Page 103 - Applied Petroleum Geomechanics

Rock strengths and rock failure criteria 95

core sample tests in laboratory experiments as described in the previous
section. However, in most cases core samples are unavailable for laboratory
testing, and empirical correlations between rock strength, geophysical, and
petrophysical data can be used for estimation. These correlations usually
are developed for some specific rock formations based on the relationships
of laboratory core tests, geophysical data, and petrophysical data. Because
there are multiple choices of strength correlations for various rock types
in different geological settings, it is necessary to understand the character-
istics of the correlations and their range of applicability before applying
them.

3.2.1 Empirical equations of rock strengths in shales
3.2.1.1 From sonic velocity
In conventional reservoirs, shales make up over 75% of the drilled for-
mations in the oil and gas industry, and over 70% of the borehole problems
are related to shale instability (Lal, 1999). The oil and gas industry still fights
borehole instability problems, particularly for drilling in geologically young
formations of shales (weak shales), for example, in Tertiary and Cretaceous
shales of the Gulf of Mexico, the North Sea, and the Gulf of Guinea. For
evaluating wellbore stability and sand production, rock strength is one of
the most important parameters. Some correlations were obtained using rock
physical data (P-wave velocity (V p ), or equivalently, interval transit time
(Dt ¼ 1/V p )), which were directly measured from sonic logs to relate to
laboratory-measured rock strengths. Using an extensive shale database, Lal
(1999) developed the following shale strength correlations tied only to
compressional sonic velocity mainly for high porosity Tertiary shales in the
Gulf of Mexico:

p ffiffiffiffiffi
c ¼ 5ðV p 1Þ= V p (3.4)
sin 4 ¼ðV p 1Þ=ðV p þ 1Þ (3.5)
Based on Eqs. (3.4) and (3.5), the UCS can be obtained:

UCS ¼ 10ðV p 1Þ¼ 10ð304:8=Dt 1Þ (3.6)
where the cohesion (c) and the uniaxial compressive strength (UCS) are in
MPa; the angle of internal friction (4) is in degrees; the compressional
sonic velocity (V p ) is in km/s; and the transit time (Dt)is in ms/ft.
Through wireline log data and laboratory triaxial compression tests
of shale samples obtained from deep boreholes from the North Sea,