Model-based design of gradient elution in liquid-liquid chromatography: Application to the separation of cannabinoids

Liquid-liquid chromatography (LLC) is a separation technique that utilizes a biphasic solvent system as the mobile and stationary phases. The components are separated solely due to their different distributions between the two liquid phases. Gradient change in the mobile phase composition during the chromatographic process is a powerful method for improving the resolution of separation or shortening the process time. Gradient elution readily applies to LLC with biphasic solvent systems in which the stationary phase composition remains nearly constant when the mobile phase composition changes. This work proposes a model-based approach to optimize gradients in LLC and circumvent tedious trial-and-error experiments. The solutes' distribution constant depends on the mobile phase composition. Thus, the distribution constants were described as a function of the content of one of the solvents (= modifier) in the mobile phase. The dispersive and mass-transfer effects in the tubing and the column are modeled with a stage model. Only a few experiments are required to determine the model parameters. After the validation of the model and its parameters, the model can be used for LLC gradient optimization. The proposed approach was demonstrated for a gradient LLC separation of a mixture of four cannabinoids. Two different gradient shapes, one-step and linear gradient, were considered. For a pre-selected minimal purity requirement, the gradient was optimized for maximum process efficiency, defined as the product of productivity and yield. An experiment conducted with the optimized gradient conditions was in good agreement with the simulation, showing the potential of the proposed method.