Abstract:

Fracture-fracture wave-induced fluid flow (FF-WIFF) is a key mechanism controlling seismic dispersion, attenuation, and hydraulic connectivity in fluid-saturated fractured rocks. Existing analytical models for intersecting fractures commonly assume two equal-length fractures, for which the normal oscillation problem can be decoupled by using a common support and exchange symmetry. Natural fracture networks, however, commonly contain intersecting fractures with unequal lengths, so that the symmetric/antisymmetric decomposition used in equal-length models is no longer directly applicable. Here we develop a frequency-dependent rock-physics model for unequal-length intersecting fractures within the framework of dynamic Biot poroelasticity and dilute fracture scattering. The fracture-fracture exchange is driven by the difference between the area-averaged pressures on the two fractures. The model distinguishes the total conductance, the reference area-normalized connectivity, and the area-normalized exchange coefficients entering the two fracture-continuity equations. Because the two fractures are defined on different radial supports, the normal response is formulated as a double-domain block system, and the short-fracture response is incorporated into the long-fracture main system through a Schur-complement feedback term. In the equal-length limit, the model degenerates to the existing equal-length intersecting-fracture model. Numerical analyses show that unequal fracture lengths can reshape P-wave velocity and attenuation spectra, but their effects depend jointly on fracture support, actual exchange capacity, and normal-response feedback. Under the short-fracture truncation protocol, increasing the length ratio breaks the equal-length geometric symmetry but simultaneously reduces the short-fracture compliance, fracture-density contribution, and total conductance. This leads to an overall increase in low-to-intermediate-frequency velocity and a weakening of intermediate-frequency FF-WIFF-related attenuation. The area-averaged pressure difference, actual exchange flux, and Schur feedback strength exhibit different frequency dependences, indicating that the pressure-driving term is not equivalent to macroscopic dissipation. Increasing the reference area-normalized connectivity shifts the FF-WIFF response to higher frequencies, whereas increasing fluid viscosity shifts the corresponding attenuation increment and Schur-feedback peaks to lower frequencies. Unequal lengths can also break the pressure-symmetry cancellation occurring in the equal-length case and reactivate the fracture-fracture pressure contrast. These results provide a theoretical basis for joint seismic rock-physics characterization of fracture-length contrast, hydraulic connectivity, and fluid effects in tight sandstone, shale, and carbonate reservoirs.

Key words: unequal-length intersecting fractures, rock-physics model, wave-induced fluid flow, FF-WIFF, Schur complement, velocity dispersion, seismic attenuation

摘要：

相交裂缝中的裂缝—裂缝波致流体流动(fracture-fracture wave-induced fluid flow，FF-WIFF)是流体饱和裂缝介质速度频散、地震衰减和水力连通性表征的重要机制。已有相交裂缝解析模型多假设两条裂缝等长，因而可利用共同支撑域和交换对称性对法向振动问题进行解耦；但天然裂缝网络中裂缝长度不一致更为常见，等长模型的对称/反对称分解不能直接适用。为此，本文在动态Biot孔隙弹性理论和稀疏裂缝散射框架下，建立非等长相交双裂缝的频率相关岩石物理模型。模型以两条裂缝面积平均压力差定义裂缝间总交换量，区分总导通系数、参考面积归一化连通性和进入各裂缝连续方程的面积归一化交换系数；针对两条裂缝径向支撑域不同导致的法向耦合问题，构建双定义域块系统，并用Schur补表征短裂缝法向响应对长裂缝主系统的反馈。等长极限下，模型可退化为已有等长相交裂缝模型。分析表明，非等长几何能够改变P波速度频散和衰减谱形，但其作用取决于几何支撑、实际交换能力和法向反馈路径的共同变化。在短裂缝截断方案下，长度比增大虽破坏等长几何对称性，但同时降低短裂缝柔度、短裂缝组裂缝密度贡献和总导通能力，使低—中频速度整体升高，并削弱中频FF-WIFF相关衰减。面积平均压力差、实际交换量和Schur反馈强度具有不同频率特征，说明压力驱动不能直接等同于宏观耗散强度。参考面积归一化连通性的增强会使FF-WIFF特征频率向高频迁移，流体黏度增大则使相关衰减增量和Schur反馈峰向低频移动。非等长几何还可破坏等长模型中的角度对称压力差抵消条件，重新激发裂缝间压力差。上述结果可为致密砂岩、页岩和碳酸盐岩储层中裂缝长度差异、水力连通性和流体性质的联合地震岩石物理表征提供理论依据。

关键词: 非等长相交裂缝, 岩石物理模型, 波致流体流动, FF-WIFF, Schur补, 速度频散, 地震衰减

CLC Number: 

• P618.13

• TE122.2