Geoscience Reference
In-Depth Information
The reservoir model
is 'data-driven' and the
Modifying the Kozeny-Carmen equation
gives:
carefully-modelled k-
transform aims to capture
the complex relationship between porosity and
permeability.
ϕ
r
k
Ø
e
Ø
e
0
:
0314
¼
Ø
e
F
zi
ð
3
:
23
Þ
1
ϕ
e
is the effective porosity
F
zi
is a function of the tortuosity,
where k is in mD and
, the shape
factor, F
s
, and the surface area per unit grain
volume, S
gv
:
˄
3.3.5 Hydraulic Flow Units
The Hydraulic Flow Unit (HFU) concept offers a
useful way of classifying properties on the k-
1
F
p
S
gv
F
zi
¼
ð
3
:
24
Þ
ϕ
cross-plot, and can be linked to the definition of
model elements in a modelling study.
Abbaszadeh et al. (
1996
) defined HFU's in
terms of a modified Kozeny-Carmen equation
in which a Flow Zone Indicator, F
zi
, was used
to capture the shape factor and tortuosity terms.
˄
The F
zi
term thus gives a formal relationship
between k and ø which is related to pore-scale
flow physics (laminar flow in a packed bed of
spherical particles).
the spatial distribution of permeability. The
two distributions appear to match quite
well - they cover a similar range and have
a similar arithmetic mean. However, analy-
sis of the data statistics reveals some strange
behaviour - the geometric and harmonic
means are quite different.
What is going on here? And is this in
fact a good model for the given data?
Exercise 3.4
Comparing model distributions to data.
The plot and table below show a compari-
son of well data with the output of a model
realisationdesignedtorepresentthedataina
geological model. The well data are from a
cored well interval identified as a deltaic
sandstone facies. The model has used
Gaussian statistical modelling to represent
0.4
Model #n
Well Data
0.3
0.2
0.1
0.0
0.1
1
10
100
1000
10000
Permeability (md)
Statistics
Well data
Model #n
Number of data values/cells
30
150
Arithmetic mean
119.9
115.7
Geometric mean
45.9
90.8
Harmonic mean
17.19
0.87
