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In previous chapters the hydrodynamics of chromatographic columns has been described with simplified assumptions: fluids and chromatographic beds were assumed to be incompressible, possible temperature effects were neglected, velocity profiles were taken to be radially uniform, axial dispersion presumed to obey a Fickian mechanism, and so on. These assumptions allowed us to model the columns either with the mixing cells in series (MC) model or with the plug flow plus axial dispersion (PD) model. These models have the merits of simplicity and flexibility as they allow a large range of dispersion situations, from perfect mixing to plug flow with only one parameter, to be represented.

The real world can be more complex, because chromatographic beds are not indefinitely stable and can plug, distributors are imperfect, velocities are not always radially uniform, temperature effects can impact dispersion, large differences in density or viscosity between the feed and the eluent can induce instabilities etc. Addressing these matters and understanding their impact on column performance is the subject of this chapter.

Modeling hydrodynamics requires addressing three subjects of specific relevance to the design of chromatographic processes:

1. • Pressure drop: a key parameter for hardware design (pumps, columns, etc.) and sometimes for protecting the adsorbent

2. • Zero (total or excluded) retention time: a key reference for chromatogram positioning that can be affected by velocity heterogeneity and fluid compressibility

3. • Hydrodynamic dispersion: to ensure that the separation ability of the chromatographic medium is not spoiled by undesirable contributions to band broadening.

After presenting the modeling of “ideal” situations, we will relax some assumptions and discuss their influence on the scale-up of real systems.

Ideal systems

As explained in Chapter 1, we define “ideal” systems as chromatographic systems in which:

1. • the properties of the chromatographic bed (porosity and permeability) are uniform along the axial and radial directions

2. • the chromatographic bed is incompressible and stable

3. • the fluid velocity and temperature are radially uniform.