Civil Engineering Reference
In-Depth Information
possible in some cases (Benzi et al.
1992
; Rothman and Zaleski
1994
). Moreover,
at this level, we cannot measure physical quantities (Bachmat and Bear
1986
).
Therefore, the porous media models are often constructed through averaging the
governing equations in continua at the microscopic level over a representative
elementary volume (REV). The statistical averaging method is another commonly
used approach which treats the porous media as a random structure. The intrinsic
medium properties are represented by statistical functions. The amounts of needed
data and statistical functions are large, which makes this approach impractical.
The terminology ''representative elementary volume'' was first used in (Bear
1972
) which is defined as the minimum randomly selected volume, which keeps
the porosity features of the entire volume of the site. In other words, if the volume
is large enough, it should account for the spatial heterogeneity of the parameter of
interest within the scale of interest. A continuum approach attempts to describe
mass, momentum and energy balance laws at macroscopic scale using REV. To
summarize, the general macroscopic balance equation governing transport phe-
nomena in porous media can be formulated as
o
qW
ot
þrð
qvW
Þr
J
qF
qG
¼
0
ð
16
:
1
Þ
where
q
mass density function
W
intrinsic thermomechanical property
v
velocity
J
flux
F
external supply
G
rate of production
The equation is volume averaged over REV as illustrated in Fig.
14
. For
example,
Z
q
a
¼
1
U
U
a
q
local
a
d
ð
U
a
Þ
ð
16
:
2
Þ
is the a-phase density function, q
local
is the microscopic density function, U
denotes the volume of REV, U
a
is the subset of U occupied by the a-phase. At each
spatial point within the porous medium, the transport properties such as density
and conductivity are averaged which reflect the corresponding microscopic
properties. Details of the presentation of various averaging rules can be found in
(Bachmat
1972
; Hassanizadeh and Gray
1979
; Whitaker
1966
,
1967
,
1969
,
1973
,
1985
; Bachmat and Bear
1986
;Bear
1972
). In the following, we present some of
the commonly used fluid heat and moisture transfer properties.
