Page 75 - Applied Petroleum Geomechanics

66 Applied Petroleum Geomechanics

2.5.4 Dynamic Young’s modulus
When rock samples are not available, the well logs and geophysical data can
be used to analyze and interpret rock physical and mechanical parameters.
The dynamic Young’s modulus (E d ) can be solved from the following
theoretical equation by knowing the elastic compressional and shear wave
velocities of the rock:

E d ¼ r V p 2 ð1 þ n d Þð1 2n d Þ (2.58)
b
ð1 n d Þ
where r b is the bulk density; V p is the compressional velocity; n d is the dy-
namic Poisson’s ratio.
The dynamic Young’s modulus can also be expressed as the following
forms if the transit time is available:

r ð1 þ n d Þð1 2n d Þ
b
E d ¼ (2.59)
t p 2 ð1 n d Þ
2r ð1 þ n d Þ
b
E d ¼ (2.60)
t 2 s
where t p and t s are the compressional and shear transit time, respectively.
Therefore, if well log data (such as density log, sonic compressional
transit time, and shear transit time) are available, the dynamic Young’s
modulus can be computed from the above equations. In the English unit,
dynamic Young’s modulus, Eq. (2.59), can be expressed as the following
form:

r ð1 þ n d Þð1 2n d Þ
4 b
E d ¼ 1:35 10 (2.61)
t 2 p ð1 n d Þ
where E d is the dynamic Young’s modulus with unit of one million psi
3
(Mpsi); t p is in ms/ft; r b is in g/cm .
From lab tests in over 400 core samples of sandstones, shales, limestones,
dolomites, and siltstones from the Gulf of Mexico, Lacy (1997) derived the
following correlation between rock dynamic Young’s modulus and the
compressional velocity:
E d ¼ 0:265V p 2:04 (2.62)

where the dynamic modulus (E d ) is measured in Mpsi; the compressional
velocity V p is in km/s and ranges from 1 to 6 km/s.