Page 358 - Numerical Analysis and Modelling in Geomechanics

RESERVOIR COMPACTION, SUBSIDENCE AND WELL DAMAGE 339
(2) assuming that the vertical stress due to the weight of the overburden does
not change and
(3) assuming that the horizontal stresses at the boundaries do not change.

These assumptions are those for the condition of plane strain and lead to the
following expression for the compaction (i.e., the change in thickness), ≥ h, of the
reservoir with initial thickness h or a rock sample of height h:

(11.33)

where C m is referred to as the one-dimensional compressibility or uniaxial
compaction coefficient:

(11.34)

Typical deep-water Gulf of Mexico (GOM) reservoirs have been reported to be
composed of unconsolidated to slightly consolidated Miocene, Pliocene and
Pleistocene age turbidite sands. 74 These sands are prone to compaction, since
they are young and under-consolidated. 62 Martin and Serdengecti 75 presented
data on the bulk compressibility of unconsolidated sandstones ranging from about
0.7 to 7.0 µ sips, they also reported that C m ranges from 0.45C bc to C . As a
bc
further approximation, if C is assumed to be much less than C , then C has an
m
r
bc
effect on C that is a function only of Poisson’s ratio. If Poisson’s ration ranges
bc
from 0.2 to 0.45 for consolidated to unconsolidated rock, then C ranges from 0.
m
5C to 0.88C .
bc
bc
Nonlinear, elastic-plastic constitutive model
Failure of rocks and soils under shear stress is well known and understood. 1,76,77
For reservoir rocks, depletion of pore pressure results in increased stress carried
by the rock matrix, reduction of pore volume, and possibly pore collapse. High
porosity, weakly cement rocks are most susceptible to pore collapse. 74,78–80 On
the micro-scale, pore collapse is the result of the failure of bonds between
particles and the subsequent rearrangement of the particles. Under sufficiently
high stress and associated high volumetric strain, rock grains can fracture or
become fragmented, a situation not often encountered in soils due to the
relatively lower overburden stress near to the Earth’s surface. For clastic rocks
with weak grain bonds, shear stress can enhance compaction by the
rearrangement of intact or fragmented particles. Pore collapse results in
unrecoverable deformation and thus plasticity theories are amenable to
developing a constitutive model. One such model, which has been used widely
and successfully for both soils and rocks, is the generalized cap model of