Page 108 - Applied Petroleum Geomechanics

100 Applied Petroleum Geomechanics

3.2.2 Empirical equations of rock strengths in sandstones
3.2.2.1 From sonic velocity and transit time
For fine grained, both consolidated and unconsolidated sandstones in the
Bowen Basin of Australia, McNally (1987) presented the following strength
estimation using sonic logs:

UCS ¼ 1200 expð 0:036DtÞ (3.17)
where UCS is in MPa and the transit time Dt is in ms/ft.
For the Tertiary reservoir sandstones in the Gulf of Mexico and the
Jurassic reservoir sandstones in the North Sea, the following correlation
exists between the lab-measured UCS and the compressional transit time
from sonic log measurements (Fig. 3.12):
2:064
UCS ¼ 156318ð1=DtÞ (3.18)

Figure 3.12 Lab-measured uniaxial compressive strengths versus sonic compressional
transit time in some deep wells in the Gulf of Mexico and the North Sea.

The same units are used as those in Eq. (3.17).
Some high-porosity (w20%) sandstones are even weaker than shales,
such as the Tertiary formations in the Gulf of Mexico. In this case, the
wellbore breakout and sand production are expected while drilling and
after reservoir production. Based on the laboratory test data in the Tertiary
formations of the Gulf of Mexico and the North Sea, Zhang (2013) ob-
tained the following empirical equation to estimate the UCS for weak
(poorly consolidated) sandstones:

2:5
UCS ¼ 0:68ð304:8=DtÞ (3.19)