Dynamic Response of a Fluid-filled 3-D Crack and its Application to Characterization of Geothermal Reservoir Cracks

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The dynamic response of a fluid-filled penny shaped crack, which was a typical example of 3-D cracks, was analyzed in detail in the framework of the theory of elasto-dynamics. It was revealed that the response was divided into tree types (Type I, II and III). Type I is the group that does not have any clear peaks in the power spectrum of the oscillation of the crack surface, and Type III is the group that has very clear peaks of fundamental modes in the power spectrum. Type II is in between Type I and Type III. Type III appears under the condition that attenuation of the wave traveling along the crack surfaces is weak and thus standing wave can be easily formed due to the reflection of the elastic wave at the crack periphery. Since Type III is far more informative than the other two and thus is preferable for the estimation of the crack parameters, it can be recommended that the reservoir pressure should be kept as higher as possible during the field experiments of active acoustic techniques.A new method is proposed for estimating the crack size, aperture and interfacial stiffness which is caused due to the asperity contact between the two crack surfaces. The method compares the frequencies of the fundamental modes of the standing wave, that are theoretically determined by the analyses just mentioned above, with the peak frequencies of the elastic waves observed during the field experiments such as hydraulic fracturing. The method was successfully applied to the field data obtained during hydraulic fracturing conducted in Hijiori and Ogachi HDR/HWR fields. Crack size and aperture in Hijiori field were estimated to be 5-11m and 1-44mm, respectively. Those in the Ogachi field are 4-28n and 10-22mm.