Numerical solution methods for coupled population balance systems for the dynamic simulation of multivariate particle processes at the example of shape-selective crystallization

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The goal of this project (six-year period) is the development of accurate and efficient methods for the numerical solution of multivariate population balance systems. As application problem, we consider an innovative shape-selective crystallization process. The final aim is the optimal process design and operation through the use of the developed numerical methods. In order to reach this goal, it is planned to develop and systematically compare techniques for the numerical treatment of the differential and integral operators appearing in population balance equations. These two types of operators are entirely different in their mathematical properties as well as in the appropriate numerical techniques for their solution. We establish benchmark problems which exhibit the desired behaviour of particle populations. These benchmarks are also realized experimentally. Through the experiments, reliable measured data become available which serve as reference values and support the evaluation of the numerical techniques. In the first project period, we closed gaps which existed concerning the evaluation of numerical techniques for the univariate case. In the second project period, we focus on the bivariate case (crystals with two internal properties), both in its experimental realization as well as in the development of suitable numerical methods and a subsequent systematic comparison of experimental and simulation results. In the third project period we plan to realize experimentally an integrated shape-selective crystallization process with several coupled process units and to simulate this process by using the developed numerical techniques. With this process we want to control the size and shape distribution of the crystal product. With respect to growth-dominated multivariate processes, improved algebraic stabilization schemes will be developed and used for the simulation of population balance systems in chemical engineering problems.Another aim of the third period is the numerical treatment of multivariate aggregation processes. It will be shown for uniform grids that aggregation integrals can be evaluated with linear costs by use of the Fast Fourier Transformation (FFT). This allows simulations on much finer grids than with conventional methods. The prerequisite for this approach is a separable approximation of the aggregation kernel - a property featured by many kernel functions of practical relevance.