Simple approximate rate law for both short- and long-chain rice Herzfeld kinetics

Many high-temperature hydrocarbon conversion processes are based on or contain an element of thermal reaction chemistry. The essential challenge in modeling these pyrolysis reactions stems from the complexity of the hydrocarbon feed. Toward this end, the elementary steps noted above can be organized into a general Rice-Herzfeld chain process comprising initiation, propagation, and termination components. The appeal of this long-chain approximation (LCA), especially for modeling the reaction of mixtures, motivated the present scrutiny of its range of applicability. The mathematical convenience of the long-chain approximation can be retained at conditions where it is a poor representation of the exact solution of RH kinetics by constructing an approximate solution as the sum of the initiation and long-chain rates. This simple strategy obviates the need for the full solution of a problem nonlinear in radical concentrations by adding the trivial initiation rate to the solution of a problem linear in radical concentrations. This approximation is expected to be quite useful in the analysis of complex pyrolysis mixtures.