CRYSTALLIZATIONCRYSTALLIZATION

CRYSTALLIZATIONCRYSTALLIZATION

a process where solid particles are formed a process where solid particles are formed from a homogeneous phasefrom a homogeneous phase

a solid-liquid separation processa solid-liquid separation process

for control:for control:– yield of crystalsyield of crystals– purity of crystalspurity of crystals– sizes and shapes of crystalssizes and shapes of crystals

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

Common methods to achieve supersaturationCommon methods to achieve supersaturation

Cooling (with some exceptions)Cooling (with some exceptions)– achieved near a heat-transfer surfaceachieved near a heat-transfer surface

Solvent evaporationSolvent evaporation– achieved near a heat-transfer surfaceachieved near a heat-transfer surface

DrowningDrowning– addition of nonsolvent, which decreases the solubility addition of nonsolvent, which decreases the solubility

of the solidof the solid

Chemical reactionChemical reaction– decreases the solubility of the dissolved solvent, decreases the solubility of the dissolved solvent,

leading to supersaturationleading to supersaturation

Progression of crystallization

EQUILIBRIUM SOLUBILITY CURVES FOR EQUILIBRIUM SOLUBILITY CURVES FOR CRYSTALLIZATIONCRYSTALLIZATION

Fig. 18-56 (Perry’s CHE Handbook, 7th Ed.) – Solubility of MgSOFig. 18-56 (Perry’s CHE Handbook, 7th Ed.) – Solubility of MgSO44xH2O in xH2O in water at 1 atmwater at 1 atm

Fig. 12.11-1 (Geankoplis, 4th Ed.) – Solubility of NaFig. 12.11-1 (Geankoplis, 4th Ed.) – Solubility of Na22SS22OO33 in water at 1 atm in water at 1 atm

Fig. 19.27 (Foust et al., 2nd Ed.) – Solubility of NaFig. 19.27 (Foust et al., 2nd Ed.) – Solubility of Na22SOSO44 in water at 1atm in water at 1atm

Fig. 19.28 (Foust et al., 2nd Ed.) – Enthalpy-concentration diagram for the Fig. 19.28 (Foust et al., 2nd Ed.) – Enthalpy-concentration diagram for the NaNa22SOSO44 - H - H22O system at 1 atmO system at 1 atm

Fig. 19.29 (Foust et al., 2nd Ed.) – Enthalpy concentration diagram for the Fig. 19.29 (Foust et al., 2nd Ed.) – Enthalpy concentration diagram for the CaClCaCl22 - H - H22O system at 1 atmO system at 1 atm

Solubilities of several solids

MATERIAL BALANCES: YIELD OF CRYSTALS

10,000 KG

30% Na2CO3

T = 293 K

C

Na2CO310H2O

SSaturated solution

Solubility :21.5 kg Na2CO3 / 100 kg H2O

S'M

MMCVx1F

M

MC

FFx

h

ahF

h

a

SCVMVF

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 Balance

Total 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, TL

HV = total enthalpy of the vapor HC = total heat of crystallization

= positive if crystallization is exothermic= evaluated as the negative of the heat of solution

VLCF HHqHH

HEAT BALANCE (Vacuum Operation)

CLFV HHHVλ

V = latent heat of vaporization of the solvent

HF – HL = sensible heat drop

Classification of Crystallization EquipmentClassification of Crystallization Equipment

According to mode of operationAccording to mode of operation– BatchBatch– ContinuousContinuous

According to method by which supersaturation According to method by which supersaturation is achievedis achieved– Crystallizers that obtain precipitation by cooling a Crystallizers that obtain precipitation by cooling a

concentrated, hot solutionconcentrated, hot solutionAgitated batch crystallizersAgitated batch crystallizers

Swenson-Walker crystallizersSwenson-Walker crystallizers

– Crystallizers that obtain precipitation by evaporating a Crystallizers that obtain precipitation by evaporating a solutionsolution

Salting out evaporatorsSalting out evaporators

Draft-tube evaporatorsDraft-tube evaporators

Oslo crystallizers Oslo crystallizers (e.g., ‘Krystal’ crystallizer for ammonium sulfate (e.g., ‘Krystal’ crystallizer for ammonium sulfate production)production)

– Crystallizers that obtain precipitation by adiabatic Crystallizers that obtain precipitation by adiabatic evaporation and coolingevaporation and cooling

Vacuum crystallizersVacuum crystallizers

TANK CRYSTALLIZERS

•Hot, 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 CRYSTALLIZERS

•An 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-CRYSTALLIZER

•combines 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 CRYSTALLIZER

•The 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 DesignCrystallizer Design

CRYSTAL SIZE DISTRIBUTIONCRYSTAL SIZE DISTRIBUTION

Crystallization is operated to maximize crystal Crystallization is operated to maximize crystal growth and restrict nucleation.growth and restrict nucleation.

Product CSD is based on kinetics and nucleation Product CSD is based on kinetics and nucleation growth of crystals. growth of crystals.

If it is assumed that nucleation does not occur If it is assumed that nucleation does not occur and that the initial CSD is not known, a rough and that the initial CSD is not known, a rough estimation of CSD can be calculated. estimation of CSD can be calculated.

The McCabe The McCabe L lawL law is commonly used to is commonly used to calculate the final CSD if initial CSD in known.calculate the final CSD if initial CSD in known.

The The L LawL LawIf all crystals in magma grow in a uniform If all crystals in magma grow in a uniform supersaturation field and at the same temperature supersaturation field and at the same temperature and if all crystals grow from birth at the rate and if all crystals grow from birth at the rate governed by the supersaturation, then all crystals governed by the supersaturation, then all crystals are not only invariant but also have the same are not only invariant but also have the same growth rate that is independent of size.growth rate that is independent of size.

L = GL = Gtt G G ≠≠ f(L) : growth rate f(L) : growth rate

t : timet : time

Calculation of CSD for a seeded crystallizer

ΔLLL SP

LP = 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)

3S3PP ΔLLρρL'm

3SS ρL'm

Combining:3

SSP L

ΔL1mm

’ = shape factor (different from the usual shape factor)

= particle density

For the entire crystal mass:

SP m

0

Ps

3

S

m

0

P mdmL

ΔL1dm

MSMPRMSMPR

MSMPR or MSMPR or MIXED-SUSPENSION MIXED-PRODUCT REMOVAL MIXED-SUSPENSION MIXED-PRODUCT REMOVAL MODELMODEL

– An idealized crystallizer model, which is a basis An idealized crystallizer model, which is a basis for identifying the kinetic parameters and for identifying the kinetic parameters and showing how knowledge of them can be applied showing how knowledge of them can be applied to calculate the performance of such crystallizer.to calculate the performance of such crystallizer.

MSMPR AssumptionsMSMPR Assumptions

Steady-stateSteady-stateCrystallizer contains a mixed-suspension magma at all Crystallizer contains a mixed-suspension magma at all times, with no product classificationtimes, with no product classificationUniform supersaturation exists throughout the magma at Uniform supersaturation exists throughout the magma at all timesall timesL law of crystal growth appliesL law of crystal growth appliesNo size-classified withdrawal systemNo size-classified withdrawal systemNo crystals in the feedNo crystals in the feedMother liquor in the product magma is saturated Mother liquor in the product magma is saturated (equilibrium)(equilibrium)No crystal breakage into finite particle sizeNo crystal breakage into finite particle size

CRYSTAL POPULATION-DENSITY FUNCTIONCRYSTAL POPULATION-DENSITY FUNCTION

ΔL

ΔN

dL

dNn

ndL

dNN

L

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.

V

ΔtQ

ΔLn

ΔLΔn

VG

ΔLQ

n

Δn

Recall the L law (i.e., L = G t). If G is in mm/h:

As both L and n approach 0, and integrating,

L

0

n

n

dLGτ

1

n

dn

0

Gτ

Lexpnn 0

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.

A solute that forms cubic crystals is to be precipitated from solution at a rate of 10,000 lb/h of solid (dry basis) using 1,000 lb/h of seed crystals. If no nucleation occurs and the seed crystals have the following size distribution, determine the product size distribution.

Tyler sieve mesh weight fraction retained

-48+65 0.10

-65+100 0.30

-100+150 0.50

-150+200 0.05

-200+270 0.05