CRYSTALLIZATIONa process where solid particles are formed from a homogeneous phasea solid-liquid separation processfor control:yield of crystalspurity of crystalssizes and shapes of crystals

A crystal is a highly organized array of atoms, molecules, or ions arranged in three-dimensional space lattices.

Common methods of reaching supersaturationCooling (with some exceptions)achieved near a heat-transfer surfaceSolvent evaporationachieved near a heat-transfer surfaceDrowningAddition of nonsolvent, which decreases the solubility of the solid.Chemical reactionDecreases the solubility of the dissolved solvent, leading to supersaturation

Progression of crystallization

EQUILIBRIUM SOLUBILITY CURVES FOR CRYSTALLIZATIONFig. 18-56 (Perrys CHE Handbook, 7th Ed.) Solubility of MgSO4xH2O in water at 1 atmFig. 12.11-1 (Geankoplis, 4th Ed.) Solubility of Na2S2O3 in water at 1 atmFig. 19.27 (Foust et al., 2nd Ed.) Solubility of Na2SO4 in water at 1atmFig. 19.28 (Foust et al., 2nd Ed.) Enthalpy-concentration diagram for the Na2SO4 - H2O system at 1 atmFig. 19.29 (Foust et al., 2nd Ed.) Enthalpy concentration diagram for the CaCl2 - H2O system at 1 atm

Solubilities of several solids

MATERIAL BALANCES: YIELD OF CRYSTALS10,000 KG30% Na2CO3T = 293 KC Na2CO310H2O

SConcentrated solutionSolubility :21.5 kg Na2CO3 / 100 kg H2O

C= mass of crystals in the product magma per unit timeMa = molecular weight of anhydrous salt or crystalMh= molecular weight of hydrated crystalxF= mass fraction of anhydrous solute in feedS= solubility of the anhydrous solute at product temperature= expressed as a weight ratio of anhydrous salt to solventF= total mass of feed solution per unit timeV= evaporation rate in mass of solvent per unit timeS= mass of saturated solution produced per unit timeM= total mass of product magma produced per unit time= mass of crystals formed + saturated solution Solute BalanceTotal Balance

HEAT BALANCE:q= total heat absorbed in the crystallization/evaporation processHF= total enthalpy of entering solution at TF, which is read off enthalpy-concentration diagramHM= total enthalpy of the crystals and saturated solution in the product magma at the final temperature, TLHV= total enthalpy of the vapor HC= total heat of crystallization = positive if crystallization is exothermic= evaluated as the negative of the heat of solution

HEAT BALANCE (Vacuum Operation)V= latent heat of vaporization of the solvent

HF HL= sensible heat drop

Classification of Crystallization EquipmentAccording to mode of operationBatchContinuous

According to method by which supersaturation is achievedCrystallizers that obtain precipitation by cooling a concentrated, hot solutionAgitated batch crystallizersSwenson-Walker crystallizersCrystallizers that obtain precipitation by evaporating a solutionSalting out evaporatorsDraft-tube evaporatorsOslo crystallizers (e.g., Krystal crystallizer for ammonium sulfate production)Crystallizers that obtain precipitation by adiabatic evaporation and coolingVacuum crystallizers

TANK CRYSTALLIZERSHot, saturated solutions are allowed to cool in open tanks. After crystallization, the mother liquor is drained and the crystals are collected. Controlling nucleation and the size of the crystals is difficult. The crystallization is essentially just "allowed to happen". Heat transfer coils and agitation can be used. Labor costs are high, thus this type of crystallization is typically used only in the fine chemical or pharmaceutical industries where the product value and preservation can justify the high operating costs.

SCRAPED-SURFACE CRYSTALLIZERSAn example may be the Swenson-Walker crystallizer consisting of a trough about 2 feet wide with a semi-circular bottom. The outside is jacketed with cooling coils and an agitator blade gently passes close to the trough wall removing crystals that grow on the vessel wall.

FORCED CIRCULATING LIQUID EVAPORATOR-CRYSTALLIZERcombines crystallization and evaporation, thus the driving forces toward supersaturation

The heated liquid flows into the vapor space of the crystallization vessel. Flash evaporation occurs, reducing the amount of solvent in the solution, thus driving the mother liquor towards supersaturation. The supersaturated liquor flows down through a tube, then up through a fluidized area of crystals and liquor where crystallization takes place via secondary nucleation. Larger product crystals are withdrawn while the liquor is recycled, mixed with the feed, and reheated. FORCED CIRCULATING LIQUID EVAPORATOR- CRYSTALLIZER

CIRCULATING MAGMA VACUUM CRYSTALLIZERThe crystal/solution mixture (magma) is circulated out of the vessel body. The magma is heated gently and mixed back into the vessel. A vacuum in the vapor space causes boiling at the surface of the liquid.

CIRCULATING MAGMA VACUUM CRYSTALLIZER

Crystallizer Design

CRYSTAL SIZE DISTRIBUTIONCrystallization is operated to maximize crystal growth and restrict nucleation.Product CSD is based on kinetics and nucleation growth of crystals. If it is assumed that nucleation does not occur and that the initial CSD is not known, a rough estimation of CSD can be calculated. The McCabe L law is commonly used to calculate the final CSD if initial CSD in known.

The L LawIf all crystals in magma grow in a uniform supersaturation field and at the same temperature and if all crystals grow from birth at the rate governed by the supersaturation, then all crystals are not only invariant but also have the same growth rate that is independent of size.L = Gt G f(L) : growth ratet : time

Calculation of CSD for a seeded crystallizerLP= characteristic crystal product dimensionLS= characteristic crystal seed dimensionL= change in dimension; constant throughout the range of sizes present

Relationship between seed mass (mS) and product mass (mP)Combining:= shape factor (different from the usual shape factor)= particle density

For the entire crystal mass:

MSMPRMSMPR or MIXED-SUSPENSION MIXED-PRODUCT REMOVAL MODELAn idealized crystallizer model, which is a basis for identifying the kinetic parameters and showing how knowledge of them can be applied to calculate the performance of such crystallizer.

MSMPR AssumptionsSteady-stateCrystallizer contains a mixed-suspension magma at all times, with no product classificationUniform supersaturation exists throughout the magma at all timesL law of crystal growth appliesNo size-classified withdrawal systemNo crystals in the feedMother liquor in the product magma is saturated (equilibrium)No crystal breakage into finite particle size

CRYSTAL POPULATION-DENSITY FUNCTIONLN

Assumptions: In t time, nL crystals are withdrawn.The effluent composition in the outflow is Q L/h, which is the same as that in the crystallizer of volume V.Recall the L law (equation 5). If G is in mm/h:As both L and n approach 0, and integrating,where = V/Q, which is the total retention time or holding time (in hours) in the crystallizer, and n0 is the population of nuclei when L = 0.

A solution of 500 kg of Na2SO4 in 2500 kg of water is cooled from 333 to 283 K in an agitated mild steel vessel of mass 750 kg, the specific heat of steel being 0.5 kJ/kg-K. At 283 K the stable crystalline phase Na2SO410H2O and at 291 K the heat of solution is -78.5 MJ/kgmol. The mean heat capacity of the solution is 3.6 kJ/kg-K. If, during cooling, 2% by mass of the water is lost by evaporation, estimate the yield of crystals formed and the heat to be removed. The solubility of the anhydrous salt at 283 K is 8.9 kg/100 kg water.