4 Dynamic Simulation of Technical Precipitation Processes
133
Fig. 20 Median of
volume-based PSD (L 50,3 )
versus the splitting factor β
and two different mixing
assumptions (ideal mixed
and micro mixing model by
[4]). Reprinted with
permission from [5]
0.0
0.1
0.2
0.3
20
40
60
80
100
120
L
50,3 (nm)
β (-)
Experiment (SLS)
SimulaƟon (id. mixed)
SimulaƟon (micro mixing model)
3.2 Validation of the Equivalent Circuit Model Concept
The two-zone experiments (Setup D, Sect. 2.2.2.2) were performed to verify whether
the assumption of a well-mixed stirred tank connected to a PFR is, in principle, a
suitable analogon for depicting the semi-batch process. As Bałdyga and Bourne [24]
did not selectively investigate this aspect before using this model idea for simulation,
we performed an “experimental simulation” by comparing particle sizes from the bulk
semi-batch and corresponding two-zone equivalent circuit experiments. This method
allows us to approximate the error which originates from this model concept. The
corresponding value of Q circ,1 was calculated for a given stirring rate N of the bulk
process by using the method published in [29]. The two-zone experiment was then
performed according to the procedure described in Sect. 2.2.2.2 over a wide range
of process conditions.
Figure 21 illustrates an exemplary result using the example of two process conditions, firstly, with 150 rpm and u prim = 0.39 m/s and, secondly, with 50 rpm and
u prim = 0.13 m/s. The resulting PSDs are quite similar with slightly larger particles generated in the two-zone process. This effect of slightly larger particles was
observed over a wide range of process conditions and two different stirrer types in
[29]. Therefore, it can be concluded that the equivalent circuit assumption and the
correlation for Q circ,1 introduces a small error on the final PSD. However, this error
is not significant in the context of process flowsheet simulations, where the simplified model assumptions only allow for a coarse estimation of the target variables.
Consequently, replacing the semi-batch process by the equivalent circuit of PFR and
well-mixed BF is a suitable modeling strategy for process flowsheet simulation.
133
Fig. 20 Median of
volume-based PSD (L 50,3 )
versus the splitting factor β
and two different mixing
assumptions (ideal mixed
and micro mixing model by
[4]). Reprinted with
permission from [5]
0.0
0.1
0.2
0.3
20
40
60
80
100
120
L
50,3 (nm)
β (-)
Experiment (SLS)
SimulaƟon (id. mixed)
SimulaƟon (micro mixing model)
3.2 Validation of the Equivalent Circuit Model Concept
The two-zone experiments (Setup D, Sect. 2.2.2.2) were performed to verify whether
the assumption of a well-mixed stirred tank connected to a PFR is, in principle, a
suitable analogon for depicting the semi-batch process. As Bałdyga and Bourne [24]
did not selectively investigate this aspect before using this model idea for simulation,
we performed an “experimental simulation” by comparing particle sizes from the bulk
semi-batch and corresponding two-zone equivalent circuit experiments. This method
allows us to approximate the error which originates from this model concept. The
corresponding value of Q circ,1 was calculated for a given stirring rate N of the bulk
process by using the method published in [29]. The two-zone experiment was then
performed according to the procedure described in Sect. 2.2.2.2 over a wide range
of process conditions.
Figure 21 illustrates an exemplary result using the example of two process conditions, firstly, with 150 rpm and u prim = 0.39 m/s and, secondly, with 50 rpm and
u prim = 0.13 m/s. The resulting PSDs are quite similar with slightly larger particles generated in the two-zone process. This effect of slightly larger particles was
observed over a wide range of process conditions and two different stirrer types in
[29]. Therefore, it can be concluded that the equivalent circuit assumption and the
correlation for Q circ,1 introduces a small error on the final PSD. However, this error
is not significant in the context of process flowsheet simulations, where the simplified model assumptions only allow for a coarse estimation of the target variables.
Consequently, replacing the semi-batch process by the equivalent circuit of PFR and
well-mixed BF is a suitable modeling strategy for process flowsheet simulation.