Minimizing nucleation

If primary nucleation occurs, the crystal size distribution (CSD) is usually quite small, often in the submicron to 50 micron range. Excessive nucleation yields too many small crystals and an unacceptable CSD. There is simply too much surface area competing for growth. Fortunately, most nuclei in an industrial crystallizer are of secondary origin.

In small vessels of around 50-100 gal., most secondary nuclei are due to crystal contact with the agitator and walls. As the vessel size increases, there are relatively more crystal-to-crystal collisions, due to the reduced surface area per unit volume.

Vessels with high slurry density (usually 25 percent solids or more) have nucleation due to crystal-to-crystal contact. For low slurry densities (usually
2%-5%), crystal-to-impeller contacts are the most important source of nuclei. It has been found that P/V is extremely important for both of these secondary sources of nucleation. Proper agitator design is required.

Primary nucleation

The circulation must be adequate to yield a supersaturation that will suppress primary nucleation by keeping all locations within the metastable zone and thereby avoiding the critical value, which will yield highly undesired primary nucleation and encrustations.

where S_max is the supersaturation and Q_c is the rate of circulation.

The required minimum circulation for the small-scale vessel can be estimated by varying the speed and observing the point of primary nucleation. For geometrically similar systems:

which qualitatively indicates equal speeds on scaleup if the small-scale unit is at the critical point. This results in high power requirements to avoid primary nucleation, which negatively impacts breakage and secondary nucleation. Thus, there is a likely choice between the possibility of primary nucleation and low secondary nucleation rates or having high levels of secondary nucleation and breakage while minimizing primary nucleation.

Secondary nucleation
Crystal-impeller

contacts have been shown to be the dominant mechanism for low slurry densities and small vessels. A qualitative model follows:

where B_ci is the nucleation rate and M_T is the slurry density.

For a given crystallizer where S_max is held constant, Q must be constant Therefore, ND³ is constant or N a D^-3. Thus,

The use of a large, slow speed impeller with a high N_Q relative to its N_P, such as a hydrofoil, can greatly reduce secondary nucleation.

Geometric similarity

When employing geometric similarity for scaleup, the following qualitative relationships are predicted for various strategies:

 

From Equation 6, the following relationships result for the chosen scaleup strategy.

Crystal-crystal impacts become controlling at high slurry densities and large scales. In such cases, it can be qualitatively shown that:

where B_CC is the nucleation rate and d_p is the particle size.

Again, this relationship emphasizes the need to minimize the P/V and, in particular, the N since:

 

Low shear, efficient hydrofoils will assist in this effort. Moderate increases in N can result in large increases in secondary nucleation. One can sometimes increase the particle size by increasing the slurry density above its natural make. This is due to the decrease in supersaturation resulting from the higher crystal surface area. However, the increased solids loading may produce more secondary nucleation.

Attrition and breakage

These phenomena may occur without supersaturation. Two general modes apply: collisional breakup and fluid mechanical breakup due to turbulent fluid flow. The efficiency of the breakage process is dictated by two opposing factors: the mechanical strength of the crystals and applied breaking forces.

The most important stresses are impact-induced stresses (e.g., crystal-crystal, crystal-wall and crystal-impeller) and fluid-induced stresses (e.g., shear stress, drag stress and pressure/normal stress). The results of these phenomena are often seen as shards and broken pieces in the crystal slurry.

Simulation and modeling

The Visimix [1] program can be helpful in analyzing the mixing parameters in a crystallization and precipitation vessel. It can be useful in investigating different scenarios for scaleup and changes in agitator and vessel configuration. The author has used this program for many systems and has found that the results often match. Table 2 presents the results for a geometric scaleup from 50 gal. to 6,250 gal. The baffled vessel was a dished head with a 45 Degrees pitched-blade turbine. A saturated aqueous mother liquor contains 15% suspended solids, and the average particle size is
125 m with the maximum size being 350 m.

 

Two cases were analyzed, the first being scaleup at constant P/V and the second being scaleup at constant tip speed, S_t.

When scaling up with a constant tip speed, as expected, the turbulence parameters predict a significant reduction in energy dissipation rates, turbulent shear rates and an increase in the microscale of turbulence. The turbulence values for scaleup at a constant P/V are quite close to each other.

The hydrodynamic values show the dramatic change in Reynolds number and mean circulation times.