Complete two dimensional population balance modelling of wet granulation in twin screw

Ismail, Hamza Y.; Singh, Mehakpreet; Albadarin, Ahmad B.; Walker, Gavin

doi:10.1016/j.ijpharm.2020.120018

Cited by 29 publications

(23 citation statements)

References 29 publications

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“…Mathematically, the proportionality constant for overlapping of the cells is calculated using the relation given below: (14) where min It can be noticed that the (15) does not give any account for the mass conservation law which is a necessary condition for any numerical method. This signifies that the above formulation cannot be used to track the true behavior of the number density and require some adjustments to predict the integral properties (zeroth-and first-order moments) accurately corresponding to the number density function.…”

Section: Numerical Schemementioning

confidence: 99%

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Finite volume approach for fragmentation equation and its mathematical analysis

Singh

Walker

2021

Numer Algor

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This work is focused on developing a finite volume scheme for approximating a fragmentation equation. The mathematical analysis is discussed in detail by examining thoroughly the consistency and convergence of the numerical scheme. The idea of the proposed scheme is based on conserving the total mass and preserving the total number of particles in the system. The proposed scheme is free from the trait that the particles are concentrated at the representative of the cells. The verification of the scheme is done against the analytical solutions for several combinations of standard fragmentation kernel and selection functions. The numerical testing shows that the proposed scheme is highly accurate in predicting the number distribution function and various moments. The scheme has the tendency to capture the higher order moments even though no measure has been taken for their accuracy. It is also shown that the scheme is second-order convergent on both uniform and nonuniform grids. Experimental order of convergence is used to validate the theoretical observations of convergence.

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Section: Numerical Schemementioning

confidence: 99%

“…Fragmentation is a well-known mechanism occur in many applications of aerosol [10], depolymerization [1,12], crystallization [31], pharmaceutical sciences [14,15] and chemical engineering [23,30]. The fragmentation process leads the formation of two or more smaller size particles after the disintegration of larger size particles.…”

Section: Introductionmentioning

confidence: 99%

Finite volume approach for fragmentation equation and its mathematical analysis

Singh

Walker

2021

Numer Algor

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“…Population balance modeling (PBM) has emerged as a powerful model-based tool not only to predict the output of the desired property but also to increases the understanding and the enhancement of continuous twin-screw granulation processes [ 12 , 13 , 14 ]. One-dimensional PBMs are still widely used in pharmaceutical manufacturing primarily tracking only one particle property at a time, partly due to the lack of suitable equipment capable of measuring two or more properties simultaneously, as well as the lack of suitable multi-dimensional kernels that take into account the specific process or the available experimental data [ 15 , 16 ].…”

Section: Introductionmentioning

confidence: 99%

“…Despite the multiple published models to simulate the twin-screw wet granulation process [ 1 , 12 , 13 , 14 , 15 , 17 , 18 , 19 , 20 ], a complete or more generic model that involves material properties, process parameters and perhaps screw configurations, is to the author’s best knowledge not available in literature [ 6 ]. This work seeks to take the first steps to address the development of a generic model, which from an industrial perspective is desirable to reduce the number of experiments required and therefore expedite the time to market for new products.…”

Section: Introductionmentioning

confidence: 99%

Improvement of a 1D Population Balance Model for Twin-Screw Wet Granulation by Using Identifiability Analysis

et al. 2021

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Recently, the pharmaceutical industry has undergone changes in the production of solid oral dosages from traditional inefficient and expensive batch production to continuous manufacturing. The latest advancements include increased use of continuous twin-screw wet granulation and application of advanced modeling tools such as Population Balance Models (PBMs). However, improved understanding of the physical process within the granulator and improvement of current population balance models are necessary for the continuous production process to be successful in practice. In this study, an existing compartmental one-dimensional PBM of a twin-screw granulation process was improved by altering the original aggregation kernel in the wetting zone as a result of an identifiability analysis. In addition, a strategy was successfully applied to reduce the number of model parameters to be calibrated in both the wetting zone and kneading zones. It was found that the new aggregation kernel in the wetting zone is capable of reproducing the particle size distribution that is experimentally observed at different process conditions as well as different types of formulations, varying in hydrophilicity and API concentration. Finally, it was observed that model parameters could be linked not only to the material properties but also to the liquid to solid ratio, paving the way to create a generic PBM to predict the particle size distribution of a new formulation.

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“…Population balance equations (PBEs) describe the behavior of particle properties' changes due to phenomena such as nucleation, growth, aggregation and breakage [1]. Many applications of PBEs can be found in the area of chemical engineering [2], depolymerization [3,4], waste water treatment [5], bubble columns [6], physics [7] and pharmaceutical sciences [8][9][10][11][12], where these mechanisms have a significant impact on the particle properties in the system. In the aggregation process, two or more smaller particles merge at a specific rate to build larger size particles.…”

Section: Introductionmentioning

confidence: 99%

Characterization of Simultaneous Evolution of Size and Composition Distributions Using Generalized Aggregation Population Balance Equation

et al. 2020

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The application of multi-dimensional population balance equations (PBEs) for the simulation of granulation processes is recommended due to the multi-component system. Irrespective of the application area, numerical scheme selection for solving multi-dimensional PBEs is driven by the accuracy in (size) number density prediction alone. However, mixing the components, i.e., the particles (excipients and API) and the binding liquid, plays a crucial role in predicting the granule compositional distribution during the pharmaceutical granulation. A numerical scheme should, therefore, be able to predict this accurately. Here, we compare the cell average technique (CAT) and finite volume scheme (FVS) in terms of their accuracy and applicability in predicting the mixing state. To quantify the degree of mixing in the system, the sum-square χ2 parameter is studied to observe the deviation in the amount binder from its average. It has been illustrated that the accurate prediction of integral moments computed by the FVS leads to an inaccurate prediction of the χ2 parameter for a bicomponent population balance equation. Moreover, the cell average technique (CAT) predicts the moments with moderate accuracy; however, it computes the mixing of components χ2 parameter with higher precision than the finite volume scheme. The numerical testing is performed for some benchmarking kernels corresponding to which the analytical solutions are available in the literature. It will be also shown that both numerical methods equally well predict the average size of the particles formed in the system; however, the finite volume scheme takes less time to compute these results.

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Complete two dimensional population balance modelling of wet granulation in twin screw

Cited by 29 publications

References 29 publications

Finite volume approach for fragmentation equation and its mathematical analysis

Finite volume approach for fragmentation equation and its mathematical analysis

Improvement of a 1D Population Balance Model for Twin-Screw Wet Granulation by Using Identifiability Analysis

Characterization of Simultaneous Evolution of Size and Composition Distributions Using Generalized Aggregation Population Balance Equation

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