Stochastic simulation allows generating multiple reservoir models that can
be used to characterize reservoir uncertainty. In many practical situations,
the large computation time needed for flow simulation does not allow an
evaluation of flow on all reservoir models. In this paper, we propose a method
to select a subset of reservoir models reflecting the same uncertainty in flow
response as the full set. Using the concept of distance, we map the reservoir
models to a low-dimensional space where kernel clustering is applied to
identify a subset of representative reservoir models of the entire set. Flow
simulation and subsequently uncertainty quantification are performed on this
subset. A case study is presented of an architecturally complex deepwater
turbidite offshore reservoir with large uncertainty in the type of depositional
Petroleum reservoirs are often modeled using well-established structural,
geostatistical, or other property modeling methods. With these methods, it is
well known that a large number of reservoir models (termed "realizations") can
be rapidly generated, each of which will respect the data (wells, seismic,
production) and geological constraints (e.g., channeling) input into the
algorithms. Uncertainty quantification in reservoir performance aims at
defining the P10, P50, and P90 statistics of the flow response of interest,
which can be quantified by evaluating a large number of reservoir models
through a flow simulator. However, because flow simulation can be extremely
time consuming, it is often not practical to run flow simulation on each model.
The engineer must then select a subset of realizations to quantify uncertainty.
The traditional way to select a subset of realizations is to rank them using
static or dynamic properties [e.g., original oil in place (OOIP), streamlines].
Ranking techniques are used to select reservoir models that represent the P10,
P50, and P90 quantiles of the response (Ballin et al. 1992; Caers 2005). This
approach has been proven efficient when the ranking measure is highly
correlated to the response of interest. However, ranking is often based on
rather simple statistics extracted from the realization (e.g., OOIP), which may
not correctly capture simulation behavior. These statistical measures often
have a poor correlation with the response measured by the flow simulator.
Moreover, the level of correlation is not known in practical studies, or can
only be guessed.
In this paper, we employ a different technique to identify a subset of
reservoir models that will be evaluated by flow simulation to compute the
statistics (P10, P50, P90) of the response of interest. This method, called the
distance kernel method (DKM), was proposed by Scheidt and Caers (2007, 2008).
It is based on the definition of a dissimilarity distance between reservoir
models, which indicates how similar any two reservoir models are in terms of
their associated response of interest. In other words, the distance is defined
such that it has a good correlation with the flow response of interest. The
principle idea is to rely on the distance to identify a few typical
realizations (in terms of flow behavior) and, thus, cover the spread of
uncertainty accurately by only performing a small number of simulations. The
small subset of realizations, therefore, is selected to have statistics similar
to those of the entire set.
© 2009. Society of Petroleum Engineers
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- Original manuscript received:
27 May 2008
- Revised manuscript received:
8 October 2008
- Manuscript approved:
15 December 2008
- Published online:
20 August 2009
- Version of record:
22 December 2009