Stoneley Waves Research Articles

Determination of Archie’s Tortuosity Factor from Stoneley Waves in Carbonate Reservoirs

One of the fundamental equations in calculate the saturation of fluid in hydrocarbon reservoirs is the Archie’s equation. In addition to the parameters measured by well logging such as porosity and resistivity, there are others parameters that called Archie’s coefficients. Archie provides constant values for this coefficient base on experimental core’s data, accordance with saturation formula in sandstone. In carbonate reservoirs nevertheless the sandstone reservoirs, high heterogeneity, variety in lithology and texture, shape and distribution of pores, due to this coefficient is not constant. So, variation of tortuosity as a coefficient that depends on the way correlation between pores, is high and considering a constant value due to error in calculation of fluid saturation. In this study, with the stoneley waves measured from DSI tools and required calculation, the value of tortuosity coefficient calculated continuously in well no.10 Darkhovin field. The regression of calculated values with the core data is 83.16 percent, that showed this method is useable for calculation the tortuosity.

The transmission problem in linear isotropic elasticity

We study the isotropic elastic wave equation in a bounded domain with boundary with coefficients having jumps at a nested set of interfaces satisfying the natural transmission conditions there. We analyze in detail the microlocal behavior of such solution like reflection, transmission and mode conversion of S and P waves, evanescent modes, Rayleigh and Stoneley waves. In particular, we recover Knott's equations in this setting. We show that knowledge of the Dirichlet-to-Neumann map determines uniquely the speed of the P and the S waves if there is a strictly convex foliation with respect to them, under an additional condition of lack of full internal reflection of some of the waves.

Extinction of Stoneley waves in stratified media with diffused interfaces

Extinction of Stoneley waves in stratified media with diffused interfaces

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.

Experimental study on attenuation of Stoneley wave under different fracture factors

To quantitatively determine the effect of different factors such as fracture width, dip angle, extension and filling material on Stoneley wave amplitude decreasing, the shock tube experiment method was changed from fixing the sample and vertically moving the sensor in the borehole to fixing the sensors along the shock tube wall and vertically moving the sample without drilling the borehole in it. The measurement accuracy and the signal-to-noise ratio of the first Stoneley wave were improved by the time corrections and amplitude corrections of Stoneley wave signals. At the same time, 21 sets of core models with different fracture parameters were processed for this measurement method by using full-diameter carbonate core, and relative amplitudes were defined to characterize Stoneley wave amplitude decreasing. The experimental results show that the relative amplitude of Stoneley wave exponentially decreases with increasing fracture width. The relative amplitude of Stoneley wave linearly decreases with increasing fracture dip angle. The relative amplitude of Stoneley wave exponentially decreases with increasing fracture extension. The relative amplitude of Stoneley wave decreases with increasing the permeability of filling material in the fracture. Under the above four conditions, the fracture width has the greatest effect on the decreasing of Stoneley wave amplitude, followed by the fracture extension and the permeability of filling material, and finally the fracture dip angle.

On disappearing Stoneley waves in functionally graded plates

Dispersion analysis of Lamb waves propagating in anisotropic functionally graded plates with transverse inhomogeneity reveals that the high frequency asymptotes associated with the interfacial Stoneley waves disappear, while in stratified plates the corresponding high frequency asymptotes exist. The analysis utilizes a variant of the Cauchy sextic formalism coupled with the exponential fundamental matrices for constructing explicit dispersion equation.

Modelling of Stoneley wave transference at the frictional interface between ice and rock medium

The present article attempts to study the propagation of surface seismic waves (Stoneley waves) in the layered structure composed of rock and ice medium. The interface between the two media (ice and rock) is considered to be frictional. Mathematical model of the present problem is formulated by adapting the Coulomb frictional boundary conditions. The frequency relation is obtained in the determinant form. The non-dispersive nature of the Stoneley wave is observed through the frequency relation. The non-dimensional phase velocity and damping parameter curves have been plotted against the non-dimensional angular frequency. Effect of different parameters (viscoelastic coefficient of the rock medium, frictional interface parameter, anisotropy parameter and initial stress of both the media) on the phase velocity and damping has been distinctly marked and shown graphically.

Acoustic fields for monopole logging while drilling with an eccentric collar

The acoustic problem of an eccentric drill collar in a fluid-filled borehole has been of interest in the field of acoustic logging while drilling (ALWD) in recent years. To reduce the effects of tool eccentricity on ALWD measurements, studies on acoustic responses under such conditions are essential. This study therefore has developed an analytical method to investigate borehole wavefields with an off-center monopole ALWD tool in fast and slow formations. By evaluating the contributions of compressional and shear branch points, the effects of the tool eccentricity on individual formation primary and shear head waves are investigated. Results illustrate that tool eccentricity only affects the excitation properties and has almost no effect on the extracted velocities. The joint analysis of synthetic full waveforms and dispersion diagrams with varying eccentricity degrees indicates that multipole modes are excited when the tool is off center, and their excitation amplitudes gradually increase with the increasing eccentricity, especially in the direction of tool movement. Moreover, the dispersion analysis reveals that the two modes with intersections in the centered case are coupled when the tool becomes eccentric. In particular, the coupling performance between the Stoneley and flexural modes is the most prominent. Furthermore, the effects of tool eccentricity on the monopole acquisition method, that is, the sum of waveforms received at four orthogonal azimuths, are evaluated. Results show that the above summation method can effectively reduce the effects of slight or moderate eccentricity. However, for large or extreme eccentricity, reducing or eliminating the effects of eccentricity on the Stoneley wave is a challenge for this method. Based on the above analyses, measurements may not be reliable for formation evaluation in the case of extreme eccentricity, especially for Stoneley wave applications.

On the influence of finite initial deformations on the surface instability of the incompressible elastic layer interacting with the half-space of an ideal fluid

The problem of the propagation of quasi-Lamb waves in a pre-deformed incompressible elastic layer that interacts with the half-space of an ideal compressible fluid is considered. The study is conducted on the basis of the three-dimensional linearized equations of elasticity theory of finite deformations for the incompressible elastic layer and on the basis of the three-dimensional linearized Euler equations for the half-space of an ideal compressible fluid. The problem is formulated, and the approach based on the utilization of representations of the general solutions of the linearized equations for an elastic solid and a fluid is developed. Applying the Fourier method, we arrive at two eigenvalue problems for the equations of motion of the elastic body and the fluid. Solving them, we find the eigenfunctions. Substituting the general solutions into the boundary conditions, we obtain a homogeneous system of linear algebraic equations for the arbitrary constants. From the condition for the existence of a nontrivial solution, we derive the dispersion equation. A dispersion equation, which describes the propagation of normal waves in the hydroelastic system, is obtained. The dispersion curves for quasi-Lamb waves over a wide range of frequencies are constructed. The effect of the finite initial deformations in an elastic layer, the thickness of the elastic layer, and the half-space of an ideal compressible fluid on the phase velocities and dispersion of quasi-Lamb modes are analyzed. It follows from the graphical material presented above that, in the case of compression with 0.54, i.e., with a 46 percent’s reduction in the length of the highly elastic incompressible body, the phase velocities of the surface waves (Stoneley waves and Rayleigh waves) vanish. This indicates that surface instability develops at 0.54 for a highly elastic incompressible non-Hookean body initially in a plane stress-strain state. We should point out that these figures agree with results obtained earlier in the theory of stability and correspond to the critical value of the contraction parameter. In the case of highly elastic incompressible bodies, the linearized wave theory makes it possible to study not only general and several specific wave processes, but also the conditions under which the surface instability begins in elastic bodies and hydroelastic systems. It also follows from the graphs that the ideal fluid slightly affects the surface instability of hydroelastic systems. The numerical results are presented in the form of graphs, and their analysis is given.

Propagation of Axisymmetric Stoneley Waves in Elastic Solids

Propagation of Axisymmetric Stoneley Waves in Elastic Solids

Stoneley wave propagation in nonlocal isotropic magneto-thermoelastic solid with multi-dual-phase lag heat transfer

In the present paper we have investigated the Stoneley wave propagation at the interface of two dissimilar homogeneous nonlocal magneto-thermoelastic media under the effect of hall current applied to multi-dual-phase lag heat transfer. The secular equations of Stoneley waves have been derived by using appropriate boundary conditions. The wave characteristics such as attenuation coefficients, temperature distribution and phase velocity are computed and have been depicted graphically. Effect of nonlocal parameter and hall effect are studied on the attenuation coefficient, phase velocity, temperature distribution change, stress component and displacement component. Also, some particular cases have been discussed from the present study.

Surface waves in layered thermoelastic medium with double porosity structure: Rayleigh and Stoneley waves

Rayleigh-type waves are investigated in a layered model composed of thermoelastic medium with double porosity structure. Using appropriate boundary conditions, the dispersion relation is obtained, which provides multi-modes, dispersive and attenuating nature of Rayleigh-type waves. This dispersion relation reduces to the dispersion equation of Stoneley-type waves, when the thickness of the overlying layer is assumed to be large enough. Some new results along with earlier known ones are reduced from the present formulation. For a particular model, the phase speed and corresponding attenuation coefficient of Rayleigh-type waves are found to be affected by the presence of thermal, pores and layer thickness. Displacements and stresses generated by the fundamental mode are also depicted graphically.

Antiplane Stoneley waves propagating at the interface between two couple stress elastic materials

We investigate antiplane Stoneley waves, localized at the discontinuity surface between two perfectly bonded half-spaces. Both half-spaces are elastic linear isotropic and possess a microstructure that is described within the theory of couple stress materials with micro-inertia. We show that the microstructure deeply affects wave propagation, which is permitted under broad conditions. This outcome stands in marked contrast to classical elasticity, where antiplane Stoneley waves are not supported and in-plane Stoneley waves exist only under very severe conditions on the material properties of the bonded half-spaces. Besides, Stoneley waves may propagate only beyond a threshold frequency (cuton), for which an explicit expression is provided. For a given frequency above cuton, this expression lends the admissible range of material parameters that allows propagation (passband). In particular, significant contrast between the adjoining materials is possible, provided that Stoneley waves propagate at high enough frequency. Therefore, micro-inertia plays an important role in determining the features of propagation. Considerations concerning existence and uniqueness of antiplane Stoneley waves are given: it is found that evanescent and decaying/exploding modes are also admitted. Results may be especially useful when accounting for the microstructure in non-destructive testing (NDT) and seismic propagation.

The quantitative measurement method for the radiation energy of the acoustoelectric converted wave field of building electricity

In order to provide the basis for the quantitative measurement of wave field radiation energy formed by building electricity and promote the development of construction industry, the quantitative measurement method for the radiation energy of the acoustoelectric converted wave field of building electricity is studied. Based on the multipole sound field of any azimuth order, the displacement potential of the sound field generated by the sound source is obtained, and the sound source model of the building electricity is established. According to the Pride theory, the acoustoelectric coupling equations are derived by using the established sound source model, and the acoustoelectric conversion of the building electricity is carried out. In this paper, the energy of Stoneley wave induced electric field in uniform medium is obtained according to the first coupling relation of acoustoelectric. The concept of electric energy density of low-frequency acoustoelectric polarization electric field is put forward, and the quantitative measurement of radiation energy of wave field is realized by deducing the specific expression. In the process of low-frequency acoustically induced polarization, the relationship between the density of electric energy and the frequency of sound wave and the permeability is obtained by simulation experiment. The results show that the energy distribution characteristics of buildings are similar when the distance between buildings is small, and the permeability and the density of electric energy are increasing.

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.

A study on the influence of salinity interfaces on borehole seismoelectric wavefields

Previous theoretical and experimental studies on seismoelectric logging suggest that the electromagnetic head wave (EH wave) is much weaker than the electric field accompanying the Stoneley wave (ESt wave). Nevertheless, recent in situ measurements show that the EH wave amplitude can be greater than that of the ESt wave. We have addressed this issue according to the simulation of borehole seismoelectric wavefields and find that the amplitude ratio of EH to ESt waves is sensitive to the salinity contrast at the interfaces. Specifically, the EH wave amplitude can be greater than that of the ESt wave if the salinity of the borehole fluid is much higher than that of the pore fluid in a homogeneous porous formation. When an impermeable mud cake layer is taken into account between the borehole fluid and the formation, the amplitude ratio of EH to ESt waves can be even larger, although the amplitudes of the EH and ESt waves become smaller. For a radially stratified porous formation, the large amplitude ratio of EH to ESt waves also occurs if the salinity of the borehole fluid is much higher than that of the pore fluid in the inner layer, or if the salinity of the pore fluid in the inner layer is much higher than that in the outer layer. The large amplitude ratio of EH to ESt waves has potential for detecting interfaces with high salinity contrast, or it can be used as an indicator of mud cake.

Multi-Basin Real-Time Perforation Assessment Using Tube Wave Measurements

This article addresses a means to improve hydraulic fracturing operations by measuring the perforation effectiveness on a stage-by-stage basis before the hydraulic fracturing process begins. Observations lead to the conclusion that pre-frac measurements provide meaningful insight about well-to-reservoir opening, allowing operators to identify the difficult-to-treat stages before the treatment begins. Based on the results of a case study from a North American unconventional basin, the limitations and conditions for employing pre-frac measurements are discussed. Background Often, perforation operations fail to initiate a well-established hydraulic communication between the wellbore and the reservoir rock. When hydraulic fracturing operations begin, a lack of wellbore to reservoir connectivity may cause unexpected difficulties such as unusually high pumping pressures, difficulty injecting the design volumes of fluid and proppant, and/or the inability to achieve design pumping rate or screenouts. The hydraulic fracturing industry is increasingly looking for an efficient, nonintrusive method for identifying poor wellbore to reservoir connectivity. Currently, step-rate tests are commonly used (Massaras et al. 2007) to give the operator an estimate of open perforations taking fluid, as well as frictional losses within the wellbore and near-field region. However, these tests are costly, time-consuming, and rarely accurately confirm the number of poor perforations (Cramer et al. 2019). Fiber-optic technologies can improve these uncertainties but are costly and susceptible to damage during installation and/or operation. How the Method Works Low-frequency hydraulic tube waves, or Stoneley waves (Stoneley 1924), are induced at the surface by equipment connected to the wellhead. Tube waves travel rapidly through the fluid within the wellbore and reflect by any changes within the hydraulically connected parts of the wellbore. In this case, the reflection off the bottom of the well influences the tube-wave properties - dispersion and attenuation of the normal modes (Hsu, Kostek, and Johnson 1997), depending on the condition and number of the perforations, the quality of their connection with the near-field region, and the quality of the near-field region itself (e.g., a region already naturally fractured) [Dunham et al. 2017].

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.