#### Transcript Document

### Crystallisation (3 periods)

### References

1. Geankoplis, C. J., Transport Processes and Separation Process Principles, 4 th edition, Prentice Hall, New Jersey, 2003.

2. Badger, W. L. and Banchero, J. T., Introduction to Chemical Engineering, McGraw-Hill, Singapore, 1957.

3. McCabe, W. L., Smith, J. C. a;nd Harriott, P., Unit Operations of Chemical Engineering, 4 th edition, McGraw-Hills, Singapore, 1985.

4. Foust, A. S., Wenzel, L. A., Clump, C. W., Maus, L. and Andersen, L. B., Principles of Unit Operations, 2 nd edition, John Wiley & Sons, New York, 1980.

### Overview

• • • • • • • • •

**Equipment for crystallisation**

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**Systems with heat transfer (external cooling systems)**

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**Adiabatic systems (Vacuum systems) Equilibrium Solubility and Solubility Curves Enthalpy-Composition Diagrams/Enthalpy-Concentration Diagrams Material Balances in Crystallisation**

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**Calculation using equilibrium solubility or solubility curves**

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**Yield of Crystallisation Process Heat Balances in Crystallisation**

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**Heat evolved and removed from the system**

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**Calculation using enthalpy-composition diagrams Nucleation of Crystals Crystal Growth Particle-Size Distribution of Crystals Model for Mixed Suspension – Mixed Product Removal (MSMPR) Crystalliser**

### Equilibrium Solubility and Solubility Curves

### Material Balances in Crystallisation

• •

**Calculation using equilibrium solubility or solubility curves Yield of Crystallisation Process**

### Enthalpy-Composition Diagrams

### Example 1 (Geankoplis, p. 819)

• A salt solution weighing 10,000 kg with 30 wt% Na 2 CO 3 is cooled to 293 K (20 be the yield of Na 2 CO 3 .10H

2 solubility is 21.5 kg anhydrous Na 2 o C). The salt crystallises as the decahydrate. What will O crystals if the CO 3 /100 kg of total water? Do this for the following cases: (a) Assume that no water is evaporated.

(b) Assume that 3% of the total weight of the solution is lost by evaporation of water in cooling.

**Heat Balances in Crystallisation**

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**Heat evolved and removed from the system**

### Example 2 (Geankoplis, p. 821)

A feed solution of 2,268 kg at 327.6 K (54.4

o C) containing o 48.2 kg MgSO 4 /100 kg total water is cooled to 293.2 K (20 C), where MgSO 4 .7H

2 O crystals are removed. Calculate the yield of crystals and make a heat balance to determine the heat evolved and removed from the crystalliser, q, assuming that no water is vaporised. (Information : The solubility of the salt is 35.5 kg Mg MgSO 4 /100 kg total water. The average heat capacity of the feed solution can be assumed as 2.93 kJ/kg.K. The heat of solution (endothermic) at 291.2 K (18 o C) is 13.31x10

3 kJ/kg mol MgSO 4 .7H

2 O.)

### Example 3 (Badger & Banchero, p. 534)

• A crystalliser is to be used to produce 1 ton/hr of copperas (FeSO 4 .7H

2 O) crystals by the cooling of a saturated solution entering at 120 o F. The slurry leaving the crystalliser will be at 80 o F. Cooling water enters the crystalliser jacket at 60 o F and leaves at 70 Btu/(hr)(ft 2 )( o o F. It may be assumed that the over-all coefficient of heat transfer for the crystalliser is 35 F). Each 10-ft section of the crystalliser has 35 ft 2 . Average specific heat of initial solution = 0.70 Btu/(lb)( o F). Heat of solution of copperas at 18 o C = 4400 cal/gmol (endothermic).

– (a) Calculate the yield – (b) Estimate the cooling water required in gpm – (c) Determine the number of crystalliser sections to be used

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**Heat Balances in Crystallisation**

**Calculation using enthalpy-composition diagrams **

### Example 4

• Solve the problem in the Example 2 using enthalpy-composition diagram.

### Problems

• • • • 1. A solution consisting of 30% MgSO 4 and 70% H 2 kg of crystals are obtained per kg original mixture?

O is cooled to 60 o F.

During cooling, 5% of the total water in the system evaporates. How many 2. A 32.5% solution of MgSO 4 at 120 o F is cooled, without appreciable evaporation, to 70 o C in a batch water-cooled crystalliser. How much heat must be removed from the solution per ton of crystals?

3. One pound each of Na 2 SO 4 and H 2 O at 50 o F are mixed and allowed to reach equilibrium at atmospheric pressure. If the system is perfectly insulated so that equilibrium is reached with no gain or loss of enthalpy, what will be the temperature and phase condition of the product?

o 4. A single-stage, continuous, Krystal crystalliser is to be used to obtain CaCl 2 .4H

2 O product from a feed containing 40 wt% CaCl 2 in water at 180 F. The vacuum system on the crystalliser will give an equilibrium magma at 90 o F. (a) What range of heat input per pound of feed solution can be used to obtain a product containing only CaCl 2 .4H

2 O crystals?, (b) What would be the maximum yield of crystal in the product (pounds of CaCl 2 as crystal per pound of CaCl 2 in feed).