Jahrestreffen der Fachgruppen Extraktion und Mehrphasenströmungen, 19-20 March 2013, Kongresshaus Baden Baden
Hanin Jildeh1, Menwer Attarakih2, Matthias Mickler1, Hans-Jörg Bart1 1
TU Kaiserslautern, Lehrstuhl für Thermische Verfahrenstechnik, Centre of Mathematical and Computational Modelling 2 University of Jordan, Department of Chemical Engineering
Parameter Estimation for Breakage and Coalescence Models in Liquid Extraction Columns Motivation
Mathematical model
Column performance prediction
Population Balance Equation (PBE)
• Steady state and dynamic response
• Classes Method (CM) [1] or Method of Moment (MOM) [2]
• Scale down or scale up
• Combination [3]: “One Primary and One Secondary Particle Method” (OPOSPM)
• Process synthesis, design and control
CM:
Problem • Model parameters (breakage & coalescence) • Column geometry • Chemical test system Aim
Inverse problem
• Interaction parameters estimation & validation independent on geometry
Parameter Estimation
Breakage model Schmidt [4], Garthe [5] • Γ = f(B1-B5, d, N), physical properties & geometry Coalescence model Coulaloglou and Tavlarides [6] • ω = f(C1-C2, ε, N), physical properties & hydrodynamics
1 2 OPOSPM [7,8]: Given Bi, Ci: S = K b [ (ϑ − 1)ΓN ] − K c ω N 2 2 learning parameters Ki
various chemical test systems & different Kühni column size
Breakage model DN 80 DN 150
DN 80 DN 150
(a) Exp. data [4,5]
(b) Exp. data [4,5]
DN 80
DN 32
(c) Exp. data [5]
(d) Exp. data [9]
Fig. 1: Breakage probability a) Schmidt and Garthe model b) re-optimized Schmidt parameters c) validation at different mother droplet size d) scale down
Coalescence model • Solving inverse population balance problem DN 150
Fig. 2: Optimization of coalescence parameters
DN 150
a) steady state
b) transient
Fig. 3: Simulated mean holdup using the CM-PBM and OPOSPM
Conclusions Droplet interaction parameters (breakage & coalescence) successful estimated (inverse PBE ) Good accord with experimental data - for different EFCE chemical test systems - for different Kühni column geometry CPU time OPOSPM ≤ 3 % CM Online Performance Prediction OUTLOOK: Validation using CFD [10] and online prediction (OMST [11]) Transfer to reactive and gas-liquid systems
Email:
[email protected]
Fig. 4: Breakage probability for EFCE reactive system ZnSO4 with 1% D2EHPA
References: [1] M. Attarakih et al. (2006), Chem. Eng. Sci. 61 (1): 113-123. [2] M. Attarakih et al. (2009), Chem. Eng. Sci. 64: 742-752. [3] M. Attarakih et al. (2009), Comp. Aided Chem. Engng 26: 1333-1338. [4] S. A. Schmidt (2006), PhD thesis, Shaker Verlag, TU Kaiserslautern. [5] D. Garthe (2006), PHD thesis, Verlag Dr Hut, TU München. [6] C. A. Coulaloglou and L. L. Tavlarides (1977), Chem. Eng. Sci. 32 (11): 1289–1297. [7] H. Jildeh et al. (2012), Comp. Aided Chem. Engng 30: 1043–1047. [8] H. Jildeh et al. (2012), Comp. Aided Chem. Engng 31: 960-964. [9] T. Steinmetz (2007), PhD thesis, TU Kaiserslautern, VDI Verlag, Düsseldorf. [10] H. Jildeh et al. (2012), Procedia Engineering 42: 1692–1710. [11] M. Mickler et al. (2013), accepted Can. J. Chem. Eng..
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