Blue Shift in the Spectrum of Arrival Times of Acoustic Signals Emitted during Laboratory Hydraulic Fracturing

Abstract

We discuss a method of detecting localised fracturing that potentially requires only one channel. The method is based on the notion that the fracture propagation involves generation of acoustic events from its contour. It is proposed that the number of events microcracks generated at each step of fracture propagation could be proportional to the fracture size to a certain power called the localisation exponent. This dependence of the number of generated events on the fracture size the event coherence leads to a shift to higher frequency the blue shift in the combined spectrum of the events as compared to the spectrum of randomly generated events. This concept was applied to the results of a laboratory test in which hydraulic fracture was driven by injecting glycerine into a x x mm block of polycrystalline gabbro. We show that there is indeed a blue shift in the spectrum of the arrival times at any one sensor that seems to correspond with the growth of a localized hydraulic fracture. The localisation exponent is able to distinguish between the cases of the fracture contour length roughly proportional to, and more slowly than proportional to, the nominal fracture radius.