Environmental Engineering Reference
In-Depth Information
S
ʱ
=
1
(5)
ʱ
=
g
,
o
,
w
n
c
1
ˉ
i
ʱ
=
,ʱ
=
,
,
1
g
o
w
(6)
i
=
p
cow
(
S
w
)
=
p
o
−
p
w
,
p
cgo
(
S
g
)
=
p
g
−
p
o
(7)
ˉ
i
ʱ
=
K
i
ʱʲ
(
p
,
T
) ˉ
i
ʲ
;
i
=
1
,...,
N
c
,ʱ,ʲ
=
g
,
o
,
w
(8)
Initial and boundary conditions
ˉ
i
ʱ
(
x
,
0
)
=
ˉ
i
ʱ
(
x
),
i
=
1
,...,
n
c
−
1
,ʱ
=
o
,
w
S
w
(
,
)
=
S
w
0
(
)
x
0
x
S
g
(
,
)
=
S
g
0
(
)
x
0
x
p
o
(
x
,
0
)
=
p
o
0
(
x
)
(9)
T
(
x
,
0
)
=
T
0
(
x
)
u
ʱ
(
x
,
t
)
=
0
,
x
∈
∂
∇
T
(
x
,
t
)
=
0
,
x
∈
∂
In Eqs. (
1
)-(
9
)
A
i
represents the reactants stoichiometric coefficients,
B
i
the
products stoichiometric coefficients,
C
s
the solid mass heat capacity,
D
i
ʱ
the diffu-
sion coefficient of component
i
in phase
,
g
is the gravity vector,
H
is the enthalpy,
k
T
is the total thermal conductivity of the porous media,
k
is absolute permeabil-
ity,
k
r
is the relative permeability,
K
i
ʱʲ
ʱ
is the equilibrium K-value of component
i
between phases
,
n
c
is the number of components,
p
is pressure,
p
cow
is
the oil-water capillary pressure,
p
cog
is the oil-gas capillary pressure,
q
is the source
volumetric rate,
q
c
is heat source rate,
q
L
is heat loss rate,
r
i
ʱ
ʱ
and
ʲ
is the rate of production
of component
i
by reactions,
S
is saturation,
T
is temperature,
U
is internal energy,
u
is velocity,
x
is position vector,
ˆ
is porosity,
ˁ
ʱ
is phase density,
ˁ
s
is solid density,
μ
ʱ
is phase dynamic viscosity,
ˉ
i
ʱ
is the mass fraction of component
i
in phase
ʱ
, and
˃
is the solid volume fraction. The subscript
ʱ(
=
g
,
o
,
w
)
represents phase
evaluated as gas, oil or water.
For more information about the mathematical model, we refer to the reader to the
STARS user's guide (see references list).
3 Homogeneous System Simulation
The model simulation was validated using experimental data from a combustion tube
reported in the work from Kumar (
1987
). In the experiment, a sand pack (mixture of
oil, water and sand) was put in the tube. An electrical igniter was used at the top of
the tube in order to generate a combustion front that propagates along the tube. For
more information, we refer the reader to the work of Kumar (
1987
).
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