Direct Discretized Kernel Identification for Continuous Agglomeration Processes

Continuous particle agglomeration processes are important size-enlargement unit operations applied in the food, pharmaceutical and agricultural industry. For the improvement of these processes predictive mathematical models are of utmost importance. A widely applied modeling framework is the population balance equation, where the agglomeration kinetics are described by the so-called agglomeration kernel. The identification of functions describing these kinetics has turned out to be a challenging task. Therefore, this article deals with identifying such a kernel function by minimizing the L2-residual between experimentally obtained particle size distributions and simulations. The application of a stochastic gradient descent algorithm with automatic differentiation for minimization allows for the direct identification of the high-dimensional matrix representing the discretized kernel function. The comparison between the simulated and measured size distribution shows that the identified kernel is able to accurately describe the evolution of the particle size distribution. The algorithm presented in this contribution can be applied to a variety of similar processes and the identified kernels can be used in process optimization and automation applications.