reservoir geomecanics

292 Reservoir geomechanics
A few more comments about the bilateral constraint
The section above that discussed empirical methods for estimating stress magnitudes at
depth focused on normal faulting areas and the determination of the minimum principal
stress. This is principally because of the need of drillers to estimate permissible mud
weights during drilling – an issue that is most important in normal faulting areas where
S hmin has the smallest values. In point of fact, techniques such as the bilateral constraint
(equation 9.3) are used more broadly for estimating stress magnitude at depth used with
tectonic stress added empirically to match measured values when available. So what
is wrong with using the bilateral constraint for predicting the least principal stress at
depth? First, diagenesis occurs over geologic time and stresses in the earth, originating
from a variety of tectonic processes (as summarized earlier in this chapter), will act
on rock to the degree that the rock can support such stresses. Thus, it is geologically
somewhat naïve to view diagenesis as occurring in the absence of either gravitational or
tectonic stress such that there is, at some point, an elastic half-space and gravitational
forces can be instantaneously applied. Second, there is appreciable horizontal strain in
the earth, especially in extending sedimentary basins. Third, the two horizontal stresses
are rarely equal as a result of the wide variety of tectonic sources of stress acting on rock
at depth (Chapter 1). The existence of consistent directions of principal stresses over
broad regions is an obvious manifestation of anisotropic magnitudes of the horizontal
stress. Moreover, these tectonic sources of stress often result in one (or both) of the
horizontal stresses exceeding the vertical stress, as required in areas of strike-slip or
reverse faulting and demonstrated previously in this chapter. Attempts to correct for
this by adding arbitrary tectonic stresses only make the matter worse by adding more
empirically determined parameters.
Figure 9.14 (after Lucier, Zoback et al. 2006) illustrates a lithologic column for a
well drilled in the central U.S. V p , V s and density logs and log-derived elastic moduli
(using equations 3.5 and 3.6 and the relations presented in Table 3.1) are also shown.
Hydraulic fracturing of the Rose Run sandstone at ∼2380 m was being considered
to stimulate injectivity. As a result, a series of mini-frac measurements were made
within the Rose Run and in the formations immediately above and below (Figure 9.15).
Moreover, as shown in the figure, estimates of S hmin and S Hmax magnitudes at other
depths were made from analysis of tensile and compressive wellbore failures in the
manner described in Chapter 7. Ingeneral, a strike-slip faulting stress state is seen.
However, note the unusually low magnitudes of S hmin and S Hmax at the depth of the
Rose Run. This indicates that this would be a particularly good interval for hydraulic
fracturing as a relatively low pressure would be needed to exceed the least principal
stress (∼35 MPa) and as long as the frac pressure did not exceed ∼42 MPa, the fracture
would not grow vertically out of the injection zone.
The data presented in Figures 9.14 and 9.15 make it possible to test the applicability
of equation (9.3), although as S Hmax is significantly greater than S hmin (and is mostly