Extended detailed balance for systems with irreversible reactions

Chemical Engineering Science

Volumn 66, Issue 21, 2011, Pages 5388-5399

  Gorban, A N ^a   Yablonsky, G S ^b  

^a UNIVERSITY OF LEICESTER   (United Kingdom)

^b Saint Louis University   (United States)

Author keywords

Detailed balance; Irreversibility; Kinetics; Microreversibility; Pathway; Reaction network

Indexed keywords

DETAILED BALANCE; IRREVERSIBILITY; MICROREVERSIBILITY; PATHWAY; REACTION NETWORK;

ALGEBRA;

CATALYTIC OXIDATION;

EID: 81155159722     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2011.07.054     Document Type: Article

References (24)

1. Benson H.E. Processing of gasification products. Chemistry of Coal Utilization 1981, 1753-1800. John Wiley and Sons, New York, USA, (Chapter 25). M. Elliot (Ed.).
2. Bertsimas D., Tsitsiklis J.N. Introduction to Linear Optimization 1997, Athena Scientific, Cambridge, MA, USA.
3. Boltzmann L. Lectures on Gas Theory 1964, University of California Press, Berkeley, CA, USA.
4. Chu Ch. Gas absorption accompanied by a system of first-order reactions. Chem. Eng. Sci. 1971, 26(3):305-312.
5. Feinberg M. Complex balancing in general kinetic systems. Arch. Rat. Mechan. Anal. 1972, 49(3):187-194.
6. Fukuda, K., Prodon, A., 1996. Double description method revisited. In: Combinatorics and Computer Science. Lecture Notes in Computer Science, vol. 1120/1996, pp. 91-111.
7. Gagneur J., Klamt S. Computation of elementary modes: a unifying framework and the new binary approach. BMC Bioinformatics 2004, 5:175.
8. Gorban A.N., Mirkes E.M., Bocharov A.N., Bykov V.I. Thermodynamic consistency of kinetic data. Combustion, Explosion, and Shock Waves 1989, 25(5):593-600.
9. Horiuti J. Theory of reaction rates as based on the stoichiometric number concept. Ann. New York Academy Sci. 1973, 213:5-30.
10. Ivanova A.N. Conditions for uniqueness of stationary state of kinetic systems related to structural scheme of reactions. Kinet. Katal. 1979, 20(4):1019-1023.
11. Mincheva M., Roussel M.R. Graph-theoretic methods for the analysis of chemical and biochemical networks. I. Multistability and oscillations in ordinary differential equation models. J. Math. Biol. 2007, 55:61-68.
12. Moe J.M. Design of water-gas shift reactors. Chem. Eng. Progress 1962, 58(3):33-36.
13. Motzkin T.S., Raiffa H., Thompson G.L., Thrall R.M. The double description method. Contributions to Theory of Games 1953, vol. 2:51-73. Princeton University Press, Princeton, NJ, USA.
14. Onsager L. Reciprocal relations in irreversible processes I. Phys. Rev. 1931, 37:405-426. II 38, 2265-2279.
15. Papin J.A., Price N.D., Wiback S.J., Fell D.A., Palsson B.O. Metabolic pathways in the post-genome era. Trends in Biochemical Sciences 2003, 28(5):250-258.
16. Prigogine I., Defay R. Chemical Thermodynamics 1962, Longmans and Green, New York, USA.
17. Schnakenberg J. Network theory of microscopic and macroscopic behavior of master equation systems. Rev. Mod. Phys. 1976, 48:571-585.
18. Schuster S., Fell D.A., Dandekar T. A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks. Nat. Biotechnol. 2000, 18:326-332.
19. Temkin O.N., Zeigarnik A.V., Bonchev D.G. Chemical reaction networks: a graph-theoretical approach 1996, CRC Press, Boca Raton, FL, USA.
20. Volpert A.I., Khudyaev S.I. Analysis in classes of discontinuous functions and equations of mathematical physics 1985, Nijoff, Dordrecht, The Netherlands.
21. Wegscheider R. Über simultane Gleichgewichte und die Beziehungen zwischen Thermodynamik und Reactionskinetik homogener Systeme. Monatshefte für Chemie/Chemical Monthly 1911, 32(8):849-906.
22. Yablonskii G.S., Bykov V.I., Gorban A.N., Elokhin V.I. Kinetic Models of Catalytic Reactions 1991, Elsevier, Amsterdam, The Netherlands.
23. Yablonsky G.S., Gorban A.N., Constales D., Galvita V.V., Marin G.B. Reciprocal relations between kinetic curves. EPL 2011, 93:20004.
24. Yang J., Bruno W.J., Hlavacek W.S., Pearson J. On imposing detailed balance in complex reaction mechanisms. Biophys. J. 2006, 91:1136-1141.