Environmental Engineering Reference
In-Depth Information
6.2 Triple-Continuum Model
The dual-continuum models are suitable for the simulation of a fractured reservoir
with low-permeability matrix blocks. However, for severely fractured reservoirs
where a dominant fracture system intercepts a less pervasive and nested fracture net-
work, which in turn is set within a porous matrix, dual-porosity/dual-permeability
models may not be appropriate. An immediate extension of the dual-porosity concep-
tualization is to triple porosity. For a triple-porosity/dual-permeability system, matrix
pores are interwoven with non-percolating fissures and they interact with open cracks
through fluid exchange among different phases. While these models are suitable for
severely fractured reservoirs with moderate permeability, in reservoirs with high per-
meability an extension of the model to a triple-porosity/triple-permeability concept
would be required. One important difference is that the triple-permeability model
allows each fluid phase
to carry its own permeability.
Another example of fractured reservoirs where the extension to a triple-continuum
model is important concerns the existence of vugs (i.e., empty holes or cavities) in
naturally fractured reservoirs. Typical fractured vuggy reservoirs consist of a large
and well connected fractured, lower-permeable rock matrix with a large number of
cavities, or vugs, of irregular shapes and sizes ranging from millimetres to metres
in diameter. Many of the small-sized cavities appear to be isolated from fractures.
Therefore, conceptual models for vugs include: (a) vugs that may be indirectly con-
nected to fractures through small fractures or microfractures; (b) vugs that are isolated
from fractures or separated from fractures by the rock matrix; and (c) the case where
some vugs are connected to fractures and some others are isolated. Triple-porosity
models for flow in vuggy matrix-fracture systems have been presented by Liu et al.
(
2003
), Kang et al. (
2006
) and Wu et al. (
2007
).
Irregular and stochastic distributions of small (
f
) and large fractures (
F
) can also
be handled using a triple-continuum model. For example, experimental observations
show that in typical fractured rocks there may be many more small fractures than
large ones (Liu et al.
2000
). Therefore, in a triple-continuum model the fracture-
matrix system can be conceptualized as consisting of a single porous rock matrix and
two types of fractures: large globally connected fractures and small fractures that are
locally connected to the large fractures and the rock matrix. As before, compositional
fluid flow and heat-transfer processes can be described using a continuum approach
for the two types of fractures and the matrix. We have now three transport equations
describing mass conservation for each component
k
in the multiphase mixture within
each of the three continua, which can be written by analogy with Eqs. (
120
) and (
121
)
as follows:
ʱ
ˆ
m
ʱ
∂
∂
S
m
,ʱ
ˁ
m
,ʱ
c
m
,
k
ʱ
+∇·
ˁ
m
,ʱ
c
m
,
k
ʱ
v
m
,ʱ
+
d
m
,
k
ʱ
t
ʱ
=
I
m
,
k
ʱ
−
F
mf
,
k
ʱ
−
F
mF
,
k
ʱ
,
(131)
ʱ
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