Modelling binary non-linear chromatography using discrete equilibrium data

The determination and description of adsorption equilibria is critical for the design of several separation processes. In some instances, the dependence of the solid phase loading on the fluid phase concentration is complex and it is difficult to find a suitable functional form to represent the adsorption equilibria. This difficulty can be overcome by the use of discrete equilibrium data, i.e., using the experimental data of solid phase loadings and the corresponding fluid phase concentrations in its discrete form, without the use of a functional form to describe the adsorption isotherms. In this work we demonstrate how discrete equilibrium data can be used to predict binary competitive equilibria using the ideal adsorbed solution theory. Two approximations to generate data outside the range of measured values are proposed. The effectiveness of these methods in predicting competitive equilibria and elution profile of binary injections is demonstrated using numerical simulations. The application of this framework to estimate the regions of achievable separation for a multi-column simulated moving bed chromatographic separation is also discussed.