Geoscience Reference
In-Depth Information
a
True k-
ˆ
relationship (unknown)
10000
1000
Analysis of k-
ˆ
data
b
100
10000
10
Reservoir Unit (N=87)
Delta lobe facies (N=12)
Sandstone 1
1000
1
Sandstone 2
0.1
100
Swanson's mean
0.01
0
5
10
15
20
25
30
35
10
Porosity
c
Modelled k-
ˆ
relationship
1
10000
k=0.0122 e
0.2969
ˆ
R
2
=0.6
0.1
1000
Cut-off
100
k=0.0022 e
0.3788
ˆ
R
2
=0.8
0.01
10
0.001
1
0
5
10
15
20
25
30
35
Porosity
0.1
0.01
0
5
10
15
20
25
30
35
Porosity
Fig. 3.20
Use of the k-
) True pore
systems exhibit a non-linear relationship with disper-
sion, (
b
)Dataanalysisissensitivetothechoiceofrock
ϕ
transform: (
a
groups and statistical analysis method; (
)Themodel
function should be constrained by data and fit-for-
purpose
c
inferred function is strongly dependent on rock
grouping and sample size. For example, in
Fig.
3.20b
, the correlation coefficient (R
2
) for a
single facies is significantly lower than for the
total reservoir unit (due to reduced sample size).
Furthermore, for the whole dataset, Swanson's
mean gives a higher permeability trend than with
a simple exponential fit to the data. The modelled
k-
We have introduced two end member
approaches to modelling:
(a) Concept-driven
(b) Data-driven
The concept-driven approach groups the data
into a number of distinct model elements, each
with their own k-
transform. Simple log
transforms and best-fit functions are used to capture
trends but k-
ϕ
transform (Fig.
3.20c
) should be designed to
both faithfully represent the data and capture
rock trends or populations (that may not be
fully represented by the measured data).
Upscaling leads to further transformations of
the k-
ϕ
cross-correlation is poor and belief in
the data support is weak. The process is 'model-
driven' and the explicitly modelled rock units cap-
ture the complex relationship between porosity and
permeability. The data-driven approach assumes a
representative dataset and a minimal number of
model elements are distinguished (perhaps only
one). Care is taken to correctly model the observed
k-
ϕ
model. In general, we should expect a
reduction in variance (therefore improved corre-
lation) in the k-
ϕ
ϕ
transform, using for example a piecewise or
percentile-based formula (e.g. Swanson's mean).
ϕ
