Chemical engineering approach to dynamic modelling of linear chromatography : A flexible method for representing complex phenomena from simple concepts

The main features of the theory of linear chromatography based on a “systems approach” are presented. The main theorem states that the transfer function of the chromatographic system (the Laplace transform of the peak equation) can be obtained by combining the transfer function of the residence-time distribution of the mobile phase, where the transfer function characterizes the reversible interaction with the stationary phase at the local level. Various models for local retention are considered: simple interaction, retention layers in series, retention sites in parallel, transient diffusion in particles of any shape and the special cases of simple and double porosity. The expressions for the transfer functions are reported in each case. An important concept is the transfer-time distribution, describing distributed exchange on sites of different activities. The case of chemical reaction in both the mobile and stationary phases can be dealt with as well. Chromatographic peaks can be obtained in the real domain by numerical inversion of Laplace transforms. An example is presented of an interaction controlled by both external mass transfer and internal diffusion, and two models are compared, a distributed-parameter model and a simple lumped-parameter model for mass-transfer resistance. It is shown that the simple model yields results close to those of the detailed one in the region of well behaved chromatographic peaks. Oversophistication of mathematical models appears to be useless in most cases. The chemical engineering approach, based on systems dynamics, thus yields models which can very flexibly be adapted to most situations.