reservoir geomecanics

385 Effects of reservoir depletion
normal faulting. Modification of equation (4.45) for depletion in a laterally extensive
reservoir yields:
[S V − (P p − P p )]
= f (µ) (12.4)
[(S hmin − S hmin ) − (P p − P p )]
where
f (µ) = ( √ µ 2 + 1 + µ) 2
Simplifying this results in:
S V − P p
S hmin − P p
=
[
1 − S ]
hmin − P p
f (µ) −
S hmin − P p
P p
S hmin − P p
(12.5)
In areas where normal faults are in frictional equilibrium, the left-hand side of equation
(12.5) isequivalent to f (µ) such that,
f (µ) = f (µ) − S hmin − P p
f (µ) − P p
S hmin − P p S hmin − P p
S hmin − P p
f (µ) =− P p
S hmin − P p S hmin − P p
S hmin − P p
=− 1
P p f (µ)
Substituting A = S hmin /P p yields the stress path, A ∗ , which if exceeded, can lead
to production-induced normal faulting:
A ∗ 1
= 1 −
( √ (12.6)
µ 2 + 1 + µ) 2
For µ = 0.6, the theoretical stress path corresponding to normal faulting will be roughly
equal to 0.67. This corresponds to the horizontal dashed line in Figure 12.2 such that
stress paths in excess of 0.67 will be unstable. In other words, sufficient depletion will
eventually result in production induced faulting. Stress paths less than 0.67 never lead
to faulting, regardless of the amount of depletion. Hence, the fields shown above the
horizontal dashed line in Figure 12.2 are located in a normal faulting environments,
where sufficient depletion could eventually induce slip on pre-existing normal faults in
the reservoir.
This is illustrated in Figure 12.4a inatype of plot we refer to as reservoir space
because it expresses the evolution of the state of stress in a reservoir in terms of pore
pressure and the least principal stress. The vertical stress is assumed to remain constant
with depletion (for the reasons stated above). The value of the least principal stress
that corresponds to the vertical stress defines the horizontal line labeled S v .Inanormal
faulting environment, we can assess the potential normal faulting on pre-existing faults
simply by defining a failure line that corresponds to equation (4.45). The diagonal line