Effect of damping boundary conditions on acoustic transmission of drill strings

Effect of damping mechanism on transient acoustical behavior of periodic drill pipes was analyzed including drilling fluid, radiation loss and downhole boundary conditions. A one-dimensional longitudinal wave equation and cylinder source radiation theory were developed to determine fluid viscous loss due to the axial motion of the pipe surfaces in the drilling fluid and radiation loss due to the radial motion coupled to the longitudinal motion. In addition, a Kelvin constitutive equation was used to model the earth layer. Then, the response of the drill strings to the excitation with down-hole viscoelastic boundary condition was discussed using a time-domain algorithm based on finite element method. The simulation results show that the radiation loss and coupled vibrations dominate the viscous acoustic damping loss, and the earth layer viscoelastic coefficients are quite sensitive to low frequency response. However, the presence of losses still keeps the comb filtering properties of drill strings.