reservoir geomecanics

280 Reservoir geomechanics
Methods for approximating S hmin in normal faulting areas
In Chapter 7 we discussed how mini-frac and leak-off tests can be used to accurately
determine the magnitude of the least principal stress, S hmin . Knowledge of the least principal
stress is not only a critical step in determining the full stress tensor (as discussed
at length in Chapters 7 and 8), it also provides important information for drilling stable
wells. During drilling, mud weights must be kept below S hmin to prevent accidental
hydraulic fracturing and lost circulation, but above both the pore pressure (to avoid taking
a kick) and the minimum mud weight required to prevent excessive wellbore failure
(i.e. the collapse pressure) as discussed in Chapter 10. Because of this, a number of
empirical techniques have been proposed for estimating the least principal stress in the
absence of direct measurements. This issue is particularly important in normal faulting
areas (such as the Gulf of Mexico) where overpressure is present at depth. As illustrated
in Figure 1.4d, in overpressured normal faulting regions, there can be extremely small
differences between P p and S hmin , which define the mud window, orthe safe range of
pressures to use while drilling.
In the sections below, the techniques summarized in Table 9.1 for estimating the
least principal stress (or least principal effective stress) in the Gulf of Mexico are
briefly discussed.
In their classic paper on hydraulic fracturing, Hubbert and Willis (1957) proposed
an empirical expression for the magnitude of the least principal stress as a function of
depth in the Gulf of Mexico region,
S hmin = 0.3(S v − P p ) + P p (9.1)
where the constant 0.3 was empirically determined from the analysis of hydraulic fracturing
data. The scientific basis for this constant can be understood in terms of frictional
faulting theory (Zoback and Healy 1984), as equation (4.45) produces essentially the
same equation for a coefficient of friction of 0.6. However, as additional data became
available for the offshore Gulf of Mexico area, Hubbert and Willis later adopted an
empirical coefficient of 0.5 indicating that observed values for the least principal stress
in the Gulf of Mexico generally exceed the values predicted using equation (4.45) with
a coefficient of friction of 0.6.
Matthews and Kelly (1967) proposed a similar relation for the fracture pressure,
or the magnitude of the pore pressure at which circulation is lost. As this requires
propagation of a hydraulic fracture away from the wellbore, this value is essentially
equivalent to the least principal stress. Thus, they proposed
S hmin = K i (S v − P p ) + P p (9.2)
where K i is a function of depth, z. Using this relation, functions for the Louisiana gulf
coast and south Texas gulf coast region were proposed that varied in a non-linear fashion