Fate and transport of species in a linear reaction network with different retardation coefficients

A response function approach is used to generate semi-analytical solutions to model the transport of species within a first-order reaction network. If the retardation coefficients of these species are not the same, product species will either be delayed or displaced forward relative to the reactants. A novel approach is used to simulate linear, kinetic response functions (KRFs) for species in plug flow, then to integrate with the conservative residence time density function (E-curve) to yield a residence time density for the reacted species. This kinetic E-curve can be used with linear operator methods such as convolution to yield the semi-analytical solution for nonuniform inputs, nonideal mixing, and complex reaction networks. Closed-form analytical solutions are presented for the linear response functions for straight, three-member reaction networks in plug flow. Only irreversible reactions are considered. Several examples with various mixing conditions are shown and compared to other analytical solutions. Although the approach is related to other transfer function models, the kinetic residence time density is a transfer function that is generated directly from the plug-flow response functions and the numerical evaluation of the E-curve. The advantage is that a wide variety of mixing conditions and reaction networks may be considered without the need to generate analytical transfer functions for each species and mixing condition.