References
- Goedecke, R. Fluidverfahrenstechnik; Wiley-VCH Verlag GmbH & Co. KGaA: Weinheim, Germany, 2006.
- Mersmann, A.; Kind, M.; Stichlmair, J. Thermische Verfahrenstechnik: Grundlagen Und Methoden, 2nd ed.; Springer-Verlag Berlin Heidelberg: Berlin, Heidelberg, 2005.
- Bart, H.-J.; Garthe, D.; Grömping, T.; Pfennig, A.; Schmidt, S.; Stichlmair, J. Vom Einzeltropfen Zur Extraktionskolonne. Chem. Ing. Tech. 2006, 78(5), 543–547. DOI: 10.1002/cite.200500146.
- Henschke, M. Auslegung Pulsierter Siebboden-Extraktionskolonnen; Shaker: Aachen, 2004.
- Ayesterán, J.; Kopriwa, N.; Buchbender, F.; Kalem, M.; Pfennig, A. ReDrop - A Simulation Tool for the Design of Extraction Columns Based on Single-Drop Experiments. Chem. Eng. Technol. 2015, 38(10), 1894–1900. DOI: 10.1002/ceat.201500097.
- Attarakih, M.; Hlawitschka, M. W.; Abu-Khader, M.; Al-Zyod, S.; Bart, H.-J. CFD-population Balance Modeling and Simulation of Coupled Hydrodynamics and Mass Transfer in Liquid Extraction Columns. Appl. Math. Modell. 2015, 39(17), 5105–5120. DOI: 10.1016/j.apm.2015.04.006.
- Attarakih, M. Solution Methodologies for the Population Balance Equations Describing the hydrodynamics of Liquid-Liquid Extraction Contactors. Dissertation, Kaiserslautern, 2004.
- Kalem, M.; Buchbender, F.; Pfennig, A. Simulation of Hydrodynamics in RDC Extraction Columns Using the Simulation Tool “Redrop”. Chem. Eng. Res. Des. 2011, 89(1), 1–9. DOI: 10.1016/j.cherd.2010.05.001.
- Garthe, D. Fluiddynamics and Mass Transfer of Single Particles and Swarms of Particles in Extraction Columns. Dissertation, München, 2006.
- Buchbender, F. Single-drop-based modelling of drop residence times in Kühni columns. Dissertation, Aachen, 2013.
- Klinger, S. Messung Und Modellierung Des Spaltungs- Und Koaleszenzverhaltens Von Tropfen Bei Der Extraktion. Dissertation, Aachen, 2007.
- Amokrane, A.; Charton, S.; Sheibat-Othman, N.; Becker, J.; Klein, J. P.; Puel, F. Development of a CFD-PBE Coupled Model for the Simulation of the Drops Behaviour in a Pulsed Column. Can. J. Chem. Eng. 2014, 92(2), 220–233. DOI: 10.1002/cjce.21933.
- You, X.; Xiao, X. Simulation of the Three-Dimensional Two-Phase Flow in Stirred Extraction Columns by Lagrangian-Eulerian Method. Chem. Biochem. Eng. Quart. 2005, 19(1), 1–11.
- Drumm, C.; Attarakih, M. M.; Bart, H.-J. Coupling of CFD with DPBM for an RDC Extractor. Chem. Eng. Sci. 2009, 64(4), 721–732. DOI: 10.1016/j.ces.2008.05.041.
- Chen, H.; Sun, Z.; Song, X.; Yu, J. A pseudo-3D Model with 3D Accuracy and 2D Cost for the CFD–PBM Simulation of A Pilot-scale Rotating Disc Contactor. Chem. Eng. Sci. 2016, 139, 27–40. DOI: 10.1016/j.ces.2015.09.023.
- Drumm, C.; Hlawitschka, M. W.; Bart, H.-J. CFD Simulations and Particle Image Velocimetry Measurements in an Industrial Scale Rotating Disc Contactor. AIChE J. 2011, 57(1), 10–26. DOI: 10.1002/aic.12249.
- Vikhansky, A.; Kraft, M. Modelling of a RDC Using a Combined CFD-population Balance Approach. Chem. Eng. Sci. 2004, 59(13), 2597–2606. DOI: 10.1016/j.ces.2004.02.016.
- Bezzo, F.; Macchietto, S.; Pantelides, C. C. A General Methodology for Hybrid multizonal/CFD Models. Comput. Chem. Eng. 2004, 28(4), 501–511. DOI: 10.1016/j.compchemeng.2003.08.004.
- Le Moullec, Y.; Gentric, C.; Potier, O.; Leclerc, J. P. Comparison of Systemic, Compartmental and CFD Modelling Approaches: Application to the Simulation of a Biological Reactor of Wastewater Treatment. Chem. Eng. Sci. 2010, 65(1), 343–350. DOI: 10.1016/j.ces.2009.06.035.
- Irizarry, R.;. Fast Compartmental Monte Carlo Simulation of Population Balance Models: Application to Nanoparticle Formation in Nonhomogeneous Conditions. Ind. Eng. Chem. Res. 2012, 51(47), 15484–15496. DOI: 10.1021/ie3011116.
- Rigopoulos, S.; Jones, A. A Hybrid CFD—Reaction Engineering Framework for Multiphase Reactor Modelling: Basic Concept and Application to Bubble Column Reactors. Chem. Eng. Sci. 2003, 58(14), 3077–3089. DOI: 10.1016/S0009-2509(03)00179-9.
- Bezzo, F.; Macchietto, S. A General Methodology for Hybrid multizonal/CFD Models. Comput. Chem. Eng. 2004, 28(4), 513–525. DOI: 10.1016/j.compchemeng.2003.08.010.
- Bauer, M.; Eigenberger, G. A Concept for Multi-scale Modeling of Bubble Columns and Loop Reactors. Chem. Eng. Sci. 1999, 54(21), 5109–5117. DOI: 10.1016/S0009-2509(99)00264-X.
- Gimbun, J.; Liew, S. Y.; Nagy, Z. K.; Rielly, C. D. Three-Way Coupling Simulation of a Gas-Liquid Stirred Tank Using a Multi-Compartment Population Balance Model. Chemical Prod. Process Model. 2016, 11(3). DOI: 10.1515/cppm-2015-0076.
- Delafosse, A.; Collignon, M.-L.; Calvo, S.; Delvigne, F.; Crine, M.; Thonart, P.; Toye, D. CFD-based Compartment Model for Description of Mixing in Bioreactors. Chem. Eng. Sci. 2014, 106, 76–85. DOI: 10.1016/j.ces.2013.11.033.
- Laakkonen, M.; Alopaeus, V.; Aittamaa, J. Validation of Bubble Breakage, Coalescence and Mass Transfer Models for Gas–Liquid Dispersion in Agitated Vessel. Chem. Eng. Sci. 2006, 61(1), 218–228. DOI: 10.1016/j.ces.2004.11.066.
- Guha, D.; Dudukovic, M. P.; Ramachandran, P. A.; Mehta, S.; Alvare, J. CFD-based Compartmental Modeling of Single Phase Stirred-tank Reactors. AIChE J. 2006, 52(5), 1836–1846. DOI: 10.1002/aic.10772.
- Wells, G. J.; Ray, W. H. Methodology for Modeling Detailed Imperfect Mixing Effects in Complex Reactors. AIChE J. 2005, 51(5), 1508–1520. DOI: 10.1002/aic.10407.
- Alexopoulos, A. H.; Maggioris, D.; Kiparissides, C. CFD Analysis of Turbulence Non-homogeneity in Mixing Vessels A Two-compartment Model. Chem. Eng. Sci. 2002, 57(10), 1735–1752. DOI: 10.1016/S0009-2509(02)00053-2.
- Gresch, M.; Brügger, R.; Meyer, A.; Gujer, W. Compartmental Models for Continuous Flow Reactors Derived from CFD Simulations. Environ. Sci. Technol. 2009, 43(7), 2381–2387. DOI: 10.1021/es801651j.
- Vrábel, P.; van der Lans, R.; Cui, Y. Q.; Luyben, K. Compartment Model Approach. Chem. Res. Design. 1999, 77(4), 291–302. DOI: 10.1205/026387699526223.
- Yu, X.; Hounslow, M. J.; Reynolds, G. K.; Rasmuson, A.; Niklasson Björn, I.; Abrahamsson, P. J. A Compartmental CFD-PBM Model of High Shear Wet Granulation. AIChE J. 2017, 63(2), 438–458. DOI: 10.1002/aic.15401.
- Bouffard, J.; Bertrand, F.; Chaouki, J. A Multiscale Model for the Simulation of Granulation in Rotor-based Equipment. Chem. Eng. Sci. 2012, 81, 106–117. DOI: 10.1016/j.ces.2012.06.025.
- Metzger, L.; Kind, M. Compartment Method for Dynamic Multi-Scale Simulation of Precip. Reactors, 2014, DOI: 10.1115/FEDSM2014-21547.
- Irizarry, R.;. Fast Monte Carlo Methodology for Multivariate Particulate systems-II: τ-PEMC. Chem. Eng. Sci. 2008b, 63(1), 111–121. DOI: 10.1016/j.ces.2007.09.006.
- Kramer, H.; Dijkstra, J. W.; Neumann, A. M.; ÓMeadhra, R.; van Rosmalen, G. M. Modelling of Industrial Crystallizers, a Compartmental Approach Using a Dynamic Flow-sheeting Tool. J. Cryst. Growth. 1996, 166(1–4), 1084–1088. DOI: 10.1016/0022-0248(96)00096-6.
- Irizarry, R.;. Fast Monte Carlo Methodology for Multivariate Particulate systems—I: Point Ensemble Monte Carlo. Chem. Eng. Sci. 2008a, 63(1), 95–110. DOI: 10.1016/j.ces.2007.09.007.
- Kulikov, V.; Briesen, H.; Marquardt, W. Scale Integration for the Coupled Simulation of Crystallization and Fluid Dynamics. Chem. Eng. Res. Design. 2005, 83(6), 706–717. DOI: 10.1205/cherd.04363.
- Zhao, H.; Zheng, C.; Xu, M. Multi-Monte Carlo Method for Coagulation and condensation/evaporation in Dispersed Systems. J. Colloid Interface Sci. 2005, 286(1), 195–208. DOI: 10.1016/j.jcis.2004.12.037.
- Misek, T.; Berger, R.; Schröter, J. Microsoft Word - Buch.doc//Standard Test Systems for Liquid Extraction, 2nd ed.; Published on behalf of the European Federation of Chemical Engineering by Institution of Chemical Engineers: Rugby, 1985.
- Amidror, I.;. Scattered Data Interpolation Methods for Electronic Imaging Systems: A Survey. J. Electron. Imaging. 2002, 11(2), 157. DOI: 10.1117/1.1455013.
- Bärwolff, G.;. Höhere Mathematik Für Naturwissenschaftler Und Ingenieure; Springer Berlin Heidelberg: Berlin, Heidelberg, 2017.
- Dahmen, W.; Reusken, A. Numerik Für Ingenieure Und Naturwissenschaftler; Springer Berlin Heidelberg: Berlin, Heidelberg, 2008.
- Crowe, C. T.;. Multiphase Flow Handbook; CRC Press: Boca Raton, FL, 2006.
- Attarakih, M.; Al-Zyod, S.; Abu-Khader, M.; Bart, H. PPBLAB: A New Multivariate Population Balance Environment for Particulate System Modelling and Simulation. Proc. Eng. 2012, 42, 1445–1462. DOI: 10.1016/j.proeng.2012.07.538.
- Coulaloglou, C. A.; Tavlarides, L. L. Description of Interaction Processes in Agitated Liquid-liquid Dispersions. Chem. Eng. Sci. 1977, 32(11), 1289–1297. DOI: 10.1016/0009-2509(77)85023-9.
- Kamp, J.; Kraume, M. From Single Drop Coalescence to Droplet Swarms – Scale-up considering the Influence of Collision Velocity and Drop Size on Coalescence Probability. Chem. Eng. Sci. 2016, 156, 162–177. DOI: 10.1016/j.ces.2016.08.028.
- Han, L.; Gong, S.; Li, Y.; Ai, Q.; Luo, H.; Liu, Z.; Liu, Y. A Novel Theoretical Model of Breakage Rate and Daughter Size Distribution for Droplet in Turbulent Flows. Chem. Eng. Sci. 2013, 102, 186–199. DOI: 10.1016/j.ces.2013.06.046.
- Rathod, H. T.; Venkatesudu, B.; Nagaraja, K. V.; Islam, M. S. Gauss Legendre–Gauss Jacobi Quadrature Rules over a Tetrahedral Region. Appl. Math. Comput. 2007, 190(1), 186–194. DOI: 10.1016/j.amc.2007.01.014.