Forward Modeling of Transducer Misalignment Effects in Ultrasonic Leaky Wave Measurements

Ultrasonic measurements performed with a pair of acoustic transducers in pitch-catch mode are of common use in the NDE field. In particular, for nearfield leaky wave (LW) measurements which are directed at precise determination of material properties of layered elastic structure in immersion. In LW measurements, the acoustic transducer beams are aligned at angles so as to phase match to one or several of the structure’s leaky (Rayleigh or Lamb) waves. The amplitude and phase of the scattered acoustic energy collected, and converted to an electrical voltage, by the phase-sensitive receiving transducer depends not only on the properties of the structure but also on the parameters of the transducers used, in particular, their apertures and alignment angles. Transducer alignment issues are especially important for transducers that radiate or receive over a narrow angular range

Guided Waves in Fluid-Elastic Concentric and Non-Concentric Cylindrical Structures: Theoretical and Experimental Investigations

Modeling and understanding the complex elastic-wave physics prevalent in fluid-elastic cylindrically-layered structures is of importance in many NDE fields, and most pertinently in the domain of well integrity evaluation in the oil and gas industry. It is believed that acoustical measurements provide one of the effective means to provide a diagnosis. Historically, the problem has been researched and addressed to a good extent for well intervals with a single steel string. For these cases, high-frequency ultrasonic imaging has been optimized and demonstrated to yield acceptable diagnosis of the annulus properties behind the first string the signal encounters. However, they fail to provide information about the outer annulus in a double or triple string geometry. To probe with more effective radial depth, lower-frequency signals are used. In a typical double-string configuration, the inner casing is eccentered with respect to the outer string which itself is also eccentered within the cylindrical hole. The annuli may or may not be filled with solid cement, and the cement may have liquid-filled channels or be disbonded over localized azimuthal ranges. The complexity of wave propagation along axial intervals is significant in that multiple modes can be excited and detected with characteristics that are affected by the various parameters in a non-linear fashion. To gain understanding of the complex wave physics and leverage it to design effective diagnosis means, we have developed modeling capabilities that address the configurations of interest. In this talk, we first establish a mathematical framework to analyze the guided wave fields in a multi-string system embedded in infinite media. We then develop and implement a Chirp Sweeping Finite Element Modeling (CSFEM) method to investigate the dispersions and modal characteristics of the complex propagating signals synthesized over an axial array of receivers. The CSFEM provides for a flexible framework to study the modal sensitivities in a multi-string system with arbitrary eccentricity, azimuthal heterogeneities, and partial bonded interfaces. We have also conducted scaled laboratory experiments to acquire reference data used to verify the range of validity of the modeling approach in predicting the guided modal characteristics of axially-propagating waves in concentric and non-concentric cylindrical structures immersed in fluid. An acoustic transmitter having four selectable, active elements at 90 degrees apart allows sourcing of all guided modes of interest and is located at one end of the string length. Received waveforms are acquired from a single receiver which is scanned axially and circumferentially inside the inner string. The acquired data set is then analyzed for spectral modal content using both Slowness-Time-Coherence and Matrix Pencil methods and compared to theoretical predictions. The comparisons indicate good agreement and provide confidence in the CSFEM capability to accurately predict the complex wave field dispersion characteristics estimated from the experimentally acquired signals in the fluid-filled double string geometries

Efficient Modeling of Finite Acoustic Beam Excitation and Detection of Interface and Bulk Waves on Planar and Cylindrical Fluid-Solid Structures

Ultrasonic (UT) nondestructive evaluation (NDE) of fluid-immersed bulk or layered elastic materials is commonly carried out with a single or a pair of acoustic transducers used in pulse-echo or pitch-catch modes. Applications range from determining material properties to identifying interior and/or surface defects. Some of the configurations often encountered in UT-NDE, and that are considered in this paper, are depicted in Figure 1. These sketches show a transmitting transducer radiating a continuous or pulsed finite beam that excites interface or bulk waves within the elastic part. Acoustic energy radiated back by the elastic part into the fluid is collected by a receiving transducer which converts it into a voltage. Quantitative modeling of this class of experiments, even under assumptions of ideal conditions (e.g. homogeneous and isotropic layers and defect-free structures), is important for design optimization purposes and for understanding and interpreting the data acquired. It also provides a first step towards tackling non-ideal configurations. There is a large body of work that address this objective through various approaches (analytical, numerical, hybrid, etc); the reader is referred to References in this issue and in past issues of the Proceedings of this conference. This paper presents recent developments in the application of analytic methods to comprehensive and efficient modeling of the type of configurations depicted in Fig. 1. Comprehensive in the sense that the methodology used can account for 1) arbitrary three-dimensional (3D) diffraction and orientation of transmitting and receiving transducers; 2) interface and layering wave effects such as the excitation of surface and modal waves in the structures inspected.</p

The Flexural (Lamb) Mode that could: Effective Imaging through Steel with an Intricate Wavephysics

Oil and gas wells are cemented before they are put in production. The cement is placed in the annulus between steel casing and rock formation to provide mechanical integrity and zonal isolation. Evaluating that the cement has indeed displaced drilling mud and has set enough to provide well integrity is a regulatory requirement. The well-honored ultrasonic pulse-echo technique was originally introduced to meet this need. The typical implementation consists of a trans-receiver housed on a fluid-immersed rotating tool to excite a casing thickness resonance whose amplitude decay is sensitive to the acoustic impedance of the annular material in contact with the casing. The technique was however shown to have limitations in (i) resolving light-weight cements with mud-like acoustic impedance as well as in (2) radially probing the entire annular space stemming from the significant impedance contrast encountered by the acoustic beam at the steel layer: less than 10% of the signal amplitude is coupled to the steel. Investigations to go beyond these limitations led to the identification of the high- frequency casing quasi-Lamb A0 (aka flexural) mode as having attractive imaging characteristics. The implemented pitch-catch measurement, named flexural wave imaging or FWI, features signals with temporally-compact (i.e., imaging-friendly) echoes: propagating axially in the casing with an amplitude attenuation informing on the material in contact with the steel as well as reflecting from interfaces deep within the cement sheath such as at the rock face, with relatively large amplitudes seemingly defying the impedance contrast premise. This presentation will focus on FWI and will describe the rich and intricate wavephysics arising from the dispersive nature of the flexural mode and that is manifested in particular with the signal propagation in the cement sheath: elastic-wave propagation and evanescence often co-exist, steel-cement bond conditions markedly affect the signal characteristics, and shear only or both compressional and shear wave reflections from the cement-rock interface whose time of flights are explainable in terms of simple ray acoustics whereas their relatively large amplitudes require elaborate scattering (non-specular) considerations. Both theoretical results and processed field data from an operating measurement tool in real wells will be presented to explain and illustrate the intricate wavephysics of FWI as well as comment on the general challenges faced in this industrial application.</p

Non-Specular Reflection of Bounded Beams From Multilayer Fluid-Immersed Elastic Structures: Complex Ray Method Revisited

The excitation of various types of leaky waves in layered elastic media by beams incident from an exterior fluid at or near the leaky wave phase-matching angle is of interest for NDE applications. In particular, much attention has been given to the non-specular reflection of beams under such conditions of incidence. While various methods have been employed to study and clarify these phenomena for well collimated beams in plane layered environments [1–11], much less has been done on the corresponding effects when the incident beams are diverging and/or when the layers are curved. To extend the plane layer results to more general conditions, it is desirable to employ analytic modeling that adapts the wave phenomenology locally from planar to curved geometries. Because the phenomena occur in the range of high frequencies, ray field modeling affords an attractive option. By the complex-sourcepoint (CSP) technique, which places a radiating source at a complex coordinate location, a conventional line or point source excited field can be converted into a two-or three-dimensional quasi-Gaussian beam field that is an exact solution of the dynamical equations [12,13]. When the CSP field interacts with a plane or cylindrically layered elastic medium, the resulting internal and external fields can be expressed rigorously in terms of wavenumber spectral integrals [14]. Asymptotic reduction of these integrals, achieved by the method of saddle points applied to deformed contours in the complex spectral wavenumber plane, accounts for all relevant wave phenomena. For the reflected field, this yields explicit waveforms which are synthesized by interacting specularly reflected beam, leaky wave, and possible lateral wave contributions.</p

Beam Parametrization of Localized Weak Debonding in a Layered Aluminum Plate

Obliquely incident (predominantly P-wave) beam inputs from an ultrasonic transducer into a layered bounded composite elastic plate are suitable for detection of weak debonds because they generate on the bond lines the tangential shear to which this kind of flaw responds. In previous studies, the beam-flaw interaction and scattering mechanisms were explored by expressing the fields in both the unflawed and flawed environments in terms of the set of P-SV coupled modes capable of propagating in the plate [1–5]. As may be anticipated, the reference data generated in this manner exhibited beam-like features of the fields in observational domains characterized by only a few P-SV coupled beam reflections between the outer boundaries of the perfectly bonded plate, thereby indicating that the normal modes do not parametrize the process in terms of the “observables” in the data. The problem is therefore re-parametrized here by direct beam tracking. As before [1,2], our model is two-dimensional and comprises a two-layer aluminum plate in vacuum, with a weak debond region modeled by a quasi-Gaussian pliability profile</p

Nonspecular reflection of rotationally symmetric Gaussian beams from shaped fluid-solid interfaces

Nonspecular reflection, which occurs when an incident beam is phase matched to a leaky wave, is an important tool for fluid-solid interface diagnostics. A recently developed complex ray analysis for modeling nonspecular reflection of two-dimensional Gaussian sheet beams [1,2] is here extended to account for rotationally symmetric three-dimensional (3D) Gaussian beams (GBs) with arbitrary collimation. As in our 2D analysis, we utilize the complex-source-point (CSP) technique by which a conventional point-source-excited field can be converted into a 3D quasi-Gaussian beam field by displacing a real point source to a complex location [3]. When the CSP field excited in the fluid interacts with a plane or cylindrically layered elastic medium, the resulting internal and external fields can be expressed rigorously in terms of wavenumber spectral integrals that are approximated explicitly by high-frequency uniform asymptotics [4]. The resulting expressions for the reflected field contain interacting specularly reflected beam and leaky wave contributions which establish the physical basis for the observed phenomena.</p

A 2D Hybrid Model for Ultrasonic Pulse-Echo Scattering from a Rough Interface Buried in a Layered Medium

Understanding and predicting the effects of surface roughness on ultrasonic pulse-echo measurements is important in a variety of applications. In particular, it is of interest for cased well evaluation in the oilfield industry where the measurement is used to investigate the cement seal placed between the casing and the formation wall (see Fig. 1(a)) [1]. Here, the acoustic transducer signal arises from multiple reflections taking place at the various interfaces of the layered (borehole fluid)-(steel casing)-cement-(rocky formation) structure. Previous numerical models, developed to account for this measurement, have been limited to canonical configurations where, in particular, the various interfaces are smooth [2]. Typically, the cement-formation interface is rough with widely varying rms height and correlation length. In order to predict the effect of roughness of arbitrary sizeon the reflection echo attributed to this interface, a frequency-domain hybrid analytical/numerical simulation model has been developed. The model has been preliminary implemented for a two-dimensional (2D) configuration where an acoustic transducer with a Gaussian profile interacts with the aforementioned structure in a planar geometry (see Fig. 1(b)). In this configuration, the transducer aperture has a finite size in the (x, z) and is infinite in the y direction. The fluid, steel layer, cement layer, and halfspace formation are assumed to be isotropic and homogeneous. The cement-formation interface, denoted by S 0, is in general irregular or rough and parameterized by the function z = h(x) describing the height of a particle on S 0 measured from the (mean) plane z = 0. A time-harmonic variation e iωt is assumed throughout.</p

Maxillary distraction of cleft lip and palate patients by internal distractors

The excitation of various types of leaky waves in layered elastic media by beams incident from an exterior fluid at or near the leaky wave phase-matching angle is of interest for NDE applications. In particular, much attention has been given to the non-specular reflection of beams under such conditions of incidence. While various methods have been employed to study and clarify these phenomena for well collimated beams in plane layered environments [1–11], much less has been done on the corresponding effects when the incident beams are diverging and/or when the layers are curved. To extend the plane layer results to more general conditions, it is desirable to employ analytic modeling that adapts the wave phenomenology locally from planar to curved geometries. Because the phenomena occur in the range of high frequencies, ray field modeling affords an attractive option. By the complex-sourcepoint (CSP) technique, which places a radiating source at a complex coordinate location, a conventional line or point source excited field can be converted into a two-or three-dimensional quasi-Gaussian beam field that is an exact solution of the dynamical equations [12,13]. When the CSP field interacts with a plane or cylindrically layered elastic medium, the resulting internal and external fields can be expressed rigorously in terms of wavenumber spectral integrals [14]. Asymptotic reduction of these integrals, achieved by the method of saddle points applied to deformed contours in the complex spectral wavenumber plane, accounts for all relevant wave phenomena. For the reflected field, this yields explicit waveforms which are synthesized by interacting specularly reflected beam, leaky wave, and possible lateral wave contributions

Forward Modeling of Transducer Misalignment Effects in Ultrasonic Leaky Wave Measurements

Ultrasonic measurements performed with a pair of acoustic transducers in pitch-catch mode are of common use in the NDE field. In particular, for nearfield leaky wave (LW) measurements which are directed at precise determination of material properties of layered elastic structure in immersion. In LW measurements, the acoustic transducer beams are aligned at angles so as to phase match to one or several of the structure’s leaky (Rayleigh or Lamb) waves. The amplitude and phase of the scattered acoustic energy collected, and converted to an electrical voltage, by the phase-sensitive receiving transducer depends not only on the properties of the structure but also on the parameters of the transducers used, in particular, their apertures and alignment angles. Transducer alignment issues are especially important for transducers that radiate or receive over a narrow angular range.</p