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In-Depth Information
because the channels have a component of
lateral migration and deposit a broader and
lower sinuosity belt of sands as they do so.
Carbonate reservoirs offer a more extreme
example of this as any original depositional
architecture can be completely overprinted by
subsequent diagenetic effects. Differential
compaction effects may also change the verti-
cal geometry of the original sediment body.
6. Do not confuse uncertainty with variability.
Uncertainty about the most appropriate ana-
logue may result in a wide spread of geomet-
rical constraints. It is incorrect, however, to
combine different analogue datasets and so
create spuriously large amounts of variation.
It is better to make two scenarios using differ-
ent data sets and then quantify the differences
between them.
7. Get as much information as possible from the
wells and the seismic data sets. Do well
correlations constrain the geometries that can
be used? Is there useful information in the
seismic?
8. We will never know what geometries are cor-
rect. The best we can do is to use our concep-
tual models of the reservoir to select a series
of different analogues that span a plausible
range of geological uncertainty and quantify
the impact. This is pursued further in Chap.
5
.
an adaptation of the algorithm called
Indicator
Kriging
.
The algorithm attempts to minimise the esti-
mation error at each point in the model grid. This
means the most likely element at each location is
estimated using the well data and the variogram
model - there is no random sampling. Models
made with indicator kriging typically show
smooth trends away from the wells, and the
wells themselves are often highly visible as
'bulls-eyes'. These models will have different ele-
ment proportions to the wells because the algo-
rithm does not attempt to match those proportions
to the frequency distribution at the wells. Indicator
kriging can be useful for capturing lateral trends
if
these are well represented in the well data set, or
mimicking correlations between wells.
In general, it is a poor method for representing
reservoir heterogeneity because the heterogene-
ity in the resulting model is too heavily
influenced by the well spacing. For fields with
dense, regularly-spaced wells and relatively long
correlation lengths in the parameter being
modelling, it may still be useful.
Figure
2.35
shows an example of indicator
Kriging applied to the Moray data set - it is
first and foremost an interpolation tool.
2.7.2.2 Sequential Indicator
Simulation (SIS)
Sequential Gaussian Simulation, SGS is most
commonly used for modelling continuous
petrophysical properties (Sect.
3.4
), but one vari-
ant, Sequential Indicator Simulation (SIS), is
quite commonly used for rock modelling
(Journel and Alabert
1990
). SIS builds on the
underlying geostatistical method of kriging, but
then introduces heterogeneity using a sequential
stochastic method to draw Gaussian realisations
using an indicator transform. The indictor is used
to transform a continuous distribution to a dis-
crete distribution (e.g. element 1 vs. element 2).
When applied to rock modelling, SIS will gen-
erally assume the reservoir shows no lateral or
vertical trends of element distribution - the prin-
ciple of stationarity again - although trends can be
superimposed on the simulation (see the important
comment on trends at the end of this section).
2.7.2 Pixel-Based Modelling
Pixel-based modelling is a fundamentally differ-
ent approach, based on assigning properties using
geostatistical algorithms on a cell-by-cell basis,
rather than by implanting objects in 3D. It can be
achieved using a number of algorithms,
the
commonest of which are summarised below.
2.7.2.1 Indicator Kriging
Kriging is the most basic form of interpolation
used in geostatistics, developed by the French
mathematician Georges Matheron and his stu-
dent Daniel Krige (Matheron
1963
). The tech-
nique is applicable to property modelling (next
chapter) but rock models can also be made using
