部分饱和孔隙岩石中声波传播数值研究

利用基于Biot理论的孔隙弹性介质的高阶交错网格有限差分算法，模拟了具有随机分布特征的多种流体饱和岩石中声波在中心频率分别为25，50，75，100kHz时的声场特点. 对于一个由两种成分（气和水）饱和的岩石模型, 假设含不同流体的孔隙介质随机分布在不同的宏观区域，该区域尺度远小于计算的声波波长；组成模型的两种随机分布介质具有相同的固体骨架参数、渗透率和孔隙度，但分别被具有不同压缩性、密度和黏滞系数特性的水和气饱和. 计算和统计分析结果表明，在两种孔隙成分随机分布的部分饱和条件下纵波速度比较复杂，除骨架参数外，其变化主要依赖于中心频率、各种孔隙成分饱和度及饱和介质的速度. 比较该随机分布模型、Gassmann理论模型和White的“气包”模型，发现三种模型得到的纵波速度和衰减规律有较好的定性对应关系. 其次，按照这种随机计算模型的处理方法，本文还首次计算了一个三种流体成分充填饱和的例子，即岩石模型中的孔隙被水、油和气部分饱和，计算时保持模型含水饱和度不变而只改变含油和含气饱和度. 在这种计算条件下，纵波速度随中心频率呈增大的趋势但有起伏变化. 声场快照显示了各种转换波在多种孔隙成分充填（两种和三种孔隙成分）岩石中的声场特征，复杂的水-油-气界面的非均匀分布对声场有重要影响，纵波能量主要转换形成了较为复杂的多种慢纵波和横波.

A numerical study of acoustic wave propagation in partially saturated poroelastic rock

Based on the Biot theory we use a high-order staggered finite-difference algorithm to carry out numerical experiments on wave propagation in rock partially saturated by multi-phase fluid with random fluid distribution. The ultrasonic source frequencies are 25,50,75kHz and 100 kHz, respectively. The first model is homogeneous isotropic sandstone partially filled with two-phase pore fluids (water and gas), which have different elastic characteristic parameters of saturation, viscosity, compressibility, and density, respectively. We assum that the two different pore-fills occupy different macroscopic regions and the wavelength of acoustic wave is much larger than the scale of these regions. The calculation results show that the P-wave velocity and the attenuation change with fluid saturations (water and gas) and central frequencies of the acoustic source. These numerical results are qualitatively in agreement with the White and Gassmann's models. The second model is partially filled with three-phase pore fluids (water, oil, and gas). We keep the saturation of water at a constant and change the saturations of oil and gas. In these conditions, the velocity of P-wave shows an increasing trend with the increasing of the saturation of oil. The snapshot of the acoustic wave field shows that the energy of P-wave is converted into several kinds of slow P-waves and S-waves which occur at the interfaces between water, oil and gas. These modeling results would be of significance in seismic exploration and acoustic well logging interpretation.