Geoscience Reference
In-Depth Information
0.20
Clean sands
Heterolithic sands
Sandy Heterolithics
Mixed Heterolithicss
0.15
Freq.
0.10
0.05
0.00
Permeability (md)
Fig. 3.9
Probe permeameter measurements from a highly variable, deeply-buried, tidal-deltaic reservoir interval
(3 m of core) from offshore Norway
Fig. 3.10
Calculation of
effective permeability
using averages for ideal
layered systems: (
) The
arithmetic average for flow
along continuous parallel
layers; (
a
) The harmonic
average for flow
perpendicular to
continuous parallel layers
(k
i
and t
i
are the
permeability and thickness
of layer i)
b
continuous parallel layers the harmonic average is
the correct solution (Fig.
3.10
).
If the layers are in any way discontinuous or
variable or the flow is not perfectly parallel or
perpendicular to the layers then the true effective
permeability will lie in between these averages.
This gives us the outer bounds to effective
permeability:
More precise limits to k
eff
have also been
proposed, such as the arithmetic mean of har-
monic means of each row of cells parallel to
flow (lower bound) and
vice versa
for the upper
bound (Cardwell and Parsons
1945
). However,
for most practical purposes the arithmetic and
harmonic means are quite adequate limiting
values, especially given that we seldom have an
exhaustive set of values to average (the sample
problem, discussed in Sect.
3.3
below).
k
harmonic
k
eff
k
arithmetic