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Because there is no general design method for depth filters, especially for layered configurations, this methodological gap is addressed here. Using optimal control theory, paths of the filter coefficient, a measure for local filtration performance, are determined along the filter depth. An analytical optimal control solution is derived and used to validate the numerical algorithm. Two optimal control scenarios are solved numerically: In the first scenario, the goal of constant deposition along the filter depth is addressed. The second scenario aims at maximizing the time until some maximal pressure drop is reached. Furthermore, a computational strategy is presented to derive discrete layers suitable for practical design from the continuous optimal control solutions. All optimized scenarios are compared to one‐layered filter designs and significant improvements are found. As this work is based on strongly validated and widely used filtration models, the presented methods are expected to have broad applicability. © 2017 American Institute of Chemical Engineers AIChE J, 63: 68–76, 2018

Bioprocesses for the production of renewable energies and materials lack efficient separation processes for the utilized microorganisms such as algae and yeasts. Dissolved air flotation (DAF) and microflotation are promising approaches to overcome this problem. The efficiency of these processes depends on the ability of microorganisms to aggregate with microbubbles in the flotation tank. In this study, different new or adapted aggregation models for microbubbles and microorganisms are compared and investigated for their range of suitability to predict the separation efficiency of microorganisms from fermentation broths. The complexity of the heteroaggregation models range from an algebraic model to a 2D population balance model (PBM) including the formation of clusters containing several bubbles and microorganisms. The effect of bubble and cell size distributions on the flotation efficiency is considered by applying PBMs, as well. To determine the sensitivity of the results on the model assumptions, the modeling approaches are compared, and suggestions for their range of applicability are given. Evaluating the computational fluid dynamics (CFD) of a dissolved air flotation (DAF) system shows the heterogeneity of the fluid dynamics in the flotation tank. Since analysis of the streamlines of the tank show negligible back mixing, the proposed aggregation models are coupled to the CFD data by applying a Lagrangian approach.

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