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missing elements. On reflection, we can see that
the aim of reproducing the statistical content of
the sample dataset brings with it a major flaw in
all the models.
Could the missing elements in Fig. 5.5 have
been foreseen, given that they were absent in the
data sample? We would argue yes, to a large
extent. From the data set it is possible to establish
a concept of hilly countryside in a temperate
climate - the 'expert judgement' of Kahneman
and Klein ( 2009 ). Having established this, there
are in fact certain aspects which are consistent
with the concept but not actually seen by the
sample data. However, these can be anticipated.
Ask yourself:
• Could there be more than one type of house?
Yes .
• Could there be a small village? Yes .
• Is there a structure to the clouds? Yes .
• Are the hills logically arranged, ones with
greater contrast in the foreground? Yes
• Could there be trees?
Taking the issue of trees specifically, these are
highly likely to be present, given the underlying
concept (grass and hills in a temperate climate).
They are also likely to be under-sampled.
The parallels with reservoir modelling are
hopefully clear: we need to use concepts to
honour the data but work beyond it to include
missing elements. If these elements are important
to the field development (e.g. open natural
fractures, discontinuous but high permeability
layers, cemented areas, sealing sub-seismic
faults, thin shales) then the presence or absence
of these features becomes the important uncer-
tainty. We should always ask ourselves: “could
there be trees?”
alternative approaches to uncertainty handling,
and lead to a general recommendation for
scenario-based approaches, along the way also
distinguishing different flavours of 'scenario'.
Scenario-based modelling became a popular
means of managing sub-surface uncertainty
during the 1990s, although opinions differ widely
on the nature of the 'scenarios' - particularly
with reference to the relative roles of determin-
ism and probability. In the context of reservoir
modelling, a scenario is defined here as a possi-
ble real-world outcome and is one of several
possible outcomes (Bentley and Smith 2008 ).
The idea of alternative, discrete scenarios
followed on logically from the emergence of
integrated reservoir modelling tools (e.g.
Cosentino 2001 ; Towler 2002 ), which
emphasised the use of 3D static reservoir
modelling, ideally fed from 3D seismic data
and leading to 3D dynamic reservoir simulation,
generally on a full-field scale.
Appreciating the numerous uncertainties
involved in constructing such field models, the
desire for multiple modelling naturally arises.
Although not universal (see discussion in
Dubrule and Damsleth 2001 ), the application of
multiple stochastic modelling techniques is now
widespread, with
alternative models
'realisations' or 'scenarios'.
The different terminologies are more than
semantic. The notion of multiple modelling has
been explored differently by different workers,
the essential variable being the balance between
deterministic and probabilistic inputs. Using
“multiple realisations” may sound more routed
in statistical theory than using some alternative
“model runs” - but is it? These concepts are best
related to differing approaches to the application
of geostatistical algorithms, and to differing
ideas on the role of the probabilistic component
(Fig. 5.6 ).
The contrasting approaches to uncertainty
handling broadly fall into three groups:
Rationalist approaches, in which a preferred
model is chosen as a base case (Fig. 5.7 ).
The model is either run as a technical best
guess, or with a range of uncertainty added
Differing Approaches
Abandoning the route of modelling for comfort
and embarking on the harder but more interesting
and ultimately more useful route of modelling
to illustrate uncertainty, we need a workflow
(see Caers 2011 , for a summary of statisti-
cal methodologies). This chapter will review
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