Xiao He

Finite-difference modeling of the monopole acoustic logs in a horizontally stratified porous formation

Monopole acoustic logs in a homogeneous fluid-saturated porous formation can be simulated by the real-axis integration (RAI) method to analytically solve Biots equations [(1956a) J. Acoust. Soc. Am. 28, 168-178; (1956b) J. Acoust. Soc. Am. 28, 179-191; (1962) J. Appl. Phys. 33, 1482-1498], which govern the wave propagation in poro-elastic media. Such analytical solution generally is impossible for horizontally stratified formations which are common in reality. In this paper, a velocity-stress finite-difference time-domain (FDTD) algorithm is proposed to solve the problem. This algorithm considers both the low-frequency viscous force and the high-frequency inertial force in poro-elastic media, extending its application to a wider frequency range compared to existing algorithms which are only valid in the low-frequency limit. The perfectly matched layer (PML) is applied as an absorbing boundary condition to truncate the computational region. A PML technique without splitting the fields is extended to the poro-elastic wave problem. The FDTD algorithm is validated by comparisons against the RAI method in a variety of formations with different velocities and permeabilities. The acoustic logs in a horizontally stratified porous formation are simulated with the proposed FDTD algorithm.

Borehole flexural modes in transversely isotropic formations: Low-frequency asymptotic velocity

Dipoleacousticloggingiswidelyusedforinsitumeasurement of formation shear velocity. This technique is based on the theoretical result in isotropic formations that the velocity ofthedispersiveflexuralmodeapproachestheshearvelocity at the low-frequency limit. Transversely isotropic TI formations frequently are encountered in petroleum engineering, so it is necessary to determine if shear velocity along the borehole can be determined from the low-frequency flexural wave in TI cases. The flexural wave in a borehole parallel to thesymmetryaxisofaTIformationisinvestigated.Theborehole acoustic field is formulated in the frequency-wavenumber domain as the sum of a direct field from the source and a reflected field from the borehole wall. Poles and branch points of the reflection coefficient are analyzed, and component waves contributed by those singularities are calculated. ThedispersionfeatureoftheflexuralmodeinsomeTIformationsdiffersfromisotropiccases.Thelow-frequencylimitof flexural-mode velocity trends to a value lower than the shear velocity when parameters of the formation satisfy c44/2c33,where and areThomsenparametersandc33 and c44 are the elastic moduli. That asymptotic value corresponds to a newly found branch point of the reflection function. Numerical results show that the low-frequency flexural wave travels slower than the shear wave in the synthetic full waveforms in Mesaverde clayshale 5501. Extracting the shearvelocityfromtheflexuralarrivalleadstoinaccuracyon theorderof10%inthisformation.

Studies on phase and group velocities from acoustic logging

It is still argued whether we measure phase or group velocities using acoustic logging tools. In this paper, three kinds of models are used to investigate this problem by theoretical analyses and numerical simulations. First, we use the plane-wave superposition model containing two plane waves with different velocities and able to change the values of phase velocity and group velocity. The numerical results show that whether phase velocity is higher or lower than group velocity, using the slowness-time coherence (STC) method we can only get phase velocities. Second, according to the results of the dispersion analysis and branch-cut integration, in a rigid boundary borehole model the results of dispersion curves and the waveforms of the first-order mode show that the velocities obtained by the STC method are phase velocities while group velocities obtained by arrival time picking. Finally, dipole logging in a slow formation model is investigated using dispersion analysis and real-axis integration. The results of dispersion curves and full wave trains show similar conclusions as the borehole model with rigid boundary conditions.

3D FINITE DIFFERENCE SIMULATIONS OF ACOUSTIC LOGS IN TILTED LAYERED POROUS FORMATIONS

A finite-difference algorithm is developed in the 3D cylindrical coordinate system. Synthetic waveforms excited by monopole and dipole acoustic sources are calculated for acoustic logging in a tilted layered formation composed of two poroelastic media. It is revealed that the existence of a tilted layer drives more acoustic energy out and therefore reduces the reflection back to the wellbore. Numerical results show that the amplitudes and the arrival times of the shear waves and flexural modes are influenced by the borehole inclination. The Stoneley modes, however, show little sensitivity to the orientation of the layer interface.

Generalized collar waves in acoustic logging while drilling

Tool waves, also named collar waves, propagating along the drill collars in acoustic logging while drilling (ALWD), strongly interfere with the needed P- and S-waves of a penetrated formation, which is a key issue in picking up formation P- and S-wave velocities. Previous studies on physical insulation for the collar waves designed on the collar between the source and the receiver sections did not bring to a satisfactory solution. In this paper, we investigate the propagation features of collar waves in different models. It is confirmed that there exists an indirect collar wave in the synthetic full waves due to the coupling between the drill collar and the borehole, even there is a perfect isolator between the source and the receiver. The direct collar waves propagating all along the tool and the indirect ones produced by echoes from the borehole wall are summarized as the generalized collar waves. Further analyses show that the indirect collar waves could be relatively strong in the full wave data. This is why the collar waves cannot be eliminated with satisfactory effect in many cases by designing the physical isolators carved on the tool.

Rough interfaces and ultrasonic imaging logging behind casing

Ultrasonic leaky Lamb waves are sensitive to defects and debonding in multilayer media. In this study, we use the finite-difference method to simulate the response of flexural waves in the presence of defects owing to casing corrosion and rough fluctuations at the cement-formation interface. The ultrasonic obliquely incidence could effectively stimulate the flexural waves. The defects owing to casing corrosion change the amplitude of the earlyarrival flexural wave, which gradually decrease with increasing defect thickness on the exterior walls and is the lowest when the defect length and wavelength were comparable. The scattering at the defects decreases the energy of flexural waves in the casing that leaks directly to fluids. For rough cement-formation interface, the early-arrival flexural waves do not change, whereas the late-arrival flexural waves have reduced amplitude owing to the scattering at rough interface.

Analysis of radial detection characteristics of monopole sonic logging

Drilling causes variation of the rock properties in the vicinity of a wellbore. In this article, we use the radial cylindrical layered model to examine monopole logging response with a two-dimensional axisymmetric finite difference method. Three variables are set, that is, the transition zone thickness, the source frequency and source-receiver spacing, respectively. We also use the slowness-time correlation-method to evaluate sound speed variations under different conditions. At last, based on the ray theory, the variation characteristics of the arrival time of the first wave under different conditions are analyzed. We conclude that the radial detection characteristics of compression waves are greatly affected by spacing. By combining different signals with various spacings, it is possible to obtain the tomography of the compressional wave velocities near wellbore.

Numerical simulation of the 3C single well imaging technique

The three-dimensional Finite Difference Time Domain (FDTD) method was used to simulate the reflections of the three-component single well imaging. The simulation results proved the efficiency of the SH wave imaging, and also pointed out the potential problems. Besides, unlike the transverse components which were commonly used, the axial component was proven to be prominent in the logging data, thus might ease the filtering process.

Numerical simulations of ultrasonic flexural waves in cased wellbores and evaluations of the cement bond quality

Cement bond quality is significant to productivity and security of a cased wellbore in the oil/gas field. The ultrasonic flexural-wave evaluation is a potential way to detect the debonding which appears at the cement sheath interfaces. In this paper, we present the ultrasonic wavefields in a multilayered cased hole and reveal the flexural wave responses to defects at the cement annulus. To excite and record Lamb waves of the flexural modes, an inclined pitch-catch sonic system is arranged inside the steel casing. The wavefields in the layered media are modeled by the 2D/3D finite difference methods. It is found that two groups of flexural waves are prominent in the wavefields. They are the primary flexural (PF) waves arriving early and the secondary flexural (SF) modes received by the transducers later. If a fluid-filled channel appears at the casing-cement interface, the PF-wave attenuation will decrease with the increasing width of the debonding. In contrast, the energy of SF waves will be greatly enhanced if the channel is located between the cement and the formation. For a 250-kHz sonic transmitter, the resolution of detection for a sector defect is about 10 degrees. Hence it is possible to effectively evaluate the bond quality of the cement annulus by extracting the properties of ultrasonic flexural waves.

Generalized collar waves and their characteristics

A good acoustic logging while drilling (ALWD) tool is difficult to be designed because of collar waves that propagate along the tool. There always exist such acoustic waves in ALWD. The collar wave arrivals can strongly interfere with formation compressional waves in wave slowness picking up. In the past years, a considerable research work has been seen in suppressing collar waves in order to accurately pick up p- and s-wave slowness, and the obtained p- and s-wave slowness accuracy is still a problem. In this work, numerical and physical experiments are conducted to tackle collar wave propagation problems. And the collar wave propagation physics is elaborated and a generalized collar wave concept is proposed. It is shown that collar waves are much complex, and they consist of two kinds of collar waves, i.e., the direct collar waves and indirect collar waves. Both of these two collar waves make the ALWD data difficult to process for formation wave slowness picking up. Because of drilling string structures...