Numerical simulation of an acoustic field generated by a phased arc array in a fluid-filled cased borehole

Transducers that are widely applied in cement bond evaluation tools, such as cement bond logs and variable density logs, cannot radiate acoustic energy directionally because of the characteristics of monopole sources. A phased arc array transmitter, which is a novel transducer that differs from monopole and dipole transducers, is presented in this study. To simulate the acoustic field generated by a phased arc array in a fluid-filled cased borehole with different channelings, a 3D finite-difference time-domain method is adopted. The acoustic field generated by a traditional monopole source is also simulated and compared with the field generated by the phased arc array transmitter. Numerical simulation results show that the phased arc array radiates energy directionally in a narrow angular range in the borehole, thereby compressing the acoustic energy into a narrow range in the casing pipe, the cement, and the formation. We present the analyses of first-arrival waveforms and the amplitudes of casing waves at different azimuthal angles for the two different sources. The results indicate that employing a directional source facilitates azimuthal identification and analysis of possible channeling behind the casing pipe.

Numerical study of dispersion characteristics of dipole flexural waves in a cased hole with different cement conditions

Crossed-dipole acoustic logging technology is mainly used to measure shear wave and determine the anisotropy or fractures of formation in the fi eld of acoustic logging.Based on the propagation characteristics of dipole flexural waves in cased holes,and the wavefi eld of fundamental flexural mode at three bonding conditions:good cement bonding,poorly bonded interface I,and poorly bonded interface II.The dispersion curves of flexural waves are calculated,and the eff ects of cement parameters(elastic parameters and geometric dimensions)on dispersion curves are investigated.The RAI method is used to calculate the dipole full waveforms in a cased hole with conventional or ultralight cement surrounded by a soft formation.Then,the weighted spectral semblance is used to conduct the dispersion analysis of the full waves.The numerical results show that the cutoff frequency of flexural waves exceeds the frequency band of the current dipole logging tools in the well-bonded cased hole with conventional cement in soft formations.However,when ultralight cement is used,the cutoff frequency shifts toward low values,and the ultralight cement bonding is conducive to measuring flexural waves in soft formations.When interface I is poorly bonded,the cutoff frequency shifts toward low values,and the change is evident in soft formations.The cutoff frequency in the case of ultralight cement bonding is more evident than that of conventional cement bonding.If only interface II is poorly bonded,regardless of the cement used,the cutoff frequencies are all below 2 kHz.The dipole full-wave analysis of diff erent bonding conditions further illustrates that the dispersion characteristics of flexural waves are sensitive to the cement bonding quality of cased holes.

Leaky modes and the first arrivals in cased boreholes with poorly bonded conditions

The generation mechanism of the first arrivals in the cased boreholes for the poorly bonded conditions is investigated. Based on the analyses of the Riemann surface structure of the characteristic function, the dispersion features, excitation spectra and contributions of modes excited in the cased boreholes with different cementing types are studied. The phase velocity dispersion studies of leaky modes show that high-order modes form "plateau" regions with one approximate velocity denoted by v separated by their cutoff frequencies, in which the phase velocity changes little with a considerable frequency range, while the group velocity keeps a relatively constant high value. Usually, the operation frequency range of a specific cementing evaluation acoustic logging tool is covered by such a "plateau" region. Mode excitation and contribution analyses show that the first arrivals in the cased boreholes for the poorly bonded conditions are the contributions from leaky modes, where the traveling velocity of the first arrivals processed by slowness time coherence(STC) method is equal to the approximated velocity v. Analyses on generation of leaky modes in the cased boreholes supplement the understanding of the generation mechanism of the first arrivals.

An acoustic-wave theory for casing bond evaluation using viscoelastic slip boundary modeling

Slip boundary condition is commonly utilized to model elastic wave propagation through layered earth media. The same approach is used here to characterize acoustic wave propagation along a cased borehole with various cement bond conditions. By modeling the cement layer between casing and formation as a viscoelastic slip interface with complex coupling rigidity parameters, one can not only reduce the complexity in the classical elastic wave modeling of the problem, but also efficiently model various complicated wave phenomena that are difficult for the existing modeling. More specifically, the new theory can well describe the effect of the cement bond condition change and the location of the change(i.e., whether it is in the first interface between casing and cement, or the second interface between cement and formation) on the acoustic waves,demonstrating the good modeling capability and predicting power. Application of the theory to field data shows that the theory can correctly model the acoustic wave characteristics and interpret the cement bond condition, thus providing a useful fundament theory for casing bond evaluation using acoustic logging.

Experimental studies of linear phased-array transmitter acoustic logging in cased wells with scaled borehole models

Laboratory cased-hole acoustic logging simulations are developed with the linear phased-array transmitter in scaled cased well models for evaluating the feasibility of extracting formation acoustic parameters through casing.The full waveforms are measured with different cement bonding models.By analyzing the measured wavetrains and the time-slowness correlation graphs,it is showed that when the generation conditions of the refracted compressional wave and the refracted shear wave are reached successively by regulating the direction of acoustic beam radiated from the linear phased-array transmitter,steered angle of the main radiation lobe with both good bonding interfaces.The refracted compressional wave and the refracted shear wave can be stimulated obviously and the casing wave can be suppressed effectively,even when the casing and cement（or the cement and formation） is not bonded.Based on these observations, it is worthwhile to apply the linear phased-array transmitter to determine formation velocities,particularly in poorly bonded cased well.The works establish the experimental and theoretical foundation for new generation cased-hole acoustic logging tool development.

The effects of bonding conditions on the propagation of acoustic waves along a cased borehole

Based on the wave equations in cylindrically layered structures and boundary conditions, the frequency equation for axisymmetric guided waves and the expression for sound fields in a cased borehole excited by a monopole or multipole source have been derived. The synthetic full waveforms excited by the monopole and dipole source are simulated using a real axis integration and FFT method. According to the axisymmetric guided wave modes, the synthetic full waveforms and the effects of the interface conditions on the sound field in a cased borehole have been analyzed and studied respectively. Numerical results indicate that it may be difficult to distinguish well bonded, poorly bonded or unbonded intermediate layer between the steel pipe and formation if only using a monopole source or dipole source. To properly estimate the case boundary conditions, a combination of monopole source logging with dipole source logging is suggested.