The influence of casing curvature and thickness on the attenuation of circumferential SH waves

Cementing plays a critical role in petroleum well completion, ensuring well integrity and zonal isolation. Conventional acoustic impedance-based logging tools face limitations in evaluating low-density cement bonding; however, these challenges can be effectively addressed using circumferential SH waves. SH waves, polarized axially along the casing and propagating circumferentially, offer distinct advantages for assessing the cement bond. In this study, the dispersion and attenuation characteristics of SH waves under casing and steel plate models are investigated using analytical methods. The radial or through-thickness variations in displacement amplitude and energy density are quantified. Key findings reveal distinct attenuation behaviors between casing and steel plate geometries due to curvature effects. While the steel plate exhibits a slight decrease in zeroth-order SH (SH0) mode attenuation with increasing frequency, the casing demonstrates a pronounced increase in SH0 attenuation under identical conditions. Particle displacement amplitude progressively intensifies from the inner to the outer casing wall as frequency increases, with SH wave energy distribution simultaneously concentrating toward the outer wall. Due to the symmetry of the steel plate’s upper and lower surfaces, displacement amplitudes and energy distributions are symmetric with respect to the middle plane. Frequency-dependent analysis reveals an inverse relationship between attenuation and frequency for SH1/SH2 modes in casing structures, accompanied by pronounced energy localization at the inner wall. Consequently, these modes demonstrate limited discriminative capability for cement impedance assessment in thick-walled casing applications. The SH0 mode attenuation demonstrates superior differentiation of cement impedance in thick-walled casing. These results are significant for applying SH waves in cementing quality evaluation under complex well conditions.