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FUNDAMENTALS OF INDUSTRIAL
CRYSTALLIZATION
AN OVERVIEWMichel COURNIL, Department of Chemical Engineering (Centre SPIN), Ecole des Mines de Saint-Etienne (France)
cournil@emse.fr 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….
Industrial crystallization
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,...
Industrial crystallization
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
Industrial crystallization
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
)
Industrial crystallization
A few fundamental aspects
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
Industrial crystallization
A few fundamental aspects
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
Industrial crystallizationA few fundamental aspects (crystallography-continued)
From works of Gilmer et Bennema)
Interfacial roughness (simulation examples)
Industrial crystallizationA few fundamental aspects (crystallography-continued)
The faces of a real crystal can be of different roughness type
Interfacial roughness (continued)
Industrial crystallizationA few fundamental aspects (crystallography-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
Industrial crystallizationA few fundamental aspects
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 :
Industrial crystallizationA few fundamental aspects
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
Industrial crystallizationThe different steps of the crystallization process
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
Industrial crystallizationThe different steps of the crystallization process
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
Industrial crystallizationThe different steps of the crystallization process
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
Industrial crystallizationThe different steps of the crystallization process
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
Industrial crystallizationThe different steps of the crystallization process
Kinetic models of homogeneous primary nucleation (continued)
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
Industrial crystallizationThe different steps of the crystallization process
Kinetic models of homogeneous primary nucleation (continued)
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
Industrial crystallizationThe different steps of the crystallization process
Kinetic models of homogeneous primary nucleation (continued)
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
Industrial crystallizationThe different steps of the crystallization process
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
Industrial crystallizationThe different steps of the crystallization process
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
Industrial crystallizationThe different steps of the crystallization process
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)
Industrial crystallizationThe different steps of the crystallization process
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)
Industrial crystallizationThe different steps of the crystallization process
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
Industrial crystallizationThe different steps of the crystallization process
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
Industrial crystallizationThe different steps of the crystallization process
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)
Industrial crystallizationThe different steps of the crystallization process
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…)
Industrial crystallizationThe different steps of the crystallization process
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
A few typical cases of growth rate laws (continued…)
Industrial crystallizationThe different steps of the crystallization process
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
A few typical cases of growth rate laws (continued…)
Industrial crystallizationThe different steps of the crystallization process
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
Industrial crystallizationThe different steps of the crystallization process
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
Industrial crystallizationThe different steps of the crystallization process
Industrial crystallizationThe different steps of the crystallization process
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
Industrial crystallizationThe different steps of the crystallization process
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
Industrial crystallizationThe different steps of the crystallization process
Agglomeration (continued)
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
Industrial crystallizationThe different steps of the crystallization process
Agglomeration (continued)
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
Industrial crystallizationThe different steps of the crystallization process
Agglomeration (continued)
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
Industrial crystallizationThe crystallization reactors
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,...)
Industrial crystallizationThe crystallization reactors
)()( ),().,(),().,(),( 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)
Industrial crystallizationThe crystallization reactors
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)
Industrial crystallizationThe crystallization reactors
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
Industrial crystallizationThe crystallization reactors
Poor mixing
Classified product removal Log(f)
DExample : potassium sulphate size distribution (continuous crystallizer)
Classification
Agglomeration
Fragmentation
The continuous crystallizers : the MSMPR limitations
Industrial crystallizationThe crystallization reactors
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
Industrial crystallizationThe crystallization reactors
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
Industrial crystallizationThe crystallization reactors
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