Reflection and transmission of tube waves in cased boreholes with layers and perforations

Abstract

At low frequencies tube or Stoneley waves represent a dominant arrival propagating along boreholes. They can be excited by the source in a well or by external source due to conversion from other wave types. Tube wave experiences reflection at the bed boundaries, borehole diameter changes and fractures or permeable zones. It was proven in previous studies that 1D effective wavenumber approach provides simple and accurate low-frequency description of tubewave propagation in open boreholes surrounded by radially homogeneous formation. Tube waves become even more dominant in cased boreholes, but casing further modifies wave propagation and reflection/transmission phenomena. In this study we apply 1D effective wavenumber approach to radially inhomogeneous media and demonstrate that it still provides excellent description of low-frequency tubewave propagation. In particular, we focus on three models representative of cased boreholes: reflection from geological interfaces behind casing, reflection from corroded casing section and reflection from idealized diskshaped perforation in cased hole. In all three cases frequency-dependent reflection coefficient obtained by 1D effective method and by finite-difference computations show excellent agreement.