Systematic design of supersaturation controlled crystallization processes for shaping the crystal size distribution

The paper presents a novel methodology for the systematic design of the setpoint operating curves for supersaturation controlled crystallization processes, which produce a desired target crystal size distribution (CSD). The population balance model is solved using the method of characteristics under the assumptions of constant supersaturation and growth dominated process, yielding a simplified analytical expression for the size distribution. A design parameter for supersaturation controlled processes is introduced as a function of the supersaturation and time. Based on the design parameter and the simplified analytical model, the supersaturation setpoint and batch time are determined using an optimization approach to obtain a target distribution with a desired shape. A methodology is also described, which can be used to obtain the temperature profiles in the time domain, corresponding to a desired target CSD, providing a systematic direct design approach for practical applications and scale-up. Additionally, a method for designing the seed distribution is proposed, which can be used in conjunction with the supersaturation setpoint design, for shaping the product CSD. The proposed methods are exemplified for the model system of potash alum in water, for which the size dependent growth kinetic parameters have been identified based on industrial experimental data.