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.
where Smax is the supersaturation and Qc 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.
where Bci is the nucleation rate and MT is the slurry density.
For a given crystallizer where Smax 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 NQ relative to its NP, such as a hydrofoil, can greatly reduce secondary nucleation.
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 BCC is the nucleation rate and dp 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
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
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, St.
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.