Dynamics of Spray Granulation in Continuously Operated Horizontal Fluidized Beds

Abstract

This chapter presents new findings on process and product design in continuous spray layering granulation in horizontal fluidized beds. The results are achieved by a multi-scale approach, combining single-particle characterization of the influence of drying conditions on layer formation and properties with meso-scale information of particle flow and recirculation between process chambers separated by weirs. On the macro-scale, population balance modeling is used to describe the overall process dynamics taking into account apparatus design and process conditions. New process regime maps are presented along with control concepts to guarantee stable and safe operation as well as desired particle properties.

1 Introduction

Spray layering (granulation) is a particle formulation process in which a solid containing liquid is sprayed onto a collection of core particles. The droplets collide with the cores and wet their surface. Supplying a heated gas flow, the liquid evaporates and the solid remains on the core particle surface. By continued spraying and evaporation, full layers can be obtained. As a consequence, the particles grow in size.

Horizontal fluidized beds are a key technology in spray layering, with widespread application in the areas of food, feed, fine chemicals and pharmaceuticals. They can be used to combine more than one operation in a single apparatus, for example layering of particles with a solid-containing liquid, followed by drying and cooling. For this, the apparatus can be compartmentalized along the apparatus length, by installation of weirs, creating different process chambers (Fig. 1).

Fig. 1

Schematics of a typical spray granulation process in a horizontal fluidized bed with multiple process chambers generated by the insertion of weirs. Additionally shown is the external screen-mill cycle for product classification [1]

Installation of weirs generates a residence time distribution (RTD) of the particles in the apparatus, as the passing of a weir by an individual particle depends on the particle properties, for example mass density, sphericity, as well as the fluidization conditions. Residence time distributions are known to cause product property distributions, for example differences in particle size in granulation, or product moisture content in drying operation.

The knowledge of the effect of an individual weir, parameterized with respect to particle properties and fluidization conditions, would allow answering a number of important design questions, for example how many weirs are required in an apparatus to obtain a desired spread of the residence time distribution, and therefore guide the design and operation of horizontal fluidized beds.

Furthermore, thermal conditions influence the dynamics of the evaporation process and thereby the dynamics of layer formation and layer properties, for instance layer thickness and porosity. These in turn influence the evolution of the particle size distribution.

Product classification in continuous operation can be performed internally and externally, for example by a screen-mill cycle. Here, the particle size distribution in the horizontal fluidized bed determines the dynamics of the process including the classification, for example the magnitude and time-scale of recycle flows or loads on screens and mill, influencing their efficiency.

Due to the multi-scale interaction, starting with single-particle layer formation dynamics over particle flows between adjacent process chambers to large-scale process and plant behavior, spray layering granulation in horizontal fluidized beds is a prototypical interconnected solids process.

The research aims of the project were:

• 1. Study the influence of thermal conditions on the dynamics of layer formation and layer properties;

• 2. Study and characterize the influence of weir design and configuration on residence time and particle property distributions;

• 3. Derive and extend population balance models to describe the temporal evolution of particle properties with respect to apparatus (weir) design and operating parameters;

• 4. Using these models, study the dynamic and steady-state behavior of the continuous spray layering in horizontal fluidized beds;

• 5. Derive, design and implement control strategies to prevent unwanted process behavior and guarantee required product properties under model uncertainties and process disturbances.

This chapter is structured as follows: In Sect. 2, the basic population balance model for continuous spray layering in horizontal fluidized beds is introduced, considering particle flows not only between adjacent process chambers but also between different functional compartments within each chamber. This is followed in Sect. 3 by experimental and simulation results on the particle exchange rates between chambers under the influence of weir design. Section 4 collects the experimental results with respect to the influence of thermal conditions on particle properties. This is followed in Sect. 5 by the presentation of a model extension, to allow predictive simulation of property development for different thermal conditions in each chamber. Using the extended model, the dynamic and steady-state behavior can be studied in detail. Section 6 presents results of the system theoretic analysis using the process model, identifying different process regimes (stable, unstable) depending on the operation and process conditions. This presentation is followed in Sect. 7 by results on control of the overall process, to stabilize operation and to guarantee desired product properties. The chapter closes with Sect. 8, a summary and outlook.

2 Basic Population Balance Model for Spray Granulation in A Multi-chamber Setup

In this section a multi-chamber and multi-compartment model of a horizontal fluidized bed apparatus for layering granulation is presented. Each chamber is designed individually and process conditions, such as spray rate, particle feed or gas temperature, can be adjusted for each chamber separately. Particle growth is described by population balance modeling. The particle exchange rates between the process chambers are determined individually to account for different weir configurations.

The growth of particles by layering is described within the population balance equation (PBE) framework as introduced for particulate processes by Ramkrishna [2].

The main idea of population balance modeling is the description of the temporal evolution of the number density function (or other density functions derived from it). For this, all relevant sub-processes that yield a change in the density have to be modelled. The density function characterizes the distribution of particle properties, for example the particle size, moisture content or temperature. Solving for the density function thereby gives information on the change of these particle properties. Population balance modeling has been used successfully to describe fluidized bed drying, agglomeration and layering granulation processes, for instance by Refs. [3,4,5,6,7].

To account for the fact that the sprayed solution or suspension can only reach a fraction of the particle bed it is necessary to divide the process chamber into compartments of different functionalities. For this purpose [8,9,10] introduced multi-compartment models for fluidized bed coating and layering granulation. Particularly, two-compartment models have been applied by Refs. [11,12,13,14] for fluidized bed layering granulation and coating processes.

A two-compartment model is integrated into the multi-chamber model to describe particle growth and all relevant particle flows in each chamber. Figure 2 illustrates the developed multi-chamber and multi-compartment model. In this model the two compartments are considered to be arranged vertically in order to account for bottom or top-spray of the solid-containing spray. In case of top-spray configuration, the upper compartment (denoted by ‘1’ in Fig. 2) is the spray compartment in which the particles are in direct contact with the sprayed liquid. In the lower zone (compartment ‘2’) only drying and mixing of the contained particles take place. In bottom-spray configuration the lower zone ‘2’ is assigned to be the spray zone and the upper zone ‘1’ the drying zone, respectively.

Fig. 2

Schematic representation of setup and particle flows in the multi-chamber, multi-compartment model

The population balance equations for the number distribution density of particles with respect to particle size L of each compartment j in each chamber i, $n_{i,j}$, are written as follows:

$$\begin{aligned} \frac{\partial n_{i,j}}{\partial t} = -\frac{ \partial \left( G_{i,j} \ n_{i,j} \right) }{\partial L}-\frac{n_{i,j}}{\tau _{i,j}} + \frac{n_{i,\bar{j}}}{\tau _{i,\bar{j}}} + \dot{n}_{i,j,in} - \dot{n}_{i,j,out}. \end{aligned}$$

(1)

The total number distribution density of each chamber $n_i$ is the sum of the number distributions of all compartments j within the chamber i,

$$\begin{aligned} n_i = \sum _{j=1}^J n_{i,j}. \end{aligned}$$

(2)

The volume fraction of the compartment, $\omega _{i,j}$, and the particle residence time in this compartment, $\tau _{i,j}$, can be determined experimentally or taken from literature (e.g. [13] or [11]). The ratio of the mean residence times of the two zones equals the ratio of the compartment volumes:

$$\begin{aligned} \frac{\tau _{i,j}}{\tau _{i,\bar{j}}} = \frac{\omega _{i,j}}{\omega _{i,\bar{j}}}. \end{aligned}$$

(3)

All particles in a chamber are contained in the two compartments, yielding the constraint:

$$\begin{aligned} \sum _{j=1}^2 \omega _{i,j} = 1. \end{aligned}$$

(4)

In the spray compartment ($j=1$ for top-spray and $j=2$ for bottom-spray configuration) the growth rate of particles, $G_{i,j}$, can be expressed by a relation proposed by Mörl et al. [15]:

$$\begin{aligned} G_{i,j} = \frac{2 \ y_{sus,s} \, M_{sus,i,j}}{\left( 1-\epsilon _{sh}(\eta _{dry,i})\right) \ \varrho _{s} \ A_{p,i,j}} \end{aligned}$$

(5)

with

$$\begin{aligned} A_{p,i,j} = \pi \int L^2 n_{i,j} (t,L)~ dL = \pi \ \mu _{2,i,j}(t), \end{aligned}$$

(6)

where $\mu _{2,i,j}$ is given by

$$\begin{aligned} \mu _{2,i,j}(t) = \int \limits _0^\infty L^2 n_{i,j}(t,L)~ dL. \end{aligned}$$

(7)

It contains the assumption that the sprayed liquid mass is distributed equally on the particle surface, $A_{p,i,j}$, which can be calculated from the second moment of number distribution density in the respective compartment, $n_{i,j}$. In case of spherical particles, the particle surface within the spray zone can be determined by Eq. (6).

The porosity of the formed shell, $\epsilon _{sh}$, depends on thermal process conditions and the material of the initial core as shown experimentally by Rieck et al. [16].

The particle number flow rates between the chambers are represented by $\dot{n}_{i,j,out}$ and $\dot{n}_{i,j,in}$:

$$\begin{aligned} \dot{n}_{i,j,out}&= \dot{n}_{out,i,j}^- + \dot{n}_{out,i,j}^+,\end{aligned}$$

(8)

$$\begin{aligned} \dot{n}_{i,j,in}&= \dot{n}_{in,i,j}^- + \dot{n}_{in,i,j}^+ , \end{aligned}$$

(9)

$$\begin{aligned} \dot{n}_{in,i,j}^-&= \dot{n}_{out,i-1,j}^+ ,\end{aligned}$$

(10)

$$\begin{aligned} \dot{n}_{in,i,j}^+&= n_{out,i+1,j}^-. \end{aligned}$$

(11)

Particle flows that enter from or leave to a previous chamber are denoted by “−”. Those that enter from or leave to a subsequent chamber are denoted by “$+$” (see Fig. 2). In case of the first and the last chamber these equations have to be modified, since there is no previous or subsequent chamber, respectively. For the first chamber the inlet flows $\dot{n}_{in,1,j}^-$ and the outlet flows $\dot{n}_{out,1,j}^-$ are 0. The same applies for the inlet flows $\dot{n}_{in,I,j}^+$ of the last chamber. The product flow is the sum of forward outlet flows of the last chamber $\dot{n}_{out,I,j}^+$.

The particle flow at the chamber inlet and outlet depends on various factors, for example particle properties, like particle size and density distribution, the fluidization regime as well as the geometric design of the weir. Weirs, therefore, may have influence on the overall movement and recirculation of particles and mixtures in a process chamber. The characterization of the weir influence can be performed experimentally by particle tracking velocimetry (PTV) as described by Meyer et al. [17] or theoretically by combination of computational fluid dynamics (CFD) and discrete element method (DEM).

3 Determination of Inter-chamber Particle Transfer

In solids processing in horizontal fluidized beds the formation of residence time distributions and subsequently of property distributions, for instance in moisture content, particle size or chemical composition, are observed. Residence time distributions are due to partial recirculation of particles against the main transport direction. It is known that the installation of weirs, thus dividing the apparatus into multiple chambers, influences the overall residence time distribution.

Weirs are rectangular plates which are installed perpendicular to the main solid transport direction. Three common designs exist, shown in Fig. 3: Over-flow weirs which are installed directly on top of the distributor plate so that particles have to overcome the weir; under-flow weirs with a defined gap between weir and distributor plate; and side-flow weirs which are similar to under-flow weirs, however, the gap only exists over a certain portion of the apparatus width.

Fig. 3

Weir designs: over-flow weir (left), under-flow weir (center), side-flow weir (right)

The effect of individual weirs on the observed dispersion has not been fully understood with respect to operation parameters, material properties or weir geometry.

Therefore, methods were developed and tested that allow investigating the particle transfer from one chamber to another and vice versa. In contrast to previous attempts to characterize the transport behavior by tracer experiments (see for instance [18,19,20,21]), particle tracking velocimetry (PTV) was utilized. The main advantage is that PTV allows the determination of exchange rates on single particle basis.

3.1 Experimental Setup

3.1.1 Two-Dimensional Fluidized Bed

The particle tracking experiments were conducted in a batch pseudo-two-dimensional fluidized bed. It is a slightly modified version of the plant already used by Refs. [22,23,24] in their studies (Fig. 4a–c). The front and back plane are made of shatterproof glass that has been treated to prevent sticking of particles. Fluidization is realised by a controlled gas mass flow through a 3 mm sintered metal plate at the bottom. The plant has been modified such that one weir can be installed, either as an under-flow or as an over-flow weir. A weir plate (thickness: 4 mm) is made of PVC and can be fixed to the front and back plane, providing the required gap for the under-flow weir (here: 20 mm) and dividing the fluidized bed into two chambers of equal size and volume. The chambers are called ‘left chamber’ and ‘right chamber’ in the following.

Fig. 4

(Used with permission by Elsevier)

Sketch, dimensions (a,c) and placement of the field-of-view (b) of the 2D-fluidized bed setup for recording of particle exchange between chambers separated by a weir

3.1.2 Materials

All experiments were conducted with porous $\gamma$-alumina particles (Sasol Germany GmbH). The material, a model substance in drying and layering experiments, was chosen because of its thermal and mechanical robustness, i.e., there is only limited breakage and abrasion of particles even after repeated particle-particle or particle-wall collisions. This simplified the tracking of particles. Two different size distributions were used: One with a mean diameter of 1.8 mm and a standard deviation of 0.1 mm, the other with a mean diameter of 3 mm and a standard deviation of 0.1 mm. The particles belong to group D in the Geldart classification with minimum fluidization velocities of 0.5 m/s (1.8 mm) and 0.81 m/s (3 mm), respectively.

3.2 Method Development: Particle Tracking Velocimetry (PTV)

Particle tracking velocimetry (see [23,24,25,26,27] for details and successful applications) involves the identification of individual particles in images, constructing individual particle trajectories and determining individual (Lagrangian) particle velocities (Fig. 5). The main advantage of PTV is that particles are tracked directly and individually, allowing also the detection of small numbers of particles moving opposite to a dominating particle flow, making PTV very suitable for the investigation of exchange rates at weirs.

Fig. 5

General idea of and processing steps in particle tracking velocimetry

3.2.1 Image Acquisition

Particle movement in the two chambers was recorded with a high-speed camera system: It consists of a 1024 $\times$ 1024 pixel Photron camera with a CMOS chip, mounted on a solid frame. Two halogen bulbs with 400 W each were positioned to provide uniform lighting of the field of view (FOV). The camera was operated at full resolution at 1000 Hz, with an exposure time of 1/31000 s and a dynamic range of 10 bits. Operating the camera at these settings allows recording of 5000 images (5 s of process time), a constraint imposed by the built-in memory chip. An objective lens (60 mm, f = 4) was used to give the desired depth of field and light exposure. The field of view (95 mm $\times$ 95 mm) was placed as sketched in Fig. 4. This position was chosen in pre-trials and allows capturing the particle movement without losing spatial resolution by the observation of empty zones or of regions where particle movement is not of interest for weir passage (far left, far right of the weir). The overall setup was controlled by the DaVis image acquisition software (LaVision GmbH, Germany).

3.2.2 Image Analysis: Monodisperse Particulate Systems

Analysis of the recorded images and particle tracking were performed following the steps shown in Fig. 6: At first, individual particles were identified by choosing and cropping a sample particle in the initial image. The sample particle is cropped to the area of highest illumination; this enables the identification of particles in close packings. Using a smaller sample particle, a larger number of particles is successfully detected [17]. In each image, the centroids of detected particles were tabulated and fed to the tracking algorithm. Particle centroids were tracked between frames by Voronoi matching, as introduced by Capart et al. [26] for dilute flows and extended by Hagemeier et al. [24] for dense particle flows. Thereby, for each identified and unambiguously tracked particle, a set of positions was generated over time, forming the individual (Lagrangian) particle trajectories.

Fig. 6

Flow-chart of operations involved in image processing to obtain particle exchange rates

To determine the exchange rates from the left to the right chamber and vice versa, the x-position (horizontal position) of the weir in the images is defined. Then the x-component of each position of each individual particle trajectory is evaluated, checking whether it passes this threshold position, i.e., it is checked whether the x-component of a particle starting in the left chamber has increased beyond the x-value defined as the weir position, or decreased below this value if the particle was initially in the right chamber. In over-flow as well as under-flow configuration the y-component (vertical position) of the particles is arbitrary in this step. Particles cannot penetrate the weir, so in over-flow configuration they can only pass from one chamber to the other above the weir, whereas in under-flow configuration the height of the installed weir prohibits particle transfer by passing the weir in over-flow. Straightforward counting of passes between frames yields the number-based exchange rates.

3.2.3 Image Analysis: Polydisperse Particulate Systems

Identification of particles of different sizes is performed by an incremental approach, i.e. applying the method for monodisperse particles several times. In the first run, the sample particle used for identification is chosen such that all particle sizes are detected, yielding a total number of particles. In the second run on the same set of images as in the first, the sample size is increased such that the smallest size (1.8 mm) is no longer detected but the larger particle size (3 mm). In this step also the detection of agglomerate structures due to overlap of two or more particles is corrected. The difference in numbers of detected particles (total and 3 mm) then gives the number of 1.8 mm particles.

In each image the centroids of detected particles are tabulated and fed to the tracking algorithm. Particle centroids are tracked between frames by Voronoi matching as described in Hagemeier et al. [24] for dense particle flows. Thereby, for each identified and unambiguously tracked particle a set of positions is generated over time, forming individual particle trajectories.

3.3 Experimental Series

Particle exchange was studied for different fluidization velocities in multiples of the minimum fluidization velocity and varying mass fraction of 1.8 and 3.0 mm particles. For the mixtures, the minimum fluidization velocity is obtained using the mean Sauter diameter of the mixture, i.e. fluidization velocities relate to multiples of the minimum fluidization velocity of the mixture. All experiments were performed at ambient temperature with non-heated fluidization gas. For under-flow experiments the weir gap height was set to 20 mm, in over-flow experiments the weir was set to height of 25 cm. In all experiments the left chamber was filled to a static bed height of 12.5 cm, the right chamber to a height of 10 cm.

In the over-flow weir scenario, both chambers were filled with particles until the static bed heights were achieved. The mass flow controller for the fluidization gas was then switched on. Following the start-up period of the mass flow controller (which can result in a small amount of particle exchange between the chambers), the high-speed recording was started and images of particle motion were taken for the next 5 s, resulting in 5000 images.

All batch experiments to study the recirculation at under-flow weirs were performed in the following way: (1) Filling both chambers of particles to a certain bed height (gap closed by a lid); (2) start of fluidization in both chambers via setting reference value for gas mass flow controller; (3) after start-up of fluidization sudden removal of lid (opening the gap) and start of image acquisition with the high-speed camera system.

An example sequence of images, showing every 500th frame, is shown in Fig. 7. These sequences form the basis for image analysis, particle tracking and the determination of the exchange rates between the chambers.

Fig. 7

Exemplary sequence of recorded high-speed images of particle transport at under-flow weir (1.8 mm particles, time resolution: 1 ms)

3.4 Results

The presentation and discussion of the results is structured as follows: First a measure for quantification of internal particle circulation is introduced. Then the results obtained from PTV measurements and Voronoi-tracking are presented for 1.8 mm particles at different fluidization velocities. Hereby results for under-flow weirs are compared to results obtained for over-flow weirs. Following is the presentation of results for 3 mm particles and a comparison with results for 1.8 mm particles, characterizing the influence of particle size on internal circulation. Finally, results for internal circulation for mixtures of 1.8 and 3 mm particles of different mass fractions are discussed to show the influence of bi-(poly-)disperse particles on transport at over-flow and under-flow weirs.

In order to quantify the internal recirculation R, we use the concept as introduced by Charlou et al. [28] in their study on residence time behavior in paddle dryers. They related the internal circulation as the ratio of particles moving ‘backwards’, B (against the dominant transport direction) to the net value of particles moving ‘forwards’, F:

$$\begin{aligned} R(t) = \frac{B(t)}{F(t)-B(t)} \end{aligned}$$

(12)

From the definition, R can take arbitrary values (positive and negative), signaling at each time whether more particles are moving ‘forwards’ or ‘backwards’. For practical evaluation, however, averaging of the quantities B and F over a representative time interval provides more insight. In case of a time average of zero in the ‘backwards’ flow, the (averaged) value of R is zero, which in turn yields plug-flow of particles in the dominant (‘forward’) transport direction. Increasing values of R quantify increasing back-flow of particles, i.e. recirculation against the transport direction. If the time averages of F and B are (almost) equal, an ideally mixed system results and the absolute value of the time average of R approaches infinity.

The internal circulation R is related to the classical Bodenstein number Bo (see [29, 30]). The Bodenstein number in turn measures the axial dispersion of particles in the chamber, i.e. by determing R from particle tracking, the coefficient of axial dispersion can be obtained.

3.4.1 Internal Recirculation of 1.8 mm Particles

The time-averaged values for the internal recirculation of 1.8 mm particles at an over-flow weir are shown in Table 1. It can be observed that with increasing fluidization velocity the value of R decreases, i.e. the system tends to a plug-flow like behavior. A similar trend, although of different magnitude is also observed in the results for the under-flow configuration also presented in Table 1. Again, with increasing fluidization velocity the internal circulation decreases and the particle transport is similar to plug-flow.

In case of the over-flow configuration the result is due to the initially different bed height in the chambers, resulting in different pressure drop and the rising velocity of formed gas bubbles that propell particles over the weir. For long times an equilibration of bed heights and also transfer rates is achieved [17]. In case of the under-flow configuration, bubble formation close to the weir and rising velocity are important. If a bubble forms in one chamber close to the weir and starts to rise (as seen in Fig. 7), it creates additional drag on the particles close to the weir in both chambers, dragging significant particle numbers through the gap towards the bubble. For long process times, again, equilibration of the transport rates between the two chambers is achieved.

Table 1 Averaged internal recirculation coefficient $R_{avg}$ for 1.8 mm particles

Table 2 Averaged internal recirculation coefficient $R_{avg}$ for 3.0 mm particles

3.4.2 Internal Recirculation of 3 mm Particles

The obtained results of internal recirculation for beds of monodisperse 3 mm particles at over-flow and under-flow weirs are shown in Table 2. While the recirculation coefficient at the under-flow weir follows the same trend as it did for 1.8 mm particles, a reverse trend is observed in terms of the over-flow weir: With increasing fluidization velocity the internal recirculation does not decrease but increase, resulting in a system that is close to an ideally back-mixed system. This behavior can also be observed visually during the measurements with many bubbles being created on both sides of the weir, propelling large amounts of particles to the adjacent chamber, due to high momentum of the gas, and quickly driving the system to an equilibrium state of equal bed heights and transfer rates in the current set-up.

Compared to 1.8 mm particles, the 3 mm particles tend to even transfer rates faster after a disturbance in the fluidization behavior, for instance due to different bed heights, for example due to feeding events in only one of the chambers, or due to bubble formation and movement inside the bed. If, however, the absolute fluidization velocities are compared, one observes that R has a similar value for both particle sizes: The ratio of the two minimum fluidization velocities $u_{mf,3.0}/u_{mf,1.8}$ is approximately 1.5. Comparing the absolute value of $u/u_{mf,3.0} = 3$ (2.43 m/s) giving an R value of 2.04 with the corresponding value of 1.8 mm (between $u/u_{mf,1.8} = 4$ and 5), the values are similar (R in [1.59, 2.71]). This means that, as long as the equilibrium has not been obtained and the fluidization conditions are equal, both particle sizes are re-circulated in the same manner. One has to note, that this does not mean that in equal times equal numbers are transported across the weir, but only that the ratio of the directed transport is equal.

3.4.3 Internal Recirculation of Bi-disperse Particle Mixtures at Over-Flow Weirs

After having studied the trends for the recirculation of mono-disperse particles at over- and under-flow weirs for different fluidization velocities, the behavior of bi-disperse particle mixtures is investigated. For this purpose, experiments with mixtures of 1.8 and 3.0 mm particles with different mass fractions were performed under otherwise the same conditions. Note that in the following $u_{mf}$ corresponds to the minimum fluidization velocity of the mixture, calculated from the Sauter mean diameter. In most experiments, the fluidization velocity corresponds to 4 $u_{mf}$; for the $50\%/50\%$-mixture results for the overall circulation are also presented for 3 and 5 $u/u_{mf}$. In addition to the over-all circulation of particles at the weirs (regardless of size), also the individual recirculation of the two particle sizes is presented and discussed.

The trends of time-averaged internal recirculation R for the $50\%/50\%$-mixture are presented in Table 3. One can observe a decrease in the value of R with increasing fluidization velocity. Comparing this trend with the two individual trends for the monodisperse material, it can be concluded that for large enough fluidization velocities the exchange behavior of the mixture is dominated by the recirculation behavior of the smaller (1.8 mm) particles.

Fixing the fluidization velocity to 4 $u_{mf}$ and varying the mass fractions of 1.8 and 3.0 mm particles, the results for the over-all recirculation also shown in Table 3 are obtained: Now an increase in the value of R can be observed, i.e. the transport tends towards back-mixed flow (resp. equilibrium state). Comparing the results for the individual recirculation of the 1.8 and 3.0 mm particles, one sees that with increasing mass fraction of small particles, the recirculation of both particle sizes increases. Again, one has to note that the minimum fluidization velocity of the mixture does correspond to neither of the minimum fluidization velocities of the particles, i.e. individual particles are experiencing higher and lower velocities than four times their individual minimum fluidization velocities. This may accelerate reaching the equilibrium state of the set-up with equal transfer rates, shifting the time-averaged values of R to higher values, i.e. apparently larger back-mixing.

Table 3 Averaged internal recirculation coefficient $R_{avg}$ of bi-disperse particle mixture at over-flow weirs

3.4.4 Internal Recirculation of Bi-disperse Particle Mixtures at Under-Flow Weirs

Following the same approach, the particle recirculation behavior of the bi-disperse mixture was studied in the under-flow configuration. Results for the $50\%/50\%$-mixture and different fluidization velocities are presented in Table 4, showing a decrease of the time-averaged value of R with increasing fluidization velocity, similar to the trends obtained for the monodisperse particles.

Again fixing the fluidization velocity to four times the minimum fluidization velocity (calculated with the Sauter mean diameter of the mixture) and varying the mass fractions of 1.8 mm and 3 mm particles, the results for the overall recirculation (regardless of particle size) and results for the individual particle sizes in Table 4 are obtained, respectively. Compared to the other scenarios, the trends with respect to variation of the mass ratios are not obvious. As a first approximation, the overall recirculation is almost constant with increasing mass fraction of small particles. The individual rates decrease non-uniformly with increasing mass fraction of small particles, still following the trend of the monodisperse particles. The non-uniformity has its sources in the bubble behavior (and the aforementioned force exerted on the particles, dragging them through the gap) as well as in the gap size. Compared to the over-flow case, however, the over-all values of R follow a different trend and are also different in magnitude, signaling that the equilibrium state was generally not achieved in the experiment, due to the influence of the gap width on the flow behavior.

Table 4 Averaged internal recirculation coefficient $R_{avg}$ of bi-disperse particle mixture at over-flow weirs

3.5 Discrete Particle Modeling

A special focus was placed on the microscopic scale of particle transport behavior between the separated chambers in horizontal fluidized beds. For this reason discrete particle modeling (DPM) was used for the characterization of the microscopic particle transport behavior. Discrete particle modeling is a very powerful tool for the investigation of flow phenomena and the particle dynamics in fluidized bed technology [31]. It can be used for the determination of the circulation frequencies and residence times in certain zones of the apparatus [32], for studying the spraying [33], mixing behavior [34,35,36] and for optimization of processes [37].

Coupled CFD-DEM simulations are used to characterize the particle exchange in a two-compartment system on the micro-scale. For the simulations OpenFOAM and LIGGGHTS have been used. For a detailed description of the theoretical background, the reader is referred to the work of Refs. [38, 39], while a profound review of the DPM for fluidized beds can be found in Deen et al. [31]. For the implementation of OpenFOAM, CFDEMcoupling and LIGGGHTS, Refs. [40, 41] provide comprehensive summaries.

3.5.1 Experimental Validation

Validation was performed with respect to the two-dimensional experimental fluidized bed, to adopt the setup for the numerical simulation without any assumptions or simplifications. In fact, the process conditions as well as the experimental setup and geometrical data were to be adopted for the simulation. Figure 4c shows the CAD geometry of the used setup for the numerical study. For the simulation the size of the particles was fixed to 1.8 mm.

The coupled CFD-DEM simulation was performed for 6 s for the over-flow configuration (see Fig. 4c) in order to compare the results regarding the particle transport between the individual chambers of the two-staged fluidized bed and validate the simulation by the PTV experiments. The experiments have been evaluated for 5 s of the recorded high-speed videos, while the simulations have been also evaluated for 5 s after the first second of initialization.

Fig. 8

Snapshots of the particle positions obtained from the experiments and the corresponding simulation at a gas inlet flow of 60 kg/h for the validation setup [42]

The snapshots in Fig. 8 show that the particle transport behavior in both, the experiment and the simulation is randomly changing from left to right and the opposite direction. The simulation and the experiment show a good agreement regarding the flow pattern of the particles within the two compartments and also the transport behavior of the particles. The quantitative exchange rate in the simulation was determined on the basis of particles crossing from one to the other chamber between two time steps (0.005 s). Similar to the PTV experiments, the horizontal trajectory of every particle that crossed the weir defined whether the particle is in the first chamber or the second. Consequently, the particle exchange between the two chambers was determined from one frame to the next.

The particle exchange rates and internal recirculation are evaluated using the particle identifiers provided by the simulation environment. Figure 9 shows the results of the individual averaged particle streams and the resulting average internal recirculation coefficient R (averaging over 5 s).

Fig. 9

Averaged particle exchange rates between the individual compartments and the average internal recirculation coefficient of the validation experiment and the simulation for a time interval of 5 s [42]

The results of Fig. 9 show that the amounts of exchanged particles in the experiment and the simulation are similar, while the recirculation coefficient has a slightly higher deviation, because of the sensitivity of the recirculation coefficient to small changes in both particle streams. Moreover, it cannot be guaranteed that the initial conditions of the experiment and the corresponding simulation were exactly the same. Despite these minor discrepancies, it can be concluded that the two methods show very good quantitative agreement. Thus, it could be proven that coupled CFD-DEM simulations are suitable for the evaluation of weir designs at the transition zone between two compartments.

3.5.2 Large-Scale Numerical Study of Particle Transfer

The simulation methodology was transferred to the study of the large-scale equipment at the Institute of Solids Process Engineering and Particle Technology at Hamburg University of Technology (Procell 25, Glatt Ingenieurtechnik GmbH). The geometry is shown in Fig. 10a, limited to two chambers to reduce numerical effort. The studied weir configurations and their dimensions are shown in Fig. 10b.

Fig. 10

(Used with permission by Elsevier)

a Scheme of the numerical setup of the two-staged horizontal fluidized bed for continuous simulations and b the dimensions of the two-staged systems for the different weir configurations [42]

Continuous throughput of particles was realized within a particle generation domain, which was attached to the inlet tube of the geometry. For the continuous discharge of particles, the outlet tube was connected to a rotary valve model domain. This model was added for keeping the hold-up mass inside the apparatus constant. The main simulation conditions and material properties are contained in Table 5. For further information on the simulation setup, see [42].

Table 5 Simulation conditions of the two-staged pilot plant simulations (detailed information is given by Diez et al. [42]).

3.5.3 Large-Scale Simulation Results

Simulations were carried out for three different weir configurations and the base case for setups with 3 mm particles of mono-disperse distributions in the two-staged system. The overall goal of this study was to analyze the impact of weir designs on the microscopic transport behavior of the particles in multi-chamber systems. After an initializing time of 10 s for reaching stationary conditions regarding the supply and discharge of the solids material inside the system the evaluation procedure was started.

Results for the average internal recirculation coefficient R (averaging time interval of 60 s) for the individual setups are shown in Fig. 11.

Fig. 11

Mean recirculation rates of each weir configuration with 3 mm particles (mono-disperse) and a fluidization velocity of 3 m/s for the two-compartment system [42]

The results in Fig. 11 show that the base (no weir) and over-flow configurations are characterized by higher particle recirculation (solids transport from the second to the first chamber), which implies more intensive axial dispersion. In contrast to this the side-flow as well as the under-flow variant show significantly lower recirculation coefficients. While in the over-flow weir design the internal recirculation decreases to about 60% of the base case, for the side-flow and under-flow a decrease to about 17% and 11%, respectively, is observed.

With regard to the weir configuration, the base (no weir) and over-flow configuration favor axial dispersion due to intense mixing between the two compartments, whereas the under-flow and side-flow weir design lead to a reduction of axial dispersion. This indicates a more directional transport for the side-flow and under-flow design. Further results are presented in Diez et al. [42], and Bachmann et al. [29] who additionally investigated the influence of gap height and particle size on particle transfer in these configurations.

Summarizing, coupled CFD-DEM simulations can be a tool for extending macroscopic particle transport approaches, like residence time experiments, by the micro-scale particle dynamics for improving solids transport models and getting comprehensive knowledge about the transport behavior of gas-solids flows, especially at high solids loading.

4 Experimental Studies on Continuous Spray Granulation in Horizontal Fluidized Beds

4.1 Experimental Setup

The experiments have been carried out in a pilot-scale horizontal fluidized bed plant (Fig. 12; ProCell 25, Glatt Ingenieurtechnik GmbH Weimar, Germany). Combined with an external pneumatic conveying and a screening-milling cycle, this process was operated continuously.

The process chamber, presented in Fig. 12a, has a length of 1 m, a width of 0.25 m and a height of about 0.40 m and can be divided into four different compartments by introducing weirs. The aim was to analyze the influence of thermal conditions on product quality. The process conditions in every stage were the same, operated with constant inlet gas velocity of 3 m/s. The solution was injected by four two-fluid nozzles in bottom-spray configuration (see Fig. 12b). Atomization was supported by compressed air. The spray solution consisted of 35 wt.-% of sodium benzoate dissolved in demineralized water. The hold-up material consisted of sodium benzoate particles in a size range of 0.5 m to 2.5 mm (undersize, product and oversize material) and an apparent density of 1440 kg/m$^{3}$.

Nuclei were exclusively produced by grinding of oversized material in a pin mill. Hence, no external feed of solid material was required in these experiments. The process was operated with a constant bed mass of 25 kg, while starting with a bed that contained 50 wt% product particles, 25 wt% oversized and 25 wt% undersized particles.

The thermal conditions of the spray granulation process can be varied, not only changing the process temperature, but also by changing the spray rate of the solution. For this reason, those two parameters, given in Table 6, have been selected as variables in the experiments.

Table 6 Parameter variations to investigate the influence of the thermal conditions on product properties [1]

Fig. 12

Photos of a the sampling devices and the installed inline probe during continuous granulation, b an installed two-fluid-nozzle within the process chamber and c the used pilot plant granulator [1]

During the experiments samples were taken from the process chamber for an off-line measurement of the moisture content of the solid material and for tracking the particle size distribution. Additionally, an inline probe (IPP 70-S, Parsum GmbH, Germany) for in-situ measurement of the particle size distribution was used.

The product granules were discharged by a two-deck tumbler screen in a size range of 2.00–2.24 mm. After three times the average solids residence time, steady-state was assumed. From this point onwards, samples were taken and analyzed according to the following characteristics:

• Solids moisture content

• Surface morphology and roughness

• Solids density and porosity

• Compression strength

• Wetting behavior.

4.2 Particle Characterization

4.2.1 Solids Moisture Content

The solids moisture content of the hold-up material was analyzed thermo-gravimetrically using the moisture analyzer Precisa EM-120 HR (Precisa Gravimetrics AG). For the analysis procedure a constant drying temperature of 105 $^\circ$C was applied and a switch-off criterion was used that stopped the measurement when the reduction in weight was less than 0.01 mg/s or a total measuring time of 10 min was reached. Due to the hydrophilic character of sodium benzoate the particle moisture content was determined immediately after sampling. Figure 13a shows that the particles were relatively dry in all experiments, except of two experiments. These results demonstrate that there has to be a certain boundary, at which the combination of the drying temperature and the spraying rate do not affect the moisture content of the particles anymore while reaching a certain equilibrium value which should be around 1 g/kg according to Fig. 13a. To identify this transition zone the drying potential $\eta$ according to Refs. [16, 43] is used:

$$\begin{aligned} \eta = \frac{Y_{sat}-Y_{out}}{Y_{sat}-Y_{in}}\; . \end{aligned}$$

(13)

The drying potential is calculated by the moisture content of the inlet gas stream $Y_{in}$ and at the outlet $Y_{out}$ of the process. These values were measured and recorded by installed sensors in the plant. The saturation moisture content $Y_{sat}$ is calculated from the following equation:

$$\begin{aligned} Y_{sat} = 0.662 \cdot \frac{p_{sat}}{p-p_{sat}}\; . \end{aligned}$$

(14)

The corresponding saturation vapor pressure $p_{sat}$ is calculated according to Wagner [44]. From Fig. 13 the transition can be identified to occur at $\eta = 0.5$.

Fig. 13

a Solids moisture content of the material inside the process chamber and b calculated drying potentials of each experiment by varying the inlet temperature and the spray rate

4.2.2 Surface Morphology and Roughness

For surface analysis of the product granules, a scanning electron microscope (LEO Gemini 1530, Carl Zeiss AG, Germany) was used. The results in Fig. 14 clearly show an influence of the process conditions on the morphological structure of the particles and are in line with findings of Refs. [16, 45]. The scanning electron microscope (SEM) images show that the increase in the drying temperature results in smoother surfaces, while a decrease leads to a higher surface roughness in combination with a more porous surface layer.

Fig. 14

(with kind permission of Elsevier)

SEM analysis of the product granule surfaces of each experiment [1]

At the highest spray rate and lowest gas inlet temperature ($\vartheta _{drying} = 100\,^\circ C$ and $\dot{m}_{spray}$ = 120 kg/h), the experiment could not be performed as agglomeration set in, i.e. particle clusters occured due to the formation of liquid bridges between particles.

The surface roughness was measured by focus-variation microscopy using an Alicona Infinite Focus microscope (Alicona Imaging GmbH), which provides a measurement of the 3D-surface structure, followed by an evaluation related to a surface-based roughness parameter. This surface-based evaluation included a projection area of $500 \times 500\, \upmu$m for each product granule, as shown in Fig. 15.

Fig. 15

Example for a focus-variation measurement of 3D-surface structure and b the height profile of the corresponding granule surface [1]

The roughness parameter $S_{dr}$ belongs to the so-called hybrid topography characteristics affected by both the texture amplitude and the structural pattern [46]. It is calculated according to DIN EN ISO 25178-2 [47]:

$$\begin{aligned} S_{dr} = \frac{1}{A} \left( \iint _{A}^{} \left( \sqrt{(1 + \left( \frac{\partial z(x,y)}{\partial x} \right) ^2 + \left( \frac{\partial z(x,y)}{\partial y}\right) ^2} -1 \right) \mathrm {d} x \mathrm {d} y\right) \; \end{aligned}$$

(15)

The results of this roughness evaluation are shown in Fig. 16. A significant increase in surface roughness is observed with increasing spray rates as well as with decreasing gas inlet temperature.

Fig. 16

Surface roughness $S_{dr}$ of the granules according to the process conditions (drying temperature and spray rate) they are produced with

The influence of operation parameters on surface roughness was discussed in detail in Rieck et al. [16], also taking into account the crystallization behavior of the sprayed salt solution.

4.2.3 Solids Density, Porosity and Compression Strength

Thermal conditions not only influence the roughness of the granules, but also the internal structure, such as the porosity and apparent density. Moreover, these characteristics are topologically related to and significantly influence other characteristics, for example the compression strength of a granule.

The apparent density of granules was measured by helium pycnometry (Multivolume Micrometrics 1305). The porosity of selected granules was measured via X-ray micro-computed tomography (CT-ALPHA, ProCon X-Ray GmbH) as described in Refs. [48, 49].

The compression strength was analyzed by single particle compression tests using a Texture Analyser TA.XT plus (Stable Micro Systems). For detailed information on the test procedure and evaluation of force-displacement curves, see [50].

Figure 17 shows results for the three characteristics. The solids density and the compression strength of the granules show an increasing trend with increasing drying potential, while the porosity reveals the opposite trend.

Fig. 17

(Used with permission by Elsevier)

a Average solids density, b granule porosity and c compression strength of the granules according to drying potential of the individual granulation process experiments [1]

These trends are in line with the results from the SEM analysis and the roughness measurements. Because of the smoother and more compact surfaces of the particles with increasing drying potential, the particles are layered more compactly, resulting in higher of solids content (see Fig. 17a) due to high nucleation rates and reduced crystal growth. In consequence, the void fraction inside the granule structure decreases, resulting in a reduction of the granule porosity (see Fig. 17b). Furthermore, the reduction of voids and defects inside the granule leads to higher compression strengths (see Fig. 17c).

5 Population Balance Model Extension: Influence of Thermal Operating Conditions

Product design is one of the key disciplines in particle formulation processes, usually driven by quality-by-design principles in combination with a fundamental process understanding, focusing on key features of solids handling properties, like flowability, the dissolution behavior, the release rates or the storage stability. Furthermore granule characteristics, like the solids density, moisture content, granule surface morphology, surface roughness, compression strength and the wetting behavior play a major role for the development of tailor-made granule properties for specific uses in pharmaceutical, food and other industrial applications. The particle properties can be influenced by several process parameters, like drying temperature, liquid feed rate as well as droplet size of the atomized liquid feed. Additionally the peripheral process units and downstream processing play a distinctive role.

Figure 14 clearly shows that the morphology of the particles is changing significantly with the thermal operating conditions. In particular, the shell porosity is increasing with increasing rate of the injected liquid from the left to the right in Fig. 14. Further it is increasing with decreasing temperature of the fluidization air from the top to the bottom in Fig. 14.

Following the ideas in Refs. [1, 16], the behavior shown in Fig. 14 was modeled by correlating the shell porosity with the drying potential $\eta$.

It turns out that for the present test system the relation between shell porosity and drying potential can be described in good approximation by a linear correlation.

$$\begin{aligned} \epsilon _{shell}(\eta )= \epsilon _{shell,0} -\Delta \epsilon _{shell}\, \eta . \end{aligned}$$

(16)

Other particle properties like surface roughness and compression strength can also be correlated with the drying potential as shown in the previous section. Alternatively, they can be obtained as a function of porosity and particle size distribution as suggested in Litster and Ennis [51].

Using the correlation between shell porosity and the drying potential according to Eq. (16), the population balance model presented in Sect. 2 can be extended to account for the influence of the thermal conditions on particle porosity [52]. For this, it is assumed that all particles share the same porosity, temperature and moisture content due to the ideal mixing of the bed, but have different sizes. The particle size distribution is described by the population balance of the particle phase introduced already in Sect. 1. Therein, the growth rate has to be modified with the shell porosity as illustrated in Fig. 18 to account for the growth of porous particles. As described above the shell porosity is correlated with the drying potential which depends on the thermal conditions inside the granulation chamber. Thermal conditions are obtained from energy balances of the fluid and the particle phase, and the material balances of the solvent in the fluid, the particle phase, the dry mass of the particles and the fluidization air. Due to the assumption of ideal mixing inside the granulation chamber, these additional material and energy balances are described by ordinary differential equations. They depend on the heat and mass transfer between the particle and the fluid phase, which depends in turn on the total surface of the particle phase according to

$$\begin{aligned} A_P=\pi \int \limits _{0}^{\infty } L^2 n(t,L) dL. \end{aligned}$$

(17)

This leads to a bi-directional coupling between the population balance of the particle phase and the ordinary differential equations describing the influence of the thermal conditions as illustrated in Fig. 18. The resulting model can be used for the design and control of processes for the production of particles with tailor-made size and porosity. The latter will be discussed in Sect. 7 of this chapter.

Fig. 18

Model extension to account for the influence of thermal conditions

So far, focus was on the granulation chamber. However, particle morphology affects also the milling of oversized particles in a continuous process with sieve mill cycle and has therefore also an effect on dynamic stability of this process configuration according to the experimental findings of Schmidt et al. [53], who have shown that a high inlet gas temperature leads to a stable steady state, whereas a low gas inlet temperature leads to an unstable steady state. This has been modeled qualitatively in Neugebauer et al. [54] by correlating the mean diameter of the milled particles with shell porosity.

Fig. 19

Simulation scenario on the influence of thermal conditions on the stability of the fluidized bed layering granulation process with sieve-mill cycle

The resulting plant dynamics is illustrated in Fig. 19 with a simulation scenario. The simulation starts at a steady state with a constant fluidization air inlet temperature of $80\,^{\circ }\text {C}$ and a constant moisture content of the fluidization air at the inlet of 6 g/(kg dry air). The mill is operated with a constant reference value $\mu _{mill,0}$ which is only changed by some portion $\Delta \mu _{mill}(\epsilon _P)$, which depends on particle porosity $\epsilon _P$ as explained above. At time $t_{sp}$ in Fig. 19 the inlet temperature of the fluidization air is reduced to $75\,^\circ \text {C}$. This leads to an increase of particle porosity, which in turn results in finer milling. As will be discussed in the next section this affects the process stability and leads to instability in the form of self sustained oscillations of the particle size distribution, which is illustrated in Fig. 19 with the Sauter diameter $d_{32}$.

At time point $t_{dist}$ in Fig. 19, the moisture content of the fluidization air at the inlet is changed from 6 to 15 g/(kg dry air). This increases the particle porosity further. As a consequence the particle size distribution is further destabilized, i.e. the amplitude of the oscillations of $d_{32}$ is further increased.

6 Systems Theoretical Analysis

Continuously operated fluidized bed layering granulation (FBLG) processes tend to be unstable, as reported by Refs. [7, 55, 56]. A rigorous experimental investigation has been given recently by Refs. [53, 57, 58]. A model based analysis helps to further deepen the understanding of the underlying mechanisms and can be used to 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 $\dot{V}_{inj}$. 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 $\alpha$, 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.

Fig. 20

Stability map and simulation scenario for FLBG with internal product classification

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 fraction is milled and fed back to the granulation chamber together with the undersized fraction. On the one hand, this mode of operation is very economic due to the recycle and re-use of the off-spec particles. On the other hand it creates instability due to the positive feedback introduced by the recycle.

The influence of the most important operational parameters on process stability of this second configuration was also studied theoretically using a two-zone model [11, 12]. Results for the case, when no additional external nuclei are fed to the granulation chamber, are shown in Fig. 21. Most important parameters are now the mean diameter of the milled particles $L_{mill}$, the relative volume of the granulation zone $\alpha$, and the time constant $\tau _2$ characterizing the exchange rate between the granulation and the drying zone. Since the bed mass is constant, $\alpha$ is also constant. $\alpha$ and $\tau _2$ depend on the plant design (nozzle type, size, and position and geometry of the granulation chamber) and the operating conditions [11]. It turned out that zone formation inside the granulation chamber has minor effect on process stability compared to $L_{mill}$. Coarse milling will result in stable steady states, whereas fine milling will lead to self sustained oscillations of the recycle flows and the particle size distribution, represented by the Sauter diameter $d_{32}$ in Fig. 21.

Fig. 21

Stability map and simulation scenario for $\tau _2=10\, s$ for FBLG with external product classification

Fig. 22

Influence of mill characteristics on the stability of FBLG with external product classification

The instability region shrinks, if additional nuclei are fed externally to the process chamber, which has a stabilizing effect as was already shown in Radichkov et al. [56].

The results in Fig. 21 were obtained for an ideal milling process described by a Gaussian distribution of the milled particle sizes around $L_{mill}$. Similar results were obtained for a more detailed model of the mill which was fitted to experimental data using a superposition of three Gaussians. However, the instability region can change its size and position in the parameter space. So that for a specific set of operating and plant parameters, oscillations are predicted by the detailed mill model whereas the idealized mill model predicts stable steady state behavior as illustrated in Fig. 22. Hence it is concluded, that for the quantitative prediction of instability of the FBLG process with sieve-mill cycle a quantitative prediction of the milling process is essential [59].

Fig. 23

Stability map for two different two stage FBLG processes with external product classification. $\dot{V}_{inj,2}=0$—suspension injected only to the first stage, $\dot{V}_{inj,2}\not =0$—suspension injected to the first and second stage

The above results were obtained for single stage FBLG processes. An extension to multi-stage FBLG processes with sieve mill cycle is illustrated in Fig. 23. The figure gives a comparison between two different two-stage processes. In the first process half of the solution is injected in each of the two stages, whereas in the second process the whole solution is injected to the first chamber. In both cases, the injected liquid is evenly distributed on the available particle surface in the respective granulation zones contributing entirely to uniform growth. Total bed mass and total injected liquid suspension is the same in both cases and the same as in Fig. 21. In a first step, transport between the chambers is assumed to be representative. In both cases, the exchange rates between the drying and the granulation zones on each stage are assumed to be high, corresponding to a low value of $\tau _2$. Therefore, stability in Fig. 23 does not change with $\alpha$ (the relative size of the granulation zones), which is consistent with the single stage process in Fig. 21 for a low value of $\tau _2$. Further, the other operational parameters are the same as in Fig. 21. With these assumptions, the first process in Fig. 23 with injection in both stages is identical to the single stage process in Fig. 21. Instability occurs for fine milling below $L_{mill}=0.725$ mm. In contrast to this, if the whole liquid is injected into the first chamber, instability occurs for fine milling below $L_{mill}=0.6$ mm. Hence, the size of the shaded instability region is reduced for the second process compared to the first process. This is due to the fact, that in the second chamber of the second process no granulation is taking place but only drying. Therefore, the second chamber acts as a buffer, which dampens the oscillatory behavior and therefore has a stabilizing effect. Hence, multi-stage processes with additional drying chambers are not only useful for additional adjustment of product properties but also have a positive effect on dynamic stability when an external sieve-mill cycle is used.

7 Control of Continuous Operation

Several control concepts were developed for single and multistage FBLG processes within this project to stabilize unstable steady states, increase the reproducibility and speed up the time consuming experiments. The developed control concepts are as follows:

• 1. Model-free controllers using auto tuning [60]. This approach was used for direct determination of the open loop stability boundaries in closed loop operation as described in Palis et al. [61].

• 2. Model-based robust [62] and nonlinear control [63] of a multi-stage FBLG process.

• 3. Adaptive control of continuous fluidized bed spray granulation with external sieve-mill cycle [64].

• 4. Decentralized cascade controllers for continuous fluidized bed spray granulation with external sieve-mill cycle. Controllers were developed step by step using a detailed plant model and also validated experimentally [54, 65].

For the latter, the plant model introduced in Sect. 2 of this chapter was extended to account for the specific plant characteristics of the pilot plant in Hamburg considered in this chapter, such as

• classifying product removal from the granulation chamber,

• size dependent milling of the oversized particles,

• a variable bed mass, to test different approaches for bed mass control of the granulation chamber with the model.

For the bed mass control, the pressure difference across the fluidized bed is determined as a direct measure for the bed mass to be controlled. Manipulated variable is the rotational speed of the rotary valve at the product withdrawal from the granulation chamber. It turned out that the performance of this control loop depends crucially on the operation of the mill. The mill is used for the grinding of the oversized particles, which are fed back to the granulation chamber as new nuclei. Stable operation of the bed mass control was not possible for the standard mode of operation, where the rotational speed of the mill is kept constant. This problem could be resolved by introducing another controller to adjust the mill power instead of its rotational speed. With this, a stable bed mass control could be achieved, which is crucial for continuous operation of the plant over a prolonged period [65].

However, even for constant bed mass, oscillations of the particle size distribution and the recycle flow rate can occur as described in the previous section. Such a scenario is shown in Fig. 24 under the label open loop dynamics. Here, the particle size distribution shows a very weakly damped oscillation so that the startup of the plant takes several days, until finally a stable steady state of the particle size distribution and the Sauter diameter is obtained. For finer milling, the steady state is even unstable and will never be reached due to permanent oscillations without damping. To solve this problems and achieve not only stable bed mass but also a stable particle size distribution, a further control loop was added. Here, the Sauter diameter is determined online with a Parsum probe and the mill power is manipulated to achieve a stable given value of the Sauter diameter within short time. The model was used for the tuning and testing of this controller before it was implemented at the plant. As shown in Fig. 24 the controller achieved a stable steady state of the particle size distribution and the Sauter diameter within short time of less than 10 hours. Further, experimental findings agree well with the theoretical predictions.

Fig. 24

Comparison of open loop and closed loop dynamics of a continuous granulation process with sieve-mill cycle during startup. Upper diagrams show the temporal evolution of the particle size distributions measured at the pilot plant in Hamburg. Lower diagrams show the corresponding time plots of the Sauter diameter $d_{32}$. Solid lines in the lower diagrams represent model predictions, whereas the bullets represent the experimental values. Figure taken from Ref. [54]

The control algorithm for the Sauter diameter in Fig. 24 is a simple linear proportional controller. It was shown that additional integral action is destabilizing and should therefore be avoided for this process. It was shown that the simple proportional controller works very well for small disturbances. For larger disturbances, however, more advanced, model-based control concepts are required as proposed for example in Refs. [66,67,68,69].

Fig. 25

Porosity control with (dashed red line) and without $d_{32}$ control (solid line)

Besides particle size, particle morphology, in particular particle porosity, is of major interest in many applications. Therefore, automatic adjustment of particle porosity by feedback control was studied in Neugebauer et al. [54]. Problem here is, that porosity cannot be controlled directly, due to a lack of available online measurement information. However, as discussed in Sect. 4, particle porosity depends directly on the drying potential which is related to the thermal conditions. The thermal conditions can be measured online easily. Therefore, the drying potential is taken as controlled variable for porosity control and the inlet temperature of the fluidization gas is taken as manipulated variable. For this control configuration a simple single loop PI controller was designed and tested using the model. For this, the plant model was extended to account for the influence of porosity on the milling of oversized particles, which is crucial for the stability of the particle size distribution.

Results taken from Neugebauer et al. [54] are shown in Fig. 25. The solid line represents a scenario where only porosity control is applied, whereas the red dashed line is for simultaneous porosity and $d_{32}$ control. In all cases, bed mass control as described above was applied. At time $t_{sp}$ in Fig. 25 the reference value of the particle porosity was changed from $\epsilon _{p,I}$ to $\epsilon _{p,II}$ and at time $t_{dist}$ a step disturbance of the moisture content of the inlet gas from 6 to 15 g/kg dry air was introduced.

In both cases, the controller adjusts the porosity within a relatively short time of about 5 hours smoothly to the new reference value $\epsilon _{p,II}$ and keeps it constant. However, without the $d_{32}$ controller, the particle size distribution represented by the Sauter diameter in the second diagram of Fig. 25 starts oscillating due to the influence of the porosity on the milling of the oversized particle. If in addition, $d_{32}$ control was applied as described above, the Sauter diameter and the particle size distribution could also be stabilized.

8 Summary and Outlook

Within this project, new insight into the dynamics of particle formulation by spray layering in continuously operated horizontal fluidized beds has been obtained. Starting from the single-particle level, using information on the particle recirculation between functional compartments and multiple chambers by weirs, the effect of thermal conditions on layer properties, dynamic and steady-state process behavior has been illuminated. Process models were derived allowing the predictive simulation of particle properties and the dynamic and steady-state behavior. This led to the derivation of process regime maps, dividing (asymptotically) stable operating points from unstable operating points. Using this information, control concepts could be derived and tested—first in simulations and later at a full-scale industrial plant.

Combined information on micro-, meso- and macro-scale behavior, i.e. from single particles to the apparatus, and its implementation in the simulation framework “Dyssol” allows for model-driven apparatus, process and control design. This enables the inverse design of process and apparatus starting from particle property requirements, by mathematical optimization.