Sonic Anisotropy Research Articles

S-wave anisotropy from two dipole sonic data processing methods, confronted with fracture permeability, logs and cores

The present paper consists in two parts, determined by the historical emerging production of Dipole Sonic Imager (DSI) measurements and results in the early 1990’s. The DSI data were processed following two methods simultaneously developed in France and in USA by Schlumberger. In the first part the early dipole sonic S-wave velocity results obtained in late 1993 are confronted with the other borehole data obtained in the scientific borehole MM-1, entirely cored and extensively logged, as part of the comprehensive scientific project named Géologie Profonde de la France (GPF), conducted by the Bureau de Recherches Géologiques et Minières (BRGM, i.e. the French Geological Survey), in Ardèche, southern France. In 1994, José Perrin summarized and integrated all the borehole information including the preliminary results from an azimuthal “rotation scan” of S-wave sonic slowness determination method quickly developed in Schlumberger-France and aiming at detecting only the presence of S-wave velocity anisotropy in a first step. The initial results were presented to the French industrial logging community in April 1994, prior to the commercialization of any S-wave splitting computer detection routine applied to dipole sonic data. The second part focuses on the comparison of the dipole sonic S-wave anisotropy detection results from two methods produced at a later time by Schlumberger, namely: a) results from the commercial S-wave anisotropy detection routine based on cross energy minimization, obtained in October 1994, and b) principal S-wave azimuth results sorted from the “rotation scan” azimuthal method, produced in 1995 and further improved in July 1997. After discussing the discrepancies of the principal fast S-wave azimuth derived from the two methods with diverse specialists in Schlumberger, over several years, and on a spare time basis, the authors expose constructive explanations in the present paper. A limited overview of the latest dipole sonic data processing developments has also been attempted to better understand the differing S-wave birefringence results obtained in MM-1, suggesting that the rock formation in the immediate borehole vicinity, up to three times the borehole radius, may not be homogeneous along the borehole depth depending on the local geological context. Besides, the Fast Azimuth split S-wave (FAZ) fits with the strike of major regional faults and parallel to the maximal horizontal palaeo-stress, which happens to be nearly orthogonal to the local present stress direction accepted by the geologists! The present case study suggests that the S-wave anisotropy results ought to become more reliable, mainly on the accuracy and precision of the FAZ. Additionally, the efficiency of the semblance parameter for S-wave attenuation anisotropy detection is pondered, where no S-wave velocity anisotropy is detected over the dipole sonic receiver array.

Fault and fracture reactivation analysis by 4D geomechanical integrated modelling in one of a depleted carbonate oil field, southwest of Iran

ABSTRACT The study field has been an oil-producing area in southern Iran for nearly 50 years. Complex geological structure and varying levels of depletion scenarios require geomechanical analysis of the reservoir to enhance its production and mitigate geomechanical risks. This paper describes creating a time-lapse (4D) integrated geomechanical model by generating 3D maps of mechanical properties and a 3D stress state that can be altered over time as pore pressure changes, then explores pressure depletion and related stress changes effects on faults and fractures reactivation. The first phase of the study was an integrated stress analysis using Image logs and sonic anisotropy interpretation. 1D–3D Mechanical Earth Model was built by gridding the reservoir and populate the model with mechanical properties. The third phase provided a distribution of stresses and associated strains under initial conditions using finite element calculations. Ultimately, stress and strain changes associated with depletion simulated by the reservoir flow model were determined during the fourth phase of study. In the resulting model, different critical coordinates points from the initial year (1992) to 2045 were selected five time-steps. Results show no critical faults reactivation but by increasing production time the instability of fractures gradually rises by stress regime changes.

Precambrian basement reservoirs: Case study from the northern Bongor Basin, the Republic of Chad

Bongor Basin in the south of Chad is a Cretaceous–Paleogene rift basin developed on Precambrian crystalline basement and is part of the central African rift system (CARS). High oil flows have been tested from five basement buried hills, indicating that the Precambrian basement is a good reservoir for hydrocarbon accumulation. Core analyses from 10 wells indicate that the basement rocks are composed of plutonic rocks (including granite, syenite, monzonite, quartz monzonite, and diorite) and orthometamorphites (including migmatitic granite, migmatitic gneiss, and granulite). Structural mapping of the top basement shows that faults in basement have a principal strike orientation of west–northwest-east–southeast and a secondary orientation of northeast–southwest. A combination of mud losses, well testing results, cores, wire-line logs, Formation MicroImager, sonic scanner logs, and three-dimensional seismic data were used to identify and detect the basement reservoirs. Two main sets of high-angle fractures, striking west–northwest-east–southeast and west–southwest-east–northeast, were identified. Three facies are divided based on the degree of weathering, intensity of fracturing, and sonic anisotropy. The basement can be divided vertically into four zones: weathered and leached, fractured, semifilled fractured, and tight zones. The weathered and leached and fractured zones are the main basement reservoirs in the study area. The effective porosities range from 3% to 10%, in places up to 25%. The porosity and permeability of basement reservoirs depend on the structural location and hydrothermal and authigenic precipitates developed during and after the basin formation. The discovery of basement reservoirs in the Bongor Basin will aid the hydrocarbon exploration of a new play in the CARS.

Novel finite-element approach applied to borehole quadrupole dispersion analysis in stress-sensitive formations

Near a borehole, stress concentration effects may cause a complex spatial variation of elastic anisotropy. Stress-induced sonic anisotropy results when moduli and velocities are stress dependent and the state of stress is nonhydrostatic. For such cases, the appropriate material model is that of an elastic orthorhombic medium with material axes aligned with the principal axes of stress. We simulate the dispersion characteristics of quadrupole waves propagating along a borehole in a stress-sensitive formation. To include sensitivity to stress in the analysis, we derive a finite-element modeling approach which includes the stress-velocity relationship, the perturbed stress and velocity field near the borehole, and solutions to the full coupled anisotropic and 3D wave equation. We characterized the anisotropy around the borehole for different in situ stress conditions, and we derived the effects on quadrupole dispersion characteristics. Of particular interest was the phase velocity of the quadrupole wave, which at low frequencies provides an estimate of formation shear-wave velocity. Results indicated that the quadrupole mode dispersion was relatively insensitive to the hoop stress effects around a borehole giving greater confidence to shear-wave estimates made from these modes. The proposed ring-element formulation, which includes Fourier expansions of the field variables in the direction of the circumference, is well suited to this analysis and can be adapted to include other effects, such as a finite-length borehole.

Relating shear sonic anisotropy directions to stress in deviated wells

We develop a model that relates the polarization direction of a dipole sonic fast shear wave propagating along the borehole (hereafter called FSA) to the relative deviatoric stress tensor for arbitrary well orientations. We first define stress quantities, or “subsidiary principal stress,” relevant for sonic dipole shear characterized sufficiently far away into the formation to be unaffected by borehole stress concentration. Next, we show analytically for wells oriented within principal stress planes and numerically for wells outside principal stress planes that the stress-induced FSA coincides with the maximum normal stress direction orthogonal to the borehole (“maximum subsidiary principal stress”) using a nonlinear elastic model for isotropic unstressed background media and plane wave solutions. This model is independent of stress sensitivity parameters. This result is a consequence of, first, the direct relationship between the stressellipsoid factor and the shear stiffness difference ratio, [Formula: see text], and, second, the almost elliptical nature of stress-induced orthorhombic media. Using published laboratory data relating stiffnesses to applied differential stress for isotropic unstressed limestone and sandstone rocks, the model is confirmed for most well orientations except in the vicinity of the stress nodal point within the maximum and minimum principal stress plane, due to small anellipticity as stress increases. The orientations near the nodal point are also the zones of weakest stress-induced anisotropy zones and are therefore the least likely to be measured in practice as long as a quality indicator depending on both the degree of anellipticity and the strength of the shear anisotropy is below 0.5. Finally, we present a synthetic example of the application of this model to estimate the relative deviatoric stress tensor using two wells with different orientations.

Fracture characterization at multiple scales using borehole images, sonic logs, and walkaround vertical seismic profile

We present a quantitative forward-modeling methodology to link and interpret several measurements relevant to mechanical properties of fractures such as borehole images, sonic anisotropy logs, and borehole seismic anisotropy. The analysis is applied to a case study from a north African tight gas field using data from a vertical well. Two studies are conducted independently using the same geological fracture data to model fracture-induced anisotropy. In the first study, we use the orientation of the natural and drilling-induced fractures interpreted on the image log to model the azimuthal fracture-induced anisotropy at the sonic scale. The mechanical effects of natural and drilling-induced fractures are treated using different compliance parameters for each fracture type. We show that modeled sonic fast shear azimuths could be biased by the presence of noncompliant fractures in each fracture type, and we propose an empirical selection criterion to reject noncompliant fractures prior to compliance estimation. Then, we estimate the fracture compliances and confirm that natural open fractures have larger compliances than drilling-induced fractures. In the second study, we apply interpreted borehole images toward modeling of the azimuthal vertical seismic profile (VSP) attributes as a function of source azimuthal position. Natural fractures inside a window of height, h, and located at depth, d, are included, and several volume sizes and positions (i.e., h and d) are considered. We find a good agreement between modeled and observed transverse-over-radial displacement trends using natural fractures within windows located at the depth of the VSP receiver, and having window heights on the order of one to two VSP shear wavelengths.

Forward modeling of fracture-induced sonic anisotropy using a combination of borehole image and sonic logs

We develop a methodology to model and interpret borehole dipole sonic anisotropy related to the effect of geologic fractures, using a forward-modeling approach. We use a classical excess-compliance fracture model that relies on the orientation of the individual fractures, the elastic properties of the host rock, and the normal and tangential fracture-compliance parameters. Orientations of individual fractures are extracted from borehole-image log analysis. The model is validated using borehole-resistivity image and sonic logs in a gas-sand reservoir over a [Formula: see text] (50 m) vertical interval of a well. Significant amounts of sonic anisotropy are observed at three zones, with a fast-shear azimuth (FSA) exhibiting 60° of variation and slowness difference between 2% and 16%. Numerous quasivertical fractures with varying dip azimuths are identified on the image log at the locations of strong sonic anisotropy. The maximum horizontal-stress direction, given by breakouts and drilling-induced fractures, is shown not to be aligned with the strike of natural fractures. We show that using just two adjustable fracture-compliance parameters, one fornatural fractures and one for drilling-induced fractures, is an excel-lent first-order approximation to explain the fracture-induced anisotropy response over a depth interval of [Formula: see text]. Given the presence of gas and the absence of clay filling within the fractures, we assumed equal normal and tangential compliances. The two inverted normal compliances are [Formula: see text] and [Formula: see text]. Predicted FSA matches measured FSA over [Formula: see text] (40 m) of the [Formula: see text] (50 m) studied interval. Predicted slowness anisotropy matches the overall variation and measured values of anisotropy for two of the three strong anisotropy zones. Analysis of the symmetries of the modeled anisotropic response shows that the medium is mostly a horizontal transverse isotropic medium, with small azimuthal variation of the symmetry axis. Analysis of each independent fracture type shows that the anisotropy is mainly driven by open or partially healed fractures, but also consistent with stress-related, drilling-induced fractures. Therefore, the measured sonic anisotropy is caused by the combination of stress and fracture effects where the predominance of one mechanism over the other is depth-dependent. This method provides a consistent approach to data interpretation by integrating borehole image and sonic logs that probe the formation at different depths of investigation around the borehole.

Studies of Compact Hard Tissues and Collagen by Means of Brillouin Light Scattering

A measure of the elastic properties of tissue can be found from the propagation of sound in the tissue. Longitudinal sonic velocities were measured for mineralized turkey leg tendon (density 1.50 g/cc), deer antler (1.77 g/cc) and cow tibia (2.05 g/cc) in the 10 GHz frequency regime by means of Brillouin light scattering using a nine pass Fabry-Perot interferometer. Wet, air dried, mineralized and demineralized specimens were tested. Sonic velocity in each tissue increased with mineral content and decreased when the tissue was wet. All wet values are higher than for wet rat tail tendon collagen, axially and radially, but with considerably less anisotropy. The results are interpreted to indicate that bone matrix collagen is more highly crosslinked than tail tendon collagen. The loss of anisotropy is taken to correspond to a much higher crosslinking density between adjacent collagen molecules in mineralized tissue compared to rat tail tendon. The axial sonic velocity of dried rat tail tendon is almost that for low density dried mineralized tissue and greater than the radial sonic velocity of these tissues, but the radial sonic velocity for dried rat tail tendon is much lower, again corresponding to less crosslinking in this tissue. Longitudinal modulus, K, is defined as the tissue density times the square of the velocity. The compliance, 1/K, was found to be a linear function of density for each of the four conditions. It suggests that a Reuss formalism describes the elastic properties. Since the difference between the compliance for wet and dry tissue is also a linear function of density, the effect of water on the compliance is additive. The axial sonic velocity for cow bone is essentially constant over a frequency range spanning 10 orders. Presumably the axial sonic velocity is controlled by the continuity of the collagen fibers lying along the bone axis. The radial velocity decreases by 30% over this frequency range, probably due to the many levels of structure observed in long bone like osteons, Haversian canals and blood vessels, as well as internal surfaces like cement lines and between lamellae. The sonic anisotropy of hard tissues decreases considerably with increasing frequency. While rat tail tendon collagen is very anisotropic both sonically and optically, hard tissues whether wet, dry, mineralized or demineralized show much less anisotropy. The optical index of refraction, both axially and radially, was found by Brillouin scattering for the air dried demineralized tissues. A close match was found between optical and sonic anisotropy for all the demineralized tissues.

Some properties of the organic matrix of a bovine cortical bone sample in various media.

Dimensional stability of a demineralized bovine cortical bone sample was found in all media whether EDTA, saline or ethanol and water solutions or even 100% ethanol. A 6% volume shrinkage was observed, in strong contrast to the reported swelling for tail tendon fiber collagen. Sonic velocity was strongly dependent on the state and the medium, varying by a factor greater than 2. The medium appears to contribute strongly to the observed velocity suggesting that the Reuss formalism is applicable with the solid collagen skeleton as one component and the liquid in the pores as the second. Sonic anisotropy was noted although the intensity varied. The radial to axial velocity was greatest (0.93) in saline and least in 100% ethanol (0.80) indicating that the rigidity of the tissue influenced the character of sonic propagation. Two sets of intermolecular linkages are inferred. One set, in common with tendon collagen, controls the elastic properties. A second set in bone collagen maintains dimensional stability.

Directional Variation of Elastic Wave Velocities in Oriented Clay

AbstractSonic anisotropy of clay resulting from particle orientation was studied by means of velocity measurements on anisotropically consolidated kaolinite. Samples were prepared from a kaolin-water slurry under consolidation pressures ranging from 80 to 400 psi, with two distinct stress histories. Directional velocity measurements were made over a wide range of water contents as saturated samples were allowed to dry by evaporation to water contents below the shrinkage limit. Directional variation was most pronounced with partial saturation, when directional velocities differed by as much as a factor of two. The degree of sonic anisotropy is seen to correlate with variation in the shrinkage limit, showing a systematic dependence on particle orientation, but no unique relation to consolidation stress exists because of the overriding influence of stress history.

SONIC VELOCITY AND PENETRABILITY OF SIMULATED LUNAR ROCK DUST

Theoretical considerations are given for the design of an ultrasonic pulsing system for noncohesive dusts. In addition, measurements of less than one percent error of sonic velocity were made in volcanic rocks of different textures. Pumice containing elongate vesicles exhibits marked sonic anisotropy. In contrast, basaltic scoria with approximately equidimensional vesicles exhibits sonic isotropy. These anisotropy contrasts may be significant in interpreting Surveyor return data and in evaluating lunar base requirements. Sonic velocity with a simultaneous recording of porosity in rock dusts under ambient conditions ranges from 150 m/sec (500 ft/sec) to 700 m/sec (2,100 ft/sec). Absolute measurements of shear strength, using the vane‐type shear tester, were made at critical density obtained by vibrating the simulated lunar dust samples for specified time periods. Relative shear strengths were also compared at maximum density obtained by long‐period vibration of dust samples. Comparson of stress curves of dusts of different grain shapes indicates that relatively little strain occurs before the plastic zone of the stress curve is reached for volcanic dust consisting of angular glass shards. For purpose of shear strength analysis, grain shapes may be grouped as spherical, prismatic, and vesiculate. Shearing resistance curves are analyzed for each of these groups, and the vesiculate shapes have the highest shear strengths at critical density. Moreover, the sliding habit during shear appears to reflect the shape of the grains. Grain shape is apparently a first‐order parameter affecting shear strength of dust particles >0.1 mm in diameter. Adhesion effects due to hard vacuum ([Formula: see text] to [Formula: see text] torr) are small but measurable for the grain sizes considered. At equivalent porosities, vacuum at [Formula: see text] torr apparently does not markedly influence the peak shear strength of dust composed of vesiculate particles greater than 0.1 mm in diameter. Once sonic velocity and shear strength data are obtained by a lunar probe or astronaut, practical studies can be made on bearing capacity, trafficability, and lunar base construction.

The Ratio of Specific Heats γ as a Fundamental Physical Property of Liquids

AbstractThe ratio of specific heats (γ) of liquids behaves with regularity in organic liquids; in homologous series; with substitution; with molecular weight etc. It also enters in processes like light‐scattering and sound absorption. In fact, the observed sound absorption of liquids can be explained only on the basis of the γ and viscosity. From these considerations it is suggested that γ is a fundamental physical property of liquid state. On account of its main contribution to sound absorption in liquids, it is suggested that γ of a liquid might be termed its „sonic anisotropy”︁.

Sound Absorption in Liquids in Relation to Light Scattering Data

AbstractUltrasonic absorption coefficient (theoretical) and light scattering properties of liquids have been correlated in a large number of liquids. It is observed that there is a definite relationship in the manner in which the values of sound absorption coefficient α/v2, light scattering intensity I and the depolarisation factor ϱ change from liquid to liquid. The study reveals a linkage between optical anisotropy and sound absorption and suggests strongly the existence of sonic anisotropy of molecules at high frequencies.