The Rock Model - Reservoir Model Design - page 50

Fig. 2.38 Rock modelling using facies trend simulation

for example, an upper shoreface passing laterally
into a lower shoreface and then into shale.
Figure 2.38 shows an example applied to the
Moray data set. The facies trend approach,
because it uses SIS, gives a more heterogeneous
pattern than indicator kriging and does not suffer
from the problem of well bulls-eyes. The latter is
because the well data is honoured at the well
position, but not necessarily in the area local to
the well.
The user can specify stacking patterns,
directions, angles and the degree of inter-
fingering. The approach can be useful, but it is
often very hard to get the desired inter-fingering
throughout the model. The best applications tend
to be shoreface environments where the logical
sequence of elements, upper to lower shoreface,
transition on a large scale. Similar modelling
effects can also be achieved by the manual appli-
cation of trends (see below).

analysed for textural content. Using a geometric
template, the frequency of instances of a model
element occurring next to similar and different
elements are recorded, as is their relative position
(to the west, the east, diagonally etc.). As the cellu-
lar model framework is sequentially filled, the
record of textural content in the training image is
referred to in order to determine the likelihood of a
particular cell having a particular model content,
given the content of the surrounding cells.
Although the approach is pixel-based, the key
step forward is the emphasis on potentially com-
plex texture rather than relatively simple
geostatistical rules. The term 'multi-point' statis-
tics compares with the 'two-point' statistics of
variography. The prime limitation of variogram-
based approaches - the need to derive simple
rules for average spatial correlation - is therefore
surmounted by modelling instead an average
texture.
In principle, MPS offers the most appropriate
algorithm for building 3D reservoir architecture,
because architecture itself is a heterogeneous
textural feature and MPS is designed to model
heterogeneous textures directly.
In spite of this there are two reasons why MPS
is not necessarily the algorithm of choice:
1. A training image is required, and this is a 3D
architectural product in itself. MPS models
are therefore not as 'instantaneous' as the
simpler pixel-based techniques such as SIS,
and require more pre-work. The example
shown in Fig. 2.39 was built using a training
data set which was itself extracted from a

2.7.3 Texture-Based Modelling

A relatively new development is the emergence
of algorithms which aim to honour texture
directly. Although there are parallels with very
early techniques such as simulated annealing
(Yarus and Chambers 1994 , Ch. 1 by Srivistava)
the approach has become more widely available
through the multi-point statistics (MPS) algo-
rithm (Strebelle 2002 ; Caers 2003 ).
The approach starts with a pre-existing training
image, typically a cellular model, which is