The Rock Model - Reservoir Model Design - page 51

Fig. 2.39 Rock modelling using MPS

model combining object- and SIS-based
architectural elements. The MPS algorithm
did not 'work alone.'
2. The additional effort of generating and
checking a training image may not be required
in order to generate the desired architecture.
Despite the above, the technique can provide
very realistic-looking architectures which over-
come both the simplistic textures of older pixel-
based techniques and the simplistic shapes and
sometimes unrealistic architectures produced by
object modelling.

in their distribution. Non-stationarity is the
geological norm, indeed, Walther's Law - the
principle that vertical sequences can be used to
predict lateral sequences - is a statement of non-
stationarity.
Deterministic trends are therefore required ,
whether to build a model using object- or pixel-
based techniques, or to build a training image for
a texture-based technique.

2.7.4.1 Vertical Trends
Sedimentary systems typically show vertical
organisation of elements which can be observed
in core and on logs and examined quantitatively
in the data-handling areas of modelling
packages. Any such vertical trends are typically
switched off by default - the assumption of
stationarity.
As a first assumption, observed trends in the
form of vertical probability curves, should be
switched on , unless there are compelling reasons
not to use them. More significantly, these trends
can be manually adjusted to help realise an archi-
tectural concept perhaps only partly captured in
the raw well data.
Figure 2.40 shows an edited vertical element
distribution which represents a concept of a
depositional system becoming sand-prone
upwards. This is a simple pattern, common in
sedimentary sequences, but will not be integrated
in the modelling process by default.
Thought is required when adjusting these
profiles because the model is being consciously
steered away from the statistics of the well data.
Unless the well data is a perfect statistical sample

2.7.4 The Importance of Deterministic
Trends

All of the algorithms above involve a probabilis-
tic component. In Sect. 2.5 the balance between
determinism and probability was discussed and it
was proposed that strong deterministic control is
generally required to realise the desired architec-
tural concept.
Having discussed the pros and cons of the
algorithms, the final consideration is therefore
how to overlay deterministic control. In statisti-
cal terms, this is about overcoming the
s tationarity that probabilistic algorithms assume
as a default. Stationarity is a prerequisite for the
algorithms and assumes that elements are ran-
domly but homogeneously distributed in the
inter-well space. This is at odds with geological
systems, in which elements are heterogeneously
distributed and show significant non-stationarity:
they are commonly clustered and show patterns