3D-printed rock models: Elastic properties and the effects of penny-shaped inclusions with fluid substitution

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. D669-D677 ◽  
Author(s):  
Long Huang ◽  
Robert R. Stewart ◽  
Nikolay Dyaur ◽  
Jose Baez-Franceschi
Keyword(s):  
3D Printing ◽  
Elastic Properties ◽  
Wave Velocity ◽  
Bedding Plane ◽  
P Wave ◽  
Fluid Substitution ◽  
S Wave ◽  
Wave Velocities ◽  
P Wave Velocity ◽  
3D Printed

3D printing techniques (additive manufacturing) using different materials and structures provide opportunities to understand porous or fractured materials and fluid effects on their elastic properties. We used a 3D printer (Stratasys Dimension SST 768) to print one “solid” cube model and another with penny-shaped inclusions. The 3D printing process builds materials, layer by layer, producing a slight “bedding” plane, somewhat similar to a sedimentary process. We used ultrasonic transducers (500 kHz) to measure the P- and S-wave velocities. The input printing material was thermoplastic with a density of [Formula: see text], P-wave velocity of [Formula: see text], and S-wave velocity of [Formula: see text]. The solid cube had a porosity of approximately 6% and a density of [Formula: see text]. Its P-wave velocity was [Formula: see text] in the bedding direction and [Formula: see text] normal to bedding. We observed S-wave splitting with fast and slow velocities of 879 and [Formula: see text], respectively. Quality factors for P- and S-waves were estimated using the spectral-ratio method with [Formula: see text] ranging from 15 to 17 and [Formula: see text] from 24 to 27. By introducing penny-shaped inclusions along the bedding direction in a 3D printed cube, we created a more porous volume with density of [Formula: see text] and porosity of 24%. The inclusions significantly decreased the P-wave velocity to 1706 and [Formula: see text] parallel and normal to the bedding plane. The fast and slow S-wave velocities also decreased to 812 and [Formula: see text]. A fluid substitution experiment, performed with water, increased (20%–46%) P-wave velocities and decreased (9%–10%) S-wave velocities. Theoretical predictions using Schoenberg’s linear-slip theory and Hudson’s penny-shaped theory were calculated, and we found that both theories matched the measurements closely (within 5%). The 3D printed material has interesting and definable properties and is an exciting new material for understanding wave propagation, rock properties, and fluid effects.

Impact of change in pore-fill material on P-wave velocity

Geophysics ◽  
2014 ◽  
Vol 79 (6) ◽  
pp. D399-D407 ◽  
Author(s):  
Nishank Saxena ◽  
Gary Mavko
Keyword(s):  
Shear Modulus ◽  
Wave Velocity ◽  
P Wave ◽  
Exact Equation ◽  
Fluid Substitution ◽  
Seismic Velocities ◽  
S Wave ◽  
Wave Velocities ◽  
Fill Material ◽  
P Wave Velocity

The problem of predicting the change in seismic velocities (P-wave and S-wave) upon the change in pore-fill material properties is commonly known as substitution. For isotropic rocks, P- and S-wave velocities are fundamentally linked to the effective P-wave and shear moduli. The change in the S-wave velocity or shear modulus upon fluid substitution can be predicted with Gassmann’s equations starting only with the initial S-wave velocity. However, predicting changes in P-wave velocity or the P-wave modulus requires knowledge of the initial P- and S-wave velocities. We initiated a rigorous derivation of the P-wave modulus for fluid and solid substitution in monomineralic isotropic rocks for cases in which an estimate of the S-wave velocity or shear modulus is not available. For the general case of solid substitution, the exact equation for the P-wave modulus depends on parameters that are usually unknown. However, for fluid substitution, fewer parameters are required. As Poisson’s ratio increases for the mineral in the rock frame, the dependence of exact substitution on these unknown parameters decreases. As a result, in the absence of shear velocity, P-wave modulus fluid substitution can, for example, be performed with higher confidence for rocks with a calcite or dolomite frame than it can for rocks with quartz frame. We evaluated a recipe for applying the new P-wave modulus fluid substitution. This improves on existing work and is recommended for practice.

scholarly journals Upscaling of elastic properties in carbonates: A modeling approach based on a multiscale geophysical data set

2020 ◽  
Author(s):  
Jerome Fortin ◽  
Cedric Bailly ◽  
Mathilde Adelinet ◽  
Youri Hamon
Keyword(s):  
Elastic Properties ◽  
Wave Velocity ◽  
Representative Elementary Volume ◽  
P Wave ◽  
Elementary Volume ◽  
Data Set ◽  
Wave Velocities ◽  
P Wave Velocity ◽  
Ultrasonic Measurements ◽  
Seismic Scale

<p>Linking ultrasonic measurements made on samples, with sonic logs and seismic subsurface data, is a key challenge for the understanding of carbonate reservoirs. To deal with this problem, we investigate the elastic properties of dry lacustrine carbonates. At one study site, we perform a seismic refraction survey (100 Hz), as well as sonic (54 kHz) and ultrasonic (250 kHz) measurements directly on outcrop and ultrasonic measurements on samples (500 kHz). By comparing the median of each data set, we show that the P wave velocity decreases from laboratory to seismic scale. Nevertheless, the median of the sonic measurements acquired on outcrop surfaces seems to fit with the seismic data, meaning that sonic acquisition may be representative of seismic scale. To explain the variations due to upscaling, we relate the concept of representative elementary volume with the wavelength of each scale of study. Indeed, with upscaling, the wavelength varies from millimetric to pluri-metric. This change of scale allows us to conclude that the behavior of P wave velocity is due to different geological features (matrix porosity, cracks, and fractures) related to the different wavelengths used. Based on effective medium theory, we quantify the pore aspect ratio at sample scale and the crack/fracture density at outcrop and seismic scales using a multiscale representative elementary volume concept. Results show that the matrix porosity that controls the ultrasonic P wave velocities is progressively lost with upscaling, implying that crack and fracture porosity impacts sonic and seismic P wave velocities, a result of paramount importance for seismic interpretation based on deterministic approaches.</p><p>Bailly, C., Fortin, J., Adelinet, M., & Hamon, Y. (2019). Upscaling of elastic properties in carbonates: A modeling approach based on a multiscale geophysical data set. Journal of Geophysical Research: Solid Earth, 124. https://doi.org/10.1029/2019JB018391</p>

Elastic reflectivity vectors and the geometry of intercept-gradient crossplots

2019 ◽  
Vol 38 (10) ◽  
pp. 762-769
Author(s):  
Patrick Connolly
Keyword(s):  
Elastic Property ◽  
Elastic Properties ◽  
Wave Velocity ◽  
Seismic Data ◽  
Measurement Errors ◽  
Rock Physics ◽  
P Wave ◽  
S Wave ◽  
P Wave Velocity ◽  
Well Log Analysis

Reflectivities of elastic properties can be expressed as a sum of the reflectivities of P-wave velocity, S-wave velocity, and density, as can the amplitude-variation-with-offset (AVO) parameters, intercept, gradient, and curvature. This common format allows elastic property reflectivities to be expressed as a sum of AVO parameters. Most AVO studies are conducted using a two-term approximation, so it is helpful to reduce the three-term expressions for elastic reflectivities to two by assuming a relationship between P-wave velocity and density. Reduced to two AVO components, elastic property reflectivities can be represented as vectors on intercept-gradient crossplots. Normalizing the lengths of the vectors allows them to serve as basis vectors such that the position of any point in intercept-gradient space can be inferred directly from changes in elastic properties. This provides a direct link between properties commonly used in rock physics and attributes that can be measured from seismic data. The theory is best exploited by constructing new seismic data sets from combinations of intercept and gradient data at various projection angles. Elastic property reflectivity theory can be transferred to the impedance domain to aid in the analysis of well data to help inform the choice of projection angles. Because of the effects of gradient measurement errors, seismic projection angles are unlikely to be the same as theoretical angles or angles derived from well-log analysis, so seismic data will need to be scanned through a range of angles to find the optimum.

Wavefield simulation and data-acquisition-scheme analysis for LWD acoustic tools in very slow formations

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. E59-E68 ◽  
Author(s):  
Hua Wang ◽  
Guo Tao
Keyword(s):  
Wave Velocity ◽  
Cutoff Frequency ◽  
P Wave ◽  
Flexural Wave ◽  
S Wave ◽  
Low Frequencies ◽  
Wave Velocities ◽  
Dipole System ◽  
P Wave Velocity ◽  
Wavefield Simulation

Propagating wavefields from monopole, dipole, and quadrupole acoustic logging-while-drilling (LWD) tools in very slow formations have been studied using the discrete wavenumber integration method. These studies examine the responses of monopole and dipole systems at different source frequencies in a very slow surrounding formation, and the responses of a quadrupole system operating at a low source frequency in a slow formation with different S-wave velocities. Analyses are conducted of coherence-velocity/slowness relationships (semblance spectra) in the time domain and of the dispersion characteristics of these waveform signals from acoustic LWD array receivers. These analyses demonstrate that, if the acoustic LWD tool is centralized properly and is operating at low frequencies (below 3 kHz), a monopole system can measure P-wave velocity by means of a “leaky” P-wave for very slow formations. Also, for very slow formations a dipole system can measure the P-wave velocity via a leaky P-wave and can measure the S-wave velocity from a formation flexural wave. With a quadrupole system, however, the lower frequency limit (cutoff frequency) of the drill-collar interference wave would decrease to 5 kHz and might no longer be neglected if the surrounding formation becomes a very slow formation, with S-wave velocities at approximately 500 m/s.

Acoustic measurements in unconsolidated sands at low effective pressure and overpressure detection

Geophysics ◽  
2002 ◽  
Vol 67 (2) ◽  
pp. 405-412 ◽  
Author(s):  
Manika Prasad
Keyword(s):  
Wave Velocity ◽  
P Wave ◽  
Acoustic Measurements ◽  
S Wave ◽  
Deepwater Drilling ◽  
Unconsolidated Sands ◽  
Wave Velocities ◽  
P Wave Velocity ◽  
Shallow Water Flows ◽  
Low Pressures

Shallow water flows and over‐pressured zones are a major hazard in deepwater drilling projects. Their detection prior to drilling would save millions of dollars in lost drilling costs. I have investigated the sensitivity of seismic methods for this purpose. Using P‐wave information alone can be ambiguous, because a drop in P‐wave velocity (Vp) can be caused both by overpressure and by presence of gas. The ratio of P‐wave velocity to S‐wave velocity (Vp/Vs), which increases with overpressure and decreases with gas saturation, can help differentiate between the two cases. Since P‐wave velocity in a suspension is slightly below that of the suspending fluid and Vs=0, Vp/Vs and Poisson's ratio must increase exponentially as a load‐bearing sediment approaches a state of suspension. On the other hand, presence of gas will also decrease Vp but Vs will remain unaffected and Vp/Vs will decrease. Analyses of ultrasonic P‐ and S‐wave velocities in sands show that the Vp/Vs ratio, especially at low effective pressures, decreases rapidly with pressure. At very low pressures, Vp/Vs values can be as large as 100 and higher. Above pressures greater than 2 MPa, it plateaus and does not change much with pressure. There is significant change in signal amplitudes and frequency of shear waves below 1 MPa. The current ultrasonic data shows that Vp/Vs values can be invaluable indicators of low differential pressures.

EXPERIMENTAL EVALUATION OF ULTRASONIC VELOCITIES AND ANISOTROPY IN THE TUSCALOOSA MARINE SHALE FORMATION

2020 ◽  
pp. 1-62 ◽  
Author(s):  
Jamal Ahmadov ◽  
Mehdi Mokhtari
Keyword(s):  
Wave Velocity ◽  
Mineralogical Composition ◽  
Organic Content ◽  
P Wave ◽  
S Wave ◽  
Velocity Anisotropy ◽  
Wave Velocities ◽  
Marine Shale ◽  
P Wave Velocity ◽  
Degree Of Anisotropy

Tuscaloosa Marine Shale (TMS) formation is a clay- and organic-rich emerging shale play with a considerable amount of hydrocarbon resources. Despite the substantial potential, there have been only a few wells drilled and produced in the formation over the recent years. The analyzed TMS samples contain an average of 50 wt% total clay, 27 wt% quartz and 14 wt% calcite and the mineralogy varies considerably over the small intervals. The high amount of clay leads to pronounced anisotropy and the frequent changes in mineralogy result in the heterogeneity of the formation. We studied the compressional (VP) and shear-wave (VS) velocities to evaluate the degree of anisotropy and heterogeneity, which impact hydraulic fracture growth, borehole instabilities, and subsurface imaging. The ultrasonic measurements of P- and S-wave velocities from five TMS wells are the best fit to the linear relationship with R2 = 0.84 in the least-squares criteria. We observed that TMS S-wave velocities are relatively lower when compared to the established velocity relationships. Most of the velocity data in bedding-normal direction lie outside constant VP/VS lines of 1.6–1.8, a region typical of most organic-rich shale plays. For all of the studied TMS samples, the S-wave velocity anisotropy exhibits higher values than P-wave velocity anisotropy. In the samples in which the composition is dominated by either calcite or quartz minerals, mineralogy controls the velocities and VP/VS ratios to a great extent. Additionally, the organic content and maturity account for the velocity behavior in the samples in which the mineralogical composition fails to do so. The results provide further insights into TMS Formation evaluation and contribute to a better understanding of the heterogeneity and anisotropy of the play.

Determining P- and S-wave velocities and Q-values from single ultrasound transmission measurements performed on cylindrical rock samples: it’s possible, when…

2020 ◽  
Author(s):  
Marc S. Boxberg ◽  
Mandy Duda ◽  
Katrin Löer ◽  
Wolfgang Friederich ◽  
Jörg Renner
Keyword(s):  
Wave Velocity ◽  
P Wave ◽  
S Wave ◽  
Standard Material ◽  
Rock Samples ◽  
Intrinsic Attenuation ◽  
Finite Element Software ◽  
Wave Velocities ◽  
P Wave Velocity

<p>Determining elastic wave velocities and intrinsic attenuation of cylindrical rock samples by transmission of ultrasound signals appears to be a simple experimental task, which is performed routinely in a range of geoscientific and engineering applications requiring characterization of rocks in field and laboratory. P- and S-wave velocities are generally determined from first arrivals of signals excited by specifically designed transducers. A couple of methods exist for determining the intrinsic attenuation, most of them relying either on a comparison between the sample under investigation and a standard material or on investigating the same material for various geometries.</p><p>Of the three properties of interest, P-wave velocity is certainly the least challenging one to determine, but dispersion phenomena lead to complications with the consistent identification of frequency-dependent first breaks. The determination of S-wave velocities is even more hampered by converted waves interfering with the S-wave arrival. Attenuation estimates are generally subject to higher uncertainties than velocity measurements due to the high sensitivity of amplitudes to experimental procedures. The achievable accuracy of determining S-wave velocity and intrinsic attenuation using standard procedures thus appears to be limited.</p><p>We pursue the determination of velocity and attenuation of rock samples based on full waveform modeling and inversion. Assuming the rock sample to be homogeneous - an assumption also underlying standard analyses - we quantify P-wave velocity, S-wave velocity and intrinsic P- and S-wave attenuation from matching a single ultrasound trace with a synthetic one numerically modelled using the spectral finite-element software packages SPECFEM2D and SPECFEM3D. We find that enough information on both velocities is contained in the recognizable reflected and converted phases even when nominal P-wave sensors are used. Attenuation characteristics are also inherently contained in the relative amplitudes of these phases due to their different travel paths. We present recommendations for and results from laboratory measurements on cylindrical samples of aluminum and rocks with different geometries that we also compare with various standard analysis methods. The effort put into processing for our approach is particularly justified when accurate values and/or small variations, for example in response to changing P-T-conditions, are of interest or when the amount of sample material is limited.</p>

Estimating shear‐wave velocities from P-wave and converted‐wave data

Geophysics ◽  
1999 ◽  
Vol 64 (2) ◽  
pp. 504-507 ◽  
Author(s):  
Franklyn K. Levin
Keyword(s):  
Wave Velocity ◽  
Seismic Data ◽  
P Wave ◽  
S Wave ◽  
Converted Wave ◽  
Wave Data ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
P Wave Velocity ◽  
Growing Body

Tessmer and Behle (1988) show that S-wave velocity can be estimated from surface seismic data if both normal P-wave data and converted‐wave data (P-SV) are available. The relation of Tessmer and Behle is [Formula: see text] (1) where [Formula: see text] is the S-wave velocity, [Formula: see text] is the P-wave velocity, and [Formula: see text] is the converted‐wave velocity. The growing body of converted‐wave data suggest a brief examination of the validity of equation (1) for velocities that vary with depth.

Seismological studies in a rock body at Chalk River, Ontario and their relation to fractures

1982 ◽  
Vol 19 (8) ◽  
pp. 1535-1547 ◽  
Author(s):  
C. Wright
Keyword(s):  
Wave Velocity ◽  
Test Site ◽  
P Wave ◽  
Seismic Velocities ◽  
S Wave ◽  
P Waves ◽  
Rock Body ◽  
Near Surface ◽  
Wave Velocities ◽  
P Wave Velocity

Seismological experiments have been undertaken at a test site near Chalk River, Ontario that consists of crystalline rocks covered by glacial sediments. Near-surface P and S wave velocity and amplitude variations have been measured along profiles less than 2 km in length. The P and S wave velocities were generally in the range 4.5–5.6 and 2.9–3.2 km/s, respectively. These results are consistent with propagation through fractured gneiss and monzonite, which form the bulk of the rock body. The P wave velocity falls below 5.0 km/s in a region where there is a major fault and in an area of high electrical conductivity; such velocity minima are therefore associated with fracture systems. For some paths, the P and 5 wave velocities were in the ranges 6.2–6.6 and 3.7–4.1 km/s, respectively, showing the presence of thin sheets of gabbro. Temporal changes in P travel times of up to 1.4% over a 12 h period were observed where the sediment cover was thickest. The cause may be changes in the water table. The absence of polarized SH arrivals from specially designed shear wave sources indicates the inhomogeneity of the test site. A Q value of 243 ± 53 for P waves was derived over one relatively homogeneous profile of about 600 m length. P wave velocity minima measured between depths of 25 and 250 m in a borehole correlate well with the distribution of fractures inferred from optical examination of borehole cores, laboratory measurements of seismic velocities, and tube wave studies.

Fluid substitution: Estimating changes in VP without knowing VS

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1750-1755 ◽  
Author(s):  
Gary Mavko ◽  
Christina Chan ◽  
Tapan Mukerji
Keyword(s):  
Wave Velocity ◽  
P Wave ◽  
Large Set ◽  
Fluid Substitution ◽  
S Wave ◽  
Shear Moduli ◽  
P Wave Velocity ◽  
The Common ◽  
Common Situation ◽  
Rock Bulk

Two methods are presented for estimating the change of seismic P‐wave velocity that accompanies pore fluid changes in a rock in the common situation when S‐wave velocity is unknown. In contrast, Gassmann’s relation operates on the rock bulk modulus, which can only be calculated when both [Formula: see text] and [Formula: see text] are measured. The first method operates directly on the P‐wave modulus and is equivalent to replacing the bulk moduli of the rock and mineral in Gassmann’s relation with the corresponding P‐wave moduli. The second method uses a graphical construction to estimate the decomposition of the measured P‐wave modulus into bulk and shear moduli, which then allows the conventional Gassmann’s formula to be used. When applied to a large set of sandstone data, the predictions of both methods, computed with [Formula: see text] only, are within a few percent of the Gassmann’s relation, using both [Formula: see text] and [Formula: see text].

Sign in / Sign up

Export Citation Format

Share Document