Page 112 - Applied Petroleum Geomechanics

104 Applied Petroleum Geomechanics

Golubev and Rabinovich (1976) proposed the following empirical
equation for the limestone and dolomite (Chang et al., 2006):

UCS ¼ 10 ð2:44þ109:14=DtÞ 145 (3.28)
In Eqs. (3.27) and (3.28), UCS is in MPa and Dt is in ms/ft.
Eq. (3.27) predicts a much lower strength than Eq. (3.28); therefore, Eq.
(3.27) may be more suitable for low-strength carbonates.
Najibi et al. (2015) presented the following rock strength correlation for
the limestones from core test data in two Iran oil fields:
UCS ¼ 3:67V p 2:14 (3.29)

where UCS is in MPa and V p is in km/s.

3.2.3.2 From Young’s modulus and porosity
Chang et al. (2006) obtained the following relation between the UCS
(in MPa) and Young’s modulus (in GPa) for the limestone with
10 < UCS < 300 MPa:
UCS ¼ 13:8E 0:51 (3.30)

For the limestone and dolomite with low to moderate porosity
(0.05 < f < 0.2) and high UCS (30 < UCS < 150 MPa) in the Middle
East, the following empirical equation was obtained (Chang et al., 2006):

UCS ¼ 143:8 expð 6:95fÞ (3.31)
Another empirical equation for 0.05 < f < 0.2 and 30 < UCS <
300 MPa is (Chang et al., 2006):

UCS ¼ 135:9 expð 4:8fÞ (3.32)
where f is porosity (fraction).
The North Sea chalk has been widely studied because of the prominent
chalk reservoirs (Ekofisk, Eldfisk, Valhall, Tommeliten, and others).
Havmøller and Foged (1996) compiled a large amount of the North Sea
reservoir and outcrop chalk data to establish correlations between mechanical
properties and porosity (Fjær et al., 2008). The overall trends they found (for
the North Sea chalk) can be summarized in the following equations:
UCS ¼ 174e 7:57f (3.33)

(3.34)
UCS z 8T 0
where UCS and tensile strength (T 0 ) are in MPa; f is in a fraction.