5 - Mass transfer

Summary

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In the previous chapters, the basics of chromatography modeling were provided under the assumption that kinetic limitations either were non-existent (Chapter 3 for non-linear chromatography) or could be modeled via a first-order approximation (Chapter 2 for linear chromatography). We have shown in Chapter 2 that, as long as kinetic limitations are not extremely strong, a good approximation for modeling chromatographic columns is to lump hydrodynamic dispersion and mass transfer limitations into a single parameter known as the plate number. We will show in the following sections and in Chapter 7 that this approach is often sufficient for modeling preparative scale chromatography. In certain situations, however, when kinetic limitations are strong, in the case of strongly non-linear chromatography or when specific precision is required because of challenging purity targets, this approximation may not be accurate enough and more detailed descriptions will be needed.

It is generally accepted that kinetic limitations can be attributed to diffusional transfer occurring either outside the beads, thus referred to as external diffusion, or inside the beads, thus referred to as internal diffusion. Usually, the adsorption step is very fast and is assumed to be kinetically instantaneous. However, because very small particle sizes are now available, the influence of diffusional limitations could in principle decrease to such an extent that, in certain rare cases, the overall kinetics of chromatography may be limited by the kinetics of the adsorption step.

We want to stress the fact that the distinction between external diffusion, internal diffusion and adsorption kinetics is not purely academic, because these three possible processes are impacted differently by operating parameters like particle size and fluid velocity. The ability to identify and properly model these different processes is thus key.

We will use the lumped model and the porous model introduced in Chapter 1 to model mass transfer around and inside particles. The lumped model clearly has the advantage of simplicity, whereas more or less complex descriptions associated with the porous model allow a better understanding of the influence of certain operating parameters on kinetics.