Page 193 - Applied Petroleum Geomechanics

188 Applied Petroleum Geomechanics

Abstract
Theoretical and practical methods for determining in situ stresses are discussed.
Measurements and interpretations of the horizontal stresses (e.g., diagnostic fracture
injection test, leak-off test, and mini-frac test) are investigated in both impermeable
and permeable rocks. Empirical equations in various petroleum basins are given to
estimate in situ stresses. Overburden stress and overburden gradient for both onshore
and offshore drilling are analyzed. Integrated methods for calculating the minimum
and maximum horizontal stresses are studied in different faulting stress regimes.
Poisson’s ratioebased stress polygons are applied to constrain in situ stresses using
both drilling-induced tensile fractures and wellbore breakouts. Methods for inter-
preting directions of horizontal stresses are also introduced.

Keywords: Hydraulic fracture test; In situ stresses; Maximum horizontal stress;
Minimum horizontal stress; Overburden gradient; Overburden stress; Poisson’s ratio and
stress polygon.

6.1 Overburden stress

6.1.1 Overburden stress from bulk density
Overburden stress, or vertical stress, is caused by the weight of the over-
lying formations. If the overlying formations have an average density of r a ,
then overburden stress (s V ) can be calculated by:

s V ¼ r gZ (6.1)
a
where g is the acceleration due to gravity; Z is the depth.
If bulk densities of the rocks vary with depth, the vertical stress can be
calculated by integration of the densities to the depth of interest, Z, i.e.,
Z
Z
s V ¼ r gZ w þ g r ðzÞdz (6.2)
w
b
Z w
where r b (z) is the formation bulk density as a function of depth and can be
obtained from density log; r w is the density of sea water; Z w is the water
depth, for onshore drilling Z w ¼ 0.
However, density log is usually not recorded at the shallow depth. Some
empirical methods can be used to estimate shallow formation bulk density.
One method is Miller’s near surface or mudline density correlation, which
can be found in Eq. (2.4) or from Zhang et al. (2008). The other was
proposed by Athy (1930) to interpolate shallow formation bulk density