Zonal rate model for stacked membrane chromatography. I: Characterizing solute dispersion under flow-through conditions

Conventional models of both packed-bed and stacked-membrane chromatography typically attribute elution band broadening to non-idealities within the column. However, when the column length to diameter ratio is greatly reduced, as in stacked-membrane chromatography, variations in solute residence times within the feed-distribution (inlet) and eluent-collection (outlet) manifolds can also contribute to band broadening. We report on a new zonal rate model (ZRM) for stacked-membrane chromatography that improves on existing hold-up volume models that rely on one plug-flow reactor and one stirred-tank reactor in series to describe dispersion of solute during transport into and out of the column. The ZRM radially partitions the membrane stack and the hold-up volumes within the inlet and outlet manifolds into zones to better capture non-uniform flow distribution effects associated with the large column diameter to height ratio. Breakthrough curves from a scaled-down anion-exchange membrane chromatography module using ovalbumin as a model protein were collected at flow rates ranging from 1.5 to 20 mL min−1 under non-binding conditions and used to evaluate the ZRM as well as previous models. The ZRM was shown to be significantly more accurate in describing protein dispersion and breakthrough. The model was then used to decompose breakthrough data, where it was found that variations in solute residence time distributions within the inlet and outlet manifolds make the dominant contribution to solute dispersion over the recommended range of feed flow rates. The ZRM therefore identifies manifold design as a critical contributor to separation quality within stacked-membrane chromatography units.