FUNDAMENTALS OF INDUSTRIAL CRYSTALLIZATION AN OVERVIEW Michel COURNIL, Department of Chemical...

FUNDAMENTALS OF INDUSTRIAL

CRYSTALLIZATION

AN OVERVIEWMichel COURNIL, Department of Chemical Engineering (Centre SPIN), Ecole des Mines de Saint-Etienne (France)

[email protected] www.emse.fr

TU Wien 18. January 2002

Definition : "Crystallization" is a sequence of physical operations which allow to obtain in the form of a crystalline solid one or several substances initially contained in a liquid or gaseous phase

Crystallization is one of the oldest unit operations of thermal separation used to prepare or concentrate a substance in the solid state

Preliminary step of crystallization process : = preparation of a supersaturated solution (= which contains "too much" dissolved solid)

Crystallization precipitation (involves chemical steps)

Industrial crystallization

Introduction

Solvent elimination Shift of the equilibrium sokid-liquid equilibrium via temperature variation

Two ways for this….


Introduction

Many physical, chemical, mechanical and rheological properties of solid materials depend on the grain size and shape

Diversity of shape and size….

examples : pigments for paintings (TiO2), catalysts, pharmaceuticals,

food products, materials for electronics,...


Introduction

The particle size distribution and the particle shape of a solid product are essential criteria for its commercial quality

To this aim, it is necessary to define and perform :the necessary physico-chemical transformations, the reactor type the operating conditions

Meeting these industrial specifications is the objective of industrial crystallization

Equilibrium conditionsSystem one grain (or crystal) + liquid solution

C = Cs(T)

T : temperatureC : solute concentration in solution Cs : saturation concentration solubility

C > Cs : supersaturated solution : crystal nucleation and growth C < Cs : non saturated solution : crystal dissolution


A few fundamental aspects

s

s

CCC - Relative

supersaturation

Equilibrium conditions (continued)

Cs(T) generally increases with temperature

Principle of "cooling crystallization" : purely thermal transition from an undersaturation state (T1) to a supersaturation state (T2)

C

T

> 0 < 0

T2 T1

Temperature (°C)Solu

bilit

y (k

g of

sol

ute/

kg o

f sol

vant

)



Cristallography (notions)

A crystal = regular sequence of ions, atoms or molecules

The different crystalline systems (minimum energy)

In practice : many deviations from the theoretical shapes :

kinetic effects, instability, impurities, agglomeration-fragmentation,….

Differential growth of the crystal faces

Instability developmentAgglomeration-fragmentation



Interfacial roughness notionCharacteristics of a crystal face at the atomic scale

smooth rough

Approach via statistical physics : energetic interactions between "first neighbours"

ss interaction :

sl interaction :

ll interaction :

Importance of "entropic factor" :

kTllsssl --2

Industrial crystallizationA few fundamental aspects (crystallography-continued)

Interfacial roughness (notion- continued)

Statistical simulations (Monte-Carlo method)

Principle : construction/destruction of the crystal interface by discrete random events the probability of which depends on the interactions between close neighbours (P1, P2, P3) P1

P2P3

Results : < 3 : rough interface> 4 : smooth interface


From works of Gilmer et Bennema)

Interfacial roughness (simulation examples)


The faces of a real crystal can be of different roughness type

Interfacial roughness (continued)


A sample of granular solid = a huge number of grains of different shape and size

Assumption : one size parameter – " mean " diameter D – of a crystal is characteristic of all its properties

The crystal population is described by function f(D) population density : f(D).dD is the crystal number per unit volume the diameter of which ranges between D and D + dD

Large variety in particle size distribution ; for monomodal distributions, simple laws with two parameters are used : mean diameter and standard deviation (dispersion)

Industrial crystallizationA few fundamental aspects

Particle size distribution

Shape of classical laws of size distribution

Different representations of the population size distribution

By number, by weight or volume :

f(D).D3.dD, by surface area : f(D).D2.dD

Log-normal

normal

f(D)

D


Particle size distribution (continued)

Overview of the different methods of particle sizingThey depend on the sizing operating mode : off-line, on line or in situ and on the size domain of the crystalsOff-line : sieving, settling, image analysis,…On line : optical methods (light scattering), visualizationIn situ : a few of the previous methods

Size range :


Particle size distribution (continued)

0.001 0.01 1010.1 100001000100 D in m

SievingSettling

Microscopy

Laser beam scattering

Light scattering

Industrial crystallizationThe different steps of the crystallization process

Nucleation : crystal creation from a supersaturated solution

Crystal growth : increase of the crystal size up to the desired size by growth from supersaturated solution

Dissolution : in non-saturated solution

Ostwald ripening : slow ageing (size evolution with time) of a crystal population in the vicinity of the saturationn

Agglomeration : formation of crystal clusters linked by crystalline bridges (in supersaturated solution)

NucleationThe first step of the crystallization process : crystal birth

Decisive influence on the crystal number and size (given mass quantity to be crystallized)

Several mechanisms of new crystal (nuclei) production : - in the absence of crystals ("clear" solution) : primary nucleation

- in the presence of crystals : secondary nucleation

A transition step : the least understood crystallization tep

The crystallization step is the most difficult to characterize experimentally : small nuclei, ill-known structure, widely non reproducible process, intimately linked to growth


Primary nucleation

A few experimental aspects…

- existence of an induction period (delay) at average supersaturation level and a metastability zone (no nucleation) at low supersaturation level

T

CMetastability

zone

- the supersaturated media contain aggregates (clusters) of solute (2 to several hundreds of units in each cluster)

Experimental evidence : spectroscopy, « anomalies » in the diffusivity values,…

Supersaturation ()

2

1

0Gly

cin

e d

iffu

sivi

ty


Kinetic models of homogeneous primary nucleationAi + A1 Ai+1 (Ri) (i 1)

A1 is a single atom (solute monomer), Ai aggregate of i atoms

Ri two opposite reactions

Ai + A1 Ai+1 (Fi)

Ai+1 Ai + A1(Bi+1)

Vfi = fi Ci

Vbi = bi+1Ci+1

transformation rate of Ai to Ai+1 : Ji = fiCi - bi+1Ci+1

i1-i -dtd JJCi mass balance of Ai

Primary nucleation


constant fi et bi+1 determination

kinetic theory of gases fi = si (i > 1) C1 si = s1 i2/3

no model to calculate bi+1 however at equilibrium : Ji = 0 for all i

eiei

e1+ie

1+i = CfCb e1+i

ei

ei

e1+i =

C

Cfb eie

ie

1+ie1+i = CfCbas

e

1+i

1+ii

ei

ei

ieiii =

CC

ff

CCCfJ

Problem of calculation of the equilibrium concentrations….

Primary nucleation


Kinetic models of homogeneous primary nucleation (continued)

Problem of calculation of the equilibrium concentrations …. iA1 = Ai

e =i -i

1i TRG xx

R iR sxiRTG si ln with 321

1 exp : hence isCCC

i

s

eei

xi minimum and Gi maximum for :

)ln( 32

3 * S

Θi

1s

T

R sx

xS 1 =

(critical nucleus)

e =i -

i TRG x

isSiRTG ln with i

Gi

ii*

xi

Primary nucleation



Back to the nucleation rate calculation…J

s C S=

C

C S

C

C S

i

i i ie ' i

i

ie ' i

i+1

i+1e 'i+1

Assuming steady state…. : constant Ci and Ji independent from i :

J =1

1

s C Si i ie ' i

i = 1, (S)27ln

4 -2

1

1 2

3

e92Ns = J

J

Metastability zone

Primary nucleation



at low supersaturation level, the nucleation process is very slow and even can be blocked in the vicinity of the critical nucleus without reaching zone i>i*

no nucleation : "metastability zone"

the induction period is the time taken by the system to cross the critical zone ; in many cases, the nucleation rate (number of nuclei produced per unit time and volume) is considered as inversely proportional to the induction period

The nucleation rate is often expressed in the simpler mathematical form : J K'n ; parameters K' and n are determined from curve-fitting of experimental data

Primary nucleation



Experimental evidence : nucleation is facilitated by the presence of impureties, dust, walls,….

Interpretation : the nuclei appear on foreign supporting surfaces which decrease their formation Gi : Ghet = f. Ghom

f : heterogeneity factor 0<f<1 : contact angle

4

)cos(1)cos(+2 = f2

Primary nucleation


The heterogeneous primary nucleation

foreign surface

Ghet < Ghom

concentrations in different aggregates are increased

heterogeneous nucleation is faster than homogeneous nucleation

reduced metastability zone

J e-

4

27ln ( +1)

3

2

similar form of kinetic law

Primary nucleation


The heterogeneous primary nucleation

in the continuous industrial crystallizers, nucleation is essentially secondary

definition : the secondary nucleation consists of the formation of new crystals in presence of crystals of the same nature ("parents") in a stirred supersaturated solution

the secondary nucleation rate depends on the properties of the "parent" crystals as well as on the crystallizer operating conditions

possible at low supersaturation level (in these conditions, primary nucleation would be impossible)

Secondary nucleation


Mechanisms of secondary nucleation : initial breeding : release into the solution of small particles of crystalline dust contact nucleation :

crystal-wall The shocks crystal-stirrer produce new fragments (nuclei)

crystal-crystal

"true" secondary nucleation : the layer adjacent to the parent crystal surface acts as a stock of nuclei liable to be released

clusters

Parent crystal

solutionPotential secondary nuclei

Secondary nucleation (continued)


Only empirical laws : BII = k b j d

BII : number of nuclei produced per unit volume and time

supersaturation level, : stirrer rotation rate ; , surface area of the parent crystals, with b = 0.5 - 2.5 ; j = 1 ; d = 0 - 8 (2 - 4)

The nuclei production rate depends on : - the input power of the stirring device

- the concentration in solid of the suspension - the supersaturation

Rate of secondary nucleation :

Secondary nucleation (continued)


The growth rate is determined by the slowest step (rate-determining step)

In crystallization, growth plays an essential influence on the crystal size and shape

The growth of a cystal face results from the progressive integration of atoms or ions into the crystal lattice

The growth kinetic process is divided in several consecutive steps

Representation of the crystal surface :

terrace

stepkink

Adsorbed species

Different adsorption sites : terrace (1 bond), step (2 bonds), kink (3 bonds)

Crystal growth


1- Transport (bulk diffusion of the solute ions or molecules towards the crystal face)

2- Adsorption onto the crystal surface potential growth units

3- Bi-dimensional diffusion of the growth units on a terrace

4- Adsorption of the growth unit onto a step

5- Unidimensional diffusion along a step

6- Adsorption of the growth unit onto a kink integration to the crystal lattice

Crystal growth (continued)The different steps of the growth mechanism


Consequence : progressive filling of the step by growth units, progression

of the step on the surface, formation of the crystal lattice layer by layer

Crystal growth mechanisms : a kinetic assumption (what rate-determining step?) and a morphological assumption (rough or smooth interface ?)

dtdLGGrowth rate = mole or mass flux or rate of linear growth

A few typical cases of growth rate laws

Growth rate with rate-determining bulk diffusion : (no influence of morphology…)

Growth rate diffusion flux concentration gradient in the interfacial layer kd (C - Cs) kd; kd mass-transfer coefficient

Crystal growth (continued)


kd expressed from correlations : example

Sh = = 2 + 0.81 Rep1/2 Sc1/3 (Sh : Sherwood number ; Sc : Schmidt number)D

Lkd

Rate-determining interfacial steps

Two different cases according to the surface roughness

rough interface : an adsorption site a kink only step 6 of the mechanism growth rate

smooth interface : Growth is possible in spite of the absence of steps and kinks

Two explanations...

• in the case of high supersaturation levels : many atoms are adsorbed on the terraces temporary aggregates bi-dimensional nuclei

Crystal growth

A few typical cases of growth rate laws (continued…)


smooth interface and low supersaturation level

microphotographs show steps in form of spirals

smooth interface and high supersaturation level (continued)

Different situations of growth of the bidimensional nucleus

Crystal growth



G K

'

2

''

tanhK

Screw-dislocations source of new steps (Burton-Cabrera-Frank "BCF" model)

smooth interface and low supersaturation level (spiral growth- continued)

Spatial structures and stationary processes

growth rate law :

Simplification :

G (high supersaturation)

G 2 (low supersaturation)

Crystal growth



Experimental evidence :

KH2PO4 growth in presence of impurity Al3+

0 ppm

5 ppm

6,5 ppm

35 ppm

50 ppm

Crystal growthInfluence of the impurities (additives) on crystal growh


The shape of a growing crystal is defined by the relative values of the growth rate of its different faces ; The more rapid the growth in a direction, the lower the lateral development of the face normal to this direction

Foreign atoms adsorbed on a terrace can reduce to a large extent the proceding rate of the steps

A foreign atom or molecule can enter into competition with a "normal" atom as far as adsorption on a site is concerned and thus block or reduce the growth rate

Molecular dynamics calculations adsorption ability of a molecule on a face

Possibility of select or define and synthetize “ tailor-made ” additives to obtain a well-defined crystal shape

Crystal growthInfluence of the impurities (additives) on crystal growh



Agglomeration

Definitions :

Agglomeration : collision then aggregation between crystals followed by the formation of crystalline bridges (in supersaturated solution )

Agregate Agglomerate

Aggregation : formation of a cluster of crystals linked by weak cohesion forces (van der Waals)

mechanisms of collision Submicronic particles (brownian motion)

collisions due to the flowParticle size

Kolmogorov microscaleIn turbulent medium :significance of the ratio

Kolmogorov scale = size of the smallest eddies (about50 m)

interactions between solid particles

R

h

R = 0,2 mInteraction range :van der WaalsElectrochemical double- layerHydrodynamic interactions


Agglomeration (continued)

attractive (London-Van der Waals) : potential : A : Hamaker constant ; R : particle radius ; h : separation between particles

hRAVA 12

+

+

répulsive (electrochemical double layer (in water)) potential :

0 : electrostatic surface potential (assimilated to potential) ; -1 :

Debye-Hückel length

++

+-

+

+

-

-- +

+

++

-+ +

+-

+

+

-

--+

+

++

-hR eRV 2

0

interactions between solid particles

hydrodynamic interactions : liquid draining-off between approaching particles



quasi-fractal model : i primary particles of radius a1 aggregate of outer radius ai

fDi S

iaa1

1

Compact agglomeratesequivalent sphere models

Ramified agglomerates

quasi-fractal models

Df : fractal dimension

consequences on : collision frequence, hydrodynamic interactions and fragmentation

agglomerate morphology



21

dd

,1 ,1,1 , kk kijijij jiji NNKNNKt

Ni

takes into account the physico-chemical and hydrodynamic interactions; it is called "capture efficiency factor"

F1 collision frequence between two particles of radii ai et aj:

For example : F1 = (case of a turbulent medium)

: dissipated turbulent power ; ai et aj : particle radii

ijjiturbij aa 3

34K

Ai + Aj Ai+j

Population balance in an agglomerating system

agglomeration dynamics



Agglomeration kernel Ki,j product of two factors F1 et

Industrial crystallizationThe crystallization reactors

The continuous crystallizers

Feed ; Ta ; Ca ; flow-rate : W ; no crystals

Removal ; Tf ; Cf ; flow-rate : W ; f(D)

C

T

Ca

TaTf

Cf

Steady feed Steady operating characteristics

Stirrer

Tf, Cf , crystals : f(D)

The continuous reactors : the MSMPR model

Simplifying assumptions of the MSMPR model Steady stateThe same shape for all crystals One grain size parameter : LGrowth rate independent from the size Constant volume of the suspension Volume /Flow-rate = V/W = (residence

time)Perfectly mixed reactor Isokinetic removal ( no classification) No crystal in the feed pipeNo ripening, no agglomeration, no fragmentation New crystals (nuclei) appear with a zero initial size

Mixed suspension mixed product removal reactor


The continuous crystallizers : population balance

The population balance is an extension of the notion and the approach of classical (mass, energy,…) balances to the extensive variable "number of entities" of a population characterized by one or several properties

This approach can be applied to the MSMPR crystallizer and its crystal population of density f(D)

Variation in the number of grains of size ranging between D and D + D during time interval t

Vf.D = [f(D, t).G(D, t).t - f(D+D, t).G(D+D, t).t]V -W.f(D,

t)D.t + (B(D, t) - D(D, t)). V.t.D

B(L): "birth" contribution (nucleation, agglomeration,...)

D(L) : "death" contribution (agglomeration, fragmentation,...)


)()( ),().,(),().,(),( DDBDtDDGtDDftDGtDftDf

tf D

)()(),().,(),( DDBDtDGtDftDf

tf D

In the case of the MSMPR at the steady state :

),(),( ),( 0 DtDftDGtDf

B(D) = 0 except for D = 0

Integration

f(D) = f0 exp(-D/G) with :

f0 = B0/G (B0 B(0))

Log(f)

D

Slope = -1/(G)

Intercept : f0

The continuous crystallizers : population balance (continued)


other characteristicskvnG volume fraction in solid L50 = 3.67 Gmean size by weight : 4 G

From the semi-log representation of f(D), the most significant parameters of the crystallization process : B0 and G, can be easily determined

The continuous crystallizers : population balance (continued)


Distribution :

-by number

- by diameter

- by surface area

- by weight

The real crystallizers present many deviations from the MSMPR assumptions and characteristics, however the MSMPR model is often taken as reference

The continuous crystallizers : the MSMPR limitations


Poor mixing

Classified product removal Log(f)

DExample : potassium sulphate size distribution (continuous crystallizer)

Classification

Agglomeration

Fragmentation

The continuous crystallizers : the MSMPR limitations


A large population of fine crystals…..= problems for filtration, agglomeration, safety,…

Feed supersaturation : crystal number : and mean size :

Residence time : less influence than expected : growth counterbalanced by fragmentation (attrition)

The continuous crystallizers : influence of the operating variables


Corresponding particle size distributionExperimental principle

A partial solution to the large population of fine particles : the fine dissolution loop

Three unit operations around the crystallizer:

crystallisation/precipitation solid /liquid separation drying

Reactor volume : 4 -2800 m3 Particle mean size : 1/10 - 10 mm Residence time : 1 hr -10 hr Stirring rate : 3-250 rpm Input power of the stirring device : 0,1-1 W/kg Large crystallizers production per hour > 10t-100 t/hr

Characteristics of the industrial crystallizers

Conclusion


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