Page 25 - Reservoir Geomechanics

10 Reservoir geomechanics

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clastic sedimentary rock has an average density of about 2.3 g/cm which corresponds
to a porosity of about 15%. This results in a vertical principal stress that increases
with depth at a rate of 23 MPa/km (or conveniently, ∼1 psi/ft). Correspondingly, the
magnitudes of the two horizontal principal stresses increase with depth. Some of the
practical problems associated with the computation of S v using equations (1.5) and (1.6)
relate to the facts that density logs frequently measure anomalously low density when
the well is rugose and density is often not measured all the way up to the seafloor when
drilling offshore. This is illustrated by the density log in Figure 1.3. The density log
(top figure) is somewhat noisy and no data are available between the seafloor (1000 ft
below the platform) and 3600 ft. This makes it necessary to extrapolate densities to the
seafloor where the density is quite low. Integration of the density log using equation (1.6)
yields the overburden stress as a function of depth (middle figure). The rate at which
the overburden stress gradient increases with depth is shown in the lower figure. Note
that because of the water depth and low densities immediately below the seafloor (or
mud line), the overburden stress gradient is only 0.9 psi/ft at a depth of 14,000 ft, even
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though density exceeds 2.3 g/cm below 8000 ft.
According to the Anderson classification scheme, the horizontal principal stresses
may be less than, or greater than, the vertical stress, depending on the geological setting.
The relative magnitudes of the principal stresses are simply related to the faulting style
currently active in a region. As illustrated in Figure 1.2, the vertical stress dominates
in normal faulting regions (S 1 = S v ), and fault slip occurs when the least horizontal
principal stress (S hmin ) reaches a sufficiently low value at any given depth depending on
S v and pore pressure (Chapter 4). Conversely, when both horizontal stresses exceed the
vertical stress (S 3 = S v ) crustal shortening is accommodated through reverse faulting
when the maximum horizontal principal stress (S Hmax )is sufficiently larger than the
vertical stress. Strike-slip faulting represents an intermediate stress state (S 2 = S v ),
where the maximum horizontal stress is greater than the vertical stress and the minimum
horizontal stress is less (S Hmax ≥ S v ≥ S hmin ). In this case, faulting occurs when the
difference between S Hmax and S hmin is sufficiently large. The angle between the principal
stress directions and the strike and dip of active faults is discussed in Chapter 5.
Third, an implicit aspect of Andersonian faulting theory is that the magnitudes of the
three principal stresses at any depth are limited by the strength of the crust at depth. An
obvious upper limit for stress magnitudes might be the compressive strength of rock.
In fact, a more realistic upper limit for the magnitudes of principal stresses in situ is the
frictional strength of previously faulted rock, as essentially all rocks at depth contain
pre-existing fractures and faults (Chapter 4).
Of critical interest in this book is the current state of stress (or perhaps that which
existed at the onset of reservoir exploitation) because that is the stress state applicable in
the problems of reservoir geomechanics considered in this book. Hence, a point about
Figure 1.2 worth emphasizing is that the figure shows the relationship between states of
stress and the style of faulting consistent with that stress state. In some parts of the world