Nonlinear liquid-liquid chromatography: A comprehensive modeling approach

In liquid-liquid chromatography (LLC), components of a mixture are separated due to their different distribution between the phases of a biphasic liquid system composed of two or more solvents. In this work, for the first time, we combine a chromatography model with a liquid-liquid equilibria thermodynamic model to simulate the propagation of the solute and the solvents along the LLC column. The model was demonstrated with the n-hexane/methanol/water/cannabidiol-system, where the first three components are used to prepare the mobile and stationary phase, and cannabidiol (CBD) is the solute. The liquid-liquid equilibria (LLE) were modeled using the NonRandom Two-Liquid (NRTL) model, whose parameters were fitted to the LLE data of the quaternary system measured in this work with an RMSE of 1.0 % between the experimental and predicted LLE data. Additionally, an overflow term was included in the mass balance equations to account for restrictions in the maximum retained stationary phase volume in the LLC column and simulate possible stationary phase transfer through and out of the column. For most simulations, a good agreement between the experimental and predicted elution profiles of pulse injection experiments with different CBD concentrations was obtained, with deviations in the predicted and experimental elution times below 3 min. The presented model, even though experimentally and computationally intensive, is a first step to a more rigorous modeling of LLC and describes the LLC operation where solute distribution between the mobile and stationary phases can no longer be regarded as independent of the solute concentration in the column.