Page 62 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

50 Reservoir Engineering

where cf is the formation (rock) compressibility with common units of psi-', V
is pore volume, p is pressure in psi, and the subscript T denotes that the partial
derivative is taken at constant temperature. The effective rock compressibility
is considered a positive quantity that is additive to fluid compressibility;
therefore, pore volume decreases as fluid pressure decreases [26,66]. Since
overburden pressure of a reservoir is essentially constant, the differential pressure
between the overburden pressure and the pore pressure will increase as the
reservoir is depleted. Thus, porosity will decrease slightly, on the order of only
one-half percent for a 1,000 psi change in internal fluid pressure [17]. For
different reservoirs, porosities tend to decrease as overburden pressure (or
depth) increases. Therefore, porosity under reservoir conditions may differ from
values determined in the laboratory [67]. For sandstones with 15% to 30%
porosity, reservoir porosity was found to be about 1% lower under reservoir
conditions; for low porosity limestones, the difference was about 10% [68J.
One of the commonly cited correlations between rock compressibility and
porosity was developed by Hall [69] (Figure 5-34} for several sandstone and
limestone reservoirs. All measurements were conducted with an external pressure
of 3,000 psi and internal pressures from 0 to 1,500 psi. Fatt [67] found no
correlation between compressibility and porosity, although the porosity range
studied (10% to 15%) was very narrow. Van der Knapp [68], citing his measure-
ments and those of Carpenter and Spencer [70], observed a general trend of
increasing pore volume compressibility with decreasing porosity. For a particular
limestone reservoir, Van der. Knapp [68] found that pore compressibility and

0 LIMESTONE -
e SANDSTONE -
-
-

22

-

-
3-
-
2- -a w- "
3d
I- -
- I 1 ' ' ' ' ' ' ' 1 ' ' I 1 ' '
0 ' ' 1 1-1 I ' I 1 __
~
0 2 4 6 8 IO 12 14 16 18 20 22 24 26
POROSITY , O/o
Figure 5-34. Effective rock compressibility vs. porosity 1691.