Assessment of the parameter identifiability of population balance models for air jet mills

Abstract

Air jet mills are ubiquitous breakage devices not only in the pharmaceutical industry, but also in food and the toner manufacturing industry. The popularity of air jet mills arises due to its self-classifying, non-contaminating, and non-degrading operation while also maintaining a narrow particle size distribution. A popular approach towards mathematically modelling comminution devices like the jet mill is the population balance model framework. Population balance model for breakage is a semi-empirical framework in which several parameters are estimated from the experimental data. In many cases the experimental data available is insufficient, or of bad quality to guarantee the estimation of unique parameters. Thus it is imperative to assess the identifiability of such models to ensure that the chosen model structure is identifiable, both structurally and practically. In this study, we analyse

Crystal Growth Kinetics of an Industrial Active Pharmaceutical Ingredient: Implications of Different Representations of Supersaturation and Simultaneous Growth Mechanisms

“…The kinetic parameters can then be estimated by regression in averaged-size models 6 or in a population balance model (PBM) 7,8 after the data from different sources are parsed and curated, and appropriate equations for the crystallization mechanisms are identified. While this workflow has been successfully applied in several accounts for the estimation of crystallization kinetics of various organic molecules, it suffers from three main limitations: (a) in almost all works, the mathematical expressions used for the supersaturation are simplified by omitting the solute activity coefficients in the saturated and supersaturated state due to difficulties in estimating states in supersaturated conditions; 9,10 (b) empirical expressions are often used to relate crystal growth kinetics to supersaturation, partly due to the lack of tools to effectively measure 3D crystal growth and also due to their mathematical flexibility 11 to act as a sort of "average" between the typically coexisting growth mechanisms, which results in loss of process insight, and (c) model structure, parameter correlation, identifiability, 12 and uncertainty are rarely considered. Such limitations may lead to large deviations (>300%) in the estimation of crystallization kinetic parameters, especially in the highly concentrated nonideal solutions 2 often employed in (batch) antisolvent crystallization systems 5 and hamper efforts toward extracting key physicochemical material attributes from the estimated (lumped) kinetic parameters.…”

On structural and practical identifiability

“…Practical identifiability can be achieved by adding new data [44,60]. The process of determining the most informative targets and time points for the new measurements is known as optimal experimental design and is frequently applied in different modelling fields, e.g.…”

Numerical Simulation of Particle Dynamics in a Spiral Jet Mill via Coupled CFD-DEM

“…Although a variety of approaches have been proposed for this inverse problem, they cannot be applied directly to the spiral jet mill models. Bhonsale et al [ 23 ] performed an identifiability analysis of a discretized spiral jet mill PBM, and showed that the convolution between classification and breakage in the jet mill led to non-identifiable parameters in the breakage kernels.…”