P‐wave dispersion and attenuation in fractured and porous reservoirs – poroelasticity approach
P‐wave dispersion and attenuation in fractured and porous reservoirs – poroelasticity approach
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DOI：
10.1111/j.1365-2478.2009.00785.x
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发表时间：
2009-03
影响因子：
2.6
通讯作者：
B. Gurevich;M. Brajanovski;R. Galvin;Tobias Malte Müller;J. Toms‐Stewart
中科院分区：
文献类型：
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作者：
B. Gurevich;M. Brajanovski;R. Galvin;Tobias Malte Müller;J. Toms‐Stewart
由于波引起的流体在孔隙和裂缝之间流动，油气藏中的天然裂缝会导致显着的地震衰减和分散。我们明确地基于比奥孔隙弹性方程的解提出了两个理论模型。第一个模型将裂缝视为无限范围的薄弱面（或高度柔顺且非常薄的层）。在第二个模型中，裂缝被建模为有限半径的薄硬币形空隙。在这两个模型中，衰减是入射压缩波能量在断裂表面转换为扩散毕奥慢波的结果，并在约 1 的归一化频率附近表现出典型的松弛峰值。这对应于第一个模型的流体扩散长度约为裂纹间距和第二个模型的裂纹直径的频率。这与对衰减本质的直观理解是一致的：当裂缝间隔紧密且规则时，裂缝产生的毕奥慢波相互干扰，干涉图案由裂缝间距控制。相反，如果裂缝的长度有限（小于间距），则裂缝将充当独立的散射体，并且衰减类似于孤立裂缝的散射模式。基于分支函数使用的近似数学方法为这两个模型提供了统一的分析框架。
Natural fractures in hydrocarbon reservoirs can cause significant seismic attenuation and dispersion due to wave induced fluid flow between pores and fractures. We present two theoretical models explicitly based on the solution of Biot's equations of poroelasticity. The first model considers fractures as planes of weakness (or highly compliant and very thin layers) of infinite extent. In the second model fractures are modelled as thin penny‐shaped voids of finite radius. In both models attenuation is a result of conversion of the incident compressional wave energy into the diffusive Biot slow wave at the fracture surface and exhibits a typical relaxation peak around a normalized frequency of about 1. This corresponds to a frequency where the fluid diffusion length is of the order of crack spacing for the first model and the crack diameter for the second. This is consistent with an intuitive understanding of the nature of attenuation: when fractures are closely and regularly spaced, the Biot's slow waves produced by cracks interfere with each other, with the interference pattern controlled by the fracture spacing. Conversely, if fractures are of finite length, which is smaller than spacing, then fractures act as independent scatterers and the attenuation resembles the pattern of scattering by isolated cracks. An approximate mathematical approach based on the use of a branching function gives a unified analytical framework for both models.