Reflection and mode-conversion of ultrasonic leaky Lamb waves at inaccessible discontinuities in layered structures

The nondestructive evaluation of cemented steel pipes in underground wells with ultrasonic imaging methods is a common oilfield industry application. In order to ensure the mechanical integrity of the well and in particular the lack of undesired hydraulic communication between different geological zones, the cement quality of the annular region around the pipe is often evaluated through guided leaky Lamb waves propagating inside the pipe. Commonly, the lowest-order pseudo-flexural and pseudo-extensional modes are excited in a fluid-coupled pitch-catch geometry. The dispersion relation of these guided acoustic waves is sensitive to the elastic properties of the inaccessible material around the pipe. Furthermore, the presence of discontinuities in the external medium leads to reflections and mode conversions of the leaky Lamb waves. This can be exploited to detect undesired fluid- or gas-filled pathways in an external cement sheath which may compromise the hydraulic isolation. We investigate the feasibility of this measurement technique by laboratory experiments and numerical modelling in simplified planar, multilayered elastic slab structures with notch-type discontinuities in the inaccessible layer behind a steel layer. Experimentally, a suitable fluid-coupled, mode-selective transducer geometry was adopted to detect the presence of the elastic discontinuities along spatial and temporal dimensions. This allows to visualize and quantify leaky Lamb wave propagation and scattering effects. Numerical acoustic wave field simulations were performed using a k-space pseudo-spectral model of linear elastic wave propagation available as an open source third party toolbox (named k-Wave) for MATLAB^®. The results demonstrate the effect of reflections and mode conversions and we discuss their use for characterizing inaccessible layers.