Environmental Engineering Reference
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where
ˉ
gO
2
is the oxygen mass fraction
in the gas,
D
gO
2
is the oxygen total mass dispersion tensor, and
R
O
2
and
R
Coke
are
the oxygen and coke mass sink/source due to chemical reactions. Moreover, phase
properties, the restriction
s
o
+
ˉ
sCoke
is the coke mass fraction in the solid,
1, and relations between phase pressures
(capillary pressures) were utilized. Additionally, two chemical reactions (cracking
and combustion) were considered as follows,
s
w
+
s
g
=
Oil
ₒ
ʷ
Coke
/
Oil
Coke
(8)
Coke
+
ʷ
O
2
/
Coke
O
2
ₒ
ʷ
IG
/
Coke
IG
+
ʷ
H
2
O
/
Coke
H
2
O
(9)
where
ʷ
i
/
j
is the stoichiometric factor between the
i
and
j
chemical species. In Eq. (
9
)
the chemical species
IG
(inert gas) represents an hypothetical mixture of
CO
x
and
N
2
. To compute chemical reactions, Arrhenius-like expressions were used.
In order to set up completely the mass, momentum and energy transport problem,
initial and boundary conditions are needed. These are the corresponding ones for
injection boundaries:
inj
n
·
ψ
=
ψ
(10)
isolation boundaries:
n
·
ψ
=
0
(11)
production boundaries
n
·∇
ψ
=
0
(12)
p
ψ
=
ψ
(13)
and continuity conditions at the matrix-fracture boundary:
m
f
n
·
ψ
=
n
·
ψ
(14)
Here the subscripts
inj
,
p
,
m
and
f
refer to the injection, production, matrix and
fracture boundaries (generally known values), respectively, and
n
is a unit vector
perpendicular to the boundary and pointing outside. For brevity, the generic variable
ψ
refers to any primary (scalar or vector) variable; for instance, for energy transport
ψ
=
T
I
(
I
being the identity tensor) or the total (convective plus conductive) heat
flux, if applicable. The same formulation applies for the each mass balance, and can
be applied also for initial conditions, i.e.
0
.
ψ
=
ψ
3 The Base Case
The benchmark case performed to validate the numerical results was carried out by
comparison of relevant results with those reported by Mamora (
1993
). The main
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