Stoneley Wave Velocity Research Articles

Stoneley wave detection by acoustic Interferometry: Estimation of shear velocity of a geological formation

Both active and passive full waveform acoustic loggings (FWAL), complemented by a flow log, were conducted in a borehole of an experimental site located in the Cher region (France).. The acoustic tool used for the FWAL experiments is a flexible monopole tool holding a pair of piezoelectric receivers and a magnetostrictive transducer. The tool was modified to perform both active and passive FWAL. For passive acoustic logging, several runs were recorded to obtain a set of acoustic noise sections. As the noise is simultaneously recorded by two receivers of the tool, an interference noise section was elaborated by correlating or deconvolving the pair of signals and then summing these pairs of acoustic traces at each depth. This procedure, which can be interpreted as an interferometry analysis, points out the presence of low-frequency waves identified as Stoneley waves. The velocity and RMS amplitude of the Stoneley wave were computed at each depth. It is shown that: 1- the Stoneley wave velocity obtained in passive mode can be used to estimate the shear velocity of the formation, 2- the RMS amplitude and velocity variations of the Stoneley waves are strongly correlated with the variations of the flowmeter.

Expressions of nonlocal quantities and application to Stoneley waves in weakly nonlocal orthotropic elastic half-spaces

In this paper, we introduce a novel model of nonlocal elasticity, called the weakly nonlocal elasticity, and provide explicit expressions of nonlocal quantities for harmonic plane waves propagating in the weakly nonlocal elastic solids. Then, we apply these expressions to investigate the propagation of Stoneley waves along the interface between two weakly nonlocal orthotropic elastic half-spaces. The half-spaces may be compressible or incompressible, and they are in welded contact. Our main aim is to derive explicit dispersion equations of Stoneley waves. First, we derive the explicit dispersion equation for the compressible case (when two half-spaces are compressible) using the surface impedance matrices of half-spaces. Then, the explicit dispersion equations for the incompressible cases (at least one half-space is incompressible) are obtained using the incompressible limit method. The simple and immediate derivation of these equations proves the convenience of the incompressible limit method. Some numerical examples are carried out to examine the effect of nonlocality and incompressibility on the Stoneley wave velocity.

Active and Passive acoustic logging applied to the detection of preferential flow in a sedimentary aquifer

Two boreholes of an experimental site located in the Cher region (France) were investigated via Full Waveform Acoustic Logging (FWAL). The acoustic tool used for the FWAL experiments is a flexible monopole tool holding two pairs of piezoelectric receivers and a magnetostrictive transducer. The tool was modified to perform both active and passive FWAL. To our knowledge, this change is a novelty. For passive acoustic logging, several runs were recorded to obtain a set of acoustic noise sections from which noise Root Mean Squared (RMS) amplitude logs and spectral amplitude logs in different frequency bandwidths were computed. The acoustic logs resulting from passive acoustic monitoring were compared with P-wave acoustic velocity, core data, and a flowmeter log. It is shown that: (1) the distribution of noise frequencies in the 0–5 kHz is strongly correlated with the variations of the flowmeter, (2) the distribution of noise frequencies and noise RMS amplitude is correlated with the lithology (core description), and the P-wave velocity log. As the noise is simultaneously recorded by two receivers of the tool, an interference noise section was elaborated by correlating and summing pairs of acoustic traces at each depth. This procedure, which can be interpreted as an interferometry analysis, points out the presence of low-frequency waves identified as Stoneley waves. It is shown that the Stoneley wave velocity obtained in passive mode can be used to estimate the shear velocity of the formation.

Dynamic fluid transport property of hydraulic fractures and its evaluation using acoustic logging

The existing acoustic logging methods for evaluating the hydraulic fracturing effectiveness usually use the fracture density to evaluate the fracture volume, and the results often cannot accurately reflect the actual productivity. This paper studies the dynamic fluid flow through hydraulic fractures and its effect on borehole acoustic waves. Firstly, based on the fractal characteristics of fractures observed in hydraulic fracturing experiments, a permeability model of complex fracture network is established. Combining the dynamic fluid flow response of the model with the Biot-Rosenbaum theory that describes the acoustic wave propagation in permeable formations, the influence of hydraulic fractures on the velocity dispersion of borehole Stoneley-wave is then calculated and analyzed, whereby a novel hydraulic fracture fluid transport property evaluation method is proposed. The results show that the Stoneley-wave velocity dispersion characteristics caused by complex fractures can be equivalent to those of the plane fracture model, provided that the average permeability of the complex fracture model is equal to the permeability of the plane fracture. In addition, for fractures under high-permeability (fracture width 10~100 μm, permeability ~100 μm2) and reduced permeability (1~10 μm, ~10 μm2 as in fracture closure) conditions, the Stoneley-wave velocity dispersion characteristics are significantly different. The field application shows that this fluid transport property evaluation method is practical to assess the permeability and the connectivity of hydraulic fractures.

Stoneley waves in mild auxetics

The current research concerns with the analysis of Stoneley waves propagation along an interface between two dissimilar homogeneous and isotropic halfspace having negative Poisson’s ratios (auxetics). The main attention is paid to the case when both contacting media satisfy the Wiechert condition ensuring the existence of Stoneley wave. Closed form expressions are derived for derivatives of the Stoneley secular equation. The velocity of Stoneley waves is analyzed both theoretically and numerically in a broad range of the Wiechert parameter variation.

Stoneley wave velocity variation

Stoneley wave velocity variation is analyzed by solving the modified Scholte secular equation for velocity of Stoneley waves, allowing to find dependency of the Stoneley wave velocity on the Wiechert parameter and construct a set of inequalities that confines region of existence for the appropriate root of the secular equation. Numerical analysis for Stoneley wave velocity dependence on the Wiechert parameter for both auxetics (materials with negative Poisson’s ratio) and nonauxetics revealed the presence of (i) asymptotes indicating degeneracy of Stoneley waves into the corresponding Rayleigh waves; and (ii) common extremums relating to degeneracy of Stoneley waves into the corresponding bulk shear waves.

Propagation characteristic of axial and circumferential interface waves and detection of the interlaminar defect in multilayered pipes

This paper focuses on the dispersion characteristic of interface waves and the detection of interlaminar defects in multilayered pipes. The interface waves propagating along axial and circumferential directions are simplified as strain problems of planes (r, z) and (r, θ), respectively. The axial interface wave is well suited to axial localization of the defect, just as the circumferential interface wave is to circumferential localization. The dispersion curves and wave structures in generalized forms are built based on double- and treble-layered examples. Both interface waves converge to the Stoneley wave velocity at high frequency, while energy is concentrated on the interface. An experimental system is built. Theoretical and experimental group velocities are compared. The results indicate that the average relative errors of these two interface waves are 0.47% and 0.53%, respectively. An interlaminar crack is detected effectively both in axial and circumferential directions, revealing that interface waves hold great potential for non-destructive evaluation.

Regions of existence for Stoneley waves in auxetic and non-auxetic media

Regions of existence for Stoneley waves are analyzed for the case when isotropic contacting media have different values of Poisson's ratios. The analysis is based on solving the secular equation in Scholte’s form for Stoneley wave velocity. It reveals substantial similarity in shapes of regions of existence at all studied values of Poisson's ratio pairs. A recently observed gap in regions of existence for media with equal Poisson’s ratios is also observed in cases when contacting media have different Poisson’s ratios including both auxetic and non-auxetic media.

Stoneley waves at the generalized Wiechert condition

A generalization of the Wiechert condition by introducing two independent dimensionless parameters instead of one parameter in the original Wiechert condition is proposed. Variation of Stoneley wave velocity at varying two parameters of the generalized Wiechert condition at different Poisson’s ratios is studied revealing a substantial discrepancy in Stoneley wave velocity profiles.

Rayleigh, Love and Stoneley waves in a transversely isotropic saturated poroelastic media by means of potential method

Investigation of propagation of surface waves, and also interfacial waves in a saturated either homogeneous or coated half-space in the framework of a simplified version of Biot theory known as u−p formulation is the target of this paper. Both the half-space and the coating are fluid-saturated transversely isotropic in both transport and elastic points of view. The coupled fluid continuity equation and equations of motion are decoupled by virtue of a set of two scalar potential functions. Based on the boundary and/or continuity conditions and appropriate form of scalar potential functions, a secular equation for determination of each of Rayleigh-, Love- and Stoneley-wave velocity and related attenuation coefficients is derived. Moreover, the characteristic equations of different waves are degenerated to explicit forms for some special cases, i.e., saturated isotropic and single-phase materials of either isotropic or transversely isotropic. Furthermore, the effects of hydraulic and mechanical parameters on elastic wave propagation are studied in detail. The dependency of wave velocities and corresponding attenuation coefficients to material parameters are shown graphically and explained in physical point of view. In addition, some wave characteristics are tabulated for a deep understanding of the physical behavior of different waves. Besides, the results are compared with previous studies in special simpler cases, where exact agreements may be discovered from which the validity of the results and the accuracy of numerical computations are evident.

Estimation of shear and Stoneley wave velocities from conventional well data using different intelligent systems and the concept of committee machine: an example from South Pars gas field, Persian Gulf

ABSTRACT Shear and Stoneley wave velocities provide useful information for petrophysical and geomechanical studies of the reservoir formation. In this study, sonic Shear and Stoneley velocities were predicted from well log data using intelligent systems including: Fuzzy logic, neural networks, neuro-fuzzy, and support vector regression. After prediction, the proposed committee machine with intelligent systems combines the first three methods in performance view. Each of these selected intelligent systems has a weight factor and the optimal combination of the weights is derived by a genetic algorithm. The study was conducted on a case study from a carbonate reservoir in South Pars gas field. The results indicate the higher performance of the committee model compared to the individual and state-of-the-art methods.

VTI Anisotropy in the Jamieson and Echuca Shoals Formations in the Browse Basin

Overburden shales that overlie and seal hydrocarbon reservoirs usually exhibit polar anisotropy, also called Vertical Transverse Isotropy (VTI). This anisotropy is important for correct seismic inversion, seismic-to-well ties as well as having geomechanical implications. P-wave anisotropy cannot usually be determined from a vertical well unless a walkaway vertical seismic profile (VSP) has been obtained, however, such measurements are still rare. S-wave anisotropy though can be estimated from logs if the speed of sound in mud and the Stoneley wave velocity in the shale are known. Then, the P-wave anisotropy can be computed using theoretical models or empirical trends. The Stoneley wave velocity is nowadays routinely measured by sonic tools and, if a reliable mud velocity is known, the horizontal shear wave velocity (parallel to and polarised in the bedding plane) can be estimated. Thomsen’s gamma parameter for S-wave anisotropy can then be calculated. If mud velocity is not known, the horizontal shear wave velocity can be obtained using calibration in an isotropic interval. Using this method, we analyse the VTI anisotropy in the Torosa-6 well in the Caswell Sub-basin of the Browse Basin, Australia. Torosa-6 drilled through the Jamieson and Echuca Shoals shaly formations where Vclay reaches ~75%. Elastic anisotropy of the shaly Jamieson and Echuca Shoals Formations has been analysed. Thomsen’s gamma shows a good correlation with the clay fraction in each of these formations. However for the same clay fraction, anisotropy is about 20% higher in the Jamieson Formation compared to the Echuca Shoals. This Jamieson Formation contains up to 15% of smectite, and we are investigating how this may lead to higher levels of VTI anisotropy compared with illitic clays predominant in the Echuca Shoals Formation.

Petrophysical characterization of carbonates (SE of Spain) through full wave sonic data

Carbonate reservoirs are characterized by strong permeability heterogeneity mainly linked to the predominant pore type. In this work, we present a case study focused on a shallow borehole (160 m depth) located at the eastern end of the Betic Cordillera, SE of Spain. This borehole sampled a marly seal (deep marine marls rich in planktonic organisms from Messinian – upper Tortonian) on top of a carbonate reservoir (algae limestone from Miocene - upper Tortonian). Laboratory analysis show that most of the samples from the reservoir correspond to grainstone and packstone limestone types, and that the quality of this reservoir is controlled mainly by its detritic composition and a high content of bioclasts. The aim of this work is to show the suitability of using standard geophysical logging to assess permeability supported by laboratory and Lugeon tests. Two approaches have been used based on Kozeny's equation (pseudo-k log) and Mari et al. (2011) work (Ik-Seis log). Both ways require obtaining specific surface which is an indicator of pore type. This calculation is based on porosity and Vp/Vs relations. Porosity has been obtained from resistivity and sonic logs constrained by laboratory measurements. Shear wave velocity has been inferred from Stoneley wave velocity since this formation is considered as slow (Vs lower than 1500 m/s). Pseudo-K and Ik-Seis logs have been scaled using the Lugeon tests results. Both logs reproduce the heterogeneities found in the in-situ test. Finally, an analysis of the dependence of different seismic attributes to the specific surface has been performed to check the suitability of using solely sonic measurements to assess permeability. This can be useful for boreholes were laboratory or field tests are not available.

Developing correlations for velocity models in vertical transverse isotropic media: Bakken case study

The vertical and horizontal mechanical properties of a Vertically Transverse Isotropic (VTI) medium can be obtained from five stiffness coefficients (C33, C44, C66, C13 and C12) using velocities at different angles and density measurements. Particularly, when using well log data for vertical wells, only three out of the five elastic constants can be calculated. The sonic tool cannot measure C13 and C12, leading to introduction and application of empirical models to estimate them. However, most of the existing empirical models employ C66, a key stiffness coefficient, whose value depends on Stoneley wave velocity measured by the sonic tool. Due to the environment present in the wellbore as well as other reasons, C66 estimated in this way contains uncertainty. This in turn impacts the other stiffness coefficients thus increasing the uncertainty in VTI characterization of shale as well as increased error margin in in-situ horizontal stress estimation. This article presents a methodology to improve our understanding of the VTI anisotropy in shale.In this paper, extensive datasets from different shale formations all around the world, have been analyzed to establish linear correlations for the stiffness coefficients C13, C11, C66, and C12, without using the Stoneley wave velocity that has lots of uncertainties. The linear correlations used the stiffness coefficients C33 or C44 as the dependent variable, and were determined for individual shale formations and all compiled shale formations.In general, correlations for C11, C66, and C12, seem to work well, providing better results when using as input C33 than C44. Specifically, correlations for C11 and C66 seem to work really well, giving R-squared values greater than 0.7. Additionally, C12 as a function of C33 showed better predictions than the C12 M-ANNIE assumption, and lastly, for C13 it is concluded that there is no correlation.Finally, the correlations have been applied to well log data from a vertical well in the Bakken Formation, and compared to the stiffness coefficients obtained using the M-ANNIE assumptions. Moreover, minimum horizontal stress is calculated and compared using ANNIE, M-ANNIE, and the proposed correlations, these last ones determined from Bakken Formation velocity measured data. Generally, the new correlations provide results for the minimum horizontal stress a little bit lower than the M-ANNIE model, but greater than the ANNIE model. It is also shown that C13 M-ANNIE assumption works really well for shales, however, C12 M-ANNIE assumption does not work for shales. Furthermore, C66 calculated and used for the ANNIE and M-ANNIE models, is based on the Stoneley wave velocity which has been indicated not to be a reliable measurement. For these setbacks, the proposed correlations provide an alternative and practical solution for the in-situ stress estimation.

Characterization of Anisotropic Elastic Moduli and Stress for Unconventional Reservoirs Using Laboratory Static and Dynamic Geomechanical Data

Summary In a vertically transverse isotropic (VTI) medium, accurate prediction of the vertical and horizontal Young's moduli (E) and Poisson's ratios (ν) is crucial to predicting minimum horizontal stress (σhmin) and hence selecting drilling mud, cement weights, and perforation locations. Fully characterizing the geomechanical properties of VTI shale requires five independent stiffness coefficients. In a vertical well, two of them are directly calculated from the velocity of the vertically propagating compressional waves (P-waves) and shear waves (S-waves), whereas a third is estimated from the Stoneley-wave velocity. To obtain the last two stiffness coefficients, an empirical model must be used. This study integrates laboratory mechanical and sonic measurements to evaluate the ANNIE and modified-ANNIE models and extend the dynamic-to-static conversion equations. The ANNIE model is a three-parameter empirical model proposed by Schoenberg et al. (1996) to interpret anisotropic stiffness coefficients. Laboratory static and dynamic geomechanical experiments were applied to multiple core plugs extracted at different depths from a target shale play. Using a laboratory ultrasonic scanner, velocities were measured in different directions to obtain the five stiffness coefficients. To compare the performance of the two empirical models, three stiffness coefficients were then applied along with the ANNIE or modified-ANNIE models for estimating the dynamic Young's modulus and Poisson's ratio. The static elastic moduli were measured using triaxial compression experiments; horizontal and vertical core plugs were tested to account for anisotropy. Static and dynamic results illustrated that horizontal Young's moduli were predominantly higher than vertical Young's moduli, which suggested a horizontal layered structure. Vertical Poisson's ratios can be greater or smaller than horizontal Poisson's ratios, which is consistent with the prediction of the modified-ANNIE model. Conversely, the ANNIE model always predicts ν (vertical) ≥ν (horizontal). Static and dynamic data illustrated that the anisotropic σhmin (minimum horizontal stress) was predominantly higher than the isotropic σhmin. This implied that using an isotropic model to predict laminated shale will underestimate σhmin. The elastic moduli measured from the dynamic method were consistently higher than those measured from the static method. The dynamic and static data were used to fit the widely used dynamic-to-static conversion equations: the Canady (2011) and Morales and Marcinew (1993) equations. The Canady (2011) equation was extended to the “very hard” (greater than 70-GPa or 10.2-Mpsi Young's modulus) regime, whereas the Morales and Marcinew (1993) equation was extended to the regime of porosity less than 10%. Mpsi = 1,000 psi. Finally, the results of σhmin predicted by the isotropic and two anisotropic models (ANNIE and modified-ANNIE) were compared with the values of σhmin calculated using full ultrasonic data measured in the laboratory, showing that modified-ANNIE improved the prediction by solving the stress-underestimation issue of the ANNIE and isotropic models.

Estimation of DSI log parameters from conventional well log data using a hybrid particle swarm optimization–adaptive neuro-fuzzy inference system

Dipole shear sonic imager (DSI) log offers valuable data for geophysical, petrophysical and geomechanical studies of the hydrocarbon bearing intervals. Compressional (Vp), shear (Vs) and Stoneley (Vst) waves are acquired through processing and interpreting the DSI data. The present study aims to present an improved approach for establishing a quantitative relationship between conventional well log data and sonic wave velocities (Vp, Vs and Vst as DSI log parameters) by coupling an evolutionary computational method based on a neuro-fuzzy inference system. Particle swarm optimization – neuro fuzzy inference system (PSO-ANFIS) model suggested in this study, is based on a combination of fuzzy rule-based system and particle swarm optimization algorithm, which simultaneously adjust both the antecedent and the consequent variables. This approach was conducted in siliciclastic/carbonate Asmari Formation of Mansuri oilfield in order to estimate the compressional, shear and Stoneley wave velocities. The conventional wireline logs from two wells were employed to build intelligent models while the third well was applied to evaluate the performance and reliability of the created models. The results indicated that the proposed hybrid scheme can satisfactorily improve the computational efficiency and performance of the DSI log parameter prediction, compared to individual intelligent systems and hybrid particle swarm optimization –neural network strategy (PSO–ANN). Finally, the workflow outlined here can be used as an efficient tool for prediction of other petrophysical rock properties, due to an enhanced estimation accuracy afforded by PSO-ANFIS model.

Experimental verification of the interface wave method to detect interlaminar damage of a metal multilayer structure

The interface wave traveling along the boundary of two materials has been studied for nearly a century. However, experiments, engineering applications, and interface wave applications to the non-destructive inspection of interlaminar composite have developed slowly. In this research, an experiment that applies Stoneley waves (a type of interfacial wave between two solid half-spaces) is implemented to detect the damage in a multilayer structure. The feasibility of this method is also verified. First, the wave velocity and wave structure of Stoneley waves at a perfectly bonded aluminum-steel interface are obtained by solving the Stoneley wave dispersion equation of two elastic half-spaces. Thereafter, an experiment is conducted to measure the Stoneley wave velocity of an aluminumsteel laminated beam and to locate interlaminar cracks by referring to the Stoneley wave velocity and echo wave time. Results indicate that the location error is less than 2%. Therefore, Stoneley waves show great potential as a non-destructive inspection method of a multilayer structure.

The Estimation of Stoneley Wave Velocity from Conventional Well Log Data: Using an Integration of Artificial Neural Networks

Stoneley wave velocity (Vst) is capable of providing accurate data for reservoir characterization objectives, such as permeability estimation, fracture evaluation, formation anisotropy identification, etc. At the first stage of this study, different types of artificial neural networks, including generalized regression neural network, radial basis neural network, and feed-forward backpropagation neural network were utilized to predict Vst from conventional well log data. Consequently, a generalized regression neural network was employed to combine results of mentioned artificial neural networks for overall estimation of Vst. This novel hybrid method can enhance the accuracy of final prediction through reaping the benefits of individual artificial neural networks. The proposed methodology, hybrid neural network, was applied in Asmari formation, which is the major carbonate reservoir rock of Iranian southern oil field. A group of 1,640 data points was used to establish the intelligent model, and a group of 800 data points was employed to assess the reliability of the constructed model. Results showed that integration of different artificial neural networks using generalized regression neural network can significantly improve the accuracy of final prediction.

Acoustoelastic effects of Stoneley waves in a borehole surrounded by a transversely isotropic elastic solid

Stoneley wave in a fluid-filled pressurized borehole surrounded by a transversely isotropic elastic solid with nine independent third-order elastic constants in presence of biaxial stresses are studied. A simplified acoustoelastic formulation of Stoneley wave is presented for the parallelism of the borehole axis and the formation axis of symmetry. Sensitivity coefficients and velocity dispersions for Stoneley wave due to the presence of stresses are numerically investigated, respectively. The acoustoelastic formulation explicitly shows that the velocity dispersions of Stoneley wave depend on seven independent third-order elastic constants in presence of biaxial stresses and on six independent third-order elastic constants in the presence of borehole pressurization alone. Numerical results of both sensitivity coefficients and velocity dispersions of Stoneley wave show that at low frequency the velocity change of Stoneley wave is sensitive to c111 and c112. Stoneley wave velocity at low frequencies can be simplified by 3 independent third order elastic constants (c111, c112 and c123) instead of nine constants. In presence of biaxial stresses, at low frequencies the speed of the Stoneley wave is similar to White’s formula.

Sonic log for rock mass properties evaluation ahead of the tunnel face — A case study in the Alpine region

Ahead of tunnel prediction of the rock mass properties and the detection of weak zones potentially related to failure zones encountered during excavation can be analyzed using acoustic logging in drilled ahead tunnel face. Indeed acoustic logging in a broad frequency band (1 kHz up to 30 kHz) may provide to estimate the compressional (P-wave), shear (S-wave), Stoneley wave velocity and amplitude. A systematic sonic logging survey was performed along a tunnel during the excavation in horizontal boreholes in Quartzite and Gypsum formations. The data processing involved the estimate of P-wave velocity, the analysis of the S-wave and the estimate of group and phase velocity of Stoneley wave. We used Stoneley wave to determine the S-wave velocity whenever the waveform did not allow the detection of converted S-wave. In soft rock the S-wave velocity can be determined using the Stoneley wave analysis from acquisitions taken at low frequency (2 kHz). We interpreted the results in terms of lithological changes between soft rock and hard rock and weak zones. Indeed, in this case study weak zones in Quartzite are well delineated by a sharply decrease of P and S-wave velocities. The reflection/diffraction effects of guided waves pointed out the presence of discontinuities and fractures. In the specific geological context the method was able to predict the lithological changes between Quartzite (higher Vp/Vs ratio) and Gypsum (lower Vp/Vs ratio).