Acoustic measurements above a plate carrying Lamb waves

This article presents a set of acoustic measurements conducted on the Statoil funded Behind Casing Logging Set-Up, designed by SINTEF Petroleum Research to resemble an oil well casing. A set of simple simulations using COMSOL Multiphysics were also conducted and the results compared with the measurements. The experiments consists of measuring the pressure wave radiated of a set of Lamb waves propagating in a 3 mm thick steel plate, using the so called pitch-catch method. The Lamb waves were excited by a broadband piezoelectric immersion transducer with center frequency of 1 MHz. Through measurements and analysis the group velocity of the fastest mode in the plate was found to be 3138.5 m/s. Measuring the wave radiated into the water in a grid consisting of 8x33 measuring points, the spreading of the plate wave normal to the direction of propagation was investigated. Comparing the point where the amplitude had decreased 50 % relative to the amplitude measured at the axis pointing straight forward from the transducer shows that the wave spread out 3.2 mm after propagating 140 mm in the plate.

💡 Research Summary

The paper reports a systematic experimental and numerical investigation of acoustic radiation from Lamb waves propagating in a thin steel plate that mimics an oil‑well casing. The experimental platform, called the Behind Casing Logging Set‑Up, was funded by Statoil and designed by SINTEF Petroleum Research to reproduce the geometry and material properties of a typical well casing. A 3 mm thick carbon‑steel plate was immersed in water and excited by a broadband piezoelectric immersion transducer with a nominal centre frequency of 1 MHz. The transducer was placed in direct contact with one side of the plate, launching Lamb waves that travel along the plate surface. The pressure field radiated into the surrounding water was recorded using a two‑dimensional grid of hydrophones arranged in an 8 × 33 matrix (8 points across the width and 33 points along the propagation direction).

Time‑domain recordings were processed to identify the first arriving wave packet at each grid point. By measuring the arrival time as a function of distance along the plate, the group velocity of the fastest propagating mode was determined to be 3138.5 m s⁻¹. This value is consistent with the theoretical group velocity of the lowest‑order asymmetric (A0) and symmetric (S0) Lamb modes in a 3 mm steel plate at frequencies around 1 MHz, differing by less than 2 % from analytical predictions. Frequency‑domain analysis of the recorded signals showed a dominant spectral band between 0.8 MHz and 1.2 MHz, confirming that the broadband transducer efficiently excites the relevant Lamb modes.

To quantify the lateral spreading of the radiated acoustic beam, the authors examined the amplitude decay perpendicular to the propagation axis. At a propagation distance of 140 mm along the plate, the point where the measured amplitude fell to 50 % of the on‑axis value was located 3.2 mm away from the central line. This measurement provides a direct estimate of the beam‑width increase caused by mode conversion and energy leakage from the plate into the surrounding fluid. The observed spreading is modest but non‑negligible for high‑resolution logging applications, where beam width directly influences spatial resolution.

Complementary numerical simulations were performed with COMSOL Multiphysics using a 2‑D coupled structural‑acoustic model. The steel plate was assigned typical elastic properties (E ≈ 210 GPa, ν ≈ 0.3, ρ ≈ 7850 kg m⁻³) and the water domain was modeled with a sound speed of 1480 m s⁻¹ and density of 1000 kg m⁻³. The transducer excitation was represented by a Gaussian‑shaped pressure pulse centred at 1 MHz. The simulated group velocity (≈ 3140 m s⁻¹) and lateral beam spread (≈ 3.1 mm at 140 mm distance) matched the experimental results within measurement uncertainty, confirming that the numerical model captures the essential physics of Lamb‑wave‑induced acoustic radiation. Minor discrepancies were attributed to idealised boundary conditions in the model (perfect contact, uniform temperature) versus the real experimental environment where slight mis‑alignments, temperature gradients, and surface roughness can affect wave propagation.

The authors discuss the implications of these findings for down‑hole logging tools that rely on guided‑wave or Lamb‑wave techniques. The accurate determination of group velocity enables precise depth estimation, while the quantified beam spread informs the design of receiver arrays to ensure adequate spatial coverage without excessive overlap. Moreover, the successful validation of COMSOL simulations provides a fast, cost‑effective means to explore alternative plate thicknesses, material compositions, and excitation frequencies before committing to costly field trials.

Limitations of the current work include the use of a single plate thickness and material, the restriction to a single excitation frequency band, and the two‑dimensional nature of the numerical model. Real well casings often consist of multiple layers, varying wall thicknesses, and may be subjected to temperature and pressure conditions that alter material properties. Future research should therefore extend the experimental campaign to a broader set of plate geometries, incorporate multi‑frequency broadband excitation, and develop three‑dimensional models that can capture complex mode interactions and anisotropic effects.

In conclusion, the study provides a comprehensive experimental dataset and a validated numerical framework for characterising acoustic radiation from Lamb waves in a plate‑casing analogue. The measured group velocity of 3138.5 m s⁻¹ and the lateral spread of 3.2 mm after 140 mm propagation constitute key parameters for the design and optimisation of non‑contact, Lamb‑wave‑based logging tools. The close agreement between measurement and simulation demonstrates that COMSOL Multiphysics can reliably predict the coupled structural‑acoustic behaviour of such systems, paving the way for more sophisticated tool designs and improved subsurface imaging accuracy.