3 Dynamics of Spray Granulation in Continuously …
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predict the influence of important operational parameters on process stability using
a numerical bifurcation analysis in combination with dynamic simulations. Main
results are summarized in the following. For the details the reader is referred to
the original publications in Refs. [11, 12, 14]. For simplicity, thermal effects are
neglected in this section. The impact of thermal effects on process stability have
been briefly discussed in Sect. 5 of this chapter.
In the remainder two different types of FBLG processes are considered:
(i) A process with internal product classification, internal seed formation and variable bed mass, (ii) A process with external product classification, where the seeds
are generated with a sieve-mill cycle and the bed mass is kept constant.
For the first type of process, focus is on top spray. Seeds are generated internally
from the overspray, i.e. some small droplets which are dried before they interact with
the surface of the fluidized particles. The amount of generated seeds crucially depends
on the amount of the injected liquid and the bed height, Following [7], the basic model
introduced in the modeling section was extended accordingly [14]. In particular, it is
assumed that a part of the injected liquid is contributing to particle growth, whereas
the other part leads to the formation of new seeds by overspray. The magnitude of the
different fractions crucially depends on the bed height. The amount contributing to
seed formation decreases linearly until the bed height reaches the nozzle height and
remains constant close to zero if the bed height is larger than the nozzle height. A
second important operational parameter which has large impact on process stability
is the product withdrawal. The product withdrawal is characterized by the mean
separation diameter L 1 , which can be adjusted by means of a countercurrent air flow
used for the considered internal product classification.
Main results of the theoretical analysis using the two-zone model from Neugebauer et al. [14] are summarized in Fig. 20. The right diagram shows the stability map
depending on the separation diameter L 1 and the injected liquid ˙
V inj . Instability in the
form of self-sustained oscillations of the bed height and the particle size distribution
occurs in the shaded region. Along the upper limiting curve, bed height h bed equals
the nozzle height h nozzle and is constant. Below this limiting curve a smooth onset
of small amplitude oscillations is observed. Besides the upper limiting curve also a
lower limit to the instability region was found. With this, the experimental findings
of Schmidt et al. [57] could be explained for the first time in a consistent way. The
experimental observations were reproduced qualitatively by dynamic simulation as
shown in the left part of Fig. 20 with the time plots of bed hight and α, the relative
size of the granulation zone which is also variable in this configuration due to the
variable bed height [14]. Simulation starts at a stable steady state corresponding to
point a in the stability map. After a shift of L 1 to point b the system decays to a
different stable steady state. It starts oscillating after another shift of L 1 to point c
within the instability region and becomes stable again after a fourth move of L 1 to
point d after crossing the lower limiting curve of the instability region.
Similar patterns of behavior can be observed for the second type of process with
external product classification and a sieve mill cycle. Here, bed mass is kept constant
and the particles which are continuously withdrawn from the granulation chamber
are classified into a product, an undersized and an oversized fraction. The oversized
97
predict the influence of important operational parameters on process stability using
a numerical bifurcation analysis in combination with dynamic simulations. Main
results are summarized in the following. For the details the reader is referred to
the original publications in Refs. [11, 12, 14]. For simplicity, thermal effects are
neglected in this section. The impact of thermal effects on process stability have
been briefly discussed in Sect. 5 of this chapter.
In the remainder two different types of FBLG processes are considered:
(i) A process with internal product classification, internal seed formation and variable bed mass, (ii) A process with external product classification, where the seeds
are generated with a sieve-mill cycle and the bed mass is kept constant.
For the first type of process, focus is on top spray. Seeds are generated internally
from the overspray, i.e. some small droplets which are dried before they interact with
the surface of the fluidized particles. The amount of generated seeds crucially depends
on the amount of the injected liquid and the bed height, Following [7], the basic model
introduced in the modeling section was extended accordingly [14]. In particular, it is
assumed that a part of the injected liquid is contributing to particle growth, whereas
the other part leads to the formation of new seeds by overspray. The magnitude of the
different fractions crucially depends on the bed height. The amount contributing to
seed formation decreases linearly until the bed height reaches the nozzle height and
remains constant close to zero if the bed height is larger than the nozzle height. A
second important operational parameter which has large impact on process stability
is the product withdrawal. The product withdrawal is characterized by the mean
separation diameter L 1 , which can be adjusted by means of a countercurrent air flow
used for the considered internal product classification.
Main results of the theoretical analysis using the two-zone model from Neugebauer et al. [14] are summarized in Fig. 20. The right diagram shows the stability map
depending on the separation diameter L 1 and the injected liquid ˙
V inj . Instability in the
form of self-sustained oscillations of the bed height and the particle size distribution
occurs in the shaded region. Along the upper limiting curve, bed height h bed equals
the nozzle height h nozzle and is constant. Below this limiting curve a smooth onset
of small amplitude oscillations is observed. Besides the upper limiting curve also a
lower limit to the instability region was found. With this, the experimental findings
of Schmidt et al. [57] could be explained for the first time in a consistent way. The
experimental observations were reproduced qualitatively by dynamic simulation as
shown in the left part of Fig. 20 with the time plots of bed hight and α, the relative
size of the granulation zone which is also variable in this configuration due to the
variable bed height [14]. Simulation starts at a stable steady state corresponding to
point a in the stability map. After a shift of L 1 to point b the system decays to a
different stable steady state. It starts oscillating after another shift of L 1 to point c
within the instability region and becomes stable again after a fourth move of L 1 to
point d after crossing the lower limiting curve of the instability region.
Similar patterns of behavior can be observed for the second type of process with
external product classification and a sieve mill cycle. Here, bed mass is kept constant
and the particles which are continuously withdrawn from the granulation chamber
are classified into a product, an undersized and an oversized fraction. The oversized