Bottom-up modeling using the rate-controlled constrained-equilibrium theory: The n-butane combustion chemistry

It is shown that when the constrained-equilibrium assumption is used, kinetic calculations can be carried out without the use of a detailed kinetic model in the outset. One starts with conservation of atomic elements, to which more constraints and rate-limiting reactions can be added to improve kinetic predictions to the desired accuracy. The idea is demonstrated for high temperature homogeneous ignition of mixtures of stoichiometric n-Butane in air. An {H/O, C1,2, C3Hx (x ≤ 6)} kinetic model, involving 41 species and 348 reactions, is taken as the foundational fuel model and the gap between the fuel molecule and this base model is bridged at five different models that use the constrained-equilibrium assumption. Comparisons of predictions of this approach with the same models that make no use of the constrained-equilibrium assumption indicate that (a) the chain of reactions could be explicitly broken without compromising the fundamental elementary nature of the model, and (b) the use of the constrained-equilibrium assumption makes the model less sensitive to the missing pathways. The results, therefore, suggest that employing the constrained-equilibrium assumption may significantly reduce the modeling task of heavy hydrocarbon fuels, where the intrinsic dimensionality of the model, multiplicity of pathways and the required rates render the modeling task intractable.