As discussed in the preceding section, the DRG method identifies unimportant species in a reaction mechanism by resolving species coupling without any system knowledge [6]. The direct species coupling is defined by the immediate error to the production rate of a species, A, introduced by the removal of another species, B, from the mechanism. Such immediate error, noted as , can be expressed as

(3–21)

where A and B indicate the species, indicates the th reaction of the mechanism, indicates the stoichiometric coefficient of species A in the th reaction, and is the reaction rate of the th reaction that can be readily obtained from Reaction Workbench. The denominator represents the total absolute contributions to the production rate of species A by all reactions in the mechanism involving species A. The numerator represents the contributions by reactions involving species B. DRG has been proved to be a very efficient mechanism reduction method for generating skeletal mechanisms.

The DRG method has been extended to the Directed Relation Graph with Error Propagation (DRGEP) method [9], [10] This method shares the same underlying principle as DRG in identifying direct species coupling using the immediate error . However, the process of deciding whether a species can be removed from the mechanism is different between these two methods. In DRG, if the error is larger than a pre-defined error tolerance level, the removal of species B will introduce an error to the production rate of species A that is beyond what is deemed acceptable, so that species B must be kept in the mechanism if A is kept in the mechanism. In addition, if the error is also larger than the tolerance level, the species C must also be kept in the mechanism because of the indirect species coupling between species A and C. In DRGEP, once species A is kept in the mechanism, all other species that are reachable from species A through direct and indirect coupling are examined using their "R-value", which is defined as

where is the set of all possible paths leading from species A to species B, and is the chain product of the weights (that is, the immediate error ) of the edges along the given path. For example, if A is connected to B through a reaction and B is connected to C through a reaction, there is a path connecting from A to C via B and the R-value of this particular path is . Based on this definition, a species B must be kept in the mechanism if there is at least one path connecting from A to B whose R-value is larger than the user-specified threshold.

The DRGEP method is the default mechanism reduction method in the Reaction Workbench. Using an efficient breadth-first search algorithm, the removal of unimportant species can be achieved in a time scale that is linearly proportional to the number of reactions in the mechanism. Our test cases have also shown that, under many conditions, the DRGEP method can generate a skeletal mechanism that contains approximately 10% fewer species than one generated using the DRG method.