FUNDAMENTALS OF INDUSTRIAL
CRYSTALLIZATION
AN OVERVIEW
Michel 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
Industrial crystallization
Introduction
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)
Two ways for this….
Solvent elimination
Shift of the equilibrium sokid-liquid equilibrium via temperature variation
Crystallization  precipitation (involves chemical steps)
Industrial crystallization
Introduction
Diversity of shape and size….
Many physical, chemical, mechanical and rheological properties
of solid materials depend on the grain size and shape
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
Meeting these industrial specifications is the objective of
industrial crystallization
To this aim, it is necessary to define and perform :
the necessary physico-chemical transformations,
the reactor type
the operating conditions
Industrial crystallization
A few fundamental aspects
Equilibrium conditions
System  one grain (or crystal) + liquid solution
C = Cs(T)
T : temperature
C : solute concentration in solution
Cs : saturation concentration  solubility
C > Cs : supersaturated solution : crystal nucleation and growth
C < Cs : non saturated solution : crystal dissolution
  C - Cs
Cs
Relative
supersaturation
Industrial crystallization
Solubility (kg of solute/kg of solvant)
A few fundamental aspects
Equilibrium conditions (continued)
Cs(T) generally increases
with temperature
Temperature
C
(°C)
>0
<0
Principle of "cooling crystallization" :
purely thermal transition from an
undersaturation state (T1) to a
supersaturation state (T2)
T
T2
T1
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 Instability development
the crystal faces
Agglomeration-fragmentation
Industrial crystallization
A few fundamental aspects
(crystallography-continued)
Interfacial roughness notion
Characteristics of a crystal face at the atomic scale
smooth
rough
Approach via statistical physics : energetic interactions
between "first neighbours"
ess interaction :
esl interaction :
ell interaction :
Importance of "entropic factor" :
 2esl-ess-ell
kT
Industrial crystallization
A 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
P2
P3
Results :
 < 3 : rough interface
 > 4 : smooth interface
Industrial crystallization
A few fundamental aspects
(crystallography-continued)
Interfacial roughness (simulation examples)
From works of Gilmer et Bennema)
Industrial crystallization
A few fundamental aspects
(crystallography-continued)
Interfacial roughness (continued)
The faces of a real crystal can be of different roughness type
Industrial crystallization
A few fundamental aspects
Particle size distribution
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 crystallization
A few fundamental aspects
Particle size distribution (continued)
Shape of classical laws of size distribution
f(D)
Log-normal
normal
D
Different representations of the population size distribution
By number, by weight or volume :
f(D).D3.dD, by surface area : f(D).D2.dD
Industrial crystallization
A few fundamental aspects
Particle size distribution (continued)
Overview of the different methods of particle sizing
They depend on the sizing operating mode : off-line, on line or
in situ and on the size domain of the crystals
Off-line : sieving, settling, image analysis,…
On line : optical methods (light scattering), visualization
In situ : a few of the previous methods
Size range :
Light scattering
Laser beam scattering
Microscopy
Settling
Sieving
0.001
0.01
0.1
1
10
100
1000
10000
D in mm
Industrial crystallization
The 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)
Industrial crystallization
The different steps of the crystallization process
Nucleation
The 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 crystallization
The different steps of the crystallization process
Primary nucleation
Metastability
zone
C
A few experimental aspects…
- existence of an induction period (delay) at average
supersaturation level and a metastability zone (no
nucleation) at low supersaturation level
- 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,…
Glycine diffusivity
T
2
1
0
Supersaturation ( + 1)
Industrial crystallization
The different steps of the crystallization process
Primary nucleation
Kinetic models of homogeneous primary nucleation
Ai + 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
Ai+1 Ai + A1
(Fi)
(Bi+1)
Vfi = fi Ci
Vbi = bi+1Ci+1
 transformation rate of Ai to Ai+1 : Ji = fiCi - bi+1Ci+1
 mass balance of Ai
dCi Ji-1- Ji
dt
Industrial crystallization
The different steps of the crystallization process
Primary nucleation
Kinetic models of homogeneous primary nucleation (continued)
constant fi et bi+1 determination
 kinetic theory of gases
 fi = bsi (i > 1) b  C1
si = s1 i2/3
 no model to calculate bi+1 however at equilibrium : Ji = 0 for all i
 bie+1 Ci+1 = fi e Ci
e
e
 bie+1 =
e

C
i
fi e
Ci+1e
as
bie+1 Ci+1e = fi e Cie
e
f

C
i
i
Ji = fi Cie e Cie+1 
 Ci fi Ci+1 
Problem of calculation of the equilibrium concentrations….
Industrial crystallization
The different steps of the crystallization process
Primary nucleation
Kinetic models of homogeneous primary nucleation (continued)
Problem of calculation of the equilibrium concentrations …. iA1 = Ai
xi =
- RGi
i
x1 e R T
-
xi = e
 Gi
RT
with
RGi  RT ilnxs +si 
with Gi  RTilnS +si 
Gi
 
2

C1 e 

hence : Cie
exp s1i3

 Cs  
i

 s1
R
T
xi minimum and Gi maximum for :

xi
2Θ
i*  3 ln(
S)
i*
i

3
(critical nucleus)
S = x1
xs
Industrial crystallization
The different steps of the crystallization process
Primary nucleation
Kinetic models of homogeneous primary nucleation (continued)
Back to the nucleation rate calculation…
 C
C i+1 
i

= 

i
i
i+1

b i si C ei S'  C ei S'
C ei+1S' 
Ji
Assuming steady state…. : constant Ci and Ji independent from i :

1
e 'i
i = 1,  b i si C i S
J=b
9 
43
1
s1N 2 2e 27ln2(S)
J
Metastability zone
J=
1

Industrial crystallization
The different steps of the crystallization process
Primary nucleation
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 curvefitting of experimental data
Industrial crystallization
The different steps of the crystallization process
Primary nucleation
The heterogeneous 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 q : contact angle

2+cos( q)1cos( q)2
f=
4
foreign surface
Industrial crystallization
The different steps of the crystallization process
Primary nucleation
The heterogeneous primary nucleation
Ghet < Ghom
 concentrations in different aggregates are increased
 heterogeneous nucleation is faster than homogeneous nucleation
 reduced metastability zone
 similar form of kinetic law
J e
43
27ln 2 ( +1)
Industrial crystallization
The different steps of the crystallization process
Secondary nucleation
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)
 in the continuous industrial crystallizers, nucleation is essentially
secondary
Industrial crystallization
The different steps of the crystallization process
Secondary nucleation (continued)
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
crystal-crystal
new fragments (nuclei)
 "true" secondary nucleation : the layer adjacent to the parent crystal
surface acts as a stock of nuclei liable to be released
solution
Potential secondary nuclei
clusters
Parent crystal
Industrial crystallization
The different steps of the crystallization process
Secondary nucleation (continued)
Rate of secondary nucleation :
 The nuclei production rate depends on :
- the input power of the stirring device
- the concentration in solid of the suspension
- the supersaturation
 Only empirical laws : BII = k b S j wd
 BII : number of nuclei produced per unit volume and time
 : supersaturation level, w : stirrer rotation rate ; S, surface area of
the parent crystals, with b = 0.5 - 2.5 ; j = 1 ; d = 0 - 8 (2 - 4)
Industrial crystallization
The different steps of the crystallization process
Crystal growth
 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
 The growth rate is determined by the slowest step (rate-determining step)
Representation of the
crystal surface :
step
kink
Adsorbed
species
Different adsorption sites :
terrace (1 bond), step (2
bonds), kink (3 bonds)
terrace
Industrial crystallization
The different steps of the crystallization process
Crystal growth (continued)
The different steps of the growth mechanism
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
Consequence : progressive filling of the step by growth units, progression
of the step on the surface, formation of the crystal lattice layer by layer
Industrial crystallization
The different steps of the crystallization process
Crystal growth (continued)
Crystal growth mechanisms :
a kinetic assumption (what rate-determining step?)
and a morphological assumption (rough or smooth interface ?)
Growth rate = mole or mass flux or rate of linear growth
GdL
dt
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
kd expressed from correlations : example
kd L
Sh = D = 2 + 0.81 Rep1/2 Sc1/3 (Sh : Sherwood number ; Sc : Schmidt number)
Industrial crystallization
The different steps of the crystallization process
Crystal growth
A few typical cases of growth rate laws (continued…)
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
Industrial crystallization
The different steps of the crystallization process
Crystal growth
A few typical cases of growth rate laws (continued…)
 smooth interface and high
supersaturation level (continued)
Different situations of growth of the
bidimensional nucleus
 smooth interface and low supersaturation level
 microphotographs show steps in form of spirals
Industrial crystallization
The different steps of the crystallization process
Crystal growth
A few typical cases of growth rate laws (continued…)
 smooth interface and low supersaturation level (spiral growth- continued)
Screw-dislocations  source of new steps
(Burton-Cabrera-Frank "BCF" model)
Spatial structures and stationary processes
Simplification :
 growth rate law :
''

 G  (high supersaturation)
K
' 2
G  K  tanh 
   G  2 (low supersaturation)
Industrial crystallization
The different steps of the crystallization process
Crystal growth
Influence of the impurities (additives) on crystal growh
Experimental evidence :
0 ppm
5 ppm
35 ppm
KH2PO4 growth in
presence of impurity Al3+
50 ppm
6,5 ppm
Industrial crystallization
The different steps of the crystallization process
Crystal growth
Influence 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
Industrial crystallization
The different steps of the crystallization process
Agglomeration
Definitions :
Aggregation : formation of a cluster of crystals linked by weak
cohesion forces (van der Waals)
Agglomeration : collision then aggregation between crystals followed
by the formation of crystalline bridges (in supersaturated solution )
Agregate
Agglomerate
Industrial crystallization
The different steps of the crystallization process
Agglomeration (continued)
mechanisms of collision
 Submicronic particles (brownian motion)
 collisions due to the flow
In turbulent medium :significance of the ratio
Particle size
Kolmogorov microscale
Kolmogorov scale = size of the smallest eddies (about50 mm)
 interactions between solid particles
h
R
R = 0,2 mm
Interaction range :
van der Waals
Electrochemical double- layer
Hydrodynamic interactions
Industrial crystallization
The different steps of the crystallization process
Agglomeration (continued)
 interactions between solid particles
V
A A R
 attractive (London-Van der Waals) : potential :
12 h
A : Hamaker constant ; R : particle radius ; h : separation between particles
 répulsive (electrochemical double layer (in water)) potential :
+ - +
+ - +
-+ +
+ - +
+ - +
+
+ - +
+ + - +
+ - +
+
+
VRRF02ekh
F0 : electrostatic surface potential (assimilated to z potential) ; k-1 :
Debye-Hückel length
 hydrodynamic interactions : liquid draining-off between approaching particles
Industrial crystallization
The different steps of the crystallization process
Agglomeration (continued)
 agglomerate morphology
 Compact agglomerates
equivalent sphere models
 Ramified agglomerates
quasi-fractal models
quasi-fractal model : i primary particles of radius a1  aggregate of outer radius ai

ai a1 i
S
1
Df
Df : fractal dimension
consequences on : collision frequence, hydrodynamic interactions and fragmentation
Industrial crystallization
The different steps of the crystallization process
Agglomeration (continued)
 agglomeration dynamics
Ai + Aj  Ai+j
dNi 1
K NN 
K NN
dt 2 j1,i1 j,i j j i j k1, i,k i k
Population balance in an
agglomerating system
Agglomeration kernel Ki,j product of two factors F1 et 
F1  collision frequence between two particles of radii ai et aj:
For example : F1 =
Kijturb43ai+a j3ij
(case of a turbulent medium)
e : dissipated turbulent power ; ai et aj : particle radii
  takes into account the physico-chemical and hydrodynamic
interactions; it is called "capture efficiency factor"
Industrial crystallization
The crystallization reactors
The continuous crystallizers
C
Feed ; Ta ; Ca ; flow-rate : W ; no crystals
Stirrer
Tf, Cf , crystals : f(D)
Ca
Cf
Tf
Ta T
Steady feed  Steady operating characteristics
Removal ; Tf ; Cf ; flow-rate : W ; f(D)
Industrial crystallization
The crystallization reactors
The continuous reactors : the MSMPR model
Mixed suspension mixed product removal reactor




Simplifying assumptions of the MSMPR model
Steady state
The same shape for all crystals
One grain size parameter : L
Growth rate independent from the size
 Constant volume of the suspension Volume /Flow-rate = V/W = t (residence time)





Perfectly mixed reactor
Isokinetic removal ( no classification)
No crystal in the feed pipe
No ripening, no agglomeration, no fragmentation
New crystals (nuclei) appear with a zero initial size
Industrial crystallization
The 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
V f. 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 crystallization
The crystallization reactors
The continuous crystallizers : population balance (continued)
f f(D,t) f(D,t).G(D,t) f(D+D,t).G(D+D,t)

+
+B(D)D(D)
t
t
D
f  f(D,t)f(D,t).G(D,t)+B(D)D(D)
t
t
D
In the case of the MSMPR at the steady state :
0
f(D,t)
t
f(D,t)
D
 G(D,t)
Integration 
f(D) = f0 exp(-D/Gt) with :
f0 = B0/G
B(D) = 0 except for D = 0
Log(f)
Intercept : f0
Slope = -1/(Gt)
(B0  B(0))
D
Industrial crystallization
The crystallization reactors
The continuous crystallizers : population balance (continued)
From the semi-log representation of f(D), the most significant parameters of
the crystallization process : B0 and G, can be easily determined
Distribution :
other characteristics
f  6 kv r n0 Gt4
f  volume fraction in solid
L50 = 3.67 Gt
mean size by weight : 4 Gt
-by number
- by diameter
- by surface area
- by weight
Industrial crystallization
The crystallization reactors
The continuous crystallizers : the MSMPR limitations
Classified product
removal
Log(f)
Poor mixing
Agglomeration
Fragmentation
Classification
The real crystallizers present many
deviations from the MSMPR
assumptions and characteristics,
however the MSMPR model is
often taken as reference
D
Example : potassium
sulphate size distribution
(continuous crystallizer)
Industrial crystallization
The crystallization reactors
The continuous crystallizers : the MSMPR limitations
A large population of fine crystals…..= problems for filtration,
agglomeration, safety,…
The continuous crystallizers : influence of the operating variables
Feed supersaturation : crystal number :  and mean size : 
Residence time : less
influence than expected :
growth counterbalanced by
fragmentation (attrition)
Industrial crystallization
The crystallization reactors
A partial solution to the large population of fine particles :
the fine dissolution loop
Experimental principle
Corresponding particle size distribution
Industrial crystallization
The crystallization reactors
Conclusion
Three unit operations around the crystallizer:
 crystallisation/precipitation
 solid /liquid separation
 drying
Characteristics of the industrial crystallizers






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