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Rock physical and mechanical properties 77

Biot’s coefficient are related to porosity. Zimmerman et al. (1986) obtained
the following empirical equation for the lower bound of Biot’s coefficient:
1

fð1 þ n s Þ
a ¼ 1 ð1 fÞ 1 þ (2.85)
2ð1 2n s Þ
where n s is drained Poisson’s ratio; f is the porosity.
Jizba (1991) presented laboratory-measured petrophysical data and bulk
moduli of 34 tight gas sandstones and 9 shales from GRI’s cooperative wells
in the Travis Peak Formation in East Texas. Using the static bulk moduli
presented by Jizba (1991) and assuming the matrix modulus is 39 GPa,
Biot’s coefficient can be computed from Eq. (2.77), and the following
correlation can be obtained for tight sandstones and shales under the
confining pressure of 20 MPa (Fig. 2.30):

a ¼ 1:278f 0:22 (2.86)

For hard formations, porosity f < 0.37, the equation in the paper of
Raymer et al. (1980) was rewritten in the following form as the empirical
equation of Biot’s coefficient by Krief et al. (1990):

3:8
a ¼ 1 ð1 fÞ (2.87)
Krief et al. (1990) also gave a more general form of empirical equation
of Biot’s coefficient:

3
a ¼ 1 ð1 fÞ 1 f (2.88)

1.0
20 MPa
0.9
0.8
Biot's coefficient 0.6
0.7

0.5
0.4
0.3
0.2
Jizba, 1991
0.1
Power (Jizba, 1991 )
0.0
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16
Porosity (fraction)
Figure 2.30 Biot’s coefficient computed from laboratory results presented by Jizba
(1991) in tight sandstones and shales under the confining pressure of 20 MPa.