-time curves were fitted to an exponential expression by means of a non-linear least-squares regression technique. The errors in the apparent velocities are estimated to be about ±50 m s–1 at short distances, diminishing to about ±10 m s–1 near the ends of the profiles. Compressional-wave velocities show only slight variations with azimuth and only over certain depth intervals, showing that constant-velocity surfaces are essentially horizontal. Shear-wave velocities, however, exhibit large variations according to azimuth and polarization, indicating that transverse isotropy is violated at least in the upper 30–40 m of the ice shelf. It is believed that the anisotropy is caused by structural details in the firn perhaps modified by preferred crystal orientation and that it may arise at least partly from anisotropic stresses in the ice shelf.

Seismic investigation of a san francisco bay mud site

1974 ◽  
Vol 64 (2) ◽  
pp. 375-385 ◽  
Author(s):  
Richard E. Warrick
Keyword(s):  
Seismic Response ◽  
Shear Wave ◽  
San Francisco ◽  
San Francisco Bay ◽  
Compressional Wave ◽  
Wave Generation ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Surface Measurements ◽  
A Site

abstract Measurements were made of the shear- and compressional-wave velocities necessary to determine the seismic response of a site on the edge of the San Francisco Bay, California. The shear wave is the most difficult to isolate because of the complications of earlier arriving energy. Downhole and surface measurements yielded shear-wave velocities of 90 to 130 m/sec and compressional-wave velocities of 1,400 m/sec for soft mud. The underlying older sediments had interval shear-wave velocities of 270 to 380 m/sec, increasing with depth. The corresponding P velocities for the older sediments were 1,600 to 1,840 m/sec. The horizontal traction technique of shear-wave generation proved to be the most successful of the methods tested.

Shear‐wave logging to enhance seismic modeling

Geophysics ◽  
1991 ◽  
Vol 56 (12) ◽  
pp. 2129-2138 ◽  
Author(s):  
M. A. Payne
Keyword(s):  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Field Data ◽  
Compressional Wave ◽  
Oil Sand ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Amplitude Versus Offset ◽  
Amplitude Versus

In an effort to understand better the amplitude variation with offset for reflections from an oil sand and the sensitivity of the AVO response to shear‐wave velocity variations, I studied synthetic and field gathers collected from an onshore field in the Gulf of Mexico basin. A wave‐equation‐based modeling program generated the synthetic seismic gathers using both measured and estimated shear‐wave velocities. The measured shear‐wave velocities came from a quadrupole sonic tool. The estimated shear‐wave velocities were obtained by applying published empirical and theoretical equations which relate shear‐wave velocities to measured compressional‐wave velocities. I carefully processed the recorded seismic data with a controlled‐amplitude processing stream. Comparison of the synthetic gathers with the processed field data leads to the conclusion that the model containing the measured shear‐wave velocities matches the field data much better than the model containing the estimated shear‐wave velocities. Therefore, existing equations which relate shear‐wave velocities to compressional‐wave velocities yield estimates which are not sufficiently accurate for making quantitative comparisons of synthetic and field gathers. Even small errors in the shear‐wave velocities can have a large impact on the output. Such errors can lead to an incomplete and perhaps inaccurate understanding of the amplitude‐versus‐offset response. This situation can be remedied by collecting shear‐wave data for use in amplitude‐versus‐offset modeling, and for building databases to generate better shear‐wave velocity estimator equations.

ULTRASONIC SHEAR‐WAVE VELOCITIES IN ROCKS SUBJECTED TO SIMULATED OVERBURDEN PRESSURE AND INTERNAL PORE PRESSURE

Geophysics ◽  
1965 ◽  
Vol 30 (1) ◽  
pp. 117-121 ◽  
Author(s):  
B. S. Banthia ◽  
M. S. King ◽  
I. Fatt
Keyword(s):  
Hydrostatic Pressure ◽  
Pore Pressure ◽  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Overburden Pressure ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
The Matrix ◽  
Internal Pore

Change in shear‐wave velocity for four dry sedimentary rocks has been studied as a function of the variation of both external hydrostatic pressure and internal pore pressure in the range 0 to 2,500 psi. The experimental method employs a beam of ultrasonic energy passing through a liquid in which a copper‐jacketed parallel‐sided slab of rock is rotated. The shear‐wave velocity is calculated from the laws of refraction and reflection of waves at a liquid‐solid boundary applied to the angle at which minimum energy is transmitted. The variation of shear‐wave velocity with pressure has been found to be a function of net overburden pressure, [Formula: see text], where [Formula: see text] hydrostatic pressure on the jacketed sample, [Formula: see text] pore pressure and n = a pressure‐dependent factor less than unity. The values of n at several differential pressures were chosen to yield a smooth curve passing through the displaced data points when the shear‐wave velocities were plotted as a function of net overburden pressure. Using the n values so obtained, the matrix compressibility [Formula: see text] for two of the sandstones has been calculated from the relation [Formula: see text]. The bulk compressibility [Formula: see text] for these two rocks had previously been obtained experimentally as a function of differential pressure. The values obtained for the matrix compressibility are in the range expected from a knowledge of the grain and cementing materials for these sandstones.

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