Modeling of solid layer growth at a constant speed in a binary melt crystallization process

Melt crystallization is an attractive separation method for the purification of organics at a large scale. Because the geometry of the rigid crystal lattice is peculiar to the particular substance, most crystallization processes form eutectic systems. The kinetics of crystallization limit the rate in which crystal growth can occur without the incorporation of undesired impurity. If the rate of heat transfer exceeds the mass transfer rate of the impurity, the impurity can solidify, contaminating the product. In practice, one would like to specify a crystallization rate and determine the temperature profile of the crystallizer wall that would achieve this rate. In this dissertation we combine analytic and numerical methods for predicting solid-layer growth from melt crystallization. First, we predict the wall temperature profile over time for achieving solid separation from the melt at a constant rate. Second, we predict the rate of crystallization (or solid formation) when the wall temperature is held constant at a certain value equal to the lowest temperature that is operationally feasible. Third, we predict the temperature distribution in each of the solid and liquid phases. By considering a temperature distribution in the solid phase and holding the liquid phase\u27s temperature constant in the radial direction, an analytic model was developed by using dimensional analysis. This model was then extended numerically to account for a temperature distribution in each of the phases, liquid and solid. Applications of the two models were demonstrated with an example involving crystallization of para-dichlorobenzene from the ortho-dichlorobenzene and para-dichlorobenzene binary melt. Results from both models were analyzed and compared. Results showed that a lower initial concentration required a higher cooling rate of the crystallizer wall in order to maintain the same crystallization rate. Hence, less time was needed to reach the wall temperature operation constraint, thus leading to less solid layer growth. By comparing the results of the two models, one can conclude that the numeric model is preferred, since more crystal growth will occur under the same conditions as for the analytic model