Mathematical Modeling and Design of a Cooling Crystallizer Incorporating Experimental Data for Crystallization Kinetics

Abstract

Crystallization is one of the approximately twenty unit operations and is considered to be among the most important due to the large number of chemical compounds it produces, as well as due to the enormous quantities of these substances being manufactured around the world. This article aims to present a mathematical model for the shortcut design of a cooling crystallization unit consisting of the crystallizer and auxiliary equipment, such as an evaporator with its preheater and condenser, a heat pump that acts as the cooling system of the crystallizer, and a crystallizer pressure regulator modeled as an expansion valve. The model estimates an extensive series of variables, including mass and volume flow rates of the streams, heat duties of each piece of equipment, sizing variables such as heat transfer areas of heat exchangers and volumes of the vessels, and product flow rates for each specific feed. It embraces equations for the calculation of a series of stream properties, such as density, specific heat capacity, and latent heat of vaporization. For the sizing of the crystallizer, which is the main equipment of the unit, both flow rates and crystallization kinetics are taken into account. The latter is estimated by experimental data taken in a laboratory crystallizer and includes the crystal’s growth rate as a function of residence time.