Development of a predictive high-shear granulation model

Within the pharmaceutical industry, high-shear granulation processes are well known for the production of drug-loaded granules. Development of such granulation processes, however, is often still more an art than a science. With the use of population balances, it is possible to link granulation rates to granule properties. Previous work demonstrated that good agreement between experimental and simulated results can be achieved [Powder Technol. 130 (2003) 162]. This enabled the granulation rates to be defined by two model parameters: the critical binder volume fraction and the aggregation rate constant. The modelling framework presented in this paper forms the basis of the kinetic analysis of granulation experiments that may lead to the development of a modelling tool that cannot only be used to simulate but also predict high-shear granulation behaviour in real-life pharmaceutical processes.     

Modelling nucleation in wet granulation

Nucleation is the first stage in any granulation process where binder liquid first comes into contact with the powder. This paper investigates the nucleation process where binder liquid is added to a fine powder with a spray nozzle. The dimensionless spray flux approach of Hapgood et al. (Powder Technol. 141 (2004) 20) is extended to account for nonuniform spray patterns and allow for overlap of nuclei granules rather than spray drops. A dimensionless nuclei distribution function which describes the effects of the design and operating parameters of the nucleation process (binder spray characteristics, the nucleation area ratio between droplets and nuclei and the powder bed velocity) on the fractional surface area coverage of nuclei on a moving powder bed is developed. From this starting point, a Monte Carlo nucleation model that simulates full nuclei size distributions as a function of the design and operating parameters that were implemented in the dimensionless nuclei distribution function is developed. The nucleation model was then used to investigate the effects of the design and operating parameters on the formed nuclei size distributions and to correlate these effects to changes of the dimensionless nuclei distribution function. Model simulations also showed that it is possible to predict nuclei size distributions beyond the drop controlled nucleation regime in Hapgood's nucleation regime map. Qualitative comparison of model simulations and experimental nucleation data showed similar shapes of the nuclei size distributions. In its current form, the nucleation model can replace the nucleation term in one-dimensional population balance models describing wet granulation processes. Implementation of more sophisticated nucleation kinetics can make the model applicable to multi-dimensional population balance models.     

The kinetics of the granulation process: Right from the early stages

In this study, experimentation and modelling were carried out to understand the granulation process. This work assesses whether there is a significant difference in the aggregation rate of the wet granulation process between the very early stages and later stages of high shear granulation. Measurements of the size distribution and binder content from the beginning of the process, just after liquid binder addition, were carried out. A population balance model based on two different kernels, the Equi Kinetic Energy (EKE) kernel and two-dimensional population balance equations with a Size Independent (SI) kernel, was applied to the high shear granulation process. It was concluded that the population balance equations with SI kernel best described the aggregation in the high shear granulation process. The value of aggregation rate constant in the early stages is smaller than aggregation kernel in the later stages.     

Incorporating experimental uncertainties into multivariate granulation modelling

A methodology that carries experimental uncertainties into model predictions is studied and applied to a multidimensional population balance model for granulation processes. This complex model contains 27 parameters. A portion of them such as material constants can be measured or estimated, whereas some of the model parameters need to be established through granulation experiments and subsequent fitting to the model. As uncertainties are associated with every measurement, these are used in the presented methodology for the computation of uncertainties in the model predictions. This allows one to assess the quality of a model and to identify outliers in the experimental observations. As the evaluation of the complex model framework is computationally expensive, the granulation process is approximated with response surfaces in the studied example, allowing the quick computation of the model response in the optimisation procedure. Using eight sets of experimental observations, model-specific rate constants for particle coalescence, compaction, breakage, and reaction are calculated. Additionally, uncertainties of these parameters are estimated, allowing for the calculation of the model prediction and its uncertainty. Whereas the a priori uncertainties are relatively large, the uncertainties are significantly reduced by the method proposed. In addition to this, a possible mismatch between the model and the experimental observations is identified, giving hints for further investigations.     

A population balance model for high shear granulation

In a previous paper, Hoornaert et al. ( Powder Technol. 96 (1998); 116-128) presented data from granulation experiments performed in a 50 L Lödige high shear mixer. In this study that same data was simulated with a population balance model. Based on an analysis of the experimental data, the granulation process was divided into three separate stages: nucleation, induction, and coalescence growth. These three stages were then simulated separately, with promising results. It is possible to derive a kernel that fit both the induction and the coalescence growth stage. Modeling the nucleation stage proved to be more challenging due to the complex mechanism of nucleus formation. From this work some recommendations are made for the improvement of this type of model.     

Optimal control and operation of drum granulation processes

Process optimisation and optimal control of batch and continuous drum granulation processes are studied in this paper. The main focus of the current research has been: (i) construction of optimisation and control relevant, population balance models through the incorporation of moisture content, drum rotation rate and bed depth into the coalescence kernels; (ii) investigation of optimal operational conditions using constrained optimisation techniques; (iii) development of optimal control algorithms based on discretized population balance equations; and (iv) comprehensive simulation studies on optimal control of both batch and continuous granulation processes. The objective of steady state optimisation is to minimise the recycle rate with minimum cost for continuous processes. It has been identified that the drum rotation-rate, bed depth (material charge), and moisture content of solids are practical decision (design) parameters for system optimisation. The objective for the optimal control of batch granulation processes is to maximize the mass of product-sized particles with minimum time and binder consumption. The objective for the optimal control of the continuous process is to drive the process from one steady state to another in a minimum time with minimum binder consumption, which is also known as the state-driving problem. It has been known for some time that the binder spray-rate is the most effective control (manipulative) variable. Although other possible manipulative variables, such as feed flow-rate and additional powder flow-rate have been investigated in the complete research project, only the single input problem with the binder spray rate as the manipulative variable is addressed in the paper to demonstrate the methodology. It can be shown from simulation results that the proposed models are suitable for control and optimisation studies, and the optimisation algorithms connected with either steady state or dynamic models are successful for the determination of optimal operational conditions and dynamic trajectories with good convergence properties.     

Model-based design and control of a continuous drum granulation process

This paper is concerned with enhanced process design and control of a multiple-input multiple-output (MIMO) granulation process. The work is based on a first-principles mechanistic three-dimensional population balance model (3D-PBM), which has been previously validated against experiments at the laboratory-scale for various operating conditions and formulations. The main objective of this study is via a novel process design, to control and operate the granulation process under more optimal conditions. Novelty of the work lies in the usage of the validated 3D-PBM to extract suitable multiple control-loop pairings from which an overall control loop performance is qualitatively and quantitatively assessed. Results show that for most existing granulation process configurations, enhanced control-loop performance is not achieved and as a result an alternative process design strategy is necessary. The proposed design demonstrates increased efficiency in the control and operation of the granulation process, which is required for further efficient control and operation of subsequent downstream processes.     

Fluidized bed spray granulation: Analysis of the system behaviour by means of dynamic flowsheet simulation

Nowadays, software tools for the flowsheet simulation of industrial processes are commonly used for design, simulation, balancing, troubleshooting and optimization purposes. Most of the tools are applicable to fluid processes only and cannot be effectively used for processes which involve solids.In this contribution we want to present the conceptual design of a new system applicable for the dynamic flowsheet simulation of complex solids processes. This system is developed as an enhancement to the existing simulation program.The novel software is able to simulate the unsteady behaviour of complex circuits of granulation processes. The transient behaviour during the start-up and changing of the process or material parameters can also be examined.As flowsheet examples, a typical spray granulation process with different schemes consisting of fluidized bed granulators, screens, mill and splitters was used. The mathematical model of the fluidized bed granulator is described by a one-dimensional population balance equation and coupled with heat and mass transfer and simple fluid dynamics.Received simulation results have shown that the proposed concept of the dynamic flowsheet simulation of granulation processes can be used effectively and has the potential to be generalized for other types of solids processes.     

A volume-based multi-dimensional population balance approach for modelling high shear granulation

A volume-based multi-dimensional population balance model based on the approach used by Verkoeijen et al. [2002. Population balances for particulate processes—a volume approach. Chemical Engineering Science 57, 2287-2303], is further developed and applied to a wet granulation process of pharmaceutically relevant material, performed in a high shear mixer. The model is improved by a generalization that accounts for initial non-uniformly distributed liquid and air among the different particle size classes. Only the wet massing period of the granulation process has been modelled and it is experimentally found that the pores in the granules are fully saturated by liquid, i.e., no air is present in the granules during this period. Hence, an alternative model formulation is used as no model for the air in the granules is needed. Particle volume distribution, liquid saturation, liquid-to-solid ratio and porosity of the granules can all be modelled, as these properties can all be expressed as combinations of three model parameters, i.e., the volume fraction of solid material, total liquid fraction and the liquid fraction inside the granules. The model is also improved by introducing a new coalescence kernel and by increasing the number of size classes used. The simulated results are compared to measurements from a series of five designed experiments where impeller speed and water content are varied. It is found that the evolution of the volume, liquid saturation and porosity distributions could all be explained by fitting the compaction and coalescence rate constants.     

Model-based analysis of a twin-screw wet granulation system for continuous solid dosage manufacturing

Implementation of twin-screw granulation in a continuous from-powder-to-tablet manufacturing line requires process knowledge development. This is often pursued by application of mechanistic models incorporating the underlying mechanisms. In this study, granulation mechanisms considered to be dominant in the kneading element regions of the granulator i.e., aggregation and breakage, were included in a one-dimensional population balance model. The model was calibrated using the experimentally determined inflow granule size distribution, and the mean residence time was used as additional input to predict the outflow granule size distribution. After wetting, the first kneading block caused an increase in the aggregation rate which was reduced afterwards. The opposite was observed in case of the breakage rate. The successive kneading blocks lead to a granulation regime separation inside the granulator under certain process conditions. Such a physical separation between the granulation regimes is promising for future design and advanced control of the continuous granulation process.     

Experimental validation studies on a multi-dimensional and multi-scale population balance model of batch granulation

In this study, a dynamic model is presented for the granulation process, employing a three-dimensional population balance framework. As a first attempt to account for the multi-scale character of the process, the nucleation and aggregation kernels used in the population balance model are derived using mechanistic representations of the underlying particle physics such as wetting kinetics and energy dissipation effects. Thus, the fundamental properties of the powder and the liquid were used as parameters in the model to predict the granulator dynamics and granule properties. The population balance model is validated against experimental data from a calcite/PVOH-H₂O recipe obtained using a lab-scale drum granulator for granule size, fractional binder content and porosity. A reasonably good agreement between experimental and simulation results were obtained for the granule size distribution under different experimental conditions. In addition, accurate model predictions were made for the evolution of the average properties (i.e., size, fractional binder content and porosity) for various operating conditions.     

Determination of coalescence kernels for high-shear granulation using DEM simulations

Discrete element method (DEM) modeling is used in parallel with a model for coalescence of deformable surface wet granules. This produces a method capable of predicting both collision rates and coalescence efficiencies for use in derivation of an overall coalescence kernel. These coalescence kernels can then be used in computationally efficient meso-scale models such as population balance equation (PBE) models. A soft-sphere DEM model using periodic boundary conditions and a unique boxing scheme was utilized to simulate particle flow inside a high-shear mixer. Analysis of the simulation results provided collision frequency, aggregation frequency, kinetic energy, coalescence efficiency and compaction rates for the granulation process. This information can be used to bridge the gap in multi-scale modeling of granulation processes between the micro-scale DEM/coalescence modeling approach and a meso-scale PBE modeling approach.     

On the general theory of solid granulation

The general population balance equation for the kinetics of granulation by simultaneous coalescence and crushing and layering mechanisms is posed and self-preserving solutions are obtained. A general similarity transformation, which contains in it all the physical information concerning the granulation process, is presented. It is clearly shown that self-preserving granule size distributions are possible for granulation by simultaneous coalescence and crushing and layering.     

Identification of models for control of wet granulation

The modeling work in this paper provides insight on improved control and design (including measurement selection) of a granulation process. Two different control strategies (MPC and PID) are evaluated on an experimentally validated granulation model. This model is based on earlier work done at The University of Sheffield, UK and Organon, The Netherlands [C.F.W. Sanders, W. Oostra, A.D. Salman, M.J. Hounslow, Development of a predictive high-shear granulation model; experimental and modeling results, 7th World Congress of Chemical Engineering, Glasgow (2005), C11-002]. The granulation kinetics were measured in a 10 liter batch granulator with an experimental design that included four process variables. The aggregation rates were extracted with a Discretized Population Balance (DPB) model. Knowledge of the process kinetics was used to model a continuous (well mixed) granulator. The controller model for the Model Predictive Controller is a linearized state space model, derived from the nonlinear DPB model. It has the four process variables from the experimental design and a feed ratio as input variables. Since the DPB model describes the whole Granule Size Distribution (GSD), candidate sets of lumped output variables were evaluated. When measuring controller performance based on the full granule size distribution, it is shown that a PID controller can actually produce results that fluctuate more than the open-loop response. An MPC controller improves stability on both process outputs and the full granule size distribution. The work shows that measuring and controlling specific number based lumped outputs result in a more stable process than when mass based lumped outputs are used. The paper describes a general strategy of using lab scale batch experiments to design and control (small or large scale) continuous granulators. The continuous experiments in this paper are based on simulation, therefore future experimental validation will elucidate further the link between batch and continuous granulation.     

Simulating the early stage of high-shear granulation using a two-dimensional Monte-Carlo approach

A two-dimensional (2-D) model of a granulation process is presented in this paper. It aims to simulate an entire granulation batch without the use of an initial experimental or fictitious 2-D density function, by taking the experimental operating conditions into account. The mass of liquid and solid in the granules are the two predicted internal variables. The 2-D population balance equation is solved by a Constant Number Monte-Carlo method. This is a stochastic technique tracking the evolution of a population, whilst performing the calculations with a fixed number of particles. This is achieved by reducing or increasing the sample volume when an event results in a net production or a net decrease in the number of particles, respectively. An original multi-population approach is developed to describe the early stage of the process, where small numbers of granules are formed amongst a large number of primary particles. It consists of separating the primary particles from the granule population. A specific intensive variable is introduced to keep track of the repartition of masses. The overall density function is reconstructed a posteriori from the combination of the two populations. This approach allows the simulation to commence from the initial addition of liquid at the start of the process, rather than to start from an early granule size distribution. The early stage of the granulation process, frequently referred as nucleation, can therefore be studied numerically. Four different mechanisms are implemented. Nucleation and re-wetting describe the addition of liquid to the system. The interactions between liquid and solid phases are modelled by a layering process. An aggregation model is also included to simulate the growth of particles undergoing frequent collisions. Finally, the relevance of this new model is demonstrated by confronting the simulations to real experimental data.     

The inverse problem in granulation modeling—Two different statistical approaches

This article is concerned with parameter estimation for a multidimensional population balance model for granulation. Experimental results were obtained by running a laboratory mixer with sodium carbonate and aqueous polyethylene glycol solutions. Subsequently, a prescan of suitable parameter combinations utilising the experimental results is performed, and a local surrogate model constructed around the best combination. For the actual estimation of the parameters and their uncertainties two different approaches are applied—a projection method and a Bayesian approach. It is found that the model predictions with the parameters obtained through both methods are similar. Furthermore, the uncertainties in the model predictions increase as the experimental uncertainties are increased. Studies of the marginal densities of two‐parameter combinations obtained through the Bayesian approach show a correlation between the collision and breakage rate constant, giving potential hints for further model development. Furthermore, a bimodal distribution of the compaction rate constant is observed. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

The importance of wet-powder dynamic mechanical properties in understanding granulation

Granule impact deformation has long been recognised as important in determining whether or not two colliding granules will coalesce. Work in the last 10 years has highlighted the fact that viscous effects are significant in granulation. The relative strengths of different formulations can vary with strain rate. Therefore, traditional strength measurements made at pseudo-static conditions give no indication, even qualitatively, of how materials will behave at high strain rates, and hence are actually misleading when used to model granule coalescence. This means that new standard methods need to be developed for determining the strain rates encountered by granules inside industrial equipment and also for measuring the mechanical properties of granules at these strain rates. The constitutive equations used in theoretical models of granule coalescence also need to be extended to include strain-rate dependent components.     

Parameter estimation in a multidimensional granulation model

A new multidimensional model for wet granulation is presented, which includes particle coalescence, compaction, reaction, penetration, and breakage. In the model, particles are assumed to be spherical and consist of two kinds of solid, two kinds of liquid, and pore volume. The model is tested against experimental results (Simmons, Turton and Mort. Proceedings of Fifth World Congress on Particle Technology, paper 9d, 2006) from the granulation of sugar particles with different PEG based binders in a bench scale mixer, being carried out for different impeller speeds, binder compositions and process durations. The unknown rate constants for coalescence, compaction, reaction, and breakage were fitted to the experiments and the sensitivities of the mass of agglomerates were calculated with respect to these parameters. This is done by employing experimental design and a response surface technique. The simulations with the established set of parameters show that the model predicts the trends, not only in time, but also for crucial process conditions such as impeller speed and the binder composition. As such it is found that more viscous binder promotes the formation of porous particle ensembles. Furthermore, the statistics of the different events such as collisions, coalescence and breakage reveal for instance that successful coalescence events outnumber the breakage events by a factor of up to three for low impeller speeds.