(636c) A Continuum Approach to Chromatography Modeling

Some chromatographic applications are dealing with ‘infinitely’ complex feedstock composed of a large number of similar species with comparable properties. The feed mixture might be so complex that analytical methods fail to identify all the solutes present in the feedstock individually. In this case, the description of large multicomponent systems requires specific mathematical tools to reach an intelligible description of the complex solute mixture. Lumping methods are  commonly used to reduce the number of solutes present in the feed mixture to a smaller number of pseudo-components with relatively homogeneous properties. This classical lumping approach is often of great help to model multicomponent systems but requires a tremendous amount of work to identify and characterize the different pseudo-components and their associated model parameters. There is often a trade-off between the precision of the lumping approach requiring a large number of pseudo-components and the experimental and computational efforts increase inherent to the modeling a multicomponent systems.

In this work, we propose to consider the solute mixture as a continuum. The continuum approach is based on the description of complex mixtures by continuous distributions instead of the classical discrete sampling. By doing so the precision of the results becomes independent of the number of considered components and of the sampling technique. Considering complex mixtures as a continuum considerably reduces the number of model parameters to the few parameters characterizing the solute distribution, and thus reduces the computational effort. The continuum modeling approach is first introduced in a general manner, and then applied to the modeling of three different chromatographic separations: polydisperse polymers by size exclusion chromatography, the mono-PEGylated lysozyme positional isomers by linear gradient elution on a strong cation-exchange media, and finally a mixture of polyclonal IgGs charge variants by IEC. The continuum model is shown to be well-suited for both isocratic and gradient elution chromatography modeling and very efficient when the number of solutes rises.