Page 229 - Applied Petroleum Geomechanics

224 Applied Petroleum Geomechanics

Normally rock formations extend very long in horizontal directions;
therefore, the strain in the minimum horizontal direction is much smaller
than the strains in the vertical stress direction. Particularly, when the
interested formations are constrained by stiffer formations, the stress state is
similar to the condition of uniaxial strain loading. In this extreme case, ε h is
equal to zero if there is no tectonic strain in the minimum horizontal stress
direction; therefore, the maximum horizontal stress can be expressed as
(Li and Purdy, 2010):

ðs h ap p Þ
s H ¼ s V þ 2ap p (6.77)
n
Eq. (6.77) is applied to estimate the maximum horizontal stress in an oil
fielddField 1 of the Visund field in the northern part of the North Sea.
The vertical stress, minimum horizontal stress, pore pressure, and mud
weight are available from Wiprut (2001). Applying Eq. (6.77) and assuming
a ¼ 1 and n ¼ 0.25, the maximum horizontal stresses at different depths are
calculated, as shown in Fig. 6.21, which are consistent with Wiprut’s results.
Eq. (6.76) can be plotted to the stress polygon diagram to constrain
in situ stresses. A stress polygon in Fig. 6.22 is drawn for Poisson’s ratio of
0.25 (or m ¼ 0.58 from Eq. 5.18) based on the lower and upper bound
horizontal stresses Eqs. (5.15) and (5.16). The following parameters are used

Figure 6.21 Calculated maximum horizontal stress (S H ) from Eq. (6.77) compared to
the results of Wiprut (2001) in Well 1S of Field 1, the Visund Field, northern North Sea.