Next Generation Geological Modeling for Hydrocarbon Reservoir Characterization - Advances in Data, Methods, Models and Their Applications in Geoscience - page 233

simulation as a tool for pre-screening geological models (Gilman et. al., 2002) or
Experimental Design (ED) techniques that optimally identify values of uncertainty and their
variation range (Prada et. al., 2005). Unfortunately, in realistic reservoir forecasting projects,
not all of the flow simulations may be necessary but the clear distinction between important
and un-important parameters is unknown a priori . A workflow aiming to identify and
isolate model realizations, relevant to reservoir forecast analysis, out of a full spectrum of
statistically probable models has recently been proposed by Scheidt and Caers, 2009
combining the following steps (Fig. 13):
 Computation of a single parameter, namely, pattern-dissimilarity distance, used to
distinguish two individual model realizations in terms of dynamic performance. The
objective is to identify a set of representative reservoir models through pattern-
dissimilarity distance analysis focusing on the dynamic properties of the realizations.
 Computation of pattern-dissimilarity distances are computed via rapid streamline
simulations carried out for each ensemble member. Analysis of pattern-distances gives
rise to a set of representative models, which are then simulated using a full-physics
finite-difference simulator.
 Derivation of the forecast uncertainty from the outcome of these intelligently selected
few full-physics simulations.
Further details are available in (Scheidt and Caers, 2009; Maučec et al., 2011b).

2.6.1 The concept of dynamic data (dis)similarity
To describe the degree of (dis)similarity between reservoir model realizations in an
ensemble it is not required to identify individual reservoir characteristics and corresponding
dynamic responses for each ensemble member as knowledge about a representative
“difference” (hereafter referred to as “distance”) between any two realizations is sufficient.
An example of pattern-dissimilarity distance θ , defined as an Euclidean measure, that
describes the degree of (dis)similarity between any two of reservoir realizations m indexed
with k and l within an ensemble of size I , in terms of geologic characteristics and pertinent
dynamic response, r  , i.e. recovery factor, oil production rate, etc.

kl

I

  

2

  ( rr  ) (9)

kl ki li

i  1

where, by definition, the pattern-dissimilarity distance honors self-similarity (

k   ) and

0

symmetry (   ). Pattern-dissimilarity distances are evaluated using rapid streamline

simulation, and assembled into a pattern-dissimilarity matrix,

kl lk

 

IxI
 Θ 

k 

, where Θ .

2.6.2 Multi dimensional scaling and cluster analysis
Multi-dimensional scaling (MDS) is used to translate the pattern-dissimilarity matrix models
into a p -dimensional Euclidean space (Borg and Groenen, 2005) where each element of the
matrix is represented with a unique point. Hereafter, Euclidean space will be simply
referred to as the E space, with individual points arranged in such a way that their distances
correspond in a least-squares sense to the dissimilarities of individual realizations.
Euclidean distances tend to exhibit strong correlation with pattern-dissimilarity distances.