Geoscience Reference
In-Depth Information
properties at a larger scale given some set of finer
scale rock properties. Upscaling methods for sin-
gle and multiphase flow are reviewed in detail by
Renard and de Marsily (
1997
), Barker and
Thibeau (
1997
), Ekran and Aasen (
2000
) and
Pickup et al. (
2005
). We will review the methods
involved and establish the principles which guide
the flow upscaling process. The term
downscal-
ing
has also been used (Doyen
2007
) to mean the
process by which smaller-scale properties are
estimated from a larger-scale property. This is
most commonly done in the context of seismic
data where, for example, a porosity value
estimated from seismic impedance is used to
constrain the porosity values of thin layers
below the resolution of the seismic wavelet. In
more general terms, if we know all the fine-scale
properties then the upscaled property can be
estimated uniquely. Conversely, if we know
only the large-scale property value then there
are many alternative fine-scale property models
that could be consistent with the upscaled
property.
We will develop the argument that upscaling
is essential in reservoir modelling - whether
implicit or explicit. There is no such thing as
the
correct
value for the permeability of a given
hydraulic flow unit. The relevant permeability
value depends on length-scale, the boundary
conditions and flow process. Efforts to define
the diagnostic characteristics for hydraulic flow
units (HFU) (e.g. Abbaszadeh et al.
1996
) pro-
vide valuable approaches to petrophysical data
analysis, but HFUs should always be related to a
representative elementary volume (REV). As we
will show it is not always simple to define the
REV, and when flow process are brought into
play different REVs may apply to different flow
processes. Hydraulic flow units are themselves
multi-scale.
The framework we will use for upscaling
involves a series of steps where smaller-scale
models are nested within larger scale models.
These steps essentially involve models or
concepts at the pore-scale, geological concepts
and models at the field-scale and reservoir
simulations (Fig.
4.3
).
The factors involved in these scale transitions
are enormous; certainly around 10
9
as we go
from the rock pore to the full-field reservoir
model (Table
4.1
), and important scale markers
involved in reservoir modelling are best
illustrated on a logarithmic scale (Fig.
4.4
).
Despite these large scale transitions, most flow
processes average out the local variations - so
that what we are looking for is the correct aver-
age flow behaviour at the larger scales. How we
do this is the rationale for this chapter.
Flow simulation of detailed reservoir models
is a fairly demanding exercise, involving many
mathematical tools for creating and handling
flow grids and calculating the flows and
pressures between the grid cells. The mathemat-
ics of flow simulation is beyond the scope of this
topic, and will be treated only in an introductory
sense. Mallet (
2008
) gives a recent review of
the processes involved in the creation of numer-
ical rock models and their use in flow simula-
tion. King and Mansfield (
1999
)alsogivea
fairly comprehensive discussion of flow simula-
tion of geological reservoir models, in terms of
managing and handling the grid and associated
flow terms (transmissibility factors). In this
chapter, we will take as our starting point the
existence of a numerical rock model, created by
some set of recipes in a geological modelling
toolkit, and will focus on the methods involved
for performing multi-scale upscaling. Before we
do that we need to introduce, or recapitulate,
some of the basic theory for multiphase fluid
flow.
4.2
Multi-phase Flow
4.2.1 Two-Phase Flow Equations
In Chap.
3
we introduced the concept of perme-
ability and the theoretical basis for estimating
effective permeability using averages and
numerical recipes. This introduced us to
upscaling for single-phase flow properties. Here
we extend this by looking at two-phase flow and
the upscaling of multi-phase flow properties.
