A kinetics-based method for constraint selection in rate-controlled constrained equilibrium

Abstract

The rate-controlled constrained-equilibrium (RCCE) method is a thermodynamics-based dimension reduction method that enables representation of chemistry involving n_s chemical species in terms of a smaller number, n_r, of constraints, and thus reduces the computational burden imposed by detailed chemical kinetics. The accuracy in the reduced description by RCCE strongly depends on the specification of constraints. In this work, the connection between the RCCE method and the conventional partial equilibrium assumption (PEA) method is revisited. It is shown that with the constraints being specified based on rate-controlling slow reactions, the RCCE method is equivalent to PEA. A criterion based on time scale analysis is then employed for the identification of fast reactions. Then the importance index, which represents the contribution of individual species to the slow dynamics of a reactive system, is proposed for the selection of species constraints in RCCE. This makes the thermodynamics-based constrained equilibrium manifolds (CEMs) a good approximation to the actual kinetics-controlled slow invariant manifolds (SIMs) in reactive systems. The method is demonstrated in the reduced descriptions of perfectly stirred reactors (PSRs) burning stoichiometric methane/air mixtures. Sample reaction states ranging from near-equilibrium conditions to the extinction turning points on the S-curve are examined for the identification of fast reactions and species constraints. Reduced descriptions of transient PSRs by RCCE are subsequently performed with their accuracy assessed against the full descriptions, in which all the chemical species are transported. The study shows that the dynamics predicted by RCCE agrees well with that from the full description and that near-limit reaction states are important for the selection of species constraints in RCCE.

Keywords:

• dimension reduction
• rate-controlled constrained equilibrium
• partial equilibrium
• detailed chemical kinetics

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work at Tsinghua University is supported by National Natural Science Foundation of China [51476087 and 91441202]. The work at University of Connecticut is supported by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, US Department of Energy [grant DE-SC0008622].