Transient, Dynamic Response of a Reservoir Crack Against an Artificial Hydraulic Stimulation

基于动态弹性线性理论和线性裂缝力学，分析了人工水力压裂作用下地下储层裂缝的瞬态弹性动态响应。在拉普拉斯变换和傅立叶变换的像空间中，问题被简化为求解一个奇异积分方程，其中奇异积分方程的主导项由有限部分积分定义，其中奇异积分方程与被困在裂缝中的流体运动耦合。在此基础上，详细研究了声发射三轴图法表征地下裂纹的方法。结论总结如下：1。对于衰减介质，三轴矢图法根据观测站相对于储层裂缝的位置，将声发射源映射为裂缝外围内部的一个点或裂缝尖端的一个点。在周向位移谱中出现的峰值频率对应于裂纹表面自身振动的最低对称模态的固有频率。因此，峰值频率的取值仅取决于裂缝的大小和裂缝的刚度，而与观测站和介质的衰减强度无关。数值结果表明，受拉型裂纹引起的弹性波能量明显小于受剪切型裂纹引起的弹性波能量。这是由于两个裂纹表面之间的摩擦引起的裂纹破坏是剪切型裂纹产生弹性波的主要原因，而不是断裂韧性。这一理论证据通过对大型岩石试件（10mx10mx10mx）水力压裂过程中获得的声发射实验数据进行网格法检验得到验证。

Transient, elastic, dynamic response was analyzed for a subsurface reservoir crack subjected to an artificial hydraulic stimulation, based on linear theory of dynamic elasticity and linear fracture mechanics. In the image spaces of Laplace and Fourier transforms, the problem was found to be reduced to solving a singular integral equation with a dominant term defined by finite part integral, where the singular integral equation was coupled with a motion of fluid trapped in the crack. Based on the analysis, characterization of a subsurface crack by the triaxial hodogram method using acoustic emission was examined in detail. The conclusion are summarized as follows :1. For a attenuating medium, the tri-axial hodogram method maps an AE source as a point inside inside the crack periphery or one of the crack tips, depending on the location of the observation station relative to the reservoir crack.2. The peak frequency which appears in the spectrum of the circumferential displacement corresponds to the natural frequency of the lowest, symmetric mode of the oscillation of the crack surface it self. Therefore, the value of the peak frequency depends only on the crack size and the crack stiffness and independent of the observation station and the intensity of attenuation of the medium.3. The energy of the elastic waves due to a tensile mode crack was found out to numerically to be significantly smaller than that due to a shear mode crack. This is due to the fact that the failure of asperities caused by rubbing between the two crack surfaces is primary cause of the elastic waves from a shear mode crack, not the fracture toughness. This theoretical evidence was verified by the examination, using the so-called grid method, of the experimental AE data obtained during hydraulic fracturing conducted in a huge, rock specimen (10mx10mx10mx).