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step-wise upscaling scheme. Structural features
are typically incorporated at the geomodel scale.
However, effects of smaller scale faults may
also be incorporated as effective properties (as
transmissibility multipliers) using upscaling
approaches. The incorporation of fault transmis-
sibility into reservoir simulators is considered
thoroughly by Manzocchi et al (
2002
). Conduc-
tive fractures may also affect sandstone
reservoirs, and are often the dominant factor in
carbonate reservoirs. Approaches for multi-scale
modelling of fractured reservoirs have also been
developed (e.g. Bourbiaux et al.
2002
) and will
be developed further in Chap.
6
.
Historical focus over the last few decades has
been on including increasingly more detail into
the geomodel, with only one upscaling step being
explicitly performed. Full-field geomodels are
typically in the size range of 1-10 million cells
with horizontal cell sizes of 50-100 m and vertical
cell sizes of order 1-10 m. Multi-scale modelling
allows for better flow unit characterization and
improved performance predictions (e.g. Pickup
et al.
2000
; Scheiling et al.
2002
). There are also
examples where a large number of grid cells are
applied to sector or near-well models reducing cell
sizes to the dm-scale. Upscaling of the near-well
region requires methods to specifically address
radial flow geometry (e.g. Durlofsky et al.
2000
).
Recent focus on explicit small-scale
lithofacies modelling includes the use of million
cell models with mm to cm size cells (e.g.
Ringrose et al.
2003
; Nordahl et al
2005
).
Numerical pore-scale modelling employs a simi-
lar number of network nodes at the pore scale
(e.g. Øren and Bakke
2003
). Model resolution is
always limited by the available computing
power, and although continued efficiencies and
memory gains are expected in the future, the use
of available numerical discretisation at several
scales within a hierarchy is preferred to efforts
to apply the highest possible resolution at one of
the scales (typically the geomodel). There is also
an argument that advances in seismic imaging
coupled with computing power will enable direct
geological modelling at the seismic resolution
scale. However, even when this is possible,
seismic-based lithology prediction (using seis-
mic
modelling of the petrophysical properties within
Upscaling methods impose further limitations
on the value and utility of models within a multi-
scale framework. In conventional upscaling -
from a geological model to a reservoir simulation
grid - there are various approaches used. These
cover a range which can be classed in terms of
the degree of simplification/complexity:
1.
Averaging of well data directly into the flow
simulation grid:
This approach essentially
ignores explicit upscaling and neglects all
aspects of smaller scale structure and flows.
The approach is fast and simple and may be
useful for quick assessment of expected reser-
voir flows and mass balance. It may also be
adequate for very homogeneous and highly
permeable rock sequences.
2.
Single-phase upscaling only in
z:
This com-
monly applied approach assumes a simulation
grid designed with the same
ʔ
y as the
geological grid. The approach is often used
where complex structural architecture
provides very tight constraints to design of
the flow modelling grid. Upscaling essentially
comprises use of averaging methods but
ensures a degree of representation of thin
layering or barriers. Also, where seismic data
gives a good basis for the geological model in
the horizontal dimensions, vertical upscaling
of fine-scale layering to the reservoir simula-
tor scale is typically required.
3.
Single-phase upscaling in
ʔ
x, the
ʔ
z:
With
this approach multi-scale effective flow
properties are explicitly estimated and the
upscaling tools are widely available (diagonal
tensor or full-tensor methods). Multiphase
flow effects are however neglected.
4.
Multi-phase upscaling in
ʔ
x
ʔ
y and
ʔ
z:
This
approach represents an attempt to calculate
effective multiphase flow properties in larger
scale models. The approach has been used
rather too seldom due to demands of time
and resources. However, the development of
steady-state solutions to multiphase flow
upscaling problems (Smith
1991
; Ekran and
Aasen
2000
; Pickup and Stephen
2000
) has
led to wider use in field studies (e.g. Pickup
et al
2000
; Kløv et al
2003
).
ʔ
x
ʔ
y and
ʔ
inversion) will
require
smaller-scale
