CRYSTALLIZER DESIGN CALCULATION

Given Data

Solute                                                                   : A

Solvent                                                                 : B

Concentration of Solute                                 : 0.25 Kg of Solute/Kg of Solvent

Temperature                                                     : 50 to 20 ^OC

Maximum allowable growth rate (G)          : 3.0 µm/min

Product Crystal Size (L_p)                                : 2000 µm

Available Seed Size (L_s)                                  : 100 µm

Production Rate Crystal (P)                          : 500 Kg

Feed Concentration (C_o)                              :0.25 Kg A/Kg B

Feed Temperature (T_o)                                 : 50 ^OC

Density of Feed Solution (ρ_o)                      : 1.05 Kg/L

Density of Mother Liquor (ρ_f)                     : 1.05 Kg/L

Density of Solute Crystal (ρ_s)                      : 1.8 Kg/L

Desired final Temperature (T_f)                   : 20 ^OC

Determine:

1. Crystallizer Volume
2.  Quantity of Seeds to be added and temperature of Seeding
3. Batch time
4. Theoretical Yield
5.  Temperature-Time Profile

 

 

Seeds and Seeding:

Assume there is no secondary nucleation is present, the total number of seeds is the same as the total number of product crystals.

The seeds have to be added to a saturated if not supersaturated solution. The saturation temperature corresponding to a feed concentration of 0.25 Kg/Kg can be calculated to be 48^OC from the solubility relationship. It is therefore necessary to cool the feed from 50 ^OC to 48^OC, seed the crystallizer with 62.5 grams of 100 µm seeds, and follow the temperature profile as determines below.

The batch cycle time can be calculated from the Constant Crystal Growth (CCG) Model:

 Theoretical yield:

Temperature Profile:

The Temperature (T)-Time profile can be calculated are as follows:

 Note:

Batch Time = 0, the solution is at its saturation, corresponding to a concentration of 0.25Kg/Kg. This cooling curve is plotted in the accompanying graph, note the cooling rate is very slow initially, followed by a faster cooling rate towards the end of the cycle.

From a practical perspective, the initially slow cooling rate provides enough super-saturation to balance growth. Typically, this would help in producing a small number of larger crystals compared to the case when the cooling rate is initially high, in the latter case, the solution will tend to cross the metastable limit for the system, resulting in spontaneous nucleation. The above analysis suggests that natural exponential cooling is typically undesirable as it tends to cool faster initially due to the larger driving force, following by slower cooling towards the end of the batch. This generally would result in spontaneous nucleation and a large number of smaller particles. 

Summary of Crystallizer:

1.       Crystallizer Volume                                                                                     : 4053 Liters

2.       Quantity of Seeds to be added and temperature of Seeding           : 62.5 grams

3.       Batch time                                                                                                    : 633 min

4.       Theoretical Yield                                                                                         : 55.99%

5.       Temperature-Time Profile                                                                        :