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For the explicit case, there are then several
options for how this may be done:
1. Discrete Fracture Network (DFN) models,
where individual fractures with explicit geom-
etry are modelled in a complex network.
2. Dual permeability models, where the fracture
and matrix permeability are explicitly
represented (but fracture geometry is implic-
itly represented by a shape factor).
3. Dual porosity models, where the fracture
and matrix porosity are explicitly represented,
but the permeability is assumed to occur
only in the fractures
b
q
w
L
Fig. 3.13 Flow in a fracture
(and the fracture
geometry is
implicitly represented by a
shape factor).
Fractured reservoir modelling is discussed in
detail by Nelson ( 2001 ) and covered in most
reservoir engineering textbooks, and in Chap. 6
we describe approaches for handling fractured
reservoir models. The important thing to keep
in mind in the context of understanding perme-
ability, is that fractures behave quite differently
(and follow different laws) from the general
Darcy-flow concept for flow in permeable (gran-
ular) rock media.
law, which for a parallel-plate geometry gives
(Mourzenko et al. 1995 ):
wb 3
12
ʔ
P
L
q
¼
ð
3
:
12
Þ
ʼ
where
q is the volumetric flow rate,
w is the fracture width,
b is the fracture aperture,
ʼ
is the fluid viscosity,
ʔ
Note that the flow rate is proportional to b 3 ,
and thus highly dependent on fracture aperture.
In practice, the flow strongly depends on the
stress state and the fracture roughness
(Witherspoon et al. 1980 ), but the underlying
concept still holds. To put some values into this
simple equation - a 1 mm wide fracture in an
impermeable rock matrix would have an effec-
tive permeability of around 100 Darcys.
Unfortunately, fracture aperture is not easily
measured, and generally has to be inferred from
pressure data. This makes fracture systems much
harder to model than conventional non-fractured
reservoirs.
In practice, there are two general approaches
for modelling fracture permeability:
￿ Implicitly, where we model the overall rock
permeability (matrix and fractures) and
assume we have captured the “effect of
fractures” as an effective permeability.
￿ Explicitly, where we represent the fractures in
a model.
3.3
Handling Statistical Data
3.3.1 Introduction
ability, or any other reservoir property, are caused
by incorrect understanding or use of probability
distributions. The treatment of probability
distributions is an extensive subject covered in a
number of textbooks. Any of the following are
suitable for geoscientists and engineers wanting to
gain deeper appreciation of statistics and the Earth
sciences: Size 1987 ; Isaaks and Srivastava 1989 ;
Olea 1991 ;Jensenetal. 2000 ,andDavis 2003 .Here
we will identify some of the most important issues
related to property modelling, namely:
￿ Understanding sample versus population
statistics;
￿ Using log-normal and other transforms;
￿ Use and implications of applying cut-off values.                             Search WWH ::

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