Extended detailed balance for systems with irreversible reactions

• Published in: Chemical engineering science Vol. 66; no. 21; pp. 5388 - 5399
• Main Authors: Gorban, A.N., Yablonsky, G.S.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01-11-2011; Elsevier
• Subjects: Algebra; Applied sciences; Balancing; Catalysis; Catalytic reactions; Chemical engineering; Chemistry; combustion; Complex systems; Detailed balance; enzymatic reactions; Exact sciences and technology; General and physical chemistry; Hulls; Hulls (structures); Irreversibility; Kinetics; Mathematical analysis; Microreversibility; Pathway; Reaction network; Reactors; Theory of reactions, general kinetics. Catalysis. Nomenclature, chemical documentation, computer chemistry; Vectors (mathematics); Irreversibility; Detailed balance; Kinetics; Reaction network; Pathway; Microreversibility; Catalytic reaction; Complex system; Combustion; Reversible reaction; Irreversible reaction; Reaction mechanism; Oxidation
• ISSN: 0009-2509; 1873-4405
• DOI: 10.1016/j.ces.2011.07.054

The principle of detailed balance states that in equilibrium each elementary process is equilibrated by its reverse process. For many real physico-chemical complex systems (e.g. homogeneous combustion, heterogeneous catalytic oxidation, most enzyme reactions, etc.), detailed mechanisms include both reversible and irreversible reactions. In this case, the principle of detailed balance cannot be applied directly. We represent irreversible reactions as limits of reversible steps and obtain the principle of detailed balance for complex mechanisms with some irreversible elementary processes. We prove two consequences of the detailed balance for these mechanisms: the structural condition and the algebraic condition that form together the
extended form of detailed balance. The
algebraic condition is the principle of detailed balance for the reversible part. The
structural condition is the convex hull of the stoichiometric vectors of the irreversible reactions has empty intersection with the linear span of the stoichiometric vectors of the reversible reactions. Physically, this means that the irreversible reactions cannot be included in oriented cyclic pathways.
The systems with the extended form of detailed balance are also the limits of the reversible systems with detailed balance when some of the equilibrium concentrations (or activities) tend to zero. Surprisingly, the structure of the limit reaction mechanism crucially depends on the relative speeds of this tendency to zero.
► We found the extended principle of detailed balance for systems with irreversible reactions. ► For such systems, this principle is equivalent to two conditions: structural and algebraic ones. ► The structural condition gives us a rigorous tool for distinguishing the prohibited mechanisms. ► Computationally, it leads to an analysis of the intersection of a polyhedron with a linear subspace.