Generic crystallizer model: 1. A model framework for a well-mixed compartment

A model framework is described for crystallization of a single solid species in a well-mixed compartment at steady state. The model framework applies to both Type I (that is, nonhigh yield) crystallization and Type II (high yield) crystallization. The framework consists of population balances incorporating nucleation, growth, aggregation, breakage, classification, and dissolution, coupled with mass and energy balances. The model allows any number of product streams, any number of feed streams, one vapor product stream, nonrepresentative sampling, but only one solid species. The numerical strategy used to solve the resulting set of nonlinear integro-differential equations transforms them into a matrix of algebraic equations. Two algorithms for the solution for Type I crystallization are proposed, both of which consist of solving the material and energy balances sequentially with the population balance and iterating around only one variable. Both algorithms use an existing material and energy balance solution package, which is linked to the population balance equations. The first solution algorithm solves the population balance equations using a Newton-Raphson solver with finite-difference approximations for the derivatives, converging around a variable related to the crystal mass and the number density for each interval. The second algorithm solves the population balance equations using a successive substitution technique with root bracketing and iterates around the suspension density. The choice of algorithm depends on the nature of the system to be modeled. A similar framework is suggested for the solution for Type H crystallization, except that the iteration variable is the growth rate at a fixed supersaturation ratio. (c) 2005 American Institute of Chemical Engineers.