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A desired goal of the PAT framework is to design and develop well-understood processes that will consistently ensure a predefined quality at the end of the manufacturing process. Such procedures would be consistent with the basic tenet of quality by design and could reduce risks to quality and regulatory concerns while improving efficiency. To support a more in-depth understanding of the design and development of a chromatographic purification process the paper discusses the general thermodynamic principles of ligand-binding and models of multi-component adsorption in ion-exchange and hydrophobic chromatography. The parameters in the models are easy to determine and have a well-defined physical significance. Examples demonstrate how the model parameters can be determined from experimental data and in order to validate the model, simulated chromatograms are compared to the corresponding experimental chromatograms. Finally it is demonstrated how a simulation can be used to explain an aberration.