## A Coupled SQMOM-CFD Population Balance Framework for Modelling and Simulation of Liquid-liquid Extraction Equipment

- The growing computational power enables the establishment of the Population Balance Equation (PBE) to model the steady state and dynamic behavior of multiphase flow unit operations. Accordingly, the twophase flow behavior inside liquid-liquid extraction equipment is characterized by different factors. These factors include: interactions among droplets (breakage and coalescence), different time scales due to the size distribution of the dispersed phase, and micro time scales of the interphase diffusional mass transfer process. As a result of this, the general PBE has no well known analytical solution and therefore robust numerical solution methods with low computational cost are highly admired. In this work, the Sectional Quadrature Method of Moments (SQMOM) (Attarakih, M. M., Drumm, C., Bart, H.-J. (2009). Solution of the population balance equation using the Sectional Quadrature Method of Moments (SQMOM). Chem. Eng. Sci. 64, 742-752) is extended to take into account the continuous flow systems in spatial domain. In this regard, the SQMOM is extended to solve the spatially distributed nonhomogeneous bivariate PBE to model the hydrodynamics and physical/reactive mass transfer behavior of liquid-liquid extraction equipment. Based on the extended SQMOM, two different steady state and dynamic simulation algorithms for hydrodynamics and mass transfer behavior of liquid-liquid extraction equipment are developed and efficiently implemented. At the steady state modeling level, a Spatially-Mixed SQMOM (SM-SQMOM) algorithm is developed and successfully implemented in a onedimensional physical spatial domain. The integral spatial numerical flux is closed using the mean mass droplet diameter based on the One Primary and One Secondary Particle Method (OPOSPM which is the simplest case of the SQMOM). On the other hand the hydrodynamics integral source terms are closed using the analytical Two-Equal Weight Quadrature (TEqWQ). To avoid the numerical solution of the droplet rise velocity, an analytical solution based on the algebraic velocity model is derived for the particular case of unit velocity exponent appearing in the droplet swarm model. In addition to this, the source term due to mass transport is closed using OPOSPM. The resulting system of ordinary differential equations with respect to space is solved using the MATLAB adaptive Runge–Kutta method (ODE45). At the dynamic modeling level, the SQMOM is extended to a one-dimensional physical spatial domain and resolved using the finite volume method. To close the mathematical model, the required quadrature nodes and weights are calculated using the analytical solution based on the Two Unequal Weights Quadrature (TUEWQ) formula. By applying the finite volume method to the spatial domain, a semi-discreet ordinary differential equation system is obtained and solved. Both steady state and dynamic algorithms are extensively validated at analytical, numerical, and experimental levels. At the numerical level, the predictions of both algorithms are validated using the extended fixed pivot technique as implemented in PPBLab software (Attarakih, M., Alzyod, S., Abu-Khader, M., Bart, H.-J. (2012). PPBLAB: A new multivariate population balance environment for particulate system modeling and simulation. Procedia Eng. 42, pp. 144-562). At the experimental validation level, the extended SQMOM is successfully used to model the steady state hydrodynamics and physical and reactive mass transfer behavior of agitated liquid-liquid extraction columns under different operating conditions. In this regard, both models are found efficient and able to follow liquid extraction column behavior during column scale-up, where three column diameters were investigated (DN32, DN80, and DN150). To shed more light on the local interactions among the contacted phases, a reduced coupled PBE and CFD framework is used to model the hydrodynamic behavior of pulsed sieve plate columns. In this regard, OPOSPM is utilized and implemented in FLUENT 18.2 commercial software as a special case of the SQMOM. The dropletdroplet interactions (breakage and coalescence) are taken into account using OPOSPM, while the required information about the velocity field and energy dissipation is calculated by the CFD model. In addition to this, the proposed coupled OPOSPM-CFD framework is extended to include the mass transfer. The proposed framework is numerically tested and the results are compared with the published experimental data. The required breakage and coalescence parameters to perform the 2D-CFD simulation are estimated using PPBLab software, where a 1D-CFD simulation using a multi-sectional gird is performed. A very good agreement is obtained at the experimental and the numerical validation levels.

Verfasserangaben: | Samer Alzyod |
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URN (Permalink): | urn:nbn:de:hbz:386-kluedo-54452 |

Betreuer: | Hans-Jörg Bart, Menwer Attarakih |

Dokumentart: | Dissertation |

Sprache der Veröffentlichung: | Englisch |

Veröffentlichungsdatum (online): | 18.12.2018 |

Jahr der Veröffentlichung: | 2018 |

Veröffentlichende Institution: | Technische Universität Kaiserslautern |

Titel verleihende Institution: | Technische Universität Kaiserslautern |

Datum der Annahme der Abschlussarbeit: | 14.12.2018 |

Datum der Publikation (Server): | 20.12.2018 |

Freies Schlagwort / Tag: | Flüssig-Flüssig-Extraktion; Hydrodynamik; Populationsbilanzen; Reaktivextraktion; Stoffaustausch; pulsierte und gerührte Kolonen; stationär; transient1D-CFD; 2D-CFD; Hydrodynamics; Liquid-liquid extraction; Mass transfer; Population balances; Reactive extraction; SM-SQMOM; SQMOM; Steady state; Transient state; pulsed and stirred columns |

GND-Schlagwort: | Liquid-Liquid Extraction |

Seitenzahl: | VI, 85 |

Fachbereiche / Organisatorische Einheiten: | Fachbereich Maschinenbau und Verfahrenstechnik |

DDC-Sachgruppen: | 6 Technik, Medizin, angewandte Wissenschaften / 620 Ingenieurwissenschaften und Maschinenbau |

Lizenz (Deutsch): | Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0) |