3D analytical simulation of full reflected waves in cased single-well imaging based on viscous linear-slip theory

Abstract Over recent decades, acoustic single-well imaging technique has attracted increasing attention within the community of oil/gas exploration. Given the prevalence of cased boreholes in oil fields, it is of great significance to investigate the reflections under the condition of cased boreholes for far-field reflector detection. However, simulating wavefields for cased single-well imaging remains challenging. Instead of using the conventional finite-difference method which is considerably time-consuming, we proposed an efficient analytical method for simulating reflections by incorporating viscous linear-slip conditions, thus providing a reliable tool for characterizing the reflections in realistic scenarios involving imperfectly bonded interfaces. The efficiency and accuracy of the proposed method are validated through comparisons with reference solutions. Based on the proposed algorithm, we conduct numerical experiments to analyze the influence of the interface stiffness and viscosity on reflections. We find that the amplitudes of reflections initially increase and then decrease as the interface stiffness decreases for dipole sources, highlighting the advantage of using dipole sources in scenarios involving poor cement bonding quality. However, for monopole sources, the reflection amplitudes decrease nearly monotonically with decreasing stiffnesses. Additionally, for both dipole and monopole sources, the reflection characteristics are dominated by the interface stiffness rather than the viscosity in the case of large stiffness (i.e., good cement bonding). However, the reflections become highly sensitive to the interface viscosity when the stiffness is small (i.e., poor cement bonding). Consequently, the proposed method serves as a powerful tool for modeling and analyzing the reflections in cased single-well imaging with imperfectly bonded interfaces, providing a theoretical guidance for developing advanced logging equipment in oil/gas field exploration.