Based on the three-phase theory proposed by Santos, acoustic wave propagation in a poroelastic medium saturated by two immiscible fluids was simulated using a staggered high-order finite-difference algorithm with a time partition method, which is firstly applied to such a three-phase medium. The partition method was used to solve the stiffness problem of the differential equations in the three-phase theory. Considering the effects of capillary pressure, reference pressure and coupling drag of two fluids in pores, three compressional waves and one shear wave predicted by Santos have been correctly simulated. Influences of the parameters, porosity, permeability and gas saturation on the velocities and amplitude of three compressional waves were discussed in detail. Also, a perfectly matched layer (PML) absorbing boundary condition was firstly implemented in the three-phase equations with a staggered-grid high-order finite-difference. Comparisons between the proposed PML method and a commonly used damping method were made to validate the efficiency of the proposed boundary absorption scheme. It was shown that the PML works more efficiently than the damping method in this complex medium. Additionally, the three-phase theory is reduced to the Biot's theory when there is only one fluid left in the pores, which is shown in Appendix. This reduction makes clear that three-phase equation systems are identical to the typical Biot's equations if the fluid saturation for either of the two fluids in the pores approaches to zero.
The longitudinal wave velocity and attenuation measurements of artificial gas hy- drate samples at a low temperature are reported. And the temperature and pressure dependence of longitudinal wave velocity is also investigated. In order to under- stand the acoustic properties of gas hydrate, the pure ice, the pure tetrahydrofuran (THF), the pure gas hydrate samples and sand sediment containing gas hydrate are measured at a low temperature between 0℃ and –15℃. For the pure ice, the pure THF and the pure gas hydrate samples, whose density is 898 kg/m3, 895 kg/m3 and 475 kg/m3, the velocity of longitudinal wave is respectively 3574 m/s, 3428 m/s and 2439 m/s. For synthesized and compacted samples, the velocity of synthesized samples is lower than that of compacted samples. The velocities increase when the densities of the samples increase, while the attenuation decreases. Under the con- dition of low temperature, the results show that the velocity is slightly affected by the temperature. The results also show that wave velocities increase with the in- crease of piston pressures. For example, the velocity of one sample increases from 3049 up to 3337 m/s and the other increases from 2315 up to 2995 m/s. But wave velocity decreases from 3800 to 3546 m/s when the temperature increases from –15℃ to 5℃ and changes significantly close to the melting point. Formation con- ditions of the two samples are the same but with different conversion ratios of wa- ter. The results of the experiment are important for exploration of the gas hydrate resources and development of acoustic techniques.
WANG DongLI DongLiangZHANG HaiLanFAN ShuanShiZHAO HaiBo
In this paper, an optimized staggered variable-grid finite-difference (FD) method is developed in veloc- ity-stress elastic wave equations. On the basis of the dispersion-relation-preserving (DRP), a fourth-order finite-difference operator on non-uniform grids is constructed. The proposed algorithm is a continuous variable-grid method. It does not need interpolations for the field variables between re- gions with the fine spacing and the coarse one. The accuracy of the optimized scheme has been veri- fied with an analytical solution and a regular staggered-grid FD method for the eighth order accuracy in space. The comparisons of the proposed scheme with the variable-grid FD method based on Taylor series expansion are made. It is demonstrated that this optimized scheme has less dispersion errors than that with Taylor's series expansion. Thus, the proposed scheme uses coarser grids in numerical simulations than that constructed by the Taylor's series expansion. Finally, the capability of the opti- mized FD is demonstrated for a complex cross-well acoustic simulation. The numerical experiment shows that this method greatly saves storage requirements and computational time, and is stable.
