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Use of Geothermal Resources: Environmental Considerations 233

where P is the pore pressure. The line labeled as P = pore pressure defines the stress condition
p
required for failure of unfractured rock in which the pore pressure is equivalent to the hydrostatic
pressure.
Pore water also affects frictional strength through chemical mechanisms. At the molecular level,
ionic interactions between polar water molecules and the mineral framework, as well as interac-
tions between certain solute species (such as acids) and the crystal lattice, result in relatively rapid
rearrangement of bonds. This can weaken the rock at fracture tips, allowing crack growth at stress
values below those that would otherwise be necessary for a fracture to propagate.
The curves in Figure 12.3 are specific to the rock that was studied (granite) and the stress condi-
tions (vertical maximum principal stress). Other rock types, or granites in different settings with
different geological histories will have curves that are different from those depicted. Nevertheless,
the relationship to stress and the relative locations of the curves will be similar for all rocks.
The general nature of these relationships provides insight into the factors that determine the condi-
tions under which failure of an intact rock, or of a fault or fracture may occur. Specifically, it is obvi-
ous that the large number of variables that influence failure (fracture and fault orientation, fracture
and fault properties such as frictional strength, pore pressure, stress), and the difficulty of obtaining
detailed descriptions of these variables several kilometers in the subsurface precludes the ability to
precisely predict the conditions under which failure, and hence seismic activity will occur.
Predicting the magnitude and manner of the energy release, and hence whether or not a felt
seismic event will occur, is just as problematic. The energy release and the nature of the movement
associated with rock failure is a direct function of the size of the area over which a fracture or fault
slips. This is a reasonably intuitive relationship—if the unfractured rock in Figure 12.3 is subjected
to a stress of 300 MPa while it is under pressure equivalent to a depth of 2 kilometers, it will fail
unequivocally. If it fails by forming a set of 1000 fractures, each with 0.1 cm in surface area with
2
equal movement on each one, the collective movement could amount to a slip of 100 cm and yet the
sample would exhibit very little movement. If instruments were monitoring the sample, a swarm
of microseismic events would be detected. If, on the other hand, only one fracture formed, but the
same total movement had to be accommodated, which is a slip of 100 cm, a much more obvious
seismic event would be recorded.
A conclusion that implicitly develops from this discussion of the mechanics of rock failure is
that it will be difficult to precisely predict where and when seismic activity will occur and what its
magnitude will be. However, several factors specific to geothermal projects allow forecasts to be
made with some confidence regarding potential seismic activity and risk.

seismic acTiviTy associaTed wiTh GeoThermal projecTs
As noted above, seismic activity has been associated with injection of cool water into hot geother-
mal reservoirs, extraction of fluid from reservoirs, and high-pressure injection of fluid to enhance
reservoir permeability. With the basic mechanics of rock failure as background, each of these is
considered in the following discussion.

seismicity associated with Injection of cool water
Most minerals respond to heating by expanding. The extent of expansion depends on the mineral
structure. Laboratory measurements of the change in molar volume as a function of temperature
allow determination of the volumetric coefficient of thermal expansion, α , which is defined as
V
α V = (ΔV/V )/ΔT, (12.4)
0

where ΔV is the change in volume from a reference state, V , over the temperature interval ΔT.
0
Table 12.2 lists the volumetric coefficient of thermal expansion for the potassium feldspars sanidine
and microcline and the sodium feldspars low- and high-albite. These minerals are among the most