Geoscience Reference
In-Depth Information
Fig. 4.25
Rock sculpture by Andrew Goldsworthy (NW Highlands of Scotland) elegantly capturing the concept of the
REV
response for a well through a reservoir interval is
the 'right average.' A statistician will know that
an arbitrary sample is rarely an accurate repre-
sentation of the truth. Valid statistical treatment
of sample data is an extensive subject treated
thoroughly in textbooks on statistics in the
Earth Sciences - e.g. Size (
1987
), Davis (
2003
),
Isaaks and Srivastava (
1989
) and Jensen et al.
(
2000
).
The challenges involved in correctly inferring
permeability from well data are illustrated here
using an example well dataset (Fig.
4.26
,
Table
4.2
). This 30 m cored-well interval is from
a tidal deltaic reservoir unit with heterolithic
lithofacies and moderate to highly variable
petrophysical properties (the same well dataset is
discussed in detail by Nordahl et al. (
2005
)).
Table
4.2
compares the permeability statistics
for different types of data from this well:
(a) High resolution probe permeameter data;
(b) Core plug data;
(c) A continuous wireline-log based estimator of
permeability for the whole interval;
(d) A blocked permeability log as might be typi-
cally used in reservoir modelling.
Statistics for ln(k) are shown as the population
distributions are approximately log normal. It is
well known that the sample variance should
reduce as sample scale is increased. Therefore,
the reduction in variance between datasets (c)
and (d) - core data to reservoir model - is
expected. It is, however, a common mistake in
multi-scale reservoir modelling for an inappropri-
ate variance to be applied in a larger scale model,
e.g. if core plug variance was used directly to
represent the upscaled geomodel variance.
Comparison of datasets (a) and (b) reveals
another form of variance that is commonly
ignored. The probe permeameter grid (2 mm
spaced data over a 10 cm
10 cm core area)
shows a variance of 0.38 [ln(k)]. The core plug
dataset for the corresponding lithofacies interval
(estuarine bar), has
2
0.99, which
represents variance at the lithofacies scale. How-
ever, blocking of the probe permeameter data at
the core plug scale shows a variance reduction
factor of 0.79 up to the core plug scale (column
2 in Table
4.2
). Thus, in this dataset (where high
resolution measurements are available) we know
that a significant degree of variance is missing
˃
ln(k)
¼
