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This work focuses on the modeling, simulation and control of particle size distribution (PSD) during nanoparticle growth with the simultaneous chemical reaction, nucleation, condensation, coagulation and convective transport in a high temperature reactor. Firstly, a model known as population balance model was derived. This model describes the formation of particles via nucleation and growth. Mass and energy balances in the reactor were presented in order to study the effect of particle size distribution for each reaction mechanisms on the reactor dynamics, as well as the evolution of the concentrations of species and temperature of the continuous phase. The models were simulated to see whether the reduced population balance can be used to control the particle size distribution in the high temperature reactor. The simulation results from the above model demonstrated that the reduced population balance can be effectively used to control the PSD. The proposed method "which is the application of reduced population balance model" shows that there is some dependence of the average particle diameter on the wall temperature and the model can thus be used as a basis to synthesize a feedback controller where the manipulated variable is the wall temperature of the reactor and the control variable is the average particle diameter at the outlet of the reactor. The influence of disturbances on the average particle diameter was investigated and controlled to its new desired set point which is 1400nm using the proportional-integral-derivative controllers (PID controllers). The proposed model was used to control nanoparticle size distribution at the outlet of the reactor.
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Tom
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5--13
Opis fizyczny
Bibliogr. 29 poz., rys., tab.
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autor
autor
autor
- Tshwane University of Technology, Department of Chemical Engineering, Faculty of Engineering and the Built Environment, SadikuO@tut.ac.za
Bibliografia
- 1. Friedlander, S.K. Smoke. (1977). Dust, and Haze: Fundamentals of Aerosol Behaviour, New York: Wiley.
- 2. Kalani, A. & Christofides, P.D. (2002). Estimation and Control of Size Distribution in Aerosol Processes with Simultaneous Reaction, Nucleation, Condensation and Coagulation. Computer and Chemical Engineering, 26(7–8), 1153–1169. DOI: 10.1016/S0098-1354(02)00032-7.
- 3. Goodson, M & Kraft, M. (2002). An Efficient Stochastic Algorithm for Simulating Nano-particle Dynamics. Journal of Computational Physics, 183(1), 210–232. DOI:10.1006/ jcph.2002.7192.
- 4. Banabalova, E. (2000). Mechanism of Nanoparticle Generation by high – Temperature Methods Vacuum. 58(2–3), 174–182(9). DOI: 10.1016/S0042-207X(00)00166-4.
- 5. Christofides, P.D., Li, M. & Madler, L. (2007). Control of Particulate Processes: Recent Results and Future Challenges. Powder
- 6. Mingheng, L. & Christofides, P.D. (2010). The Control Hand Book, Second edition, Control System Applications. U. S. A: Edited by William S. Levine, CRC.
- 7. Taluka, S.S. & Swihart, M.T. (2004). Aerosol Dynamics Modelling of Silicon Nanoparticle Formation during Silane Pyrolysis: A Comparison of three Solution Method. Journal of Aerosol Science, 35, 889–908. DOI:10.1016/j.jaerosci.2004.02.004.
- 8. Jeong, J.I. & Choi, M. (2001). A Sectional Method for Analysis of the Growth of Polydisperse non – spherical particles undergoing Coagulation and Coalescence. Journal of Aerosol Science, 5(5), 565–582. DOI:10.1016/S0021-8502(00)00103-8.
- 9. Tsantilis, S., Kammler, H.K. & Pratsinis, S.E. (2002). Population Balance Modeling of Flame Synthesis of Titania Nanoparticles. Chemical Engineering Science. 57(12), 2139–2156. DOI:10.1016/S0009-2509(02)00107-0.
- 10. Spicer, P.T. Chaoul, O., Tsantilis, S. & Pratsinis, S.E. (2002). Titania Formation by Ticl4 Gas Phase Oxidation, Surface Growth and Coagulation. Journal of Aerosol Science, 33(1), 17–34. DOI: 10.1016/S0021-8502(01)00069-6.
- 11. Dorao, C.A. & Jakobsen, H.A. (2006). A least square methods for the solution of population balance problems. Computers and Chemical Engineering, 30(3), 535–547. DOI:10.1016/j.compchemeng.2005.10.012.
- 12. Langston, P.A. (2002). Comparison of least – square method and Baye’s theorem for de-convolution of mixture composition. Chemical Engineering Science. 57(13), 2371-2379. DOI: 10.1016/S0009-2509(02)00133-1.
- 13. Landau, D.P. & Binder, K. (2005). A guide to Monte Carlo Simulations in Statistical Physics, second edition, New York, Cambridge University Press.
- 14. Mazo-Zuluaga, J., Restrepo, J. & Mejia-Lopez, J. (2007). Surface Anisotropy of a Fe3O4 Nanoparticle: A simulation approach. Physica B; 398(2), 187–190. DOI: 10.1016/j. physb.2007.04.070.
- 15. Iglesias, O. & Labarta, A. (2006). Monte Carlo Simulation Study of Exchange Biased Hysteresis loops in Nanoparticles. Physica B. 372(12), 247-250. DOI:10.1016/j.physb.2005.10.059.
- 16. Efendiev, Y. & Zachariah, M.R. (2002). Hybrid Monte Carlo Method for Simulation of Two – Component Aerosol Coagulation and Phase Segregation. Journal of Colloid and Interface Science. 249, 30 43. DOI:10.1006/jcis.2001.8114.
- 17. Shi, D., El-Farra, N.H., Mhaskar, P. & Christofides, P.D. (2005). Predictive Control of Crystal size Distribution in Protein Crystallization. Nanotechnology, 16, S562–574. DOI:10.1088/0957-4484/16/7/034.
- 18. Pepper, D.W. & Heinrich, J.C. (1992). The finite element method: Basic concepts and applications (Series in Computational and Physical Processes in Mechanics and Thermal Sciences). U. S. A. Hemisphere Publishing Corporation.
- 19. Baker, J. & Christofides, P.D. (2000). Finite-Dimension Approximation and Control of Non-linear Parabolic PDE Systems. International Journal of Control, 73(5), 439–4569. DOI: 10.1080/002071700219614.
- 20. Armaou, A. & Christofides, P.D. (2001). Finite-Dimensional Control of Nonlinear Parabolic PDE Systems with Time – Dependent Spatial Domains using Empirical Eigenfunctions. Int. J. Appl. Math. Comput. Sci., 11(2), 287–317.
- 21. Roussos, A.I., Alexpoulos, A.H. & Kiparissides, C. (2006). Dynamic Evolution of PSD in a Continuous Flow Process: A Comparative Study of Fixed and Moving Grid Numerical Techniques. Chemical Engineering Science. 61, 124–134. DOI: 10.1016/j.ces.2004.12.056.
- 22. Dorao, C.A. & Jakobsen, H.A. (2006). The Quadrature Method of Moments and its Relationship with the Method of Weighted Residuals. Chemical Engineering Science. 61, 7795- 7804. DOI: 10.1016/j.ces.2006.09.014.
- 23. Diemer, R.B. & Ehrman, S. H. (2005). Pipeline Agglomerator Design as a Model Test Case. Powder Technology, 156(2–3), 129–145. DOI:10.1016/j.powtec.2005.04.016.
- 24. Barret, J.C & Webb, N.A. (1998). A Comparison of some Approximate Methods for Solving the Aerosol Dynamic Equation. Journal of Aerosol Science, 29(1), 31–39. DOI: 10.1016/S0021-8502(97)00455-2.
- 25. Gerber, A.G. & Mousavi, A. (2007). Application of Quadrature Method of Moments to the Polydispersed Droplet Spectrum in Transonic Steam Flows with Primary and Secondary Nucleation. Applied Mathematical Modelling. 31(8), 1518–1533. DOI:10.1016/j.apm.2006.04.011.
- 26. Wright, D.L., McGraw, R. & Rosner. D.E. (2001). Bivariate Extension of the Quadrature Method of Moments for Modelling Simultaneous Coagulation and Sintering of Particle Populations. Journal of Colloid and Interface Science, 236, 242–251. DOI: 10.1006/jcis.2000.7409.
- 27. Oliver, R. I. & Markus, K. (2007). Adsorption, Diffusionand Desorption of Chlorine on and from rutile TiO2 {110}: A Theoretical Investigation. ChemPhysChem, 8, 444–451. DOI: 10.1002/cphc.200600653.
- 28. Kalani, K. & Christofides, P.D. (1999). Nonlinear Control of Spatially Inhomogeneous Aerosol Processes. Chemical Engineering Science. 54(13), 2669–2678. DOI: 10.1016/S0009- 2509(98)00315-7.
- 29 Sergey, E.L. (2003). Engineering and Scientific Computation using Matlab; Rochester Institute of Technology, New Jersey. Wiley Interscience some Approximate Methods for Solving the Aerosol Dynamic Equation. Journal of Aerosol Science, 29(1), 31–39. DOI: 10.1016/S0021-8502(97)00455-2.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPS2-0064-0035