7 Dynamic Simulation of Mechanical Fluid Separation in Solid …
261
V cyl = π
R
2
d − R
2
w
L cyl ,
(27)
is decisive for the calculation of the volumetric filling level. The mass balance for
solid, liquid and particle size distribution is the same for the dynamic modeling of
decanter and tubular centrifuges. At this point, it should be noted that the rotating
gas core and thus the gas liquid-interphase are not considered in the dynamic model
presented. Additionally, no particle breakage occurs in the feed zone of the tubular
centrifuge. Moreover, the slurry rotates as a rigid body. This means that an insufficient
pre-acceleration is not taken into account by the presented approach.
5.2 Modeling of the Sediment Zone
Since a tubular centrifuge is a semi-continuous apparatus, the process behavior for
sediment build-up differs from that of a decanter centrifuge. Here, the solid accumulates continuously on the inner rotor wall until the apparatus is completely filled. As
a result, the solids mass balance in a compartment of the sediment zone simplifies
as follows:
dm s,sed,i
dt
= ˙
m s,sed,i .
(28)
The continuous supply of solids during the entire process leads to a complete
filling of the rotor up to the maximum volumetric filling level theoretically. For the
prediction of the radial position of the sediment surface for the compartments i = 1,
…, N the solids mass balance is transformed into a volume balance of solids:
dV s,sed,i
dt
= Q s,sed,i .
(29)
The dynamic simulation of the sediment build-up along the axial position of the
rotor allows the temporal prediction of the sediment distribution. The accumulated
volume of the sediment is used to determine the radial position of the sediment
surface
R s,i (t) =
R
2
d −
V sed,i (t)
ππl
0.5
,
(30)
for each compartment (index i). The radial position of the sediment surface is then
used to calculate the volume of the sedimentation zone in Eq. (26) and thus to map
the residence time behavior which deviates with process time. Stahl et al. [29] show
that the sediment in tubular centrifuges only increases up to a critical volumetric
filling level of U max = 0.95. This means that the sediment does not emerge from
261
V cyl = π
R
2
d − R
2
w
L cyl ,
(27)
is decisive for the calculation of the volumetric filling level. The mass balance for
solid, liquid and particle size distribution is the same for the dynamic modeling of
decanter and tubular centrifuges. At this point, it should be noted that the rotating
gas core and thus the gas liquid-interphase are not considered in the dynamic model
presented. Additionally, no particle breakage occurs in the feed zone of the tubular
centrifuge. Moreover, the slurry rotates as a rigid body. This means that an insufficient
pre-acceleration is not taken into account by the presented approach.
5.2 Modeling of the Sediment Zone
Since a tubular centrifuge is a semi-continuous apparatus, the process behavior for
sediment build-up differs from that of a decanter centrifuge. Here, the solid accumulates continuously on the inner rotor wall until the apparatus is completely filled. As
a result, the solids mass balance in a compartment of the sediment zone simplifies
as follows:
dm s,sed,i
dt
= ˙
m s,sed,i .
(28)
The continuous supply of solids during the entire process leads to a complete
filling of the rotor up to the maximum volumetric filling level theoretically. For the
prediction of the radial position of the sediment surface for the compartments i = 1,
…, N the solids mass balance is transformed into a volume balance of solids:
dV s,sed,i
dt
= Q s,sed,i .
(29)
The dynamic simulation of the sediment build-up along the axial position of the
rotor allows the temporal prediction of the sediment distribution. The accumulated
volume of the sediment is used to determine the radial position of the sediment
surface
R s,i (t) =
R
2
d −
V sed,i (t)
ππl
0.5
,
(30)
for each compartment (index i). The radial position of the sediment surface is then
used to calculate the volume of the sedimentation zone in Eq. (26) and thus to map
the residence time behavior which deviates with process time. Stahl et al. [29] show
that the sediment in tubular centrifuges only increases up to a critical volumetric
filling level of U max = 0.95. This means that the sediment does not emerge from