The C-matrix augmentation in a multi-route reaction mechanism

When the dimensional complexity of the chemical reaction mechanism arises, it needs special arrangements to deal with such issues. We propose an effective linear algebraic technique to split a complex reaction mechanism into different reaction completion routes to overcome this complexity. Here, three key matrices, the molecular, stoichiometric, and Horiuti matrices, are discussed in detail to deal with the whole mechanism as well as the different reaction routes. The C-matrix procedure is based on calculating the Reduced Row Echelon Form (RREF) for reducing each augmented matrix. This approach is efficient to find the typical results in chemical kinetics and engineering of chemical reactions, i.e., reaction routes, key, and non-key components, key and non-key elements, dependent and independent reaction steps, and overall reaction free from the catalyst. This procedure is very useful to develop new software tools for analyzing complex chemical networks.