Identifying coherent flow structures in chemical reactors is crucial for understanding the mixing dynamics and therefore for optimising reactor performance. In this study, a transfer operator method is applied to Lagrangian trajectory data from a lab-scaled stirred tank reactor in order to find coherent flow structures such as almost-invariant sets and coherent sets, which are characterised by minimal mixing with the surrounding fluid.
Both simulated and experimental trajectories were evaluated. The experimental tracks were recorded by four-dimensional particle tracking velocimetry of around 38,000 fluorescent tracer particles in a vessel agitated by two Rushton turbines, while the simulated tracks were obtained from a lattice Boltzmann large eddy simulation of the same geometry. Five prominent almost-invariant sets appeared in both data sets, three of them close to the top of the reactor, one in the centre and one at the bottom, with little transport between them.
The proposed method further enables a detailed analysis of the mixing behaviour by computing expected residence times and mixing times. Material stayed longest in the bottom compartment, with a mean residence time of about 9.6 stirrer rotations, and a scalar released there required roughly 208 rotations to mix, compared with 82 rotations for a scalar released between the middle and the bottom compartment.
Additionally, a Markov state model describes the macroscopic transport dynamics between the compartments in the reactor. Such data-driven compartment models open a route towards digital twins of stirred reactors, in which reaction pathways can be assessed without further costly experiments or time-consuming flow simulations.
The study is a collaboration between the Institute of Mathematics and its Didactics at Leuphana University Lüneburg, the Heinrich Blasius Institute at Hamburg University of Applied Sciences and the Institute of Multiphase Flows at Hamburg University of Technology, carried out within the Collaborative Research Centre CRC 1615 (SMART Reactors), with the experimental data recorded using the major instrumentation MUST at HAW Hamburg.
Anna Klünker, Thanh Tung Thai, Eike Steuwe, Christian Weiland, Yvonne Schade, Alexandra von Kameke, Kathrin Padberg-Gehle (2026). Dynamical Compartments in Stirred Tank Reactors and Markov State Modeling for Mixing Quantification: A Transfer Operator Approach. Ind. Eng. Chem. Res., Articles ASAP.
