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Rock physical and mechanical properties 67

If the formation bulk density (r b ) is also known from density logs, a
more accurate estimate for the dynamic modulus can be made by using the
following equation (Lacy, 1997):
E d ¼ 1:13 10 r t 2 p (2.63)
4

b
3
where E d is in Mpsi; t p is in ms/ft; r b is in g/cm . This correlation is a simpli-
fication of the theoretical equation of Eq. (2.61) with Poisson’s ratio of
n d z 0.248.
2.5.5 Relations of dynamic and static Young’s moduli

In general, the dynamic values of Young’s modulus have been found to be
greater than the static values. The discrepancy between the dynamic and
static moduli is far greater in the soft rock (such as shale) than that in the
hard rock (such as granite) (Howarth, 1984), and it has been widely
attributed to microcracks and pores in the rocks. It is also believed that the
differences in strain amplitude between static and dynamic measurements is
the primary cause for the difference between static and dynamic moduli in
dry rocks (e.g., Martin and Haupt, 1994). There are many empirical re-
lations to correlate the dynamic and static Young’s moduli. Some corre-
lations derived from petroleum basins are listed below, Eqs. (2.64)e(2.67),
where the units of the static and dynamic elastic moduli are one million psi
(Mpsi, 1 Mpsi z 6.895 GPa).
From ultrasonic test data of 600 core samples in the Gulf of Mexico,
Lacy (1997) obtained the following correlation for sandstones:
2
E s ¼ 0:0293E þ 0:4533E d (2.64)
d
A similar correction exists for shales (Lacy, 1997):
2
E s ¼ 0:0428E þ 0:2334E d (2.65)
d
From the test data in sandstones, shales, limestones, and dolomites, the
generalized correlation can be expressed as follows (Lacy, 1997):
2
E s ¼ 0:018E þ 0:422E d (2.66)
d
Ohen (2003) gave the following relation between dynamic and static
moduli for the shales in the Gulf of Mexico:
E s ¼ 0:0158E 2:74 (2.67)
d