On Cooperative Behavior of Open Homogeneous Chemical Reaction Systems in the Extent Domain

Material balance equations describe the dynamics of the species in open reaction systems and contain information regarding reaction topology, kinetics and operation mode. For reaction systems, the state variables (the numbers of moles, or concentrations) have recently been transformed into decoupled reaction variants (extents of reaction), and reaction invariants (extents of flow) (Amrhein et al., AIChE Journal, 2010). This paper analyses the conditions under which an open homogeneous reaction system is cooperative in the extents domain. Further, it is shown that the dynamics of the extents of flow exhibit cooperative behavior. Further, we provide the conditions under which the dynamics of the extents of reaction exhibit cooperative behavior. Our results provide physical insights into cooperative and competitive nature of the underlying reaction system in the presence of material exchange with surrounding (i.e., inlet and outlet flows). The results of the article are demonstrated via examples.