Resumen
A knowledge of wave propagation in boreholes with gas hydrate-bearing sediments, a typical three-phase porous medium, is of great significance for better applications of acoustic logging information on the exploitation of gas hydrate. To study the wave propagation in such waveguides based on the Carcione?Leclaire three-phase theory, according to the equations of motion and constitutive relations, a staggered-grid finite-difference time-domain (FDTD) scheme and a real axis integration (RAI) algorithm in a two-dimensional (2D) cylindrical coordinate system are proposed. In the FDTD scheme, the partition method is used to solve the stiff problem, and the nonsplitting perfect matched layer (NPML) scheme is extended to solve the problem of the false reflection waves from the artificial boundaries of the computational region. In the RAI algorithm, combined with six boundary conditions, the displacement potentials of waves are studied to calculate the borehole acoustic wavefields. The effectiveness is verified by comparing the results of the two algorithms. On this basis, the acoustic logs within a gas hydrate-bearing sediment are investigated. In particular, the wave field in a borehole is analyzed and the amplitude of a Stoneley wave under different hydrate saturations is studied. The results indicate that the attenuation coefficient of the Stoneley wave increases with the increase of gas hydrate saturation. The acoustic responses in a borehole embedded in a horizontally stratified hydrate formation are also simulated by using the proposed FDTD scheme. The result shows that the amplitude of the Stoneley wave from the upper interface is smaller than that from the bottom interface.