Optimal control of a two-stage reactor system
-
T. Hirmajer
and
M. Fikar
Abstract
Optimal operation policies were investigated for a batch reactor system with two different operation stages. At the end of the first nonisothermal stage one of the reactants was added. Since that moment the reactor was operated isothermally. In each stage behavior of the reactor was described by a set of differential equations. The maximum conversion problem was investigated subject to various operating constraints. Dynamic optimization based on the control vector parametrization was used to find the optimal control profile. Gradients of the resulting nonlinear programming problem were obtained by adjoint method based on the optimal control theory.
[1] Srinivasan, B., Palanki, S., and Bonvin, D., Comput. Chem. Eng. 27, 1 (2003). http://dx.doi.org/10.1016/S0098-1354(02)00116-310.1016/S0098-1354(02)00116-3Search in Google Scholar
[2] Bonvin, D., J. Process Control 8, 355 (1998). http://dx.doi.org/10.1016/S0959-1524(98)00010-910.1016/S0959-1524(98)00010-9Search in Google Scholar
[3] Dostál, P., Bakošová, M., and Bobál, V., Chem. Pap. 58, 184 (2004). Search in Google Scholar
[4] Lin, S. H. and Cheng, K. W., Desalination 133, 41 (2001). http://dx.doi.org/10.1016/S0011-9164(01)00081-910.1016/S0011-9164(01)00081-9Search in Google Scholar
[5] Zhao, H., Isaacs, S. H., Søeberg, H., and Kümmel, M., Water Res. 28, 535 (1994). http://dx.doi.org/10.1016/0043-1354(94)90004-310.1016/0043-1354(94)90004-3Search in Google Scholar
[6] Zhao, H., Isaacs, S. H., Søeberg, H., and Kümmel, M., Water Res. 29, 535 (1995). http://dx.doi.org/10.1016/0043-1354(94)00174-610.1016/0043-1354(94)00174-6Search in Google Scholar
[7] Coelho, M. A. Z., Russo, C., and Araújo, O. Q. F., Water Res. 34, 2809 (2000). http://dx.doi.org/10.1016/S0043-1354(00)00010-510.1016/S0043-1354(00)00010-5Search in Google Scholar
[8] Isaacs, S., Water Sci. Technol. 35, 225 (1997). http://dx.doi.org/10.1016/S0273-1223(96)00900-610.1016/S0273-1223(96)00900-6Search in Google Scholar
[9] Barton, P. I., Banga, J. R., and Galán, S., Comput. Chem. Eng. 24, 2171 (2000). http://dx.doi.org/10.1016/S0098-1354(00)00586-X10.1016/S0098-1354(00)00586-XSearch in Google Scholar
[10] Schlegel, M. and Marquardt, W., J. Process Control 16, 275 (2006). http://dx.doi.org/10.1016/j.jprocont.2005.06.00810.1016/j.jprocont.2005.06.008Search in Google Scholar
[11] Manon, P., Roubinet, C. V., and Gilles, G., Cont. Eng. Prac. 10, 133 (2002). http://dx.doi.org/10.1016/S0967-0661(01)00123-X10.1016/S0967-0661(01)00123-XSearch in Google Scholar
[12] Bemporad, A. and Morari, M., Automatica 35, 407 (1999). http://dx.doi.org/10.1016/S0005-1098(98)00178-210.1016/S0005-1098(98)00178-2Search in Google Scholar
[13] Avraam, M. P., Shah, N., and Pantelides, C. C., Comput. Chem. Eng. 22, 221 (1998). http://dx.doi.org/10.1016/S0098-1354(98)00058-110.1016/S0098-1354(98)00058-1Search in Google Scholar
[14] Biegler, L. T., Cervantes, A. M., and Wächter, A., Chem. Eng. Sci. 57, 575 (2002). http://dx.doi.org/10.1016/S0009-2509(01)00376-110.1016/S0009-2509(01)00376-1Search in Google Scholar
[15] Cuthrell, J. E. and Biegler, L. T., AIChE J. 33, 1257 (1987). http://dx.doi.org/10.1002/aic.69033080410.1002/aic.690330804Search in Google Scholar
[16] Logsdon, J. S. and Biegler, L. T., Ind. Eng. Chem. Res. 28, 1628 (1989). http://dx.doi.org/10.1021/ie00095a01010.1021/ie00095a010Search in Google Scholar
[17] Feehery, W. F., Ph.D. Thesis. Massachusetts Institute of Technology, Cambridge, 1998. Search in Google Scholar
[18] Rosen, O. and Luus, R., Comput. Chem. Eng. 15, 273 (1991). http://dx.doi.org/10.1016/0098-1354(91)85013-K10.1016/0098-1354(91)85013-KSearch in Google Scholar
[19] Caracotsios, M. and Stewart, W. E., Comput. Chem. Eng. 9, 359 (1985). http://dx.doi.org/10.1016/0098-1354(85)85014-610.1016/0098-1354(85)85014-6Search in Google Scholar
[20] Vassiliadis, V. S., Sargent, R. W. H., and Pantelides, C. C., Ind. Eng. Chem. Res. 33, 2111, 2123 (1994). http://dx.doi.org/10.1021/ie00033a01410.1021/ie00033a014Search in Google Scholar
[21] Ruban, A. I., J. Comput. Syst. Sci. Int. 36, 536 (1997). Search in Google Scholar
[22] Goh, C. J. and Teo, K. L., Automatica 24, 3 (1988). http://dx.doi.org/10.1016/0005-1098(88)90003-910.1016/0005-1098(88)90003-9Search in Google Scholar
[23] Bryson, A. E. and Ho, Y. C., Applied Optimal Control — Optimization, Estimation and Control. Hemisphere Publishing Corporation, Washington, 1975. Search in Google Scholar
[24] Hirmajer, T. and Fikar, M., Technical Report, FCFT SUT, Bratislava, Slovakia, 2005. Search in Google Scholar
[25] Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., and Mishchenko, E. F., The Mathematical Theory of Optimal Processes. Wiley, New York, 1962. Search in Google Scholar
[26] Fikar, M. and Latifi, M. A., Technical Report, LSGC CNRS, Nancy, France; FCFT SUT, Bratislava, Slovakia, 2001. Search in Google Scholar
[27] Petzold, L. R. and Hindmarsh, A. C., Technical Report, LLNL, California, 1997. Search in Google Scholar
[28] Schittkowski, K., Technical Report, University of Bayreuth, Bayreuth, Germany, 1981. Search in Google Scholar
© 2006 Institute of Chemistry, Slovak Academy of Sciences
Articles in the same Issue
- FTIR study of gamma-irradiated cis-1,4-polyisoprene
- Comparison of betaine and l-stachydrine as phase-transfer catalysts in Michael addition and Darzens reaction
- Synthesis and cyclization reactions with pyrazolopyrimidinyl keto esters part I. Reactivity of pyrazolopyrimidinyl β-keto ester and pyrazolopyrimidinyl α,β-unsaturated ketones
- Electrodeposition of mercury film on electrodes modified with clay minerals
- Properties of Ni-W alloy coatings on steel substrate
- Effect of chloride ions on the kinetics of nitrobenzene reduction by powdered iron
- Displacement washing of pulp with urea solutions
- Methane esterification in oleum
- Momentum transfer in an agitated vessel with off-centred impellers
- Optimal control of a two-stage reactor system
- Effect of span 20 concentration on oxalic acid production from post-refining fatty acids by Aspergillus niger XP
- Citric acid production from raw glycerol by acetate mutants of Yarrowia lipolytica
- Phosphonium ionic liquids as new, reactive extractants of lactic acid
Articles in the same Issue
- FTIR study of gamma-irradiated cis-1,4-polyisoprene
- Comparison of betaine and l-stachydrine as phase-transfer catalysts in Michael addition and Darzens reaction
- Synthesis and cyclization reactions with pyrazolopyrimidinyl keto esters part I. Reactivity of pyrazolopyrimidinyl β-keto ester and pyrazolopyrimidinyl α,β-unsaturated ketones
- Electrodeposition of mercury film on electrodes modified with clay minerals
- Properties of Ni-W alloy coatings on steel substrate
- Effect of chloride ions on the kinetics of nitrobenzene reduction by powdered iron
- Displacement washing of pulp with urea solutions
- Methane esterification in oleum
- Momentum transfer in an agitated vessel with off-centred impellers
- Optimal control of a two-stage reactor system
- Effect of span 20 concentration on oxalic acid production from post-refining fatty acids by Aspergillus niger XP
- Citric acid production from raw glycerol by acetate mutants of Yarrowia lipolytica
- Phosphonium ionic liquids as new, reactive extractants of lactic acid
