Page 48 - Applied Petroleum Geomechanics

Rock physical and mechanical properties 39

2.2.2 Depth-dependent porosity and normal compaction
Field tests and lab experiments have shown that rock porosity decreases as
the burial depth increases. The following equation, first proposed by Athy
(1930), is the most commonly used one to describe porosity and depth
relationship:

f ¼ ae bZ (2.14)
where a and b are constants; Z is the depth; a ¼ f 0 ; and f 0 is the porosity
when Z is zero. For example, in the Northern North Sea the constants are
a ¼ 0.49 and b ¼ 2.7 10 4 for sandstones and a ¼ 0.803 and
4
b ¼ 5.1 10 for shales, if Z is in meters (Schön, 1996).
Zhang and Wieseneck (2011) analyzed the porosity data measured from
wireline density logs in several wells of the Bossier and Haynesville shale gas
formations in North Louisiana and obtained the following relation in
normally compacted shales:
f ¼ 0:5e 0:00036Z (2.15)

where f is in fractions; Z is the true vertical depth in feet.
Athy’s compaction equation indicates that porosity reduces exponen-
tially with depth because of normal compaction of the formations, causing
formations to be more compacted and consolidated. Porosity is not only
dependent on depth (decreasing with depth) but also controlled by different
mudstone mineralogy (Mondol et al., 2007). The smectite, compared to
other clay minerals, has the largest porosity and is less compacted (the curve
19 in Fig. 2.5). It can be also observed in Fig. 2.5 that the normal
compaction trends are very different for different shales, and this behavior is
particularly important when one uses normal compaction trends for pore
pressure prediction.

2.2.3 Stress-dependent porosity
Lab experimental tests show that rock porosity decreases as the applied
stress increases. For example, lab measurements in sandstone specimens
cored 1000 m below the sea floor (Peng and Zhang, 2007) show that the
stress and porosity have a negative exponential relation, i.e.,
f ¼ 0:336e 0:0023s (2.16)

where f is the porosity (fraction); s is the axial stress (MPa).