Environmental Engineering Reference
In-Depth Information
Assumptions:
1 Neglect porosity of packing (solid particles)
2 No chemical reactions in the packed bed
3 Neglect changes in radial direction.
The differential mass balance on the fluid phase is:
t
=−∇·
N
z
+
R
0
∂
c
,
∂
where
D
∂
c
N
z
=
v
−
c
∂
z
c
v
=
convective transport
D
∂
c
−
z
=
axial dispersion
.
∂
Open tube (no packing):
∂
c
V
0
∂
c
D
0
∂
2
c
t
=−
z
+
z
2
,
∂
∂
∂
where
D
0
=
axial dispersion coefficient
V
0
=
superficial velocity (
Q
/
A
)
and
Q
=
volumetric flowrate
A
=
cross-sectional area.
Packed tube:
2
c
∂
c
t
=−
v
∂
c
D
∂
z
+
∂
∂
∂
z
2
v
0
α
v
=
D
0
α
D
=
α
=
void fraction.
Rearranging, we obtain the model equation:
α
∂
V
0
∂
D
0
∂
2
c
c
c
t
=−
z
+
∂
∂
∂
z
2
I.C.
c
(
z
≥
0
,
t
≤
0)
=
0
B.C.
c
(
z
=
0
,
t
>
0)
=
c
0
(
t
)
c
(
z
→∞
,
t
>
0)
=
finite.
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