**2. Hydraulic fracturing**

Numerical modeling of fracture systems has made significant advances and is being applied to attempt to assess the extent of these uncertainties and how they may affect the outcome of practical fracturing programs. Geophysical observations including both micro-seismic activ‐ ity and P- and S-wave velocity changes during and after stimulation are valuable tools to assist in verifying model predictions and development of a better overall understanding of the process of hydraulic fracturing on the field scale. Fundamental studies supported by lab‐

Given the widening application of hydraulic fracturing to situations where there is little pri‐ or experience (e.g., Enhanced Geothermal Systems (EGS), gas extraction from 'tight shales' by fracturing in essentially horizontal wellbores, etc.) development of a greater understand‐ ing of the mechanics of hydraulic fracturing in naturally fractured rock masses should be an industry-wide imperative. HF 2013 International Conference for Effective and Sustainable

This lecture will describe examples of some current attempts to address these uncertainties and gaps in understanding. And, it is hoped, it will stimulate discussion of how to achieve

The term 'rock' covers a wide variety of materials and widely different rheological properties often proximate to each other in the subsurface. Tectonic and gravitational forces, sustained over millions of years, have deformed and fractured the rock on many scales. These forces are transmitted in part through the solid skeleton of the rock, and in part through the fluids under pressure in the pore spaces. Long-term circulation through rock at high temperatures at depth involves dissolution and precipitation along the fluid pathways, producing changes in the

Rock in situ is 'pre-loaded' and in a state of changing equilibrium. Any engineering activity changes this equilibrium (see Appendix 1). Often the changes can be accommodated in stable

The rock mass is opaque. Although geophysics is making impressive advances in defining large structures such as faults and bedding planes, most of the features that influence the rock response to engineering activities remain hidden. Mining and civil engineering activities allow three-dimensional access to the underground and direct observation of smaller features such as fracture networks, but most of the newer engineering applications involve essentially onedimensional access by borehole. Rock engineering problems fall into the 'data –limited' category, as defined by Starfield and Cundall (1988), and strategies to address them must follow a different strategy than engineering problems where detailed and precise design

chemical composition of the fluids and modifying the overall fluid circulation.

more effective practical design of hydraulic fracturing treatments.

oratory investigations can also contribute significantly to improved understanding.

Hydraulic Fracturing is very timely!

48 Effective and Sustainable Hydraulic Fracturing

fashion, but serious instabilities can develop.

information is available.

**1. Introduction**

Hydraulic fracturing first was used successfully in the late 1940's to increase production from petroleum reservoirs (Howard and Fast, 1970). The technology has evolved since and is now a major, essential technique in oil and gas production. This and other impressive oil industry developments, such as directional drilling, have attracted interest in application of these technologies to a variety of other subsurface engineering operations. Enhanced Geothermal Energy (EGS) is a notable example. Geothermal Energy is a huge resource. Commenting on the EGS resource in the USA, Tester et al. (2005), state:

<sup>&</sup>quot;….we have estimated the total EGS resource base to be more than 13 million exajoules (EJ)1 . Using reasonable assumptions regarding how heat would be mined from stimulated EGS reservoirs, we also estimated the extractable portion to exceed 200,000 EJ or about 2,000 times the annual consumption of primary energy in the United States in 2005. With technology improvements, the economically extractable amount of useful energy could increase by a factor of 10 or more, thus making EGS sustainable for centuries." 2

<sup>1 1</sup> exajoule =1018 joules = 1018 watt.seconds.

<sup>2</sup> Future of Geothermal Energy (2005) Synopsis and Executive Summaryp.1-4 (2).

"At this point, the main constraint is creating sufficient connectivity within the injection and production well system in the stimulated region of the EGS reservoir to allow for high per-well production rates without reducing reservoir life by rapid cooling." 3

But would the crack continue to extend and lead to macroscopic failure? To address this question, Griffith invoked the *Theorem of Minimum Potential Energy,* which may be stated as "The stable equilibrium state of a system is that for which the potential energy of the system is a minimum." For the particular application of this theorem to brittle rupture, Griffith added the statement*,* "The equilibrium position, if equilibrium is possible, must be one in which rupture of the solid has occurred, if the system can pass from the unbroken to the broken

Fractures and Fracturing: Hydraulic Fracturing in Jointed Rock

http://dx.doi.org/10.5772/56366

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Griffith's classical work has provided the foundation for the field of "Fracture Mechanics" [Knott (1973); Anderson (2005)] responsible for major continuing advances in the development

Since we will make reference later to this specific definition by Griffith, it is useful to re-state

"The stable equilibrium state of a system is that for which the potential energy of the system is a minimum. The equilibrium position, if equilibrium is possible, must be one in which rupture of the solid has occurred, if the system can pass from the unbroken to the broken condition by a process involving a continuous decrease of potential energy."

Although much of classical Fracture Mechanics has emphasized applications to problems of Linearly Elastic Fracture Mechanics (LEFM) it is important to recognize that the theorem of

As used classically in petroleum engineering, hydraulic fracturing involves sealing off an interval of a borehole at depth in an oil or gas bearing horizon, subjecting the interval to increasing fluid pressure until a fracture is generated, injecting some form of granular proppant into the fracture as it extends a considerable distance from the borehole into the

5 Hydraulic fractures generated in classical petroleum applications typically extend (2b) of the order of 25m ~ 50m from a wellbore. The fracture aperture (2a) at the wellbore then will be typically of the order of 0.01 m. Thus, the tensile stress

6 In his second paper, Griffith (1924), demonstrated that tensile stresses also developed around similar cracks loaded in compression, provided the cracks were inclined to the direction of the major principal (compressive) stress.(He also assumed that the cracks did not close under the compression.) For the optimum crack inclination, an applied compressive stress of eight times the magnitude of the tensile strength was required to develop a tensile stress on the crack boundary (close to, but not at the apex of the crack) equal to the limiting value in the tensile test. He concluded that the uniaxial compressive strength of a brittle material should be eight times greater than the tensile strength. Interestingly, he did not invoke his second (minimum potential energy) criterion. It was later determined that although a tensile crack could initiate in a compressive stress regime as predicted by Griffith (1924), the crack was stable (i.e., did not satisfy the minimum potential energy criterion). The compressive/tensile strength ratio is greater than 8 (see Hoek and Bieniawski, 1966).

condition by a process involving a continuous decrease of potential energy."6

of high-performance fabricated materials.

**4. Theorem of minimum potential energy**

minimum potential applies equally to inelastic problems.

**5. Mechanics of hydraulic fracturing**

concentration at the tip is very high of the order of 103.

it here.

Field experiments to extract geothermal energy from rock at depth by hydraulic fracturing were started in 1970 by scientists of the Los Alamos National Laboratory, USA. Two boreholes were drilled into crystalline rock (one 2.8 km deep, rock temperature 195°C; the other 3.5 km rock, 235°C) at Fenton Hill, New Mexico. Hydraulic fracturing was used to develop fractures from the boreholes in order to create a fractured region through which water could be circulated to extract heat from the rock. The experiment was terminated in 1992. Commenting on what was learned from the Fenton Hill study, Duchane and Brown (2002) note:

"The idea that hydraulic pressure causes competent rock to rupture and create a disc-shaped fracture was refuted by the seismic evidence. Instead, it came to be understood that hydraulic stimulation leads to the opening of existing natural joints that have been sealed by secondary mineralization. Over the years additional evidence has been generated to show that the joints oriented roughly orthogonal to the direction of the least principal stress open first, but that as the hydraulic pressure is increased, additional joints open."

This is an early indication that pre-existing fractures mass significantly affect how hydraulic fractures propagate in a rock mass.
