Handling Model Uncertainty - Reservoir Model Design - page 150

Cloud (light)

Cloud (light)

Rock (light)

Cloud (dark)

Rock (dark)

Rock (light)

Grass (heterogeneous)

Grass (massive)

House

Grass (dark)

Fig. 5.1 An undersampled picture - our task is to determine the image

could produce the stochastic result shown in
Fig. 5.2 . This representation is statistically con-
sistent with the underlying data, and would pass a
simple QC test comparing frequency of
occurrences in the data and in the model, yet
the result is clearly meaningless.
Application of logical deterministic trends to
the modelling process, as described in Chap. 2 ,
would make a better representation, one which
would at least fit an underlying landscape con-
cept: the sky is more likely to be at the top, the
grass at the bottom (Fig. 5.3 ). Furthermore, there
is an anisotropy ratio we can use so that we can
predict better spatial correlation laterally (the sky
is more likely to extend across much of the
image, rather than up and down). If the texture
from this trend-based approach is deemed unrep-
resentative of landscapes, an object-based alter-
native may be preferred (Fig. 5.4 ). Grass is
accordingly arranged in clusters, broadly ellipti-
cal, as are sky colours (clouds) and the rocky
areas are arranged into 'hills', anchored around
the data points they were observed in. A rough
representation is beginning to take shape.
The model representations in Figs. 5.2 , 5.3 ,
and 5.4 each adhere to the same element

proportions, and in this sense all 'match' the
data, although with strongly contrasting textures.
Assuming we then proceeded to add “colours”
for petrophysical properties (Chap. 3 ) and re-
scale the image for flow simulation (Chap. 4 ) ,
these images would produce strongly contrasting
fluid-flow forecasts.
Using these different images as possible alter-
native realisations could be one way of exploring
uncertainty, but we argue this would be a poor
route to follow. Reference to the actual image
(Fig. 5.5 ) reveals a familiar theme:

data model truth

6¼ 6¼

Even though most aspects of the image were
sampled, and the applied deterministic trends
were reasonable, there are significant errors in
the representation - object modelling of the sky
was inappropriate, hierarchical organisation was
missed, and even some aspects of the
characterisation (grass vs. rocks) were over-
simplified. There are also some modelling
elements missing, most noticeably: there were
no trees . Rearranging the data and detailed anal-
ysis of the original samples does not reveal the