Multiscale Simulation of Agglomerate Breakage in Fluidized Beds

Article pubs.acs.org/IECR

Multiscale Simulation of Agglomerate Breakage in Fluidized Beds Maksym Dosta,* Sergiy Antonyuk, and Stefan Heinrich Institute of Solids Process Engineering and Particle Technology, Hamburg University of Technology, Denickestrasse 15, 21073 Hamburg, Germany ABSTRACT: In this contribution a multiscale simulation strategy is proposed which is able to simulate an industrial scale fluidized bed spray agglomeration process considering the breakage of agglomerates. A set of novel simulation approaches and hierarchically distributed models were developed and implemented into the multiscale simulation environment for solids processes. The population balance model (PBM) was used for the simulation of the global production process on the macroscale. On the microscale the coupling between discrete element method (DEM) and the computational fluid dynamics (CFD) system was employed to calculate the particle dynamics in the granulator. The material-based parameters for the PBM, such as breakage probability and breakage function, were derived from the process description on the lowest hierarchical scale, where the agglomerate was described as a system of primary particles bonded by a solid binder.

1. INTRODUCTION The fluidized bed agglomeration process is widely used in industry for the production of granular materials with desired properties, such as particle size distribution, bulk and particle density, and composition of the product. During agglomeration the suspension or solution is injected into the apparatus through one or several nozzles and wets the bed material, which is situated in fluid-like state. Collision of wetted solid particles in the bed can lead to particle sticking, formation of liquid bridges, and bridge solidification during drying. In this case, the agglomerate growth occurs. However, loading of agglomerates in the gas flow and their interactions in the apparatus can lead to destruction of the bonds between primary particles and consequently to agglomerate breakage. In recent years, a lot of work has been done in the area of detailed simulation of the aggregation process. In many investigations the focus was on the aggregation kinetics,1−3 while the breakage process was poorly considered or totally neglected. In other papers the breakage process of agglomerates was described by physical models.4−8 However, neither of the proposed models can be effectively applied for a broad variety of industrial fluidized bed agglomeration processes, which often consist of interconnection of different apparatuses and process substeps. Nowadays, the usage of flowsheet simulation tools for analysis of the behavior of industrial production processes is state of the art. These systems are employed to solve the energy and mass balances in all streams and to obtain the numerical solution of the scheme in an appropriate time. Especially for solids processes the systems for the steady-state9 and dynamic10 simulation have been developed in recent years. Here, on the scale of the global production process, the population balance models (PBM) are used for the description of the agglomeration or breakage processes. The PBM in its general form is a partial integro-differential equation,11 where microprocesses such as aggregation, growth, nucleation, breakage, or attrition can be simultaneously considered. There exist different numerical approximation schemes to solve these equations in appropriate time.12−14 © 2013 American Chemical Society

However, the PBM contains a set of empirical or semiempirical parameters such as coalescence kernel, breakage function, etc., which in most cases are experimentally obtained for a certain set of parameters. Therefore, such models cannot be effectively employed outside of strictly limited parameter domain. In order to overcome this limitation and to significantly extend the application areas of the models, the multiscale concept can be employed, whereby the process is simultaneously described on different time and length scales. In recent years a multiscale modeling concept has been applied for modeling of different solids processes and apparatuses such as drum granulator, fluidized bed reactor,15 crystallizer, gas−solid fluidization,16 paddle mixer-coater,17 fluidized bed spray granulator,18 and rotor-based granulator19 as well as for a general aggregation process.3 However, no simulation framework does exist which could be applicable to general solids processes, and many effects are neglected or poorly considered. In order to overcome these problems a novel multiscale simulation methodology is proposed in this contribution.

2. SYSTEM ARCHITECTURE The general representation of the architecture of the multiscale environment is shown in Figure 1. Here, the models which are located on the different hierarchy scales are used to calculate the process on various time intervals. The developed architecture is based on the previously proposed multiscale simulation environment18 which has been extended with an additional modeling tool on the submicroscale to perform a detailed simulation of agglomerate breakage in the fluidized bed apparatus. Special Issue: Multiscale Structures and Systems in Process Engineering Received: Revised: Accepted: Published: 11275

January 22, 2013 March 11, 2013 March 12, 2013 March 13, 2013 dx.doi.org/10.1021/ie400244x | Ind. Eng. Chem. Res. 2013, 52, 11275−11281

Industrial & Engineering Chemistry Research

Article

Figure 1. The architecture of the multiscale simulation environment.

On the upper hierarchy level the process is represented as a set of interconnected apparatuses and calculated by the flowsheet simulation system SolidSim-Dynamics.10 The PBM and semiempirical models of heat and mass transfer are applied to predict the particle size distribution (PSD) in different parts of the flowsheet. The submodels on the lower scales (Figure 1) are generated according to the calculated macroscopic process parameters such as bed mass, PSD in the apparatus, etc. The main focus of this contribution is on the investigation of the breakage characteristics of agglomerates; that is why the mesoscale model,18 which has been previously developed to calculate the particle wetting and heat and mass transfer, was not considered in this work. Therefore, the parameters which are required for the description of aggregation kinetics on the macroscale were taken from literature. The calculated properties from the flowsheet system were directly transferred into the microscale, where the coupling of the discrete element method (DEM) and the CFD system has been used to simulate agglomerate dynamics in a fluidized bed apparatus. In the DEM each particle is considered as a separate entity, and for each particle the Newtonian equations of motion are solved.20 Due to a two-way coupling of the DEM with the computational fluid dynamics (CFD) system the particle dynamics in the fluidized bed apparatuses can be predicted.21 The internal structure of agglomerates formed in a fluidized bed process can be effectively represented in the DEM as a set of primary particles which are connected by solid bonds7,22 of a binding agent. However, if such representation of agglomerates will be used on the microscale, where the large number of agglomerates is simulated, then this will lead to an exponential increase of computational time. Therefore, a simplification was made in this work that on the microscale the agglomerates were

modeled as ideally spherical objects. These calculations were carried out in the program EDEM, which has been coupled with the CFD system of ANSYS Fluent. More detailed description of this coupling can be found in Fries et al.21 To save the information about particle dynamics in the apparatus, the EDEM system has been coupled through a set of application programming interfaces to the separate postprocessing subsystem. This subsystem was employed to save trajectories of all agglomerates and to save characteristics of collisions between particles. Finally, the following characteristics have been obtained during the microscale simulation and transferred into the submicroscale: • parameters of contacts between the particles in the fluidized bed (distributions of the impact velocity and collision frequency); • parameters of particle contacts with apparatus walls; • particle residence time in different zones of the apparatus. On the submicroscale level the internal agglomerate structures were reproduced, and further modeling of mechanical interaction of agglomerate has been performed. Finally, on the basis of the data from this study, the breakage characteristics of agglomerates were derived, which afterward can be used on the macroscale as material based parameters of the PBM.

3. FLOWSHEET SIMULATION OF A GLOBAL PROCESS On the macroscale, the processes which occur in the fluidized bed apparatus are described by the one-dimensional PBM with the particle volume v as an internal property coordinate. The general form of this equation is given in eq 1 11276

dx.doi.org/10.1021/ie400244x | Ind. Eng. Chem. Res. 2013, 52, 11275−11281


Article

Figure 2. Scheme of the agglomerate collision simulation in the MUSEN-DEM system.

∂n(t , v) = niṅ (t , v) − nout ̇ (t , v) + Bagg (t , v) − Dagg (t , v) ∂t + Bbreak (t , v) − Dbreak (t , v)

Bbreak (t , v) =

(1)

1 2

∫0

v

β(t , v′, v − v′) ·n(t , v′) ·n(t , v − v′)dv′

The coalescence kernel β(t, v, u) is an important parameter in the PBE, which represents the aggregation rate of particles with volumes v and u forming the particle with the volume v + u. This kernel is symmetrical (β(t, v, u) = β(t, u, v)), continuous, and positive (β(t, v, u) ≥ 0, ∀v, u > 0). Various types of empirical and experimentally obtained coalescence kernels are available in the literature. In this contribution the kernel proposed by Kapur23 has been used. The death term Dagg(t, v) defines the velocity at which the particles of volume v are aggregating with other particles in the apparatus. The continuous form of the death events can be expressed as

∫0

(4) (5)

4. AGGLOMERATE BREAKAGE ON THE SUBMICROSCALE The developed simulation system “MUSEN-DEM” is applied to approximate the breakage characteristic of agglomerates on the lowest hierarchy scale. In the modeling framework all primary particles and solids bonds of the agglomerate are represented as separate objects. Therefore, the unique microparameters can be specified for each object that significantly increases the applicability of the system. In order to obtain the breakage function of agglomerates by different collision parameters and agglomerate properties like agglomerate size, velocity, and angle of impact, a set of simulation studies has been performed in MUSEN-DEM. In each case study, at the beginning of the DEM simulation one primary agglomerate is generated in the center of a relatively small computation volume, as it is shown in Figure 2. This agglomerate has a zero initial translational and rotational velocity. Afterward, a supplementary collision partner is generated, which also consists of primary particles connected by solid bonds (Figure 2), and the collision of both agglomerates is simulated. These calculations are carried out on the submiscroscale (Figure 1) for a time interval in the

∞

β(t , v , v′) ·n(t , v′) ·n(t , v)dv′

b ̅ (v , v′) ·S(v′) ·n(t , v′)dv′

In order to perform detailed modeling of agglomerate breakage, the values of fragmentation rate and breakage function have been approximated from the submicroscale. The numerical solution of the population balance equation (eq 1) has been calculated with the help of the Cell-Average technique,14 which is based on the well-known fixed pivot technique.11 The material streams in the flowsheet simulation system are described by multidimensional distributed parameters. The treatment of such streams in a fluidlike manner will cause a loss of information. For the correct handling of solids streams the concept of a transformation matrix is employed in the SolidSim9 and SolidSim-Dynamics10 systems. Therefore, the Cell-Average technique was not directly implemented into the simulation system. Instead of this, the transformation matrix has been generated from the Cell-Average approach, and in each simulation time step this matrix has been applied to apparatus holdup to simulate agglomeration and breakage processes.

(2)

Dagg (t , v) =

∞

Dbreak (t , v) = S(v) ·n(t , v)

where ṅin(t, v) and ṅout(t, v) are input and output streams entering and leaving the apparatus respectively; Bagg(t, v), Bbreak(t, v) and Dagg(t, v), Dbreak(t, v) are the birth and death terms due to the particle aggregation and breakage events, respectively. For example, if two particles with volumes v1 and v2 aggregate, then this will induce death events Dagg(t, v1), Dagg(t, v2) and the birth event Bagg(t, v1 + v2). Contrary to this, if some agglomerate of a volume u0 breaks into two parts with volumes u1 and u2, then this will lead to the birth events Bbreak(t, u1), Bbreak(t, u2) and the death event Dbreak(t, u0). It is assumed in the model that the agglomerates are spherical and their equivalent mass and volume after aggregation are equal to the total mass and volume of primary particles. In this case the birth rate during aggregation can be calculated by the integration throughout a volume coordinate as Bagg (t , v) =

∫v

(3)

To consider the breakage process in the PBM, the fragmentation rate S(v) and the breakage function b̅(v,v′) are used. This function describes the volume of fractions which are formed during the breakage of particles and represents the average number of particles with the volume v appearing after the fracture of particles with the volume v′. The rate S(v) is the breakage frequency of particles of specified volume. The birth and death rate can be defined as 11277



Article

As the bond breakage criteria the maximum of shear and tensile stresses in the bonds are used. If one of them exceeds the corresponding bond strength, then the bond breaks and is removed from the calculation procedure. Such a discrete event can lead to divergence in the system if the simulation step specified by the user is too big. Therefore, the analysis of the system state is carried out after each iteration, and the maximal particle velocity vmax is analyzed. As a consequence, the time step size is reduced if the maximal distance which can pass the particle in one step vmax · Δt is larger than the predefined critical distance. The detection of the contacts between particles is one of the most time-consuming operations in the DEM calculation. In the MUSEN-DEM system an approach based on the Verlet lists has been implemented, where each particle stores the information about all neighbor particles. Hence, the contact detection is performed only between particles within a given cutoff distance (Verlet distance) that sufficiently reduces computation time. To store the actual information about relative particle positions the recalculation of the Verlet lists is performed. These lists are updated not after every time step but only after a specified time interval, which depends on the Verlet distance and on the maximal particle velocity in the system.

range between 0.01 and 1 s with the typical simulation step of the DEM, which is on the order of 1−100 ns. To reflect the agglomerate breakage behavior at different tangential and normal impacts the following parameters are varied in the performed case studies: the initial position and velocity (v)̅ of the second agglomerate, the rotation angle (φ̅ ), and rotational velocity (ω̅ ) of both colliding agglomerates. The variation range of the impact and rotation velocities is selected related to the distributions of these collision parameters in the fluidized bed apparatus, which are calculated on the microscale (Figure 1). To consider different scenarios of the oblique impact the initial position of the second agglomerate is changed depending on the size of both agglomerates, as it is schematically represented in Figure 2. The following set of operations is sequentially performed within each simulation time step of the submicroscale: • Calculation of forces and moments in all solid bonds and verification of the breakage criterion for the bonds • Detection of contacts between primary particles and calculation of interparticulate forces by the Hertz-Mindlin contact model • Estimation of the total force acting on each primary particle • Calculation of Newtonian equations of motion and determination of new particle positions, translational velocities, and rotational velocities • Updating of Verlet lists (if it is necessary) • Calculation of the new value of the time step For the calculation of forces and moments in the solid bonds, which are caused by the relative motion of aggregated primary particles, the solid bridge bond model24 has been implemented into MUSEN-DEM. In each successive simulation step (i+1) the forces and moments in the bonds are calculated as an increment to the values from previous iteration (i). The forces in tangential and normal direction are determined as Fb̅ i +, t 1 = T ·Fb̅ i , t − vrel̅ , t ·Δt ·kt ·Ab

(6)

Fb̅ i +, n1 = kn·Ab ·(Linit − Lcur ) · rn̅

(7)

5. APPLICATION EXAMPLE The developed simulation approach has been applied for the multiscale simulation of the process which is shown in Figure 3.

Figure 3. Flowsheet of fluidized bed agglomeration process.

This process is used for the production of γ-Al2O3 agglomerates and consists of four main connected apparatuses. The agglomeration of particles is performed continuously in a cylindrical fluidized bed apparatus by atomization of a liquid binder. The output flow from the fluidized bed is fractionated via two screens. The oversize of the first screen is milled, mixed with the undersize of the second screen, and recycled into the agglomerator. The coarse fraction of the second screen leaves the flowsheet as the product. Additional flux of primary particles is added into the fluidized bed as external nuclei stream. In order to describe the aggregation process by the PBM, the experimentally validated coalescence kernel has been taken from the literature.23 To obtain the breakage characteristics the simulation on the lower scales has been used. The particle size distribution of the external nuclei flow has been described by the Gaussian function, with a median diameter of 0.4 mm and a deviation of 0.1 mm. For the modeling of both screens the separation function (eq 11), proposed by Molerus and Hofmann,26 has been used 1 T (d ) = 2 ⎤⎞ ⎛ 2 ⎡ d d 1 + dsc ·exp⎜ksc ⎢1 − d ⎥⎟ sc ⎦⎠ ⎝ ⎣ (11)

where Linit and Lcur are the initial and current length of the bond, Ab is the bond cross-cut surface area, rn̅ is the unit vector between bonded particles, kn and kt are the normal and tangential stiffness of the bond, and Δt is the size of the time step. In order to consider the motion of the contact partners in the space, the values calculated during the previous iteration are multiplied by a transformation matrix T. The length of the bond L depends on the distance between centers of particles Lpp, on the radii of bonded particles R1, R2, and on the bond radius Rb: L = Lpp −

R12 − R b2 −

R 22 − R b2

(8)

The moments acting in the bonds in tangential and normal directions were calculated as M̅ bi +, t 1 = T ·M̅ bi , t − ωrel ̅ , t ·Δt ·kn·I

(9)

M̅ bi +, n1 = T ·M̅ bi , n − ωrel ̅ , n ·Δt ·kt ·J

(10)

where ω̅ rel,n and ω̅ rel,t are relative rotational velocities between bonded particles in normal and tangential directions, I is the moment of inertia, and J is the polar moment of inertia of the bond cross-section.

( )

11278

( )



Article

and, as a consequence, this leads to the significant mass flow of the recycle streams in the scheme. The microscale model has been generated according to the obtained macroscopic results for simulation of 105 particles for a time interval of three seconds. The particle size distribution in the fluidized bed apparatus (Figure 4) was represented in the DEM by three size classes with diameters of 0.5 mm, 0.9 mm, and 1.5 mm. With the help of the microscale model the impact characteristics of the particles were obtained and afterward transferred to the submicroscale. In Figure 5 the vectors

where T(d) determines the mass fraction of the feed particles with diameter d which leaves the screen as oversize, ksc is the separation efficiency, and dsc is the separation diameter. The cumulative mass-related particle size distribution of fragments Q3(d) after the milling was described by the RRSB function as ⎛ ⎡ d ·ln(2)1/ n ⎤n⎞ ⎥ ⎟⎟ Q 3(d) = 1 − exp⎜⎜ −⎢ d50 ⎦⎠ ⎝ ⎣

(12)

where d50 is the median of the distribution, and the parameter n is calculated depending on the distribution steepness kmill by n=

log[log(0.75)/log(0.25)] log(kmill)

(13)

The agglomeration kinetics in the agglomerator has been obtained with the empirical coalescence kernel proposed by Kapur23 in eq 14. This kernel has been effectively used to predict the experimentally observed dynamics of agglomeration of microcrystalline cellulose in the work of Peglow et al.27 and of γAl2O3 particles by Hampel25 β(t , v , v′) = β0(t )

(v + v′)a (v ·v′)b

(14)

where β0(t) is the time-dependent aggregation efficiency, v and v′ are the volumes of contact partners, and a and b are adjustment parameters. The main process parameters of the modeled flowsheet (Figure 3) are listed in Table 1. The process was calculated up

Figure 5. Instantaneous particle velocities in the apparatus calculated on the microscale.

representing the particle velocities are illustrated. The vectors are colored according to the absolute translational velocity. The results show that the particle velocities are larger in the upper layers of the bed than in the bottom. Figure 6 represents the distribution of the collision rates between particles of different size classes depending on the

Table 1. Main Simulation Parameters of the Fluidized Bed Agglomeration Process external nuclei mass flow aggregation kinetics bed mass screen 1 screen 2 mill

1 kg/h a = 0.71; b = 0.06; β0 = 5.8 · 10−7 2 kg ksc = 8; dsc = 1 mm ksc = 4; dsc = 0.9 mm kmill = 0.7; d50 = 0.6 mm

to the steady-state regime. Figure 4 shows the obtained particle size distributions of the different streams. It can be concluded that the distribution of the final product is much narrower than material in the fluidized bed agglomerator. It is caused by double screening of the agglomerates after the fluidized bed, Figure 6. Collision rates between particles of different size.

impact velocity. The particles with diameter 0.9 mm, for example, collide with 1.5 mm particles within the range of impact velocities 0.3−0.4 m/s with the frequency of 0.151 collisions per second. The obtained results show that due to the clustered motion of particles the most part of impacts occurs at low collision velocities. Furthermore, the impact velocities are higher between particles of smaller fractions because the mean velocity of the particles in the bed increases with decreasing particle size. The calculations have shown that there is no breakage at the velocities smaller than 0.1 m/s. Therefore they were not shown on the diagram.

Figure 4. Cumulative mass-related PSDs of the different streams in steady-state. 11279



Article

contact partners, the breakage probability increased with increasing agglomerate size and increasing impact velocity. The similar dependencies between breakage probability and kinetic energy have been experimentally observed for different irregularly shaped particles.28 By combining the results about breakage probabilities with the collision rates from Figure 6 the breakage rate S(v) in eq 4 and eq 5 can be calculated for the particles of different size classes. The breakage function b̅(v, v′) can be approximated on the basis of the obtained particle size distributions of fragments. Different velocities of the impacts between agglomerates cause various breakage patterns. Figure 8 shows the change of the average particle size distribution of fragments forming during impacts between two 1.5 mm agglomerates. Each point of this three-dimensional plot represents the fractions of fragments of specified size which appear after collision with specified velocity. The simulation results have shown that the amount of fragments in the size region from 0.45 mm to 1.4 mm were negligibly small or even equal to zero. Therefore, this region is hidden in the plot, and only the PSD for two intervals from 0.25 mm to 0.45 mm and from 1.4 mm to 1.5 mm is shown. The submicroscale modeling has been performed with primary particles of 0.2 mm; therefore, in Figure 8 there are no fractions with the size less than 0.2 mm The significant change of the PSD has been obtained only above 0.4 m/s, as it is shown in Figure 8. Further increase of the impact velocity leads to the larger destruction of the agglomerates, and, as a consequence, more significant change of the width of the particle size distribution can be found.

On the submicroscale the numerical calculations of the impacts between agglomerates of different size classes have been carried out. For this purpose only one representative spherical agglomerate has been generated for each size class. From the microscale simulation it was noted that the most collisions take place with velocities up to 1.2 m/s and the collision frequency at the impact velocity higher than 1.2 m/s was less than 10−3 collisions per second. Consequently, during submicroscale simulations, the collision velocity has been varied from 0.1 to 1.2 m/s with an interval step of 0.05 m/s. For each impact velocity a set of calculations consisting of approximately 8200 tests has been carried out. The two-dimensional grid of the initial positions, which is schematically shown in Figure 2, consists of 16 points. The initial angle of rotation has been varied throughout three axes with an iteration step of 45°. The submicroscale simulation results are shown in Figure 7 and Figure 8. The obtained average breakage probability for the

Figure 7. Breakage probabilities during collisions at different velocities.

6. CONCLUSIONS In the performed study the architecture of the multiscale simulation environment for the modeling of the breakage process in fluidized beds has been developed. The novel environment consists of submodels on different time and length scales that allow for performing detailed numerical simulation of the investigated process and obtaining results within an appropriate time. Additionally to the breakage process, the novel system can be effectively used for the simulation of fluidized bed spray granulation and agglomeration processes. The detailed modeling of the breakage process is carried out on three different scales. On the upper hierarchical level the process is described by the one-dimensional population balance model. Its material specific parameters needed for the

impact between agglomerates with different sizes (Figure 7) describes the probability that at least one of the contact partner will break during collision into two or more separate fragments. Here, the simplification has been made that the plastic deformation and internal structure changing of the agglomerates due to destruction of individual solid bonds were not considered. For more detailed simulation the influence of the number of successive impacts i.e. loading history on the breakage probability should be investigated in the future work. For example, the breakage probability during impact between two agglomerates of the same size of 0.9 mm with the collision velocity 1 m/s equals 68%. The results of this study indicate that there is no agglomerate breakage by impacts with velocities less than 0.3 m/s. Moreover, due to the larger kinetic energy of

Figure 8. Influence of the impact velocity on the particle size distribution of forming fragments for collision between two agglomerates of 1.5 mm size. 11280



Article

(14) Kumar, S.; Ramkrishna, D. On the solution of population balance equation by discretization - I. A fixed pivot technique. Chem. Eng. Sci. 1996, 51, 1311−1332. (15) Balaji, S.; Du, J.; White, C. M.; Ydstie, B. E. Multi-scale modelling and control of fluidised beds for the production of solar grade silicon. Powder Technol. 2010, 199, 23−31. (16) Ge, W.; Wang, W.; Yang, N.; Li, J.; et al. Meso-scale oriented simulation towards virtual process engineering (VPE) - The EMMS Paradigm. Chem. Eng. Sci. 2011, 66, 4426−4458. (17) Freireich, B.; Li, J.; Litster, J.; Wassgren, C. Incorporating particle flow information from discrete element simulation in population balance models of mixer-coaters. Chem. Eng. Sci. 2011, 66, 3592−3604. (18) Dosta, M.; Antonyuk, S.; Heinrich, S. Multiscale simulation of the fluidized bed granulation process. Chem. Eng. Technol. 2012, 35, 1373−1380. (19) Bouffard, J.; Bertrand, F.; Chaouki, J. A multiscale model for the simulation of granulation in rotor-based equipment. Chem. Eng. Sci. 2012, 81, 106−117. (20) Cundall, P. A.; Strack, O. D. L. A discrete numerical model for granular assemblies. Geotechnique 1979, 47−65. (21) Fries, L.; Antonyuk, S.; Heinrich, S.; Palzer, S. DEM-CFD modelling of a fluidized bed spray granulation. Chem. Eng. Sci. 2011, 66, 1340−1355. (22) Mishra, B. K.; Thornton, C. Impact breakage of particle agglomerates. Int. J. Miner. Process. 2001, 61, 225−239. (23) Kapur, P. C. Kinetics of granulation by non-random coalescence mechanism. Chem. Eng. Sci. 1972, 27, 1863−1869. (24) Potyondy, D. O.; Cundall, P. A. A bonded-particle model for rock. Int. J. Rock Mech. Min. 2004, 41, 1329−1364. (25) Hampel, R. Beitrag zur Analyse von kinetischen Einf lüsen auf die Wirbelschicht-Sprühagglomeration, Dissertation, Magdeburg, 2010. (26) Molerus, O.; Hoffmann, H. Darstellung von Windsichtertrennkurven durch ein stochastisches Modell. Chem. Ing. Tech. 1969, 41, 340−344. (27) Peglow, M.; Kumar, J.; Heinrich, S.; Warnecke, G.; Tsotsas, E.; Mö rl, L.; Wolf, B. A generic population balance model for simultaneous agglomeration and drying in fluidized beds. Chem. Eng. Sci. 2007, 62, 513−532. (28) Aman, S.; Tomas, J.; Müller, P.; Kalman, H.; Rozenblat, Y. The investigation of breakage probability of irregularly shaped particles by impact tests. KONA 2011, 29, 224−235.

calculation of the breakage process were obtained from the lower scales. On the microscale the coupling of DEM and CFD systems is employed to predict the particle dynamics in the fluidized bed apparatus. On this scale the agglomerates are assumed as ideally spherical particles. The size and internal structure of agglomerates are considered properly on the submicroscale, where their breakage characteristics are obtained. As results from the submicroscale, the breakage probabilities and breakage functions under different impact conditions have been calculated. Combination of these characteristics with results from the microscale allows for approximating parameters of population balance model. In the current version of the multiscale simulation environment there still exists a large amount of simplifications and assumptions. However, the developed framework has a flexible architecture and can be easily extended with additional submodels or functional dependencies.

■

AUTHOR INFORMATION

Corresponding Author

*Phone: +4940428782143. Fax: +4940428782678. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Liu, L. X.; Litster, J. D. Population balance modelling of granulation with a physically based coalescence kernel. Chem. Eng. Sci. 2002, 57, 2813−2191. (2) Gantt, J. A.; Cameron, I. T.; Litster, J. D.; Gatzke, E. P. Determination of coalescence kernels for high-shear granulation using DEM simulations. Powder Technol. 2006, 170, 53−63. (3) Reinhold, A.; Briesen, H. Numerical behavior of a multiscale aggregation model − coupling population balances and discrete element models. Chem. Eng. Sci. 2012, 70, 165−175. (4) Ramachandran, R.; Immanuel, C. D.; Stepanek, F.; Litster, J. D.; Doyle, F. J., III A mechanistic model for breakage in population balances of granulation: Theoretical kernel development and experimental validation. Chem. Eng. Res. Des. 2009, 87, 598−614. (5) Antonyuk, S.; Tomas, J.; Heinrich, S.; Mörl, L. Breakage behaviour of spherical granulates by compression. Chem. Eng. Sci. 2005, 60, 4031−4044. (6) Antonyuk, S.; Khanal, M.; Tomas, J.; Heinrich, S.; Mörl, L. Impact breakage of spherical granules: experimental study and DEM simulation. Chem. Eng. Process. 2006, 45, 838−856. (7) Antonyuk, S.; Palis, S.; Heinrich, S. Breakage behaviour of agglomerates and crystals by static loading and impact. Powder Technol. 2011, 206, 88−98. (8) Rozenblat, Y.; Grant, E.; Levy, A.; Kalman, H.; Tomas, J. Selection and breakage functions of particles under impact loads. Chem. Eng. Sci. 2012, 71, 56−66. (9) Pogodda, M. Development of an advanced system for the modeling and simulation of solids processes; Aachen: Shaker Verlag, 2007. (10) Dosta, M.; Heinrich, S.; Werther, J. Fluidized bed spray granulation: Analysis of the system behaviour by means of dynamic flowsheet simulation. Powder Technol. 2010, 204, 71−82. (11) Ramkrishna, D. Population balances. Theory and applications to particulate systems in engineering; London: Academic Press: 2000. (12) Hounslow, M. J.; Ryall, R. L.; Marshall, V. R. A discretized population balance for nucleation growth and aggregation. AIChE J. 1988, 34, 1821−1832. (13) Kumar, J.; Peglow, M.; Warnecke, G.; Heinrich, S.; Mörl, L. Improved accuracy and convergence of discretized population balance for aggregation: The cell average technique. Chem. Eng. Sci. 2006, 61, 3327−3342. 11281


Multiscale Simulation of Agglomerate Breakage in Fluidized Beds

Recommend Documents