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

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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).