Solution of Inverse Problem using Droplet Population Balance Models for Liquid Extraction Columns

Summary

 Liquid extraction column simulation has difficulties due to continuous change in the droplet properties such as Sauter mean droplet diameter, hold-up and concentration profiles for organic and aqueous phases. Therefore, the droplet population balance model (DPBM) takes into account droplet transport and droplet interactions from droplet breakage, coalescence and interphase mass transfer. These droplet interactions are responsible for the evolution of the droplet size in multiphase flow. Different models in literature are studied and developed in the past decade to express these interactions but they are mostly dependent on column type, size and internal geometry besides the chemical test system. For these models most of them contain parameters that require fitting. So what is necessary is to have models and parameters that are independent on the column geometry which is essential for design of extraction column especially during scale up and scale down.

The parameter estimation problem is necessary to provide the droplet-droplet breakage and coalescence kernels or any other relevant parameters that could not be measured directly. Depending on experimental data availability, such as in industrial cases usually the only available data are the inlet and outlet conditions and few intermediate data along the equipment height. In such cases, the DPBM for both hydrodynamics and mass transfer has to be solved. Therefore, not only the size of the system is considerably increasing, but also the computational time due to the slow mass transfer process. For estimating the required parameters a solution of inverse DPBM problem is used, which is a well-known ill-conditioned problem and a careful algorithm design is required. Therefore, the parameter estimation is done by using the classes method (CM), and for an online process prediction and control the recent developed numerical model by Attarakih et al. (2009) so called One Primary One Secondary Particle Method (OPOSPM) is used and compared to the CM-PBM. The simulation results show that the OPOSPM can easily simulate the liquid extraction column with less than 3% of the total simulation time required by CM-PBM. Different breakage and coalescence correlations will be studied to estimate the necessary parameters for extraction column simulations, for validation EFCE reactive and nonreactive test system are used. Then these estimated parameters are used for simulation and scale up of industrial scale liquid extraction columns.

 Literature

• Attarakih, M. M., Jaradat, M., Drumm, C., Bart, H.-J., Tiwari, S., Sharma, V. K., Kuhnert, J. & Klar, A. (2009), Solution of the population balance equation using the One Primary and One Secondary particle Method (OPOSPM), Proceedings of  ESCAPE 19, Jezowski J., Thullie, J. (eds), Cracow, Poland. 
• Garthe, D., (2006), Fluid dynamics and Mass Transfer of Single Particles and Swarms of Particles in Extraction Columns, Lehrstuhl für Fluidverfahrenstechnik, TU München, München.
• Jildeh, H. B., Attarakih, M., Mickler, M. and Bart, H.-J. (2012a), An Online Inverse Problem for the Simulation of Extraction Columns using Population Balances. In: Ian David Lockhart Bogle and Michael Fairweather (Hg.): Computer Aided Chemical Engineering: 22nd European Symposium on Computer Aided Process Engineering, Bd. 30: Elsevier, 1043–1047, (DOI: 10.1016/B978-0-444-59520-1.50067-1).
• Jildeh, H. B., Hlawitschka, M. W., Attarakih, M. and Bart, H.-J. (2012b), Solution of inverse problem with the one primary and one secondary particle model (OPOSPM) coupled with computational fluid dynamics (CFD), CHISA 2012, Procedia Engineering, 42, 1692–1710 (DOI: 10.1016/j.proeng.2012.07.562).

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