Page 79 - Applied Petroleum Geomechanics

70 Applied Petroleum Geomechanics

2.6 Poisson’s ratio
2.6.1 Static Poisson’s ratio
Poisson’s ratio is the ratio of transverse strain to corresponding axial strain
on a material stressed along one axis. For a rock core subjected to an axial
load, Poisson’s ratio (n) can be expressed in the following:
ε l
n ¼ (2.73)
ε a
where ε l and ε a are the lateral and axial strains, respectively. Therefore, static
Poisson’s ratio can be determined by measuring the lateral and axial defor-
mations of the uniaxial compression test in the rock sample.
Static Poisson’s ratio in a rock depends on lithology, confining stress,
pore pressure, and porosity of the rock. Laboratory test results show that
static Poisson’s ratio increases as porosity increases (Fig. 2.26). This porosity-
dependent Poisson’s ratio is not difficult to understand because the dynamic
Poisson’s ratio is theoretically dependent on V p /V s (refer to Eq. 2.76), and
V p /V s is directly related to porosity (Fig. 2.7 and Eq. (2.28)). The trend line
in Fig. 2.26 is:

n ¼ 0:2 þ 0:61f (2.74)

2.6.2 Poisson’s ratio anisotropy
Similar to Young’s moduli, Poisson’s ratios are also anisotropic. Fig. 2.27
presents static vertical and horizontal Poisson’s ratios in the Haynesville

0.4
Static Poisson’s ratio 0.3 Carbonates Siltstones

0.2

0.1
0 0.05 0.1 0.15 0.2 0.25
Porosity (fraction)
Figure 2.26 Poisson’s ratio versus porosity for carbonates and siltstones (Yale and
Jamieson, 1994).