Combined Population Balance Research Articles

Quantitative analysis of the effects of multi-component formulation parameters on granule and tablet properties via a combined population balance and statistical predictive model

In pharmaceutical drug product manufacturing, the use of multi-component mixtures in the formulation is a common practice. However, the introduction of each material alters the powder blend properties and affects the granule growth mechanisms in a wet granulation process. In this study, we quantified the effects of varying formulation parameters on granule growth rate, expressed by the liquid amount required for granulation to reach completion, and on granule and tablet quality attributes. Process models, including population balance and statistical models, were developed to represent the granulation, milling, and tableting process, and predict relevant granule and tablet properties. Overall, prediction of granule properties had an accuracy of above 80% and the prediction of different tablet properties ranged from an R2 of 0.68 to 0.9. These models are computationally efficient and can be simulated serially to predict the performance of different multi-component formulations by using the pre-blend properties as model inputs.

Particle surface moisture content estimation using population balance modelling in fluidised bed agglomeration

The objective of this study was to investigate the effect of particle surface moisture content on growth rate during fluidised bed agglomeration. In order to establish the relationship between process conditions and particle surface moisture content, the combined population balance and thermodynamic model, as described by Ronsse et al. (2007a,b), was used but was modified to include the degree of wetting and surface moisture content as variables in the population balance. Growth kinetics were experimentally verified by fluidised bed agglomeration tests using 100μm glass beads and maltodextrin based aqueous binder solutions, under varying process conditions. Studied process variables included binder concentration, fluidisation air temperature, liquid binder feed rate and liquid binder atomisation pressure. With the exception of varying binder concentrations, it was observed that a clear correlation existed between the model-predicted surface moisture content and the experimentally obtained growth rates. This work clearly demonstrates that, in population balance modelling of fluidised bed agglomeration, constant rate agglomeration kernels are insufficient and need to be sensitised to surface moisture content and binder concentration.

On the Coupled Solution of a Combined Population Balance Model Using the Least-Squares Spectral Element Method

In this work, a cross-sectional averaged two-fluid model combined with a population balance model is applied to simulate the flow field and the bubble size distributions in a two-phase bubble column. The Martinez-Bazan breakage kernel and a modified Prince and Blanch coalescence kernel have been chosen to describe bubble breakage and bubble coalescence, respectively. In the present study, we discuss the use of a higher-order spectral element method—the least-squares method—to compute the system of equations in a coupled manner. The least-squares method is highly accurate and has a number of advantages over the conventional numerical methods like the finite difference and finite volume methods. In contrast to the finite volume method, when desinging an overall solution algorithm, this least-squares method ensures that all the continuity equations are satisfied individually and it deals with both the convective and diffusive terms stably and accurately. The novel iterative algorithm solves the flow and the ...

Batch top-spray fluid bed coating: Scale-up insight using dynamic heat- and mass-transfer modelling

A mathematical model was developed for batch top-spray fluid bed coating processes based on Ronsse et al. [2007a, b. Combined population balance and thermodynamic modelling of the batch top-spray fluidised bed coating process. Part I—model development and validation. Journal of Food Engineering 78, 296–307; Combined population balance and thermodynamic modelling of the batch top-spray fluidised bed coating process. Part II—model and process analysis. Journal of Food Engineering 78, 308–322]. The model is based on one-dimensional discretisation of the fluid bed into a number of well-mixed control volumes. In each control volume, dynamic heat and mass balances were set up allowing the simulation of the contents of water vapour, water on core particles and deposited coating mass as well as fluidisation gas, particle and chamber wall temperature. The model was used to test different scale-up principles by comparing simulation results with experimental temperature and humidity data obtained from inorganic salt coating of placebo cores in three pilot fluid bed scales being a 0.5 kg small-scale (GEA Aeromatic-Fielder Strea-1), 4 kg medium-scale (GEA Niro MP-1) and 24 kg large-scale (GEA MP-2/3). Results show good agreement between simulated and experimental outlet fluidisation air temperature and humidity as well as bed temperature. Simulations reveal that vertical temperature and humidity gradients increase significantly with increasing scale and that in fluid beds as the simulated 900 kg (RICA-TEC Anhydro) production-scale, the gradients become too large to use the simple combined drying force/relative droplet size scale-up approach without also increasing the inlet fluidisation air temperature significantly. Instead, scale-up in terms of combinations of the viscous Stokes theory with simulated particle liquid layer profiles (obtained with the model) is suggested. In this way, the given fluid bed scale may be optimised in terms of low agglomeration tendency for a given process intensity across scale.

Population balance and computational fluid dynamics modelling of ice crystallisation in a scraped surface freezer

Ice crystallisation in a scraped surface freezer is exceedingly complex and there is very limited fundamental understanding of the influences of fluid flow and heat transfer on ice crystal size, number and shape. This paper presents a computer modelling study that combines population balance method and computational fluid dynamics method. Ice crystal nucleation and growth kinetics has been described by discrete population balance equation. Algorithms for solving the coupled equations of fluid flow, heat transfer and discrete population balance of ice crystallisation have been developed and implemented into a commercial code. Demonstrated is a 2-D computer simulation of ice crystallisation in a scraped surface freezer. Although the simulation makes several assumptions including simplified fluid flow conditions, the predicted ice crystal size distribution is comparable to the experimental data. It is shown that with combined computational fluid dynamics and population balance modelling much insight into the interaction of fluid flow, heat transfer and ice crystallisation in the scraped surface freezer can be obtained.

Combined population balance and thermodynamic modelling of the batch top-spray fluidised bed coating process. Part I—Model development and validation

A combined population balance and thermodynamic model was developed for the batch top-spray fluidised bed coating process. The model is based on the one-dimensional discretisation of the fluidised bed into different control volumes, in which the dynamic heat and mass balances for air, water vapour, core particles and coating material were established. The calculation method involves a Monte Carlo technique for the simulation of the particle exchange in combination with the first-order Euler’s method for solving the heat and mass balances. The model enables the prediction of both the dynamic coating mass distribution and the one-dimensional thermodynamic behaviour of the fluidised bed during batch operation. The simulation results were validated using the results from tests on a Glatt GPCG-1 fluidised bed unit.

Combined population balance and thermodynamic modelling of the batch top-spray fluidised bed coating process. Part II—Model and process analysis

In part I of this study, a mathematical model for the top-spray fluidised bed coating process was presented. In this second part, the capabilities of the model are illustrated by performing a detailed sensitivity analysis. The results clearly show that, besides the fluidisation air temperature and volumetric flow rate, the atomisation air pressure and temperature have a significant impact on the fluidised bed’s thermodynamic operation point. Considering the sensitivity of both the thermodynamic characteristics of the bed and the energetic efficiency of the coating process, the spraying rate was found to be main control variable for future model-based control applications in fluidised bed coating. Finally, increasing the relative size of the spraying region or increasing particle mixing has a narrowing effect on the coating mass distribution, which could be used in obtaining particles with a required coating distribution.