Estimation of aggregation kernels based on Laurent polynomial approximation

Eisenschmidt, Holger; Soumaya, Moudar; Bajçinca, Naim; Borne, Sabine Le; Sundmacher, Kai

doi:10.1016/j.compchemeng.2017.03.018

Cited by 11 publications

(14 citation statements)

References 20 publications

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“…In order to get more precise process approximation another kernel functions of more degrees of freedom, e.g. Laurent polynomials of two variables [6] , bilinear basis functions [5] , or time dependency of the agglomeration efficiency 0 ( ) can be taken into account.…”

Section: Discussionmentioning

confidence: 99%

Influence of drying conditions on process properties and parameter identification for continuous fluidized bed spray agglomeration

Strenzke

Golovin

Wegner

et al. 2018

Proceedings of 21th International Drying Symposium

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Agglomeration is a particle formulation process in which at least two primary particles are combined to form a new one. The growth of agglomerates depends on interactions of particles covered with wet spots that generated by depositions of binder droplets. This work experimentally compares the influence of external feed rate and sprayed binder content on product properties and process stability with internal separation at different drying conditions. Due to the identification of parameters a populations balance model (PBM) is developed. The PBM includes the agglomeration kernel function, which characterizes the kinetics, i.e. the rate at which primary particles build agglomerates. Keywords: spray fluidized bed agglomeration; drying; continuous process; internal separation; population balances

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Section: Discussionmentioning

confidence: 99%

Influence of drying conditions on process properties and parameter identification for continuous fluidized bed spray agglomeration

Strenzke

Golovin

Wegner

et al. 2018

Proceedings of 21th International Drying Symposium

View full text Add to dashboard Cite

show abstract

“…These are either physically motivated, e.g., the Brownian motion coalescence kernel and kernel based on equipartition of kinetic energy (EKE kernel), or rather empirical, e.g., Kapur kernel and volume-independent (constant) kernel. Additionally, abstract parametric approaches, e.g., Laurent-polynomials [23], can be used. The kernel candidates studied in this contribution are summarized in Table 2.…”

Section: Mathematical Modelingmentioning

confidence: 99%

“…Thus, only the agglomeration efficiency p est = β 0 has to be estimated from experimental data. Besides these simple kernel candidates, the fifth formulation in the table represents a more complex parametric model candidate based on Laurent polynomials of rank K = 2 [23]:…”

Section: Parameter Identificationmentioning

confidence: 99%

“…In this contribution, a number of physically motivated or heuristically derived kernel candidates ( [19] and references therein) will be used. This results in a set of model candidates, which can be fitted individually to experimental data [20][21][22][23] by minimization of an objective function. To ensure that the obtained estimates are unique, i.e., there is a unique set of parameters achieving a minimum value of the objective function for the given measurements, identifiability of the parameters for the different models has to be checked [24,25].…”

Section: Introductionmentioning

confidence: 99%

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Parameter Identification For Continuous Fluidized Bed Spray Agglomeration

et al. 2018

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Agglomeration represents an important particle formation process used in many industries. One particularly attractive process setup is continuous fluidized bed spray agglomeration, which features good mixing as well as high heat and mass transfer on the one hand and constant product throughput with constant quality as well as high flow rates compared to batch mode on the other hand. Particle properties such as agglomerate size or porosity significantly affect overall product properties such as re-hydration behavior and dissolubility. These can be influenced by different operating parameters. In this manuscript, a population balance model for a continuous fluidized bed spray agglomeration is presented and adapted to experimental data. Focus is on the description of the dynamic behavior in continuous operation mode in a certain neighborhood around steady-state. Different kernel candidates are evaluated and it is shown that none of the kernels are able to match the first six minutes with time independent parameters. Afterwards, a good fit can be obtained, where the Brownian and the volume independent kernel models match best with the experimental data. Model fit is improved for identification on a shifted time domain neglecting the initial start-up phase. Here, model identifiability is shown and parameter confidence intervals are computed via parametric bootstrap.

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“…fitting exponents in rational functions [12]. Laurent polynomials were used in [7] to approximate the aggregation kernel. All these works determine coefficients for an approximation of a kernel on (0, ∞) × (0, ∞).…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of low-rank aggregation kernels in univariate population balance equations

Ahrens

Borne

2021

Adv Comput Math

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The dynamics of particle processes can be described by population balance equations which are governed by phenomena including growth, nucleation, breakage and aggregation. Estimating the kinetics of the aggregation phenomena from measured density data constitutes an ill-conditioned inverse problem. In this work, we focus on the aggregation problem and present an approach to estimate the aggregation kernel in discrete, low rank form from given (measured or simulated) data. The low-rank assumption for the kernel allows the application of fast techniques for the evaluation of the aggregation integral ($\mathcal {O}(n\log n)$ O ( n log n ) instead of $\mathcal {O}(n^{2})$ O ( n 2 ) where n denotes the number of unknowns in the discretization) and reduces the dimension of the optimization problem, allowing for efficient and accurate kernel reconstructions. We provide and compare two approaches which we will illustrate in numerical tests.

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Estimation of aggregation kernels based on Laurent polynomial approximation

Cited by 11 publications

References 20 publications

Influence of drying conditions on process properties and parameter identification for continuous fluidized bed spray agglomeration

Influence of drying conditions on process properties and parameter identification for continuous fluidized bed spray agglomeration

Parameter Identification For Continuous Fluidized Bed Spray Agglomeration

Reconstruction of low-rank aggregation kernels in univariate population balance equations

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