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岩石孔隙中常常含有两相或多相流体, 了解弹性波作用下流体压力扩散对弹性波频散和衰减的影响对于地球资源探测至关重要. 本文建立了由一种骨架和两种流体组成的非饱和双重孔隙介质模型, 推导了考虑毛细管压力作用的, 包含宏观全局流和中观局域流两种机制的弹性波传播方程. 利用平面波分析的方法分析了三种纵波(P1, P2和P3波)和一种横波(S波)的频散和衰减特性, 并重点讨论了嵌入体半径、饱和度、渗透率和孔隙度等孔隙介质参数对其中P1波传播特性的影响. 经理论分析验证, 该模型在特定参数条件下可退化为经典Biot饱和流体孔隙模型. 根据数值模拟结果, 低频P1波速度会出现低于Gassmann-Wood低频极限的现象, 这是由于在考虑宏观尺度上流体间毛细管力作用的情况下, 全局流和局域流的耦合作用加速了孔隙压力的平衡过程, 使得岩石不排水的基本假设不再成立; 孔隙介质参数与弹性波频散和衰减之间是复杂的非线性关系; 与仅考虑宏观全局流机制的Santos模型相比, 本模型预测的岩石弹性模量在低频段与实际岩心测量数据较吻合, 证实了该模型在地震勘探速度场建模方面具有更好的可靠性.Rock pores often contain two-phase or multi-phase fluids, so it is important to understand how the wave-induced fluid pressure diffusion affects dispersion and attenuation of elastic waves for resource exploration. To describe the propagation of elastic wave in a double-porosity medium saturated by two-phase fluids, a wave propagation model, including both global and local flow mechanisms and considering the effect of capillary pressure, is derived. The dispersion and attenuation characteristics of three longitudinal waves (P1, P2, P3) and one transverse wave (S wave) are investigated by analyzing a plane wave, and the effects of physical parameters, such as inclusion radius, water saturation, permeability and porosity, on the propagation characteristics of P1 wave are investigated. Theoretical analysis shows that the model derived in this work can be degenerated into the Biot model under specific conditions. According to the numerical simulation results, due to the coupling of global flow and local flow, the P1 wave velocity may decrease below the Gassmann-Wood limit. The physical explanation of this phenomenon is as follows: when considering the effect of capillary pressure, the coupling effect of global flow and local flow will break the basic assumption that rock is undrained. The relationship between physical parameters of porous medium and the dispersion and attenuation characteristics of elastic wave is complicated and nonlinear. Compared with Santos model, elastic modulus predicted by Santos-Rayleigh model is in good agreement with the experimental data in the low frequency band, which proves that this model has good reliability in modeling the velocity field of seismic exploration.
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Keywords:
- porous media /
- capillary pressure /
- local flow /
- dispersion and attenuation
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Google Scholar
[2] Biot M A 1956 J. Acoust. Soc. Am. 28 168
Google Scholar
[3] Biot M A 1962 J. Appl. Phys. 33 1482
Google Scholar
[4] 巴晶 2013 岩石物理学进展与评述 (北京: 清华大学出版社) 第151页
Ba J 2013 Progress and Review of Rock Physics (Beijing: Tsinghua University Press) p151 (in Chinese)
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[11] Dutta N C, Odé H 1979 Geophysics 44 1777
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Zhao H B 2007 Ph. D. Dissertation (Beijing: Graduate University of Chinese Academy of Sciences) (in Chinese)
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图 1 一种骨架和两种流体组成的非饱和双重孔隙介质示意图. 红色虚线箭头和黑色实线箭头分别表示波传播方向上的全局流矢量和嵌入体径向的局域流矢量
Fig. 1. Schematic diagram of unsaturated double-porosity medium composed of one type skeleton and two types of fluids. The velocity vectors of global flow and local flow are indicated by red dashed and black solid arrows respectively.
图 2 Santos模型和Santos-Rayleigh模型预测的P1波速度与衰减随频率变化曲线对比 (a) P1波相速度; (b) P1波逆品质因子
Fig. 2. Comparison of P1 wave velocity and attenuation as the function of frequencies predicted by Santos and Santos-Rayleigh models: (a) Phase velocity of P1 wave; (b) dissipation factor of P1 wave.
图 3 Santos模型和Santos-Rayleigh模型预测的P2和P3波速度与衰减随频率变化曲线对比 (a) P2, P3波相速度; (b) P2, P3波逆品质因子
Fig. 3. Comparison of P2 and P3 wave velocities and attenuations as the function of frequencies predicted by Santos and Santos-Rayleigh models: (a) Phase velocity of P2 and P3 wave; (b) dissipation factor of P2 and P3 wave.
图 4 Santos模型和Santos-Rayleigh模型预测的S波速度与衰减随频率变化曲线对比 (a) S波相速度; (b) S波逆品质因子
Fig. 4. Comparison of S wave velocity and attenuation as the function of frequencies predicted by Santos and Santos-Rayleigh models: (a) Phase velocity of S wave; (b) dissipation factor of S wave.
图 5 不同嵌入体半径下Santos-Rayleigh模型P1波速度与衰减随频率变化曲线 (a) P1波相速度; (b) P1波逆品质因子
Fig. 5. P1 wave velocity and attenuation predicted by Santos-Rayleigh model with different radii of inclusion: (a) Phase velocity of P1 wave; (b) dissipation factor of P1 wave.
图 6 不同含水饱和度下Santos-Rayleigh模型P1波速度与衰减随频率变化曲线 (a) P1波相速度; (b) P1波逆品质因子
Fig. 6. P1 wave velocity and attenuation predicted by Santos-Rayleigh model with different water saturations: (a) Phase velocity of P1 wave; (b) dissipation factor of P1 wave.
图 7 不同渗透率下Santos-Rayleigh模型P1波速度与衰减随频率变化曲线 (a) P1波相速度; (b) P1波逆品质因子
Fig. 7. P1 wave velocity and attenuation predicted by Santos-Rayleigh model with different permeabilities: (a) Phase velocity of P1 wave; (b) dissipation factor of P1 wave.
图 8 不同孔隙度下Santos-Rayleigh模型P1波速度与衰减随频率变化曲线 (a) P1波相速度; (b) P1波逆品质因子
Fig. 8. P1 wave velocity and attenuation predicted by Santos-Rayleigh model with different porosities: (a) Phase velocity of P1 wave; (b) dissipation factor of P1 wave.
图 9 Santos-Rayleigh模型与实际数据对比
Fig. 9. Comparison of measured data with Santos-Rayleigh model.
表 1 非饱和孔隙介质物性参数表
Table 1. Physical parameters of unsaturated porous media model.
参数 值 固体基质体积模量/GPa 36 固体基质密度/(kg ·m–3) 2650 骨架体积模量/GPa 6.21 骨架剪切模量/GPa 4.55 孔隙度 0.33 渗透率/m2 4.935×10–12 润湿相流体体积模量/GPa 2.223 润湿相流体密度/(kg·m–3) 1000 润湿相流体黏度/(Pa·s) 0.001 非润湿相流体体积模量/GPa 0.022 非润湿相流体密度/(kg·m–3) 100 非润湿相流体黏度/(Pa·s) 15×10–6 
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表 2 Berea砂岩及流体物性参数表
Table 2. Physical parameters of Berea sandstone and fluids.
参数 值 固体基质体积模量/GPa 30 固体基质密度/(kg·m–3) 2600 骨架体积模量/GPa 11.7 骨架剪切模量/GPa 11.1 孔隙度 0.196 渗透率/m2 0.266×10–12 地层水体积模量/GPa 2.23 地层水密度/(kg·m–3) 997.67 地层水黏度/(Pa·s) 0.00091 二氧化碳体积模量/GPa 1.17×10–3 二氧化碳密度/(kg·m–3) 17.21 二氧化碳黏度/(Pa·s) 1.5×10–5
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[1] Müller T M, Gurevich B, Lebedev M 2010 Geophysics 75 75A147
Google Scholar
[2] Biot M A 1956 J. Acoust. Soc. Am. 28 168
Google Scholar
[3] Biot M A 1962 J. Appl. Phys. 33 1482
Google Scholar
[4] 巴晶 2013 岩石物理学进展与评述 (北京: 清华大学出版社) 第151页
Ba J 2013 Progress and Review of Rock Physics (Beijing: Tsinghua University Press) p151 (in Chinese)
[5] Santos J E, Douglas J, Corberó J, Lovera O M 1990 J. Acoust. Soc. Am. 87 1439
Google Scholar
[6] Santos J E, Corberó J M, Douglas J 1990 J. Acoust. Soc. Am. 87 1428
Google Scholar
[7] Lo W C, Sposito G, Majer E 2005 Water Resour. Res. 41 W02025
Google Scholar
[8] 王婷, 崔志文, 刘金霞, 王克协 2018 物理学报 67 114301
Google Scholar
Wang T, Cui Z W, Liu J X, Wang K X 2018 Acta Phys. Sin. 67 114301
Google Scholar
[9] Mavko G, Nur A 1975 J. Geophys. Res. 80 1444
Google Scholar
[10] White J E 1975 Geophysics 40 224
Google Scholar
[11] Dutta N C, Odé H 1979 Geophysics 44 1777
Google Scholar
[12] Wang Y, Zhao L, Cao C, Yao Q, Yang Z, Cao H, Geng J 2022 Geophysics 87 MR247
Google Scholar
[13] Johnson D L 2001 J. Acoust. Soc. Am. 110 682
Google Scholar
[14] Tserkovnyak Y, Johnson D L 2003 J. Acoust. Soc. Am. 114 2596
Google Scholar
[15] Qi Q, Müller T M, Gurevich B, Lopes S, Lebedev M, Caspari E 2014 Geophysics 79 WB35
Google Scholar
[16] Ciz R, Shapiro S A 2007 Geophysics 72 A75
Google Scholar
[17] Müller T M, Gurevich B 2005 J. Acoust. Soc. Am. 117 2732
Google Scholar
[18] Dvorkin J, Nur A 1993 Geophysics 58 524
Google Scholar
[19] Pride S R, Berryman, Harris J M 2004 J. Geophys. Res. 109 B01201
Google Scholar
[20] 巴晶, Carcione J M, 曹宏, 杜启振, 袁振宇, 卢明辉 2012 地球物理学报 55 219
Google Scholar
Ba J, Carcione J M, Cao H, Du Q Z, Yuan Z Y, Lu M H 2012 Chin. J. Geophys. 55 219
Google Scholar
[21] Sun W T, Ba J, Carcione J M 2016 Geophys. J. Int. 205 22
Google Scholar
[22] Ba J, Xu W, Fu L Y, Carcione J M, Zhang L 2017 J. Geophys. Res. Solid Earth 122 1949
Google Scholar
[23] Zhang L, Ba J, Carcione J M, Wu C F 2022 J. Geophys. Res. Solid Earth 127 e2021JB023809
Google Scholar
[24] 李红星, 张嘉辉, 樊嘉伟, 陶春辉, 肖昆, 黄光南, 盛书中, 宫猛 2022 物理学报 71 089101
Google Scholar
Li H X, Zhang J H, Fan J W, Tao C H, Xiao K, Huang G N, Sheng S Z, Gong M 2022 Acta Phys. Sin. 71 089101
Google Scholar
[25] Murphy W M 1984 J. Geophys. Res. Solid Earth 89 11549
Google Scholar
[26] Batzle M L, Han D H, Hofmann R 2006 Geophysics 71 N1
Google Scholar
[27] Chapman S, Borgomano J V M, Quintal B, Benson S M, Fortin J 2021 J. Geophys. Res. Solid Earth 126 e2021JB021643
Google Scholar
[28] Ravazzoli C L, Santos J E, Carcione J M 2003 J. Acoust. Soc. Am. 113 1801
Google Scholar
[29] 赵海波 2007 博士学位论文 (北京: 中国科学院研究生院)
Zhao H B 2007 Ph. D. Dissertation (Beijing: Graduate University of Chinese Academy of Sciences) (in Chinese)
[30] Carcione J M, Cavallini F, Santos J E, Ravazzoli C L, Gauzellino P M 2004 Wave Motion 39 227
Google Scholar
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