Equilibrium Model of a Continuous Crystallization Process for Separation of Substances Exhibiting Solid Solutions

Three general types of phase diagrams characterizing solid-liquid equilibria are relevant for solution crystallization: simple eutectic, intermediate compound-forming, and solid solution systems. Among these, a system capable to form solid solutions is very difficult to separate into its pure components. However, gradual fractional crystallization of two-component solid solutions in a solvent is of large interest for the production of highly purified substances. A few publications suggest separation opportunities based on exploiting a cascade of batch crystallizers. A model-based description of such a process by means of ternary phase diagrams is complicated. Due to the Gibbs phase rule there remains one degree of freedom in the region below the solubility curve, when temperature and pressure are fixed. This implies that the conodes, connecting one solid and one liquid state, do not converge into a pure component corner of the phase diagram. In this case, the specific courses of the conodes have to be determined experimentally. A simple empirical description of a phase diagram involving solid solutions is introduced and illustrated. Subsequently, a multistage crystallization process will be explained and modeled, based on the phase diagrams and the relevant mass balances.