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This paper details the advancements made in the modeling of open column and packed bed pressure-flow. The theoretical description is a one-dimensional elasticity model. By accounting for the loss of intra-particle porosity through empiricism, and by systematically selecting the functional form of the elastic modulus from stress-strain data, this model can accurately predict several kinds of large-scale behavior from small-scale data: packed pressure-flow, open column pressure-flow, and critical velocity. The robustness of the model has been demonstrated for MabSelect, SP 650M, Butyl Sepharose 4 FF and several other agarose-based and polymethacrylate-based resins. The predicted critical velocities are on average within +/-5% of observations. A simple modification to the Blake-Kozeny permeability expression allows accurate prediction of packed bed pressure-flow explicitly from compression factor, packed bed height, and settled bed inter-particle porosity. The model provides limits on mobile phase velocity and on operating pressure-flow as a function of bed height, particle size, and resin rigidity, and allows exploration of commercial manufacturing scenarios to identify scalable process time and cycle number. |
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