Environmental Engineering Reference
In-Depth Information
+
s
i
+
1
=
1
∂
∂
r
n
∂
r
n
∂
D
eff
ρ
g
∂
∂
r
n
r
n
t
ε
ρ
g
Y
i
ε
ρ
g
Y
i
u
ε
r
Y
i
ð
Eq
:
4
:
54
Þ
∂
r
∂
r
where Y
i
is the mass fraction of component i in the gas phase; u is the gas convection
velocity in radial direction;
D
eff
is the effective gas diffusivity, here assumed to be
independent on the species; and
s
i
is the source or sink term. The subscript i denotes
any gas component (T for tar, G for light gas, and I for inert gas). Comparing with the
general form of the species transport equation Equation (4.1), the following features
can be pointed out: the effect of the presence of porosity, only one-dimensional equa-
tion in appropriate coordinate system, Fick
'
s law for diffusion, and notation of source
ω
i
to
s
i
.
The source terms are given by
term changed from
s
T
=k
2
ρ
B
−
ε
k
4
ρ
T
−
ε
k
5
ρ
T
s
C
=k
1
ρ
B
+
ε
k
4
ρ
T
:
:
ð
Eq
4
55
Þ
s
I
=0
Again, the porosity appears in order to take into account that the density of gas referred
to the total volume is smaller than the intrinsic density of the gas inside the pores. The
total gas-phase continuity equation is obtained by summation of the species equations
and has the form
t
ε
ρ
g
+
1
=
s
g
∂
∂
r
n
∂
r
n
ε
ρ
g
u
ð
Eq
:
4
:
56
Þ
∂
r
with
s
g
=k
1
ρ
B
+k
2
ρ
B
−
ε
k
5
ρ
T
ð
Eq
:
4
:
57
Þ
The flow of gas inside the particle can be described as flow in a porous medium.
In a porous medium, convection is caused solely by the pressure gradient. The
area-averaged velocity through a cross-sectional plane through the medium is related
to the local pressure drop by Darcy
'
s law:
B
η
∂
p
∂
u
=
−
ð
Eq
:
4
:
58
Þ
r
where
B
is the solid permeability [m
2
],
η
is the dynamic viscosity of the gas [Pa
s], and
p
is the gas pressure given by the ideal gas law:
p
=
ρ
g
R
u
T
MW
g
ð
Eq
:
4
:
59
Þ
The permeability
B
can be written as the mass-weighted average of the permeability of
the biomass part and the char part of the porous medium:
B
=
ρ
B
ρ
B
0
B
C
−
ρ
B
ρ
B
0
B
B
+1
ð
Eq
:
4
:
60
Þ
During conversion, the fraction of biomass decreases and the char part increases.
The subscript 0 indicates the initial state, before conversion to char. The local velocity
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