Crystallization of monohydrate citric acid. 2. Modeling through population balance equations

Experimental data about both the liquid and the solid phases during seeded batch crystallizations of citric acid (CA) in water were obtained using in situ Raman spectroscopy and image acquisition. These experimental results were reported in a previous paper in this issue (Caillet, A., et al. Cryst. Growth Des. 2007, 7, 2080-2087). The present paper is now focused on the mathematical modeling of the desupersaturation process during the crystallization of monohydrate citric acid (MCA), which is the stable form at 15 degrees C. Both the crystallization of MCA (monohydrate) and the dissolution of the anhydrous (ACA) form were investigated. The model is based upon population balance equations (PBEs) describing the evolution of the crystal size distribution (CSD) during batch seeded operations. The estimation of the kinetic parameters of MCA nucleation and growth, and of the dissolution of ACA, was performed using nonlinear optimization techniques. For various operating conditions (modifications of the initial supersaturation and of the seed amount), the two PBE models represent satisfactorily the experimental behavior of the process. In particular, activated secondary nucleation is shown to explain particular features of the solute/solvent system that were observed previously.