Page 307 - Reservoir Geomechanics

284 Reservoir geomechanics

the measured stress values by 1400 psi at higher stress levels. Hence, the line fitting the
data in Figure 9.8b also incorporates a depth-varying tectonic stress.
While using empirically determined Poisson’s ratios of tectonic stress to characterize
stress magnitudes in a given region may have some local usefulness, such methods
clearly have little or no predictive value. In fact, the data shown in Figure 9.8 are part of
the same data set presented in Figure 9.5 for the Travis Peak formation where it was seen
that frictional faulting theory (equation 4.45) does an excellent job of predicting the
magnitude of the least principal stress – without empirically determining an effective
Poisson’s ratio and tectionic stress.
With respect to the Gulf of Mexico, to fit the deep water stress magnitude data

ν
presented in Figure 9.7b with a model, ν would need to range from 0.2 (to fit
1 − ν
the lowest values of the least principal stress) to 0.47 (to fit the highest). As was the case
just described for the Travis Peak, however, these values do not match values measured
with sonic logs, but represent effective values of ν, known only after the measurements
were made.
Breckels and Van Eekelen (1981) proposed a number of empirical relations between
the magnitude of the least principal stress and depth (in units of psi and feet) for various
regions around the world. For the Gulf of Mexico region, they argue that if pore pressure
is hydrostatic
S hmin = 0.197z 1.145 (9.4)

fits the available data and for depths z < 11,500 ft and for z > 11,500 ft, they argue for
the following
S hmin = 0.167z − 4596 (9.5)

Implicitly, this assumes a specific increase in the rate of pore pressure change with
depth as well as an average overburden density. To include overpressure, they add a
term equal to 0.46 (P p −P h )to each equation, where P h is hydrostatic pore pressure.
Zoback and Healy (1984) analyzed in situ stress and fluid pressure data from the Gulf
Coast in an attempt to show that, as illustrated above for the Nevada test site, Travis
Peak formation in east Texas and the Ekofisk and Valhall crests, the state of stress in
the Gulf of Mexico is also controlled by the frictional strength of the ubiquitous active
normal faults in the region. We rewrite equation (4.45)to compare it with equations (9.1)
and (9.2):

S hmin = 0.32(S v − P p ) + P p (9.6)

Compilations of data on the magnitude of the least principal stress in the Gulf of
Mexico show that at depths less than about 1.5 km (where pore pressure is hydro-
static), S hmin is about 60% of the vertical stress (as previously discussed in context of
equation 4.45). In other words, equation (9.6) (or 4.45)is essentially identical to the