A new approach to diagnostics of ideal and non-ideal flow patterns: I. The concept of reactive-mixing index (REMI) analysis

A new approach is proposed allowing to characterize the hydrodynamic regime in the presence of chemical reactions, through small pulse-response experiments using a reacting component as a tracer instead of inert components which are used in the traditional Danckwerts-type experiment.Theoretically, our approach is based on the escape time defined as the mean exit age of molecules that escaped all reactions, and uses the original concept of the reactive mixing index (REMI), which is the ratio of the normalized difference between the escape time (ET(X)=M1(X)/M0(X))(ET(X)=M1(X)/M0(X)) in the presence and in the absence of reaction, to conversion X  : REMI(X)=(1-ET(X)/ET(0))/XREMI(X)=(1-ET(X)/ET(0))/X.Experimentally, the observed values are the numbers of additional exiting molecules per second as a function of time, F(t)F(t) (mol/s). Based on these values, the moments M0(X)M0(X) and M1(X)M1(X) can be computed and REMI calculated.This REMI is a global, macroscopic, external, model-free characteristic and to our knowledge has not been introduced or studied before. This value is identical to 1 for perfectly mixed continuous-flow reactors, and identical to zero for ideal plug flow reactors (PFR). For non-ideal PFR, the REMI depends on two independent characteristic dimensionless numbers, the Péclet number and the conversion or, equivalently, the Damköhler number. Expressions for these dependencies are developed.The smallness of the perturbations allows to use a linearized kinetic model. The theory of this new index is developed; application to experimental data will be the subject of future articles.