(in accord with equations 4.45, 4.46 and 4.47) as pore pressure changes (as illustrated).
But this is not true of the ratios (or differences) in the absolute stress magnitudes (as shown in Figure 4.29) such that the higher the pore pressure, the lower the principal stress differences. At extremely high pore pressure, relatively small stress perturbations are sufficient to change the style of faulting from one stress regime to the other (for example, to go from normal faulting to reverse faulting). This is dramatically different from the case in which pore pressure is hydrostatic. The second point to note is that perturbations of pore pressure associated with depletion (or injection) will also affect stress magnitudes through the types of poroelastic effects discussed in Chapter 3. Hence, the size and position of the Mohr circle is affected by the change in pore pressure. This can have an important influence on reservoir behavior, especially in normal faulting regions (Chapter 12).
R E V E R S E FAU LT I N G
N F S S
Sv 3
2
1
70 MPa (~3 km depth)
70 MPa (~3 km depth)
Sv
3)
2)
1) a .
SHmaxSHmax
Shmin
Shmin
b.
H Y D RO S TAT I C P O R E P R E S S U R E
H I G H P O R E P R E S S U R E H Y D RO S TAT I C P O R E P R E S S U R E
shmin
shmin sv
sv
sv sHmax
sHmax
Figure 4.31. Polygons which define possible stress magnitudes at a given depth are shown for a depth of 3 km for (a) hydrostatic pore pressure and (b) pore pressure equal to 80% of the overburden. After Zoback, Mastin et al. (1987) and Moos and Zoback (1990).
the stress polygon. If the state of stress is in frictional failure equilibrium, the state of stress falls on the outer periphery of the polygon, depending, of course, on whether the stress state is normal, strike-slip or reverse faulting. As demonstrated in Chapter 9, in situ stress measurements from sedimentary basins around the world confirm the fact that the differences in stress magnitudes are frequently limited by the frictional strength of pre-existing faults that are well-oriented for slip in the current stress field and coefficients of friction of 0.6–0.7 seem to work quite well. In terms of Figure 4.31, this means that the stress state in situ is often found to lie around the periphery of the figure.
Figure 4.31b again illustrates the fact that elevated pore pressure reduces the differ- ence between principal stresses at depth as shown previously in Figure 4.30. When pore pressure is elevated, all three principal stresses are close in magnitude to the vertical stress and relatively small changes in the stress field can cause a transition from one style of faulting to another. Moos and Zoback (1993) hypothesize that because of ele- vated pore pressure at depth in the vicinity of Long Valley caldera, the style of faulting goes from NF/SS faulting on one side of the caldera to RF/SS faulting on the other side as the direction of the horizontal principal stresses change.
The stress polygon shown in Figure 4.31a permits a very wide range of stress values at depth and would not seem to be of much practical use in limiting stress magnitudes.
However, as extended leak-off tests or hydraulic fracturing tests are often available to provide a good estimate of the least principal stress (Chapter 6), the polygon is useful for estimating the possible range of values of SHmax. As noted above, we will illustrate in Chapters 7 and 8 that if one also has information about the existence of either compres- sive or tensile wellbore failures, one can often put relatively narrow (and hence, useful) bounds on possible stress states at depth. In other words, by combining the constraints on stress magnitudes obtained from the frictional strength of the crust, measurements of the least principal stress from leak-off tests and observations of wellbore failure place strong constraints on the in situ stress state (Chapters 6–8) which can be used to address the range of problems encountered in reservoir geomechanics addressed in Chapters 10–12.
In this chapter I consider a number of topics related to faults and fractures in rock.
Faults and fractures exist in essentially all rocks at depth and can have a profound effect on fluid transport, mechanical properties and wellbore stability. As discussed in Chapter 4 (and later demonstrated through a number of case studies), frictional slip along pre-existing fractures and faults limits in situ stress magnitudes in a predictable – and useful – way.
To begin this chapter, I distinguish between opening mode (Mode I) fractures and faults, and briefly discuss the importance of faults in influencing fluid flow in low per- meability rock. The influence of faults on permeability is discussed at length in Chapter 11, as well as the sealing (or leakage) potential of reservoir-bounding faults. The man- ner in which slip along weak bedding planes can affect wellbore stability is discussed in Chapter 10. I briefly discuss wellbore imaging devices as it is now routine to use such devices to map fractures and faults in reservoirs, and then discuss common techniques for representing fracture orientation data, including stereonets and three-dimensional Mohr diagrams, when the state of stress is known. Faulting in three dimensions is revisited in Chapter 11. I conclude this chapter by briefly discussing earthquake focal mechanisms and their use in determining approximate stress orientations and relative stress magnitudes.
There are a number of books and collections of scientific papers on the subject of fractures and faults in rock. Of particular note are the compilations by Long et al.
(1996); Jones, Fisher et al. (1998) Hoak, Klawitter et al. (1997) and the collec- tions of papers on the mechanical involvement of fluids in faulting (Hickman, Sibson et al. 1995; Haneberg, Mozley et al. 1999; Faybishenko, Witherspoon et al. 2000;
Vigneresse 2001; Jones, Fisher et al. 1998; Davies and Handschy 2003). Hence, the purpose of this chapter is not to provide a comprehensive review of this subject. Rather, my goal is to cover a number of basic principles about the nature of fractures and faults at depth and provide a basis for concepts discussed in subsequent chapters. For reasons that will soon be apparent, we will be principally concerned with faults; planar discontinuities associated with shear deformation. As the topic of this book is geome- chanics, I consider only mechanical discontinuities at depth and not those associated with chemical processes – dissolution features, stylolites, etc. – which are encountered 140
Mode I
Normal
Strike-slip
Reverse
Map view Stereonet Mohr circle Cross-section Focal mechanism
T
P B
P P
B
B T
T sv
sv
sv
sHmax shmin
sHmax shmin
2b t
t
t
2b 2b t
shmin sHmax
m = 0.6
SS/RF SS/NF
SS SHmax
Shmin
SHmax Shmin
SHmax Shmin
SHmax Shmin
X shmin
shmin sv
b
sHmax
sv
a .
d . c . b .
Figure 5.1. Schematic illustration of the orientation of various types of fractures and faults with respect to the orientation of SHmaxand Shmin. (a) Mode I fractures and joints are expected to form parallel to SHmaxand normal to Shmin. (b) Conjugate strike-slip faults are expected to be vertical and strike∼30◦from the direction of SHmax(forµ∼0.6). (c) Reverse faults are expected to dip∼30◦ (forµ∼0.6) and strike normal to the direction of SHmax. (d) Conjugate normal faults are expected to dip∼60◦(forµ∼0.6) and strike parallel to the direction of SHmax. Because fractures and faults are introduced during multiple deformational episodes (depending on the age and geologic history of the formation) it is common for formations to contain numerous fractures at a variety of orientations.
in carbonate rocks, although such features may play a role in localizing subsequent shear deformation.
The relationship between the in situ state of stress and the orientation of hydraulically conductive fractures is frequently viewed in the context of Mode I fractures – extensional fractures oriented perpendicular to the least principal stress (Secor 1965; du Rouchet 1981; Nur and Walder 1990). There are a number of excellent papers on joints and Mode I fractures in rock (see the review by Pollard and Aydin 1988) and a number of papers on the application of the theory of fracture mechanics to rock (including utilizing shear fracture Modes 2 and 3 representations of faults) is presented by Atkinson (1987).
As illustrated in Figure 5.1a, if the least principal stress is Shmin(as is true in normal and strike-slip faulting regimes), Mode I fractures would be expected to form in the
SHmax−Sv plane. If such fractures were to form in the current stress field and have an appreciable effect on fluid flow in otherwise low permeability reservoirs, it would result in a simple relationship between fracture orientation, stress orientation and permeability anisotropy. Moreover, the simplistic cartoon shown in Figure 5.1a has straightforward implications for using geophysical techniques such as seismic velocity anisotropy, shear-wave splitting, and amplitude versus offset (AVO) to identify in situ directions of permeability anisotropy (e.g. Crampin 1985; Winterstein and Meadows 1995). The subject of the relationships among freacture orientation, stress orientation and shear velocity will be revisited at the end of Chapter 8.