Page 90 - Reservoir Geomechanics

74 Reservoir geomechanics

a. b.
Instantaneous vs. time-dependent strain Cumulative instantaneous and creep strain
dry Wilmington sand dry Wilmington sand
0.02 0.04

0.035 Total strain
for MPa increasing pressure increments 0.01 Cumulative axial strain (in/in) 0.025
Instantaneous strain
0.015
0.03
Axial strain (in/in) 0.015
0.02

Creep strain
0.005
0.01
0.005 Creep strain

0 0
5 10 15 20 25 30 35 5 10 15 20 25 30 35
Confining pressure (MPa) Confining pressure (MPa)
Figure 3.9. (a) Incremental instantaneous and creep strains corresponding to 5 MPa incremental
increases in pressure. The data plotted at each pressure reflect the increases in strain that occurred
during each increase in pressure. Note that above 15 MPa the incremental creep strain is the same
magnitude as the incremental instantaneous strain (from Hagin and Zoback 2004b). The cumulative
instantaneous and total (instantaneous plus creep) volumetric strain as a function of pressure.
Note that above 10 MPa, both increase by the same amount with each increment of pressure
application.

stress that is greater than the sample experienced in situ.However, as will be shown
below, once the previous highest load experienced has been exceeded, viscoplastic
compaction can be quite appreciable. One would dramatically underpredict reservoir
compaction from laboratory experiments on uncemented sands if one were to neglect
viscoplastic effects.
In an attempt to understand the physical mechanism responsible for the creep in
these samples, Figure 3.8b illustrates an experiment by Chang, Moos et al.(1997)
that compares the time-dependent strain of Wilmington sand (both dry and saturated)
with Ottawa sand, a commercially available laboratory standard that consists of pure,
well-rounded quartz grains. Note that in both the dry and saturated Wilmington sand
samples, a 5 MPa pressure step at 30 MPa confining pressure results in a creep strain of
4
2% after 2 × 10 sec (5.5 hours). In the pure Ottawa samples, very little creep strain is
observed, but when 5% and 10% montmorillonite was added, respectively, appreciably
more creep strain occurred. Thus, the fact that the grains in the sample were uncemented
to each other allowed the creep to occur. The presence of montmorillonite clay enhances
this behavior. The Wilmington samples are composed of ∼20% quartz, ∼20% feldspar,
20% crushed metamorphic rocks, 20% mica and 10% clay. Presumably both the clay
and mica contribute to the creep in the Wilmington sand.