Tropfenpopulationsbilanzen: Modellierung und Validierung
Final Report Abstract
The research project focused on the solution of Population Balance Model (PBM) based on the concept of primary and secondary particles. In the finite difference methods the particle size is discretized into a finite number of sections (Npp), where the population in each section is considered to behave like a single particle. In the Primary Secondary Particle Method (PSPM) framework of discretization, this single particle will be called the primary particle and it will be responsible for the reconstmction of the distribution. The interaction between the primary particles in different sections, due to breakage and coalescence events, results in a new primary particle with no representative size due to the discrete approximation of the distribution. The key idea in this work is to represent the distribution by a secondary particle capable of conserving two low-order moments of the distribution. The mean position of the particle is related algebraically to the total volume and number concentrations. In the framework of the SQMOM the secondary particle coincides exactly with the primary particle. A mathematical model based on the population balance equation and the primary-secondary particle concept is developed for any type of liquid extraction columns. A discrete framework is introduced for simulating the particulate physical systems governed by population balance equations (PBE) with particle splitting (breakage) and aggregation based on accurately conserving (from theoretical point of view) an unlimited number of moments associated with the particle size distribution. The basic idea is based on the concept of primary and secondary particles, where the former is responsible for distribution reconstruction while the latter is responsible for different particle interactions such as splitting and aggregation. The method is found to track accurately any set of low-order moments with the ability to reconstruct the shape of the distribution. The method is given the name: the sectional quadrature method of moments (SQMOM) and has the advantage of being not tied to the inversion of large sized moment problems as required by the classical quadrature method of moments (QMOM). A finite difference scheme (FDS) has been developed, that retains the advantages of the QMOM without destroying the shape of the distribution. In the following the fundamental framework to combine the FDS and the QMOM is introduced. The numerical implementation and thoroughly testing using available analytical solutions when available is the working program of the final project extension. In future, models for breakage and coalescence can be easily integrated and will allow for a prediction of the drop size distribution. Main drawback of the currently available commercial codes is the two-fluid model where the influence of the different drop sizes is blurred, since all droplets in the secondary phase move at the same velocity based on a idem Sauter mean diameter. This drawback could be eliminated when more primary particles (classes) are used in SQMOM and the dispersed phase is divided into a number of different velocity groups or classes, where each of the classes is characterized by its own velocity field. For every primary particle 3 to 4 moments have to be solved within each class. Other authors tried a similar approach with the drawback that their approach is based on the CPU time consuming (classes method, CM), which normally needs more than 20 classes even for a narrow distribution. The Sectional Quadrature Method of Moments was implemented in the CFD code. As a start, only one primary particle was used in SQMOM resulting in the well known QMOM. First simulations of the coupled algorithms were conducted for the RDC extractor in which droplet coalescence and breakage (with constant kernels) are used. The constant kernels were compared to experimental data and predict suitable results. CFD-PBM simulations were also carried out in the framework of Fluent in a new DFG-project. The CM and QMOM are already implemented in FLUENT® version 6.3. Different models for coalescence and breakage were implemented as user defined functions and tested using the two solution methods. The same two-way coupling was applied using also a two-fluid model as in FPM. Good agreement was obtained compared to the experimental drop holdup, path of the droplets and velocity fields, showing that the coupled model can predict the hydrodynamics in a stirred extraction column. The current results already show that the coupled PSPM (SQMOM) algorithm is a suitable design and scale-up tool. Besides, this software could be also applied to other industrial liquid-liquid systems; also it is valid for online control purposes.
Publications
- (2008). CFD-PBM coupled model using the finite point set method and the SQMOM. In: SOLVENT EXTRACTION - Fundamentals to Industrial Applications, Bruce A. Moyer (Ed.), 1177-1182, Can. Inst. Min. Met., Montreal, 2008
Drumm, C., Tiwari, S., Attarakih, M. M., Kuhnert, J., Bart, H.-J.
- (2008). Dynamic Modeling of a Rotating Disk Contactor Using the Primary and Secondary Particle Method (PSPM). ESCAPE 18. Lyon-France
Menwer M. Attarakih, Moutasem Jaradat, Hussein Allaboun, Hans-Jörg Bart, & Naim M. Faqir
- (2008). LLECMOD A Bivariate Population Balance Simulation Tool for Liquid-Liquid Extraction Columns. The Open Chemical Engineering J., 2, 10-34
Menwer M. Attarakih, Hans-Jörg Bart, Tilmann Steinmetz, Markus Dietzen, & Naim M. Faqir
- (2008). Process Intensification with reactive extraction columns. Chem. Eng. Process., 47, 745-754
Bart, H.-J. , Drumm, C. , Attarakih, M.M.
- (2008). Solution of the population balance equation using the sectional quadrature method of moments (SQMOM). Chemical Engineering Science, 64, 742-752
Menwer M. Attarakih, Christian Drumm, & Hans-Jörg Bart
- (2009). A Multivariate Population Balance Model for Liquid Extraction Columns. 19th European Symposium on Computer Aided Process Engineering-ESCAPE19. Poland
Menwer Attarakih, Moutasem Jaradat, Christian Drumm, Hans-Jörg Bart, Sudarshan Tiwari, Vikash K. Sharma, et al.
- (2009). Solution of the Population Balance Equation using the One Primary and One Secondary Particle Method (OPOSPM). 19th European Symposium on Computer Aided Process Engineering - ESCAPE 19. Poland
Menwer Attarakih, Moutasem Jaradat, Christian Drumm, Hans-Jörg Bart, Sudarshan Tiwari, Vikash K. Sharma, et al.
