Geoscience Reference
In-Depth Information
side boundary condition, forces the result to be a
diagonal tensor. This is useful, but may not of
course represent reality. Renard and de Marsily
(
1997
) give an excellent review of effective per-
meability, and Pickup et al. (
1994
,
1995
) give
examples of the permeability tensor estimated
for a range of realistic sedimentary media.
In reality, the permeability in a rock medium is
a highly variable property. In sedimentary basins
as a whole we expect variations of at least 10
orders of magnitude (Fig.
3.8
), with a general
decrease for surface to depth due to compaction
and diagenesis. Good sandstone units may have
permeabilities typically in the 10-1,000 mD
range, but the silt and clay rich units pull the
permeability down to around 10
3
mD or lower.
Deeply buried mudstones forming cap-rocks and
seals have permeabilities in the microdarcy to
nanodarcy range. Even within a single reservoir
unit (not including the shales), permeability may
range by at least 5 orders of magnitude. In the
example shown in Fig.
3.9
the wide range in
observed permeabilities is due both to lithofacies
(heterolithic facies tend to be lower than the sand
facies) and due to cementation (each facies is
highly variable mainly due to the effects of vari-
able degrees of quartz cementation).
3.2.3 Permeability Variation
in the Subsurface
There is an extensive literature on the measurement
of permeability (e.g. Goggin et al.
1988
;Hurstand
Rosvoll
1991
;Ringroseetal.
1999
) and its appli-
cation for reservoir modelling (e.g. Begg et al.
1989
; Weber and van Geuns
1990
; Corbett et al.
1992
). All too often, rather idealised permeability
distributions have been assumed in reservoir
models, such as a constant value or the average of
a few core plug measurements.
No-flow boundary
Open boundary
3.2.4 Permeability Averages
Due to its highly variable nature, some form of
averaging of permeability is generally needed.
The question is which average? There are well-
known limits for the estimation of k
eff
in ideal
systems. For flow along continuous parallel layers
the arithmetic average gives the correct effective
permeability, while for flow perpendicular to
P
1
P
2
P
1
P
2
Fig. 3.7
Simple illustration of flow boundary conditions:
P1 and P2 are fluid pressures applied at the
left
and
right
hand sides
and
arrows
illustrate flow vectors
Permeability (md)
10
−
6
10
−
3
10
3
1
Holocene aquifers:
Fluvial sand
1
1
Silty clay
Clay
1
Fig. 3.8
Typical ranges of
permeability for near-
surface aquifers and North
Sea oil reservoirs:
1
¼
Holocene aquifers
(From Bierkins
1996
),
2
¼
Example North Sea
datasets (anonymous)
North Sea oil reservoirs:
Fluvial
2
Deltaic
2
?
Deep Basin mudstones
