Matthias Mickler

The OPOSPM as a Nonlinear Autocorrelation Population Balance Model for Dynamic Simulation of Liquid Extraction Columns

Abstract Dynamic simulation and online control problems in liquid extraction columns are still unresolved issues due to the two-phase flow and the particulate character of the dispersed phase. In this work, the One Primary and One Secondary Particle Model (OPOSPM) with two autocorrelation parameters is used as an alternative to the full population balance model. The model presents the base hierarchy of the SQMOM and consists only of two transport equations for droplet number and volume concentrations. Using the full population balance model or online experimental data, the autocorrelation parameters are identified using a constrained weighted nonlinear least square method. Compared to the experimental data in RDC and Kuhni columns, the autocorrelated OPOSPM predicts accurately the dynamic and steady state mean population properties with a simulation time amounts to only 3% of that required by the detailed model.

An Online Inverse Problem for the Simulation of Extraction Columns using Population Balances

Abstract Parameter estimation and online control problems in liquid extraction columns are still unresolved issues due to the two-phase flow in such equipment. In this work, the One Primary and One Secondary Particle Model (OPOSPM) is used as an alternative to the computationally expensive full population balance model, which describes in details the two-phase flow. The model is derived from the SQMOM and consists simply of two transport equations for total number and volume concentrations. For reduction purposes, the model has two learning parameters that can be easily determined using the detailed model or on-line measured data as a reference solution. Once the model is learnt, it is used to identify the droplet coalescence parameters and hence can be viewed as the solution of an online inverse problem. Despite its simplicity, the OPOSPM predicts accurately the mean population properties along a Kuhni extraction column height with a simulation time amounts to only 3% of that required by the detailed model.