**Abstract**

[90] Verdon, J.P, Kendall, J-M, White, D.J., Angus, D.A., Fisher, Q.J. and Urbancic, T., 2010. Passive seismic monitoring of carbon dioxide storage at Weyburn. Leading

[91] Waldhauser, F., and Ellsworth, W. L., 2000, A Double-Difference Earthquake Loca‐ tion Algorithm: Method and Application to the Northern Hayward Fault, California:

[92] Walter, W.R. and Brune, J.N., 1993. Spectra of seismic radiation from a tensile crack.

[93] Warpinski, N., 2009. Microseismic Monitoring: Inside and Out. Journal of Petroleum

[94] Xuan, R., and Sava, P., 2009. Probabilistic micro-earthquake location for reservoir monitoring: SEG Houston International Exposition and Annual Meeting: 1637-1641.

[95] Zoback M. and Zoback M. 1980. State of stress in the conterminous United States.

Edge, 29, 200-206.

466 Effective and Sustainable Hydraulic Fracturing

Bull. Seis. Soc. Am., 90, 1353-1368.

J. Geophys. Res., 98: 4449-4459.

Journal of Geophysical Research 85, 6113–6156.

Technology, 61(11), 80-85.

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 200x200x120mm 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.

### **1. Introduction**

Hydraulic fracturing is a technique often used in subsurface geotechnical engineering for production stimulation in petroleum and geothermal reservoirs, for caving stimulation in the mining industry, and for stress measurements in the Earth's crust. Since the size and orienta‐ tion of the hydraulic fracture and the number of fractures induced by a given injection depend on potentially complicated conditions of rock mass structure and the stress state, they are often

© 2013 Dyskin et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

difficult to predict. This necessitates the development of methods for detecting the geometry and location of the hydraulic fracture(s) and/or monitoring the process of its propagation. A number of methods were proposed for this purpose (see review [1]). They include treating pressure response (e.g. [2, 3]), tracing the fracture fluid (e.g. [3]), microseismic mapping (e.g. [1, 4-8]), crosswell seismic detection (e.g. [9, 10]), vertical seismic profiling (e.g. [11, 12]), borehole overcoring [1], borehole cameras (e.g. [13]), surface tilts (e.g. [8, 14, 15]).

**2. Blue shift indicator**

ture propagation.

random arrival times {t<sup>k</sup>

localisation and purely random arrival times:

*n*

(r)} are

*M*

Consider a hydraulic fracture, which propagates emitting acoustic pulses from its process zone that is small compared to the fracture size R(t), Figure 1. We do not specify the particular shape of the fracture as long as it propagates in plane in all directions and its diameter and perimeter are proportional to the size, R. It is natural to assume that the hydraulic fracture is produced in quasi-static regime, that is the time intervals between successive steps of fracture propaga‐ tion are considerably larger than the time needed for the stress waves to traverse the process zone along the contour of the fracture and effect the interaction between the acoustic events. Similarly, it is natural to assume that the time step of fracture propagation is much larger than the time needed for the acoustic signal to reach the acoustic sensor such that one can regard the signal emitted at one step of fracture propagation as being received almost simultaneously.

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

http://dx.doi.org/10.5772/56448

469

**Figure 1.** Hydraulic fracture and acoustic events at its contour produced almost simultaneously during a step in frac‐

Suppose we have recorded a set of arrival times Θ={*t1, t2,.. tM*}, where M is the number of generated acoustic pulses. Then, according to [16], we can regard tk as a time shift with respect to zero and relate the Fourier transform exp(-iωtk) to it. We compute the 'spectrum' of arrival times by adding their Fourier transforms and calculate the energy the spectrum possess in the frequency range (0, Ω), where Ω is a certain frequency. The blue shift indicator is a measure of the difference between the energy associated with arrival times synchronised due to the

( ,,) ( ,) ( ,,) ( )

*r SM S M*

where the'energies' of the truncated spectrum (up to frequency Ω) of arrival times Θ and the

*S M* QW - W

*r*

S QW = (1)

The methods based on microseismic monitoring are attractive because they are capable of providing real-time information about the growth of the region that is impacted by stress and pore pressure changes that lead to the release of seismic energy during injection. Currently these methods are based on locating the microseismic events. Accurate locations of the sources require simultaneous, recording the events using multiple sensors together with accurate measurements of the wave propagation velocities in multiple directions in the rock mass.

In contrast, Pasternak and Dyskin [16] proposed a method of detecting the localised fracturing which potentially requires only one channel. The method is based on the notion that the propagation of a localised fracture process (e.g., the process zone of the hydraulic fracture) involves generation of microcracks from the contour of a propagating localised zone or a fracture. The microcrack generation is almost instantaneous as compared to the time of crack propagation since the interaction between the main fracture or localisation zone and the microcracks occurs with the speed of the stress waves. As a result the number of events (microcracks) generated at each step of fracture propagation should be proportional to the length of the contour and hence proportional to the radius of the propagating fracture. This dependence of the number of generated events on the fracture radius (the event coherence) leads to the blue shift (i.e. shift to higher frequencies) in the combined spectrum of the events as compared to the spectrum of randomly generated events. The blue shift can even be detected in the 'spectrum of arrival times' that is the Fourier transform of the time delays between the arriving signals.

Obviously single sensor data will never lead to event locations. Instead, the goal of the Blue Shift approach is to enable using a relatively inexpensive single sensor array in order to detect localization and, ultimately, to be able to infer something about the dimensionality of the leading edge of the fracture. We hope to distinguish among, for example: 1) height constrained (i.e. PKN) type growth where the length of the propagating leading edge is essentially fixed at the height of the reservoir, 2) quasi-radial growth where the length of the leading edge grows proportionally to the nominal radius, and 3) diffuse or network-type growth where the combined length of the fractures' leading edges grows more rapidly than proportionality to the nominal radius of the fractured zone.

In this paper we report the results of a first-stage laboratory test conducted in order to provide guidance to the ongoing development of the Blue Shift approach. The following section, Section 2 describes the essentials of this approach. Section 3 describes the experiments and the measurements and Section 4 shows the application of the blue shift indicator to analyse the recorded acoustic emission.
