Port-Hamiltonian modeling of non-isothermal chemical reaction networks
Authors
Li Wang, Bernhard Maschke, Arjan van der Schaft
Abstract
Motivated by recent progress on the port-Hamiltonian formulation of isothermal chemical reaction networks and of the continuous stirred tank reactor, the present paper aims to develop a port-Hamiltonian formulation of chemical reaction networks in the non-isothermal case, and to exploit this for equilibrium and stability analysis.
Keywords
Chemical reaction networks; Port-Hamiltonian systems; Network dynamics; Irreversible thermodynamic systems
Citation
- Journal: Journal of Mathematical Chemistry
- Year: 2018
- Volume: 56
- Issue: 6
- Pages: 1707–1727
- Publisher: Springer Science and Business Media LLC
- DOI: 10.1007/s10910-018-0882-9
BibTeX
@article{Wang_2018,
title={{Port-Hamiltonian modeling of non-isothermal chemical reaction networks}},
volume={56},
ISSN={1572-8897},
DOI={10.1007/s10910-018-0882-9},
number={6},
journal={Journal of Mathematical Chemistry},
publisher={Springer Science and Business Media LLC},
author={Wang, Li and Maschke, Bernhard and van der Schaft, Arjan},
year={2018},
pages={1707--1727}
}
References
- N Balabanian. N. Balabanian, T.A. Bickart, Linear Network Theory: Analysis, Properties, Design and Synthesis (Matrix Pub, York, 1981) (1981)
- Bollobás, B. Modern Graph Theory. Graduate Texts in Mathematics (Springer New York, 1998). doi:10.1007/978-1-4612-0619-4 – 10.1007/978-1-4612-0619-4
- H Callen. H. Callen, Thermodynamics (Wiley, New York, 1960) (1960)
- Couenne, F., Jallut, C., Maschke, B., Breedveld, P. C. & Tayakout, M. Bond graph modelling for chemical reactors. Mathematical and Computer Modelling of Dynamical Systems vol. 12 159–174 (2006) – 10.1080/13873950500068823
- Eberard, D., Maschke, B. M. & van der Schaft, A. J. An extension of Hamiltonian systems to the thermodynamic phase space: Towards a geometry of nonreversible processes. Reports on Mathematical Physics vol. 60 175–198 (2007) – 10.1016/s0034-4877(07)00024-9
- Favache, A., Dochain, D. & Maschke, B. An entropy-based formulation of irreversible processes based on contact structures. Chemical Engineering Science vol. 65 5204–5216 (2010) – 10.1016/j.ces.2010.06.019
- Favache, A., Dos Santos Martins, V. S., Dochain, D. & Maschke, B. Some Properties of Conservative Port Contact Systems. IEEE Transactions on Automatic Control vol. 54 2341–2351 (2009) – 10.1109/tac.2009.2028973
- Feinberg, M. Complex balancing in general kinetic systems. Archive for Rational Mechanics and Analysis vol. 49 187–194 (1972) – 10.1007/bf00255665
- Feinberg, M. Chemical reaction network structure and the stability of complex isothermal reactors—I. The deficiency zero and deficiency one theorems. Chemical Engineering Science vol. 42 2229–2268 (1987) – 10.1016/0009-2509(87)80099-4
- Feinberg, M. Necessary and sufficient conditions for detailed balancing in mass action systems of arbitrary complexity. Chemical Engineering Science vol. 44 1819–1827 (1989) – 10.1016/0009-2509(89)85124-3
- Feinberg, M. The existence and uniqueness of steady states for a class of chemical reaction networks. Archive for Rational Mechanics and Analysis vol. 132 311–370 (1995) – 10.1007/bf00375614
- Hoang, H., Couenne, F., Jallut, C. & Le Gorrec, Y. The port Hamiltonian approach to modeling and control of Continuous Stirred Tank Reactors. Journal of Process Control vol. 21 1449–1458 (2011) – 10.1016/j.jprocont.2011.06.014
- Hoang, H., Couenne, F., Jallut, C. & Le Gorrec, Y. Lyapunov-based control of non isothermal continuous stirred tank reactors using irreversible thermodynamics. Journal of Process Control vol. 22 412–422 (2012) – 10.1016/j.jprocont.2011.12.007
- Horn, F. Necessary and sufficient conditions for complex balancing in chemical kinetics. Archive for Rational Mechanics and Analysis vol. 49 172–186 (1972) – 10.1007/bf00255664
- Horn, F. & Jackson, R. General mass action kinetics. Archive for Rational Mechanics and Analysis vol. 47 81–116 (1972) – 10.1007/bf00251225
- B. Jayawardhana, S. Rao, A.J. Van der Schaft, Balanced chemical reaction networks governed by general kinetics, in Proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems, Melbourne, Australia (2012)
- Jillson, K. R. & Erik Ydstie, B. Process networks with decentralized inventory and flow control. Journal of Process Control vol. 17 399–413 (2007) – 10.1016/j.jprocont.2006.12.006
- Jongschaap, R. & Öttinger, H. C. The mathematical representation of driven thermodynamic systems. Journal of Non-Newtonian Fluid Mechanics vol. 120 3–9 (2004) – 10.1016/j.jnnfm.2003.11.008
- Keenan, J. H. Availability and irreversibility in thermodynamics. British Journal of Applied Physics vol. 2 183–192 (1951) – 10.1088/0508-3443/2/7/302
- B. Maschke, A.J. Van der Schaft, Port-controlled Hamiltonian systems: modelling origins and system theoretic properties, in Nonlinear Control Systems Design, vol. 25 (1992), pp. 359–365
- Otero-Muras, I., Szederkényi, G., Alonso, A. A. & Hangos, K. M. Local dissipative Hamiltonian description of reversible reaction networks. Systems & Control Letters vol. 57 554–560 (2008) – 10.1016/j.sysconle.2007.12.003
- Picó-Marco, E., Boada, Y., Picó, J. & Vignoni, A. Contractivity of a genetic circuit with internal feedback and cell-to-cell communication. IFAC-PapersOnLine vol. 49 213–218 (2016) – 10.1016/j.ifacol.2016.12.128
- Qian, H. & Beard, D. A. Thermodynamics of stoichiometric biochemical networks in living systems far from equilibrium. Biophysical Chemistry vol. 114 213–220 (2005) – 10.1016/j.bpc.2004.12.001
- Ramirez, H., Gorrec, Y. L., Maschke, B. & Couenne, F. Passivity Based Control of Irreversible Port Hamiltonian Systems. IFAC Proceedings Volumes vol. 46 84–89 (2013) – 10.3182/20130714-3-fr-4040.00012
- Ramirez, H., Maschke, B. & Sbarbaro, D. Irreversible port-Hamiltonian systems: A general formulation of irreversible processes with application to the CSTR. Chemical Engineering Science vol. 89 223–234 (2013) – 10.1016/j.ces.2012.12.002
- H. Ramırez, D. Sbárbaro, B. Maschke, Irreversible port-Hamiltonian formulation of chemical reaction networks, in 21st International Symposium on Mathematical Theory of Networks and Systems, Groningen, The Netherlands, 7–11 July 2014
- Rao, R. & Esposito, M. Nonequilibrium Thermodynamics of Chemical Reaction Networks: Wisdom from Stochastic Thermodynamics. Physical Review X vol. 6 (2016) – 10.1103/physrevx.6.041064
- Rao, S., van der Schaft, A. & Jayawardhana, B. A graph-theoretical approach for the analysis and model reduction of complex-balanced chemical reaction networks. Journal of Mathematical Chemistry vol. 51 2401–2422 (2013) – 10.1007/s10910-013-0218-8
- Rao, S., der Schaft, A. van, Eunen, K. van, Bakker, B. M. & Jayawardhana, B. A model reduction method for biochemical reaction networks. BMC Systems Biology vol. 8 (2014) – 10.1186/1752-0509-8-52
- van der Schaft, A. Port-Hamiltonian systems: an introductory survey. Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006 1339–1365 (2007) doi:10.4171/022-3/65 – 10.4171/022-3/65
- AJ Schaft Van der. A.J. Van der Schaft, B. Maschke, The Hamiltonian formulation of energy conserving physical systems with external ports. Arch. Elektron. Übertrag. 49(5–6), 362–371 (1995) (1995)
- van der Schaft, A., Rao, S. & Jayawardhana, B. On the Mathematical Structure of Balanced Chemical Reaction Networks Governed by Mass Action Kinetics. SIAM Journal on Applied Mathematics vol. 73 953–973 (2013) – 10.1137/11085431x
- van der Schaft, A. J., Rao, S. & Jayawardhana, B. On the network thermodynamics of mass action chemical reaction networks. IFAC Proceedings Volumes vol. 46 24–29 (2013) – 10.3182/20130714-3-fr-4040.00001
- ON Temkin. O.N. Temkin, A.V. Zeigarnik, D.G. Bonchev, Chemical Reaction Networks: A Graph-Theoretical Approach (CRC Press, Boca Raton, 1996) (1996)
- Varma, A. & Palsson, B. O. Metabolic Flux Balancing: Basic Concepts, Scientific and Practical Use. Bio/Technology vol. 12 994–998 (1994) – 10.1038/nbt1094-994
- Wang, L., Maschke, B. & van der Schaft, A. Irreversible port-Hamiltonian Approach to Modeling and Analyzing of Non-isothermal Chemical Reaction Networks. IFAC-PapersOnLine vol. 49 134–139 (2016) – 10.1016/j.ifacol.2016.12.115