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Item type:Publication, Access status: without files , Numerical methods for coupled population balance systems applied to the dynamical simulation of crystallization processes(Springer, 2020-06-21); ; ; ; Uni- and bi-variate crystallization processes are considered that are modeled with population balance systems (PBSs). Experimental results for uni-variate processes in a helically coiled flowtube crystallizer are presented.Asurvey on numerical methods for the simulation of uni-variate PBSs is provided with the emphasis on a coupled stochastic-deterministic method. In this method, the equations of the PBS from computational fluid dynamics are solved deterministically and the population balance equation is solved with a stochastic algorithm. With this method, simulations of a crystallization process in a fluidized bed crystallizer are performed that identify appropriate values for two parameters of the model such that considerably improved results are obtained than reported so far in the literature. For bi-variate processes, the identification of agglomeration kernels from experimental data is briefly discussed. Even for multi-variate processes, an efficient algorithm for evaluating the agglomeration term is presented that is based on the fast Fourier transform (FFT). The complexity of this algorithm is discussed as well as the number of moments that can be conserved.Publicationtype: Book Part99 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Estimation of aggregation kernels based on Laurent polynomial approximationThe dynamics of particulate processes can be described by population balance equations which are governed by the phenomena of growth, nucleation, aggregation and breakage. Estimating the kinetics of the latter phenomena is a major challenge particularly for particle aggregation because first principle models are rarely available and the kernel estimation from measured population density data constitutes an ill-conditioned problem. In this work we demonstrate the estimation of aggregation kernels from experimental data using an inverse problem approach. This approach is based on the approximation of the aggregation kernel by use of Laurent polynomials. We show that the aggregation kernel can be well estimated from in silico data and that the estimation results are robust against substantial measurement noise. The method is demonstrated for three different aggregation kernels. Good agreement between true and estimated kernels was found in all investigated cases.Publicationtype: Journal Article143 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Image-based analytical crystal shape computation exemplified for potassium dihydrogen phosphate (KDP)(2016-01-12); ; The evolution of the shape of growing crystals is a process that depends on various factors including crystalline material and process conditions. Toward the objective to control not only the size of crystals but also their shape, it is necessary to observe its evolution process as a basis for understanding and modeling the underlying growth kinetics. Online microscopy provides 2D projections of 3D crystal shapes. In this paper, we present a technique to reconstruct the original 3D shapes from measured 2D projections of KDP crystals. The algorithm requires the projection to be bounded by a convex polygon with six or eight vertices. Numerical results are presented both for synthetic data as well as for experimental data. They show a good agreement between true and estimated values both for highly accurate as well as perturbed projections.Publicationtype: Journal Article93 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Fast evaluation of univariate aggregation integrals on equidistant grids(2015-03-04); ; A variety of production processes in chemistry and biotechnology are concerned with particles dispersed in an environmental phase. The particle distribution is mathematically described by the solution of population balance equations of integro-differential type. We are concerned with the aggregation process: it invokes an integral term that is usually numerically expensive to evaluate and often dominates the total simulation cost. We will expose the algorithmic details of an efficient approach based on a separable approximation of the aggregation kernel and a subsequent fast Fourier transformation. This approach reduces the originally quadratic complexity to an almost optimal complexity O(nlogn) in the dimension of the approximation space. We include numerical tests illustrating its application to representative aggregation kernels from the literature. While originally developed in the context of a discretization with piecewise constant functions, we illustrate how these ideas can be applied in the setting of the popular sectional methods.Publicationtype: Journal Article114