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

基于线性动弹性理论和线性断裂力学，分析了地下储层裂缝在人工压裂作用下的瞬态弹性动力响应。在拉普拉斯和傅立叶变换的像空间中，问题被归结为求解一个奇异积分方程，该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裂纹中流体的运动相耦合。在此基础上，利用声发射三轴矢端图方法对亚表面裂纹进行了详细的表征。主要结论如下：1.对于衰减介质，三轴速端图方法将AE源映射为裂纹周边内部的一个点或裂纹尖端之一，这取决于观察站相对于储层裂纹的位置。出现在周向位移频谱中的峰值频率对应于裂纹表面自身振动的最低对称模式的固有频率。因此，峰值频率的大小只取决于裂纹尺寸和裂纹刚度，而与观测台站和介质衰减强度无关.由于拉伸模式裂纹的弹性波的能量被发现，数值上是显着小于由于剪切模式裂纹。这是由于两个裂纹表面之间的摩擦引起的凹凸体的失效是剪切型裂纹的弹性波的主要原因，而不是断裂韧性。这一理论证据得到了验证的检查，使用所谓的网格方法，在一个巨大的，岩石标本（10mx10mx10mx）进行水力压裂过程中获得的实验AE数据。

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).