Page 141 - Reservoir Geomechanics

124 Reservoir geomechanics

Because of his extensive research on friction (Coulomb 1773), equation (4.39)is
sometimes referred to as the Coulomb criterion. One can define the Coulomb failure
function (CFF) as
(4.40)
CFF = τ − µσ n
When the Coulomb failure function is negative, a fault is stable as the shear stress is
insufficient to overcome the resistance to sliding, µσ n .However, as CFF approaches
zero, frictional sliding will occur on a pre-existing fault plane as there is sufficient shear
stress to overcome the effective normal stress on the fault plane. Again, the CFF in this
manner presupposes that the cohesive strength of a fault is very small compared to the
shear and normal stresses acting upon it. As will be illustrated below, this assumption
appears to be quite reasonable.
As mentioned above, equation (4.39) predicts that raising pore pressure would tend
to de-stabilize faults and encourage slip to take place by raising the ratio of shear to
normal stress on any pre-existing fault. While there have been many examples of seis-
micity apparently induced by fluid injection in oil fields (see the review by Grasso
1992), two experiments in the 1960s and 1970s in Colorado first drew attention to this
phenomenon (Figure 4.22) and provided implicit support for the applicability of Amon-
tons’ law/Coulomb failure to crustal faulting. A consulting geologist in Denver named
David Evans pointed out an apparent correlation between the number of earthquakes
occurring at the Rocky Mountain Arsenal and the volume of waste fluid being injected
into the fractured basement rocks at 3.7 km depth. Subsequently, Healy, Rubey et al.
(1968) showed there to be a close correlation between the downhole pressure during
injection and the number of earthquakes (Figure 4.22a). The focal mechanisms of the
earthquakes were later shown to be normal faulting events. This enabled Zoback and
Healy (1984)to demonstrate that the magnitudes of the vertical stress, least principal
stress and pore pressure during injection were such that equation (4.39)was satisfied
and induced seismicity was to be expected for a coefficient of friction of about 0.6 (see
below). A similar study was carried out only a few years later at Rangeley, Colorado
(Figure 4.22b) where water was being injected at high pressure in an attempt to improve
production from the extremely low permeability Weber sandstone (Raleigh, Healy
et al. 1976). In this case, it could be seen that a downhole pressure of 3700 psi (25.5
MPa) was required to induce slip on pre-existing faults in the area, as predicted by
equation (4.39) (Zoback and Healy 1984).
As mentioned above, friction is a material property of a fault and Byerlee (1978)
summarized numerous laboratory experiments on a wide variety of faults in different
types of rock. He considered natural faults in rock, faults induced in triaxial compression
tests and artificial faults (i.e. sawcuts in rock) of different roughness. His work (and that
of many others) is summarized in Figure 4.23 (modified from Byerlee 1978). Note that
for an extremely wide variety of rock types, Byerlee showed that at elevated effective
normal stress (≥∼10 MPa), friction on faults is independent of surface roughness,