Handling Model Uncertainty - Reservoir Model Design - page 164

exercises tend to be more focussed and, paradox-
ically, tend to be quicker to execute than the very
large, very detailed base-case model builds.

The type of design depends on the purpose of
the study and on the degree of interaction between
the variables. A simple approach is the Plackett-
Burmann formulation. This design assumes that
there are no interactions between the variables
and that a relatively small number of experiments
are sufficient to approximate the behaviour of the
system. More elaborate designs, for example D-
optimal or Box-Behnken (e.g. Alessio et al. 2005 ;
Cheong and Gupta 2005 ; Peng and Gupta 2005 ),
attempt to analyse different orders of interaction
between the uncertainties and require a signifi-
cantly greater number of experiments. The value
of elaboration in the design needs to be assessed -
more is not always better - and depends on the
model purpose, but the principles described below
apply generally.
A key aspect of experimental design is that the
uncertainties can be expressed as end-members.
The emphasis on making a base case or a best
guess for any variable is reduced, and can be
removed.
The combination of Plackett-Burmann exper-
imental design with the scenario-based approach
is illustrated by the case below from a mature
field re-development plan involving multiple-
deterministic scenario-based reservoir modelling
and simulation (Bentley and Smith 2008 ). The
purpose of the modelling was to build a series of
history-matched models that could be used as
screening tools for a field development.
As with all scenario-based approaches, the
workflow started with a listing of the uncertainties
(Fig. 5.15 ), presumed in this case to be:

5.9 Linking Deterministic Models

with Probabilistic Reporting

The next question is how to link multiple-
deterministic scenarios with a probabilistic
framework? Ultimately we wish to know how
likely an outcome is. In reservoir modelling,
probability is most commonly summarised as
the percentiles of the cumulative probability dis-
tribution - P90, P50, and P10, where P90 is the
value (e.g. reserves) which has a 90 % probabil-
ity of being exceeded, and P50 is the median of
the distribution. With multiple-deterministic
scenarios, as each scenario is qualitatively
defined, the link to statistical descriptions of the
model outcome ( e.g . P90, P50 and P10) can be
qualitative (e.g. a visual ranking of outcomes) or
formalised in a more quantitative manner.
An important development has been the merg-
ing of deterministically-defined scenario models
with probabilistic reporting using a collection of
approaches broadly described as 'experimental
design'. This methodology offers a way of
generating probabilistic distributions of
hydrocarbons in place or reserves from a limited
number of deterministic scenarios, and of relating
individual scenarios to specific positions on the
cumulative probability function (or 'S' curve). In
turn, this provides a rationale for selecting specific
models for screening development options.
Experimental design is a well-established tech-
nique in the physical and engineering sciences
where it has been used for several decades ( e.g .
Box and Hunter 1957 ). It has more recently
become popular in reservoir modelling and simula-
tion ( e.g . Egeland et al. 1992 ; Yeten et al. 2005 ;Li
and Friedman 2005 ) and offers a methodology for
planning experiments so as to extract the maximum
amount of information about a system using the
minimum number of experimental runs. In subsur-
face modelling, this can be achieved by making a
series of reservoir models which combine
uncertainties in ways specified by a theoretical
template or design.

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