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双重孔隙介质模型考虑了岩石非均质性诱发的介观流对弹性波频散和衰减的影响, 在非均质储层地震资料定量解释中取得良好的应用效果. 基于双重孔隙介质理论模型, 利用数值算法开展弹性波模拟工作不仅可以直观显示波的传播特征, 同时也为后期地震反演成像工作奠定基础. 本文基于Santos-Rayleigh部分饱和双重孔隙介质模型, 利用交错网格有限差分算法模拟并分析了双重孔隙介质中的波场快照和波形曲线. 采用Zener黏弹性模型近似表征介观流机制, 结果表明Zener模型能够较好地反映快纵波传播特征, 却无法表征慢纵波P3波在低频段的衰减特征. 利用时间分裂法解决波动方程的刚性问题, 提高计算效率. 利用解析解验证了有限差分算法正确性的基础上, 模拟了均匀介质和分层介质中的波场快照和波形曲线, 清晰直观地反映了快纵波在地震频段的强衰减特征, 与双重孔隙理论模型预测结果一致. 模拟结果有助于进一步理解非均匀部分饱和孔隙介质中的弹性波传播特征.Double-porosity poroelastic model takes into account the effect of mesoscopic flow induced by rock heterogeneity on dispersion and attenuation of elastic waves, and has obtained good application results in the quantitative explanation of seismic data in heterogeneous reservoirs. Wavefield simulation based on double-porosity model not only helps visualize the propagation characteristics of the elastic waves but also lays the foundation for seismic imaging. In this work, we perform wavefield simulation and analysis based on the Santos-Rayleigh model which incorporates mesoscopic and global flow in a partially-saturated double-porosity medium. Specifically, the mesoscopic flow mechanism is represented with a Zener viscoelastic model. The comparison shows that the Zener model can accurately capture the propagation characteristics of fast P-wave, but fails to describe the attenuation characteristics of slow P3 wave in the low-frequency band. It implies that Zener viscoelastic model and slow wave modes follow different mechanisms. Then the staggered grid finite-difference method is used to simulate wave propagation in a double-porosity medium, and the stiff problem is solved with a time-splitting algorithm, which can significantly improve computational efficiency. Based on the above methods, the correctness of our algorithm is verified with derived analytical solution for a P-wave source in a uniform partially saturated poroelastic medium. Analytical and numerical solutions are in good agreement and mean error is 0.33%. We provide some examples of wavefield snapshots and seismograms in homogeneous and layered heterogeneous media at seismic and ultrasonic frequencies. The simulation results demonstrate the strong attenuation of fast P-wave and no change of S-wave in the seismic band due to mesoscopic flow mechanism, which is consistent with the theoretical prediction of double-porosity model. Moreover, the energy of fast P-wave is concentrated in solid phase while slow waves are stronger in fluid phase. This work contributes to the understanding of broadband elastic wave propagation in a heterogeneous partially saturated porous medium and can be applied to the reservoir imaging with broadband geophysical data.
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符号 参数 层1 层2 Ks 基质体积模量/GPa 36 40 ρs 基质密度/(kg·m–3) 2650 2800 Km 骨架体积模量/GPa 6.21 9.5 μm 骨架剪切模量/GPa 4.55 6.2 ϕ 孔隙度 0.33 0.2 κ 渗透率/m2 4.93×10–12 2.96×10–12 ${K}_{\mathrm{{f}}}^{(1)} $ 润湿相流体体积模量/GPa 2.223 $ {\rho}_{\mathrm{{f}}}^{(1)}$ 润湿相流体密度/(kg·m–3) 1000 ${\eta}_{\mathrm{{f}}}^{(1)} $ 润湿相流体黏度/(Pa·s) 0.001 ${K}_{\mathrm{{f}}}^{(2)} $ 非润湿相流体体积模量/GPa 0.022 ${\rho}_{\mathrm{{f}}}^{(2)} $ 非润湿相流体密度/(kg·m–3) 100 ${\eta}_{\mathrm{{f}}}^{(2)} $ 非润湿相流体黏度/(Pa·s) 1.5×10–5 
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