Why this chapter is important

As crystallization is concerned with the phase change in solid–liquid systems, analysis of crystallization processes starts with consideration of phase diagrams. In this chapter we will show how phase diagrams help to select a crystallization method, and to determine the yield and the temperature of a crystallization process. The industrially relevant features of the main crystallization methods are also presented.

We next consider the state of the liquid phase during crystallization processes. The solution is said to be supersaturated with respect to the crystallizing compound, meaning the solute concentration is higher than the solid–liquid equilibrium value. The degree of supersaturation is important because it is the driving force for the elementary rate processes of crystallization, such as nucleation and crystal growth. Therefore, expressions to determine the degree of supersaturation are presented, both rigorous expressions based on thermodynamics and less rigorous expressions commonly found in practice.

In order to calculate the degree of supersaturation, thermodynamic models that provide the activity coefficients of the solute are required. The main models available are compared, so that the most suitable model may be chosen, depending on the accuracy, the ease of obtaining model experimental parameters and the types of building units (simple organic molecules, biomolecules, electrolytes, etc.).

Phase diagrams

Phase diagrams display all the possible thermodynamic states of a system: the proportion and the composition of each coexisting phase. The thermodynamic states are described by a set of independently fixed variables, such as the pressure, the temperature and the mass fractions of all components but one (since the sum of the mass fractions of all components must be unity). For a binary system at constant pressure, the phase diagram may be represented by a two-dimensional T–x plot, where T is the system temperature and x is the mass fraction of one of the components, as exemplified for the silver nitrate–water system at atmospheric pressure in Figure 1.1.

Why this chapter is important

There are a number of situations where batch operation is chosen instead of continuous operation (see Chapter 3). Batch processing is more economical for small production capacities of approximately 1 m3 of product per day or less, for processing of expensive materials (because product offspec losses are low) such as pharmaceuticals, as well as for processing batches of different materials in the same industrial unit. Batch crystallization is also chosen for processing of compounds that form encrustations on the crystallizer walls, because the encrustations can be washed off after each batch cycle. The major advantage of batch crystallization is the ability to produce uniformly sized particles.

Seeding is an important tool to control the product size, so the seeding technique will be treated in detail. Batch crystallization can be quantitatively described by means of population balances coupled with mass and energy balances as well as with kinetic expressions for the elementary processes. These mathematical models can be used to help understand batch processes, as well as to develop operational policies (temperature, evaporation and reactant addition trajectories throughout a batch process) aiming at improved product quality, low cost, and low raw material and energy usage.

Phenomenological description of batch crystallization processes

A batch cycle starts with a solution that is slightly undersaturated with respect to the solute to be crystallized. Crystallization is achieved by any of the methods described in Chapter 1, i.e., cooling, solvent evaporation, anti-solvent addition or chemical reaction (precipitation). Usually seeds of the crystallizing material are added early in the batch process in order to improve reproducibility and product quality. When the desired amount of solid has been formed, the slurry is transferred to a solid–liquid separation unit. The crystallizer is then washed, and fresh solution is added and brought to the desired temperature to start a new batch cycle.

The main elementary processes taking place during batch crystallization are described next. Cooling crystallization will be treated here, but the analysis can equally well be applied to evaporative crystallization.