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Modeling of particle formation in pan granulators with sieve-mill recycle
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Fertilizers are commonly used to improve the soil quality in both conventional and organic agriculture. One such fertilizer is dolomite for which soil application in granulated form is advantageous. These granules are commonly produced from ground dolomite powder in continuous pan transfer granulators. During production, the granulator’s operation parameters affect the granules’ properties and thereby also the overall performance of the fertilizer. To ensure product granules of certain specifications and an efficient overall production, process control and intensification approaches based on mathematical models can be applied. However, the latter require high-quality quantitative experimental data describing the effects of process operation parameters on the granule properties. Therefore, in this article, such data is presented for a lab-scale experimental setup. Investigations were carried out into how variations in binder spray rate, binder composition, feed powder flow rate, pan inclination angle, and angular velocity affect particle size distribution, mechanical stability, and humidity. Furthermore, in contrast to existing work samples from both, pan granules and product granules are analyzed. The influence of operation parameter variations on the differences between both, also known as trajectory separation, is described quantitatively. The results obtained indicate an increase in the average particle size with increasing binder flow rate to feed rate and increasing binder concentration and the inclination angle of the pan. Compressive strength varied significantly depending on the operating parameters. Significant differences in properties were observed for the product and the intermediate (pan) samples. In fact, for some operation parameters, e.g., binder feed rate, the magnitude of the separation effect strongly depends on the specific value of the operation parameter. The presented concise data will enable future mathematical modeling of the pan granulation process, e.g., using the framework of population balance equations.
Fluidized bed spray agglomeration is an important industrial particle formation process. In particular, the continuous operation mode is able to provide a constant stream of product particles with constant quality in terms of particle properties. Mathematical process modeling represents a valuable tool for a thorough analysis of the involved mechanistic processes and can further be used for process intensification and control. Sophisticated models describing the quantitative effect of process conditions on particle properties are particularly important. Therefore, in this contribution the influence of the seven most important operational parameters on the particle size distribution is modeled, including fluidization and binder properties. To this end, a population balance process model with the three-parametric Kapur kernel is fitted to experimental data. The first main result of this contribution is the quantitative description of the dependency between the agglomeration rate and the process conditions by multidimensional paraboloids. The second main result is the introduction of a general method by which this quantitative formulation is obtained.
Population balance modeling is an established framework to describe the dynamics of particle populations in disperse phase systems found in a broad field of industrial, civil and medical applications. The resulting population balance equations account for the dynamics of the number density distribution functions and represent (systems) of partial differential equations which require sophisticated numerical solution techniques due to the general lack of analytical solutions. A specific class of solution algorithms, so-called moment methods, is based on the reduction of complex models to a set of ordinary differential equations characterizing dynamics of integral quantities of the number density distribution function. However, in general a closed set of moment equations is not found and one has to rely on approximate closure methods. In this contribution a concise overview of the most prominent approximate moment methods is given.
This paper is concerned with an experimental and theoretical study of dynamics and control of fluidized bed layering granulation with external screen mill cycle. To achieve quantitative agreement between model calculations and experiments an extended dynamic process model is proposed. In contrast to previous work by Dreyschultze etal. [1] specific plant characteristics are taken explicitly into account including a more detailed model of the milling process and a classifying particle withdrawal from the granulation chamber. The model is then used to develop new control strategies. First, a novel bed mass controller is designed and validated. Afterwards, a second control loop is introduced to dampen the oscillatory behavior of the of the particle size distribution. It is shown that the new control concepts achieve stable steady-state operation within short time and thereby improve the process dynamics significantly. Theoretical predictions and experimental results are shown to be in good agreement.
Population balance modeling is undergoing phenomenal growth in its applications, and this growth is accompanied by multifarious reviews. This review aims to fortify the model's fundamental base, as well as point to a variety of new applications, including modeling of crystal morphology, cell growth and differentiation, gene regulatory processes, and transfer of drug resistance. This is accomplished by presenting the many faces of population balance equations that arise in the foregoing applications. Expected final online publication date for the Annual Review of Chemical and Biomolecular Engineering Volume 5 is June 07, 2014. Please see http://www.annualreviews.org/catalog/pubdates.aspx for revised estimates.
Granulation in fluidized beds is an important unit operation in chemical engineering, finding widespread use in the production of food, fertilizer and pharmaceuticals in particulate form. The main particle size-enlargement mechanisms during this process are layering growth and agglomeration. Regarding the former, the possible occurrence of self-sustained oscillations during continuous operation with sieve-mill-cycle is well known. For agglomeration such phenomena have not been observed yet. The goal of this contribution is to investigate process stability for simultaneous layering growth and agglomeration. Therefore in this contribution a population balance based bifurcation analysis is conducted. It can be shown that for a wide range of process conditions an increased partition of agglomeration has a stabilizing effect on the process dynamics.
Pan granulation is a particle formation process with widespread practical applications such as fertilizer and pharmaceutical manufacturing. The continuous operation mode is especially promising with respect to industrial demands. For process automation and intensification, a suitable dynamical process model is required. Therefore, the focus of this contribution is on identification of agglomeration kernel parameters in a population balance model based on empirical data. To this end, an objective functional, representing the error between model and measurement data, is minimized. It is shown that the steady state particle size distribution of a lab-scale process can be reproduced accurately using the population balance with the identified parameters.
Agglomeration is a particle formation process taking place in many health- and food-related processes. It describes the formation of larger assemblies out of smaller entities, for instance, from dust to grain. Due to this formation, many properties of the agglomerate will differ from the properties of the individual entities, for example, the instant behavior of food powders or the risk of inhaling small airborne particles. The main physical effects leading to the formation of agglomerates are discussed, and the influences of formation on product quality are identified. Various measurement techniques to characterize the agglomerate properties are presented, as well as the main industrial-size equipment where particle formation by agglomeration takes place.
A new discretization for simultaneous aggregation, breakage, growth and nucleation is presented. The new discretization is an extension of the cell average technique developed by the authors [J. Kumar, M. Peglow, G. Warnecke, S. Heinrich, and L. Mörl. Improved accuracy and convergence of discretized population balance for aggregation: The cell average technique. Chemical Engineering Science 61 (2006) 3327–3342.]. It is shown that the cell average scheme enjoys the major advantage of simplicity for solving combined problems over other existing schemes. This is done by a special coupling of the different processes that treats all processes in a similar fashion as it handles the individual process. It is demonstrated that the new coupling makes the technique more useful by being not only more accurate but also computationally less expensive. At first, the coupling is performed for combined aggregation and breakage problems. Furthermore, a new idea that considers the growth process as aggregation of existing particle with new small nuclei is presented. In that way the resulting discretization of the growth process becomes very simple and consistent with first two moments. Additionally, it becomes easy to combine the growth discretization with other processes. The new discretization of pure growth is a little diffusive but it predicts the first two moments exactly without any computational difficulties like appearance of negative values or instability etc. The numerical scheme proposed in this work is consistent only with the first two moments but it can easily be extended to the consistency with any two or more than two moments. Finally, the discretization of pure and coupled problems is tasted on several analytically solvable problems.