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64 Applied Petroleum Geomechanics

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Haynesville shale
Exp on. (Haynesville shale)
Y oung's modulus (GPa) 40
50

30

20

10
R² = 0.5628
0 y = 50.777e -0.178x
0 2 4 6 8 10 12 14
Porosity (%)
Figure 2.22 Porosity versus Young’s modulus obtained from the uniaxial compression
tests in the Haynesville shale gas formation.

The results of uniaxial compression tests in the Haynesville shale gas
formation (porosity <14%) of several wells indicate that Young’s modulus
is highly dependent on porosity (Fig. 2.22). Young’s modulus increases as
porosity decreases and the following correlations are obtained:
E s ¼ 50:777e 17:8f (2.53)

16:511
Or E s ¼ 48:943ð1 fÞ (2.54)
where Young’s modulus E s is in GPa and the porosity f is in fractions.
Using the laboratory test data and the P-wave transit time measured
from the sonic log, t p , Horsrud (2001) obtained the following correlations
for the shale samples cored in the North Sea boreholes:
3:23
E s ¼ 0:076ð304:8=t p Þ (2.55)
where E s is in GPa; t p is the P-wave transit time from the sonic log, in ms/ft.
E s ¼ 0:076V p 3:23 (2.56)

where E s is in GPa; V p is the P-wave velocity, in km/s.
Using the empirical equations, continuous estimates of rock properties
can be obtained directly from the sonic log for different rock intervals. To
apply those empirical equations into a different field, calibrations are
needed. That is, the empirical equations need to be calibrated to available
lab data and to adjust parameters in the empirical equations to match the
lab data.