Geology Reference
In-Depth Information
a)
b)
35
35
Nel A
WOS
Mio Gulf
Rot A
Rot B
Nel B
North Sea
Cooper
Rot C
SNS C
30
30
25
25
20
20
15
15
10
10
5
5
0 0
0 0
20
40
60
80
20
40
60
80
Eff Pressure (MPa)
Eff Pressure (MPa)
Figure 8.33 Dry rock parameters of sandstones and their sensitivity to effective pressure (trend data from MacBeth ( 2004 ).
P ðÞ¼ κ
1+
the effect may well be less than that shown by labora-
tory measurements (C. MacBeth, personal communi-
cation). Drawdown in the overpressured situation
results in the dry rock frame taking more of the
weight of the overburden and thus the frame stiffens.
In a normally pressured situation the effect is minim-
ised as the rock frame already supports the overbur-
den. In contrast to this, where pore pressures increase
during hydrocarbon production (around water inject-
ors), large changes in seismic amplitude have been
observed (e.g. Sayers, 2006 ).
Whilst laboratory data are important in assessing
the dry rock sensitivity to effective pressure variations
it should be noted that even when these data are
available there is always some doubt as to the rele-
vance of high-frequency measurements on small
samples (micro-fabric measurement) to a field wide
response under the influence of subsurface stress
regimes. For example, the response in the low effect-
ive pressure regime may be dominated by micro-
cracks which may be natural or generated through
pressure release of core material. The reader is
referred to McCann and Southcott ( 1992 ) for a review
of the issues in laboratory measurements.
κ
Ε κ exp P e
P k
ðÞ¼ μ
1+
μ
P e
,
ð
8
:
38
Þ
Ε μ exp P e
P
μ
κ
μ
where
are the bulk and shear modulus at
effective pressure P e ,
and
μ are the asymptotic
high-pressure values, and P κ and P μ are constants that
characterise the rollover point beyond which the rock
frame becomes
κ and
relatively insensitive to pressure
increase.
Vernik and Hamman ( 2009 ) published similar
models for clean sandstones, parameterised in terms
of dry velocities;
h
i
exp dP e
ð
Þ
V pd ¼
V p0 +b p P e
c
:
h
i ,
exp dP e
ð
Þ
V sd ¼
V s0 +b s P e
c
:
ð
8
:
39
Þ
where b, c and d are fitting parameters with physical
meaning as follows. c correlates with microcrack
density; when pressure is high enough to close the
microcracks in the rock then c is zero and the equa-
tions become linear, with slopes b that are inversely
related to the level of consolidation and cementation.
Note that d is related to the dominant aspect ratio of
the microcracks.
In general it appears that rocks which are over-
pressured and are relaxed through pressure draw-
down will show relatively large dry rock changes
consistent with laboratory measurements. However,
if a normally pressured reservoir is drawn down then
8.2.6 Contact models
Contact models are based on mathematical principles
of the interaction of granular materials and are
applicable to sandstones. They are generally con-
structed by determining high- and low-porosity dry
rock end members which are then interpolated, often
using modified Hashin
174
-
Shtrikman ( 1964 ) bounds.
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