Page 186 - Applied Petroleum Geomechanics

180 Applied Petroleum Geomechanics

basins. When the measured data are not available, the depletion-induced
minimum stress reduction may be estimated based on the assumption of
the minimum horizontal stress in the uniaxial strain boundary condition in
the following equation (Aadnoy, 1991; Engelder and Fischer, 1994):

1 2n

Ds h ¼ a Dp p (5.24)
1 n
where Ds h and Dp p are the incremental minimum stress and reservoir pres-
sure, respectively. It should be noted that Poisson’s ratio may also change
after depletion. From Eq. (5.24) the depletion-induced stress path can be
expressed as:
1 2n

c ¼ a (5.25)
1 n
where c ¼ Ds h /Dp p . It can be seen that the stress path is dependent on Pois-
son’s ratio or the lithology.
After depletion the minimum horizontal stress may also be estimated
from the following equation, if the pore pressure after depletion is known:
s hd ¼ kðs V ap pd Þþ ap pd (5.26)

where s hd and p pd are the minimum horizontal stress and the reservoir pres-
sure after depletion, respectively; k is a parameter that can be obtained from
the measured data, such as DFIT.
Several attempts have been made to experimentally predict the in situ
stress changes with depletion and injection (Teufel et al., 1991; Rafieepour
et al., 2017). However, laboratory-measured stress paths under uniaxial
strain condition have large discrepancies with field stress measurements
from hydraulic fracturing tests. For example, the stress path measurements
via hydraulic fracturing stimulation in the Ekofisk Field (Teufel et al., 1991)
are very different from laboratory-derived stress paths under uniaxial strain
conditions (c z 0.8 from the field and c ¼ 0.5 e 0.6 from the lab). These
discrepancies might be due to several factors such as scale effects, stress
arching, and faulting contributions (Addis, 1997; Holt, 1999). Holt (1999)
argued that the damaged core and scale effects are two sources of dis-
crepancies between the lab and field measurements. Another important
parameter contributing the difference between the field and lab measure-
ments might be the fact that the dominant boundary condition in the
reservoir is not the generalized uniaxial strain. Experimental results
(Rafieepour et al., 2017) show that the changes of stress paths are larger for