Variation Of Acoustic Velocity Research Articles

Deep Dive into the factors influencing acoustic velocity in the Dalan-Kangan formations, the central Persian Gulf

The propagation of acoustic waves in rocks is directly influenced by the rocks’ elastic properties. To evaluate petrophysical properties from acoustic data, it is essential to understand the factors that influence the variations in acoustic velocity of sedimentary rocks. Carbonate reservoirs are heterogeneous, and their evaluation is complicated. A closer look at the factors affecting the elastic properties of these rocks is essential because they reveal important information about the reservoir properties and their formation evaluation. Rock physics modeling relies on laboratory-measured acoustic data. This study, however, employs acoustic logs to elucidate the key factors influencing sonic velocity, offering a more comprehensive and field-applicable perspective. Samples were prepared from the Permian–Triassic Upper Dalan and Kangan formations. Porosity, permeability, sedimentary textures, mineralogy, and pore types were investigated. Furthermore, compressional, shear, and Stoneley well-logs data were recorded and converted to acoustic velocity in the sampled interval. Porosity-velocity modeling based on the differential effective medium (DEM) theory was performed for different values of equivalent pore aspect ratio (EPAR). The results show that there is a strong inverse relationship between acoustic velocities and porosity. Acoustic velocities also exhibit an inverse correlation with permeability, but the strength of these relationships is relatively weak. Acoustic velocities are not affected by carbonate textures. A specific texture may exhibit different velocities due to the influence of diagenetic processes. Mineralogy has only a minor influence on acoustic velocities. Dolostones have a slightly higher velocity than limestones, but the difference is insignificant. Stoneley log values are slightly different in limestone and dolostone, because this wave propagates along the mud-borehole interface. The velocities were affected by the variations in pore types within the studied formations. Therefore, in carbonate rocks, porosity, and the pore types play a significant role in controlling acoustic velocities. The value of EPAR = 0.15 can be considered as the boundary between stiff pores (moldic and vuggy) and soft pores (interparticle, intercrystalline, micro-intercrystalline, and microporosity). The lower EPAR value of interparticle pores in limestones compared to dolostones can be attributed to diagenetic processes such as dolomitization and compaction. The findings of this study can help to better understand what factors affect acoustic velocity in carbonate rocks. This study also shows that acoustic logs data can be effectively used in rock physics modeling and pore type identification. By identifying the pore types, it is possible to recognize diagenetic processes and determine the rock types to control the heterogeneity and estimate reservoir quality.

Determining the effectiveness of using acoustic velocity as an indirect measurement of branchiness in standing longleaf pine

Branches reduce stem quality, and the level of the effect is determined by the geometry, size, and number, of associated knots. Quantifying branchiness is difficult, as visual estimates are subjective, and mechanical measurements are impractical. Acoustic velocity (AV) is a relatively novel measurement capturing the speed stress travels through wood. AV is correlated with wood stiffness and is affected by internal characteristics like knots. This project tested AV as an indirect branchiness metric by measuring AV, height, diameter, and counting branches classified by diameter on 255 standing 8 year old longleaf pine ( Pinus palustris). AV was highly correlated with height (r = 0.76, p < 0.0001) and slenderness (r = 0.52, p < 0.0001). AV was moderately correlated with large living branches (diameter > 2.54 cm) (r = −0.27, p < 0.0001), but not correlated with total branches. Height, slenderness, and the count of large living branches (diameter > 2.54 cm) were included in the selected model for AV. Inclusion of dead or small (diameter < 2.54 cm) branches reduced model power. The best model captured 11% of the variation in AV, of which branches explained 5%. We conclude that AV does not appropriately quantify individual tree branchiness, but may be suitable for comparing populations such as families or provenances.

Integrated multipole acoustic modeling and processing in general stressed formations, Part 1: An effective approach study

Velocity variation around the borehole due to stress is widely important for borehole stability, hydraulic fracturing and sanding prevention during hydrocarbon production. Theoretical formulation of the acoustic velocity variation around the borehole under stress condition is derived. The formation around the borehole is considered as an rock with two orthogonal crack sets caused by the drilling operation. The relationship between fracture shape and near-borehole stress is established. The effective modulus of elasticity of the above media is derived. The finite difference method is then used to model the acoustic properties. The modeling results show that in a stressed formation, shear wave splitting and dispersion crossover would occur for a monopole and dipole source, respectively. It also explains that the dipole wave-dispersion crossover may not be clear which is more suitable for the field data observation. The modeling results can be used as a guide to understand and interpret the acoustic measurements in stressed formations.

Inversion of Full Waveform Sonic Data Assists Calibration of Geomechanics Model

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 202260, “Inversion of Advanced Full Waveform Sonic Data Provides Magnitudes of Minimum and Maximum Horizontal Stress for Calibrating the Geomechanics Model in a Gas Storage Reservoir,” by Zachariah J. Pallikathekathil, SPE, Xing Wang Yang, and Saeed Hafezy, Schlumberger, et al., prepared for the 2020 SPE Asia Pacific Oil and Gas Conference and Exhibition, originally scheduled to be held in Perth, Australia, 20–22 October. The paper has not been peer reviewed. In 1D geomechanics projects, calibration of stress is extremely important in the construction of a valid mechanical earth model (MEM). The effective minimum horizontal stress (Shmin) data usually are available from traditional measurements, but these have a few deficiencies. The complete paper presents a technique for deriving stresses in which the radial variation of acoustic velocity from an advanced dipole sonic logging tool is inverted to obtain stress. These derived stresses are then used to calibrate the 1D MEM for a gas storage field. Regional Geology The field is in the Otway Basin in Western Victoria. Gas is trapped in the Late Cretaceous Waarre formation at depths between 1155 and 1200 m subsea. The reservoir is sealed by the overlying marine Belfast mudstone, which is the common seal in the stratigraphy across the onshore Otway Basin. The reservoir has excellent reservoir quality and has proved ideal for gas storage. Challenge Posed by the 1D MEM Challenge Posed by the 1D MEM Well 1 was recently drilled in the basin. A 1D MEM - a numerical representation of the geomechanical properties and stress state of the earth at any depth - was planned to be constructed to obtain the current-day far-field principal stresses (Shmin), effective maximum horizontal stress (SHmax), and effective vertical stress (SV)] in the Belfast and Waarre formations. Understanding the stress field was important, especially in the caprock (Belfast) and in the reservoir (Waarre) so that the pressure limits for safe gas-storage operation could be defined better. However, for a variety of reasons, no conventional stress measurements were available to calibrate the modeled stress in the 1D MEM. Without any calibration of the stress, the geomechanics model would feature high uncertainty to be used to define the pressure operational limits for gas-storage operation. Fortunately, a new wireline sonic tool was recorded in the reservoir section and the overburden sections of the borehole in Well 1. A quick dispersion analysis of the waveforms showed that the Paaratte formation, above the Belfast formation, was acoustically stress-sensitive and that advanced processing could be performed to invert the acoustic information to stress values.

Physical properties of Cretaceous to Eocene platform-to-basin carbonates from Albania

Understanding acoustic velocities of sedimentary deposits is crucial for realistic subsurface imaging. The velocities rely on mineralogy, density, as well as pore volume (porosity) and pore structure. In carbonate rocks, both depositional and diagenetic histories exert a significant control on these characteristics. In order to determine this control, petrographic analysis (thin sections) associated with the analysis of the carbonate content, grain density, permeability, porosity, and acoustic measurements were performed on samples from Cretaceous to Eocene carbonate platform-to-basin series of Albania. Rock facies showed two depositional associations and four pore-type associations. Very low average permeability (<1 mD) and variable porosity values (0–14%) characterize the samples. Pore type and diagenetic alteration steered the porosity-permeability distribution. Modelling of the velocity-porosity relationship, using the differential effective medium theory (DEM), revealed that variations in the acoustic velocity were mainly driven by variations in porosity and pore type, while facies and mineralogy were of minor importance.The Albanian dataset was compared with petrophysical data retrieved from time- and deep-water facies equivalent carbonate series of the Gargano Promontory in Italy. The comparison demonstrates that the variation in acoustic velocity is limited within the Albanian samples due to the pronounced infill of primary and secondary pores. Acoustic velocity data, on the other hand, are more scattered for the Gargano and this is essentially related to the higher porosity due to the preserved primary macro-intergranular and micro-intercrystalline pores, and/or to significant development of secondary mouldic pores.This study contributes to the understanding of heterogeneities and spatial distribution of pore types resulting in different petrophysical signatures of Cretaceous platform to deep-water carbonates. The data provide a better insight into possible variations in reservoir quality and seismic signature of these types of carbonates in subsurface reservoirs.

Detecting Pipeline Anomalies and Variations in Acoustic Velocity in Multiphase Flow Regimes Using Computational Fluid Dynamics

The use of hydrodynamic pressure wave generated from the action of a fast acting valve as well as acoustic reflectometry in the detection of anomalies like leaks, deposits and blockages in a pipe or fluid flow system in the context of the prevailing scientific theories in fluid flow is discussed. The focus of this paper is the application of the theories to more complex scenarios involving multi-phase fluid flow, specifically, two-phase and two-component fluid flow. The principal concern is the determination of acoustic velocity in a two-phase flow regime; which is problematic because it varies with mixture composition along multiphase flowlines. A technique for simulating flow regimes in the laboratory using stacked S-shaped pipes is presented as well as a discussion of the results from a computational fluid dynamics model.

Coupled temperature and γ-radiation effect on silica-based optical fiber strain sensors based on Rayleigh and Brillouin scatterings.

Coupled temperature and γ-ray influence on Brillouin (PPP-BOTDA) and Rayleigh (TW-COTDR) scatterings are quantified. Aging tests of these distributed strain measuring systems are performed on-line, up to 1 MGy, at room temperature, 80 ∘C, 100 ∘C and 120 ∘C. Brillouin and Rayleigh frequency shifts remain identical regardless of the temperature: 3 MHz (2 MHz) and 7 GHz (3 GHz) for Ge-doped (respectively F-doped) fiber at 1 MGy. Meanwhile, radiation-induced attenuation is diminished because of the higher temperature; hence, the maximal distance range is less deteriorated. These tests help to explain the origin of the Brillouin frequency shift under γ-rays, with an acoustic velocity variation of about 1 m/s in 1 MGy irradiated samples.

The effect of pore structure complexity and saturation history on the variations of acoustic velocity as function of brine and oil saturation in carbonates

Time lapse seismic is a major technique that has been successfully implemented to monitor reservoir dynamics (such as changes in fluid saturation) in sandstones but its applicability in carbonate rocks is not well understood yet. This study aims to improve our understanding of the time lapse seismic signature in carbonates oil reservoirs by investigating how acoustic velocity changes as a result of variations in the brine and oil saturation. To this scope, we utilize a core flooding system to perform brine-oil displacement experiment in three reservoir carbonate samples, while monitoring the acoustic velocity as function of brine saturation (Sw) changes. The fluid displacement experiment included injection of oil into the fully brine saturated samples until reaching irreducible brine saturation, followed by injection of brine until reaching the residual oil saturation. We also characterize the pore structure complexity of the samples using nuclear magnetic resonance (NMR) and micro-CT scans to investigate its effect on the velocity-saturation relationship. We finally compare the measured acoustic velocity as function of saturation with the predictions of Gassmann theory while considering both uniform and patchy fluid distribution styles.Our results show that both P- and S-wave velocity (Vp and Vs respectively) decrease as oil displaces brine and then they both increase as brine displaces oil. Nevertheless, the velocity-saturation relationship exhibits a hysteresis: velocities measured at a given saturation during brine injection tend to be higher than those measured during oil injection. Our analysis shows that the Vp-Sw trend during oil injection into brine saturated samples follows the lower bound predicted by Gassmann theory (i.e., uniform fluid distribution), while the brine flooding data follows the upper bound of Gassmann theory (i.e., patchy fluid distribution). The transition from the uniform to patchy fluids distribution seems to occur around the irreducible brine saturation. Since oil production or enhanced oil recovery can be represented by the process of brine displacing oil, our results suggest that patchy fluid distribution should be considered in Gassmann theory when performing feasibility studies to predict changes in Vp as function of saturation changes. This study also highlights the importance of pore structure in controlling the changes of saturation and the corresponding changes in acoustic velocity. Larger changes and hysteresis in the measured velocity as function of saturation seem to correlate with lower pore stiffness (i.e., more micro cracks and less content of intraparticle rounded pores).

Experimental study of water-based drilling fluid disturbance on natural gas hydrate-bearing sediments

Natural gas hydrates (NGH) are widely considered as a promising important substitute energy resource. Some countries are trying to drill and develop NGH; however, the disturbance effect of water-based drilling fluid on the stability of NGH-bearing sediments is unclear, especially the water-based drilling fluid with a thermodynamics hydrate inhibitor. To understand the disturbance effect, this paper studies the affecting patterns of drilling fluid temperatures and thermodynamics hydrate inhibitors on NGH-bearing samples with different hydrate saturations through an experimental study of drilling disturbance induced by water-based drilling fluids and by measuring the acoustic velocity variation of NGH-bearing sediments. The results show that the acoustic velocity of the natural gas hydrate-bearing sediments increases with the growing hydrate saturation. The gas hydrate dissociation is accelerated by the increase in drilling fluid temperatures. However, this acceleration effect declines after hydrate saturation exceeds 50%. The NGH dissociation inside the formation is also affected by the micro distribution of natural gas hydrates. Addition of thermodynamics hydrate inhibitors into the drilling fluid can apparently boost the gas hydrate dissociation, and the greater the concentration of inhibitors, the more obvious the effect. The boost effects of salt-type inhibitors are markedly stronger than the effects of alcohol-type inhibitors. This means that the better inhibition effect of the inhibitors is, the greater the disturbance effect on NGH-bearing sediments. Therefore, the drilling fluid that is suitable for NGH-bearing sediments should not only be capable of suppressing the NGH generation in the wellbore but also should have eased stimulation of the NGH dissociation inside the drilled formation. The findings will provide help with drilling fluid design that is suitable for NGH-bearing sediments and provide a scientific basis for achieving safe drilling through NGH-bearing sediments.

Analysis on acoustic velocity characteristics of sediments in the northern slope of the South China Sea

To understand the spatial characteristics of the acoustic velocity within sediments in the northern slope of the South China Sea, an ultrasonic technique was employed to measure the vertical and horizontal acoustic velocities of sediment core samples. Combined with the physical and mechanical properties test results of sediments, the relationships between acoustic velocity and physical properties were analyzed. The research results showed that the acoustic velocity presented irregular variations at the same depth among different stations, and that, in general, the acoustic velocities in the vertical direction were greater than those in the horizontal direction. For different sampling stations and different depths, the acoustic velocities showed a great variability; they exhibited large differences and there was almost no relation between the vertical and horizontal velocities. In addition, the results clearly exhibited strong anisotropic characteristic among the acoustic velocities. This variation of acoustic velocity was due to complex changes of physical and mechanical properties of seabed sediments in the study area. The results of the study also showed that there was a large deviation between the measured and the predicted acoustic velocities. The predicted results were calculated by empirical equations using the relationships between single geotechnical parameters and the acoustic velocity. The research results improve the understanding of engineering geological properties of the sediments in the study area.

Evaluation of the Sensitivity of an in vitro High Frequency Ultrasound Device to Monitor the Coagulation Process: Study of the Effects of Heparin Treatment in a Murine Model

This study evaluates the sensitivity of a new in vitro high frequency ultrasound test of the whole blood coagulation process. A rat model of anticoagulant treatment is reported. Many recent studies of the role of red blood cells in the whole blood coagulation process have revealed an increasing demand for global tests of the coagulation process performed on whole blood instead of plasma samples. In contrast to existing optical tests, high frequency ultrasound presents the advantages of characterizing the mechanical properties of whole blood clotting. Ultrasound longitudinal wave velocity and integrated attenuation coefficient (IAC) were simultaneously assessed in a 10 to 30 MHz frequency range during the whole blood coagulation process in vitro in rats under anticoagulant therapy. Differences between humans and rats were also clearly emphasized in non-clotting blood and in clotting blood using specific criteria deduced from acoustic parameters (ultrasound velocity for non-clotting blood: = 1574 ± 2 m/s for rats and 1583 ± 3 m/s for humans and IAC = 2.25 ± 0.14 dB/cm for rats and 1.5 ± 0.23 dB/cm for humans). We also measured the coagulation time t 0 from the acoustic velocity ( t 0 = 11.15 ± 7 min for control rat blood and 43.3 ± 11.4 min for human blood). Different doses of heparin were administered to rats. The sensitivity of the ultrasound device to the effects of heparin was evaluated. Differences between non-treated rats and chronically and acutely treated rats were recorded and quantified. We particularly noted that the slope S and the amplitude I of the variations in acoustic velocity were linked to clot retraction, which is a good indicator of the platelet function. The amplitude of the variations in S was between (20 ± 8) × 10 –3 m/s 2 for control group rats, and (0.92 ± 0.35) × 10 –3 m/s 2 for chronic heparin-treated group rats. The values of I were 15 times higher for control group rats than for chronic heparin-treated group rats. (E-mail: rachel.libgot@univ-tours.fr)

Brillouin gain suppression in photonic crystal fibers with random acoustically microstructured cores

Finite-element calculations of the Brillouin gain spectrum in photonic crystal fibers (PCFs) with cores incorporating random arrangements of regions with discrete acoustic velocities are presented. The peak Brillouin gain coefficient for PCFs with cores with an acoustic domain size of approximately 0.26 microm(2) and an acoustic velocity variation of 3% was calculated to be 3.3 x 10(-12) m/W with a Brillouin gain spectrum FWHM of 280 MHz. This corresponds to a decrease in the peak Brillouin gain coefficient of 7.4 dB relative to a PCF with an acoustically homogeneous core.

Elastic relaxations associated with the – transition in LaAlO3: II. Mechanisms of static and dynamical softening

Brillouin spectra have been collected in situ at temperatures up to∼1000 K for different crystallographic directions from two single crystal plates ofLaAlO3 perovskite. Elastic moduli derived from these, together with heat capacity, spontaneousstrain and Raman data from the literature, have then been used to calibrate the coefficientsin a classical Landau free energy expansion for the second order phase transition at Tc = 817 K. The static strain/order parameter coupling model provides aquantitative description of elastic softening between room temperature and∼700 K, butfrom ∼700 K up to Tc additional elastic softening correlates with the development of a central peak in the Brillouinspectra. The presence of quasi-elastic scattering, which reaches maximum intensity∼5–15 Kbelow Tc, implies a strong dynamical component to the phase transition. Relaxationtimes estimated from the width of the central peak are of the order of∼10–100 ps and appear to be more or less constant between∼700 and 800 K, which is consistent with an intrinsic origin associated withphonon density fluctuations. Central peak width variations and an irregularpattern of acoustic velocity variations in a 20 K temperature interval belowTc are interpreted in terms of flipping of clusters of tilted octahedra between different⟨111⟩,⟨011⟩ and⟨001⟩ tilt axes. The additional softening beyond that expected from the classical strain/orderparameter coupling model can be understood in terms of coupling of acoustic modes withthe central peak mode(s).

Effect of elastic collisions on acoustic wave propagation in simplified nuclear glass: Molecular dynamics simulation

A novel method based on classical molecular dynamics was used to measure acoustic velocities in simplified glasses and in pure silica. The method was then applied to observe the acoustic velocity variation in a simple glass subjected to displacement cascades. The Rayleigh velocity and Young’s modulus were observed to decrease; this behavior is consistent with experimental results obtained for the same glass irradiated by heavy ions. The increasing disorder and reduction in atomic density resulting from elastic collisions are thus directly related to the drop in the Rayleigh velocities and Young’s modulus.

Investigation of An Acoustic Temperature Transducer and its Application for Heater Temperature Measurement

Recent developments in temperature measurement have encouraged researchers to develop low-cost, simple structure, computerized generic transducers for environmental monitoring and industrial process control. The research presents a computerized technique which allows to measure temperature according to the variation of acoustic velocity (frequency) in a closed waveguide. Signal conditioning and processing was carried out using labVIEW (G Language) VIs. In order to evaluate the time characteristic of the transducer its response was compared with that of a reference detector (PT 100) for the same step input. Static characteristics of the transducer show a quasi-linear relationship between the measured temperature and the resonance frequency. Results of practical experiments show that in order to improve the response curve of the transducer and decrease the rising time interval it is advisable to implement thin-wall glass tubes or another material with lower thermal impedance.

Variations in acoustic velocity and density with age, and their interrelationships in radiata pine

Acoustic velocity by the Fakopp time of flight (ToF) tool was used to estimate outerwood stiffness of trees within stands and between stands of different age classes (ages 8, 16 and 25). The TOF acoustic velocity measured in the standing trees was generally higher than the acoustic velocity measured by the Hitman (resonance) tool on the associated logs. The difference between the two velocities tended to be greater in the older and large diameter trees. The large variability in acoustic velocity, or preferably V 2, makes it an efficient wood quality variable for screening trees. Wood density variables did not exhibit any relationship with acoustic velocity or modulus of elasticity (MoE) within each age-class. The classic pseudo-relationship observed with pooled data from all stand ages is mainly due to a stand age-effect and so one should be cautious in relying on any significant association between density and MoE.

Kinematic Coupling Effects on Heat-Release Transfer Function of a Premixed Flame

The effect of acoustic excitation on the heat-release characteristics of a two-dimensional premixed flame is studied. Past researchers have assumed that the acoustic nearfield and kinematics of the flame surface are uncoupled. However, recent studies by the authors have shown that the acoustic nearfield is significantly affected by flame-surface wrinkling and hence the coupling between flame-surface kinematics and the acoustic field cannot be neglected. The acoustic-velocity nearfield of the flame surface is determined by using a boundary integral equation (BIE) modified to include the effects of flame-front wrinkling on the acoustic field. A linearized G equation is solved to obtain an expression for the flame-surface wrinkling in terms of the acoustic velocity at the flame front. This equation is then solved simultaneously with the BIE by using a Newton-Raphson scheme to obtain simultaneously the flame-surface shape and the acoustic-velocity variation for the case of a two-dimensional dump-stabilized flame. The results show that the transfer function is controlled by two parameters, the flame Strouhal number and the half-angle at the apex of the flame, θ. The computed transfer function is compared with the transfer functions from two other models. The first model assumes a one-dimesional variation of acoustic velocity along the axial direction. The second model assumes a two-dimensional acoustic-velocity field while neglecting kinematic coupling. The inclusion of kinematic coupling leads to the prediction of a different value of the magnitude of the transfer function at low frequencies. This difference in predicted magnitudes depends on the excitation velocity amplitude. The predicted magnitudes increase with decrease in 0. The predicted phase is observed to be insensitive to changes in 0. Kinematic coupling also results in the reduction of the predicted spatial variation of the magnitude of the normalized acoustic velocity along the flame.

Influence of overpressure on formation velocity evaluation of Neogene strata from the eastern Bengal Basin, Bangladesh

Interpretation of sonic log data of anticlinal structures from eastern Bangladesh reveals significant variations of acoustic velocity of subsurface strata. The amount of variation in velocity is 32% from Miocene to Pliocene stratigraphic units in Titas and Bakhrabad structure, whereas 21% in Rashidpur structure. Velocity fluctuations are influenced by the presence of gas-bearing horizons, with velocities of gas-producing strata 3–7% lower than laterally equivalent strata at similar depth. Average velocities of Miocene Boka Bil and Bhuban formations are, respectively, 2630 and 3480 m/s at Titas structure; 2820 and 3750 m/s at Bakhrabad; and 3430 and 3843 m/s at the Rashidpur structure. From the overall velocity–depth distribution for a common depth range of 915–3000 m, the Titas, Bakhrabad and Rashidpur structures show a gradual increase in velocity with depth. In contrast, the Sitakund anticline in SE Bangladesh reveals a decrease in velocity with depth from 3000 to 4000 m, probably due to the presence of overpressured mudrocks of the Bhuban Formation. Tectonic compression, associated with the Indo-Burmese plate convergence likely contributed the most toward formation of subsurface overpressure in the Sitakund structure situated in the Chittagong–Tripura Fold Belt of the eastern Bengal basin, Bangladesh.

Revisiting the Wyllie time average equation in the case of near‐spherical pores

We suggest a generalized form of the Wyllie equation to better describe acoustic velocity variation with porosity in rocks with a mixture of intercrystalline and near‐spherical pores. Introducing a pore shape factor in the Wyllie equation allows different weights to be applied to the solid‐phase P‐wave velocity to account for rock frame stiffness. This is demonstrated in carbonate and igneous rocks having variable amounts of spherical porosity, ranging from 0% to 80% of the bulk porosity. The generalized equation describes a velocity–porosity envelope instead of the simple line given by the Wyllie equation. The lower limit of the velocity envelope is for rocks that have only interparticle or intercrystalline porosity (Wyllie equation behavior), and the upper limit is when all pores are spherical or near spherical. This upper limit corresponds to the Hashin‐Shtrikman upper bound for porosities up to 30%. The realization portrays Wyllie's velocity–porosity relationship as one particular case in which all pores are intercrystalline or interparticle with a pore shape factor equal to unity. An increase in the amount of high‐aspect‐ratio pores leads to higher pore shape factor. We suspect that this factor may be generalized to include fracture porosity with values less than unity. We suggest that this factor represents the acoustic equivalent of the cementation factor in Archie's law for resistivity measurements. The velocity calculated by the modified model correlates well with both the measured velocity and the calculated velocity using the Kuster‐Toksöz theoretical model. Various factors controlling acoustic velocity in carbonates can be quantified, based on this modification.

Microstructural control on the elastic properties of thermally cracked granite

Compressional waves velocity V P was measured during long-term experiments in a high-pressure vessel (in the range [10–75] MPa for confining and pore pressures). Experiments were carried out on a granite specimen prepared by a controlled heating treatment at 510 °C, which generated thermal cracks. Data analysis is proposed by using an effective medium approach based on Kachanov's [Appl. Mech. Rev. 45 (1992)304] model. The elastic behaviour of the cracked rock is controlled by the crack density parameter which varies with confining and pore pressures due to crack closure. In order to model the progressive closure of cracks, we assume elliptical cracks with major axis 2 c and aspect ratio α. By using a conformal mapping technique, we derive the variation of the crack aspect ratio as a function of effective pressure, the effective pressure coefficient η depending on α and Poisson's ratio ν 0. As a result, we compute the crack density parameter and the elastic moduli of the cracked rock as a function of confining and pore pressures. To take into account the heterogeneity of the rock sample, a peak-like distribution of crack aspect ratios is introduced, which allows us to calculate the acoustic velocity V P for various effective pressures. Comparison is made between theoretical and experimental values and shows that this simple model captures the essential features of the acoustic velocity variation: an increase of V P when pore pressure is decreased followed by a plateau for a threshold pore pressure. Best consistency between theoretical and experimental velocity values is obtained by introducing a second crack population with a higher mean aspect ratio and an irreversible closure mechanism as effective pressure is cycled.