Download In situ optical methods for particle size determinations

Optical methods for in-situ particle sizing
Michel COURNIL, Department of Chemical Engineering
(Centre SPIN), Ecole des Mines de Saint-Etienne (France)
[email protected]
www.emse.fr
TU Wien 18. January 2002
Introduction
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)
Introduction
Particle size distribution
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
Introduction
How to monitor (continuously) a crystallization process ?
A difficult experimental problem
- problem of sampling (off-line and on-line characterisations) :
general problem of sample withdrawal (isokinetic character)
hydrodynamic perturbations
crystal or aggregate fragility
- interest of in-situ characterizations
process control
better mastering of the product quality
understanding of the processes
In situ particle size distribution determinations from optical measurements
 spectral turbidimetry ( pseudo-absorbance) for dilute suspensions
 analysis of backscattered light for concentrated suspensions
In situ optical methods for particle size determinations
Light scattering fundamentals
Scattering angle q and and mean scattering angle q
i q
Incident ray
Scattered ray
q
q
small particle dp <   isotropic scattering
Anisotropy factor
large particle dp >  anisotropic scattering
Scattering cross section

m  2 iq cosq sinq dq
4 sca 0
Phase function

Csca 2 iq sinq dq
4 0
iq 
pq 
2 Csca
In situ optical methods for particle size determinations
Spectral turbidimetry measurement principle
EXPERIMENTALS
THEORY
D
L
IL
I0
1
I
   ln 0
L IL
Intensity
0,50
Turbidity
Intensity
Turbidity

0,45
0,40
II 0
2,5
0

0,35
3,0
2,0
0,30
0,25
1,5
0,20
ILI
0,15
1,0
L
0,10
0,5
[nm]
0,05
A
L
G
O
R
I
T
H
M
I0

 
290
340
390
440
490
540
590
640
690
740
 Qsca ( , D, m)D
4
2
f ( D)dD
2,50E+8
f (D) population density function f (D)
Crystal
2,00E+8
1,50E+8
1,00E+8
5,00E+7
DD
0,0
240

0
 (nm)
0,00
IL
0,00E+0
In situ optical methods for particle size determinations
Backscattering measurement principle
optical fiber bundle A
bundle B
photodiode
laser diode
holder
bundle A + B
receiving fiber
slurry
emitting fiber
In situ optical methods for particle size determinations
Fundamentals of spectral turbidimetry (1)
Suspension of monodisperse non-absorbing spherical particles

dI
 NC sca I
dx
: Light intensity at abscissa x
I
N
: Particle number per unit volume [#/cm3]
C sca : Scattering area [cm2]
Scattering coefficient :
Csca
Q
C géom
C géom : area of particle cross-section
C géom 
 D2
4
for a spherical particle
In situ optical methods for particle size determinations
Fundamentals of spectral turbidimetry (2)
Case of a monodisperse suspension of non-absorbing spherical particles :
   QND
2
4
Case of a polydisperse suspension of non-absorbing spherical particles :


   Qf DD2 dD
40
In situ optical methods for particle size determinations
Fundamentals of spectral turbidimetry (3)
Determination of scattering coefficient Q : Mie theory
Q : function of wavelength , particle diameter D, and m
particle refractive index
m
dispersing medium refractive index
Different possible approximations
0
1
  D 
2

2-3
1 : Rayleigh
2 : Rayleigh-Debye (Gans)
2-3 : Anomalous diffraction
m 1

1-4
MIE
4
3
3 : Fraunhoffer scattering
4 : Total reflection
1-4 : Optical resonance
Elsewhere : : MIE (no
approximation)
Example :
methane hydrate crystals in water
Qsca
3,5
3
2,5
2
1,5
1
0,5
0
0
5
10
15
 2 m1D

20
In situ optical methods for particle size determinations
Particle size distribution calculation from turbidity spectra (1)
“Direct” calculation for a polydisperse suspension
 

4

2
Q


,
D
,
m

f

D

D
dD


0
TM   , ,..., 
 1 1
M 
t

   
 
f  f D , f D ,..., f D
1
2
N

t
TM  A  f with A  Q , D, m D 2   1,..., M ; D  D ,..., D
No particular difficulty in the “direct” problem
1
N
In situ optical methods for particle size determinations
Particle size distribution calculation from turbidity spectra (2)
“Direct” calculation for a polydisperse suspension : example
Suspension water/polystyrene latex particles
mean diameter Dp=0.778 mm ; nearly monodisperse
In situ optical methods for particle size determinations
Particle size distribution calculation from turbidity spectra (3)
The "inverse" problem
Experimental data :
   350  750nm
Discretization of the turbidity spectrum (M values)
“Turbidity vector” definition :

TM   , ,...,
 1 1
M 
Data to obtain : population density function f D
Restriction to size range
Dmin , Dmax 
Discretization of the diameter range (N values)
“Population density vector” definition
   
 
f  f D , f D ,..., f D
1
2
N
t
t
In situ optical methods for particle size determinations
Particle size distribution calculation from turbidity spectra (4)
The "inverse" problem : derivation of f from experimental TM
TM = A.f
1st method : simple inversion:
2nd method : least square
f̂  A1 TM
 
f̂  A A
t
1
t
Catastrophic !
A TM
Small variation in TM
large variation in f
An ill- conditioned problem : Matrix A nearly singular
A solution…..
Constrained least-square method: Min( ||TM - Af||2 + g q(f))
(Twomey, 1977; Eliçabe and Garcia Rubio, 1989)
In situ optical methods for particle size determinations
Examples of application of turbidimetry
Crystallization of methane hydrate in pressurized reactor [30-100 bars]
Methane + water  Methane hydrate
(gas) (liquid)
(solid)
Crystallization of titanium oxide in a two-jet reactor
Titanium chloride + water  Titanium dioxide + HCl
(gas)
(gas)
(solid)
In situ optical methods for
particle size determinations
Example of application of
turbidimetry : crystallization of
methane hydrate
TEMPERATURE
PRESSION
WEST
6100
2105
2130
1
2
SET AT ALM
WEST
1
2
AL1
AL2
AL3
SET AT ALM
65 b
AL1
AL2
AL3
MIN
MAX
MIN
MAX
Analyseur
AL1
AL2
AL3
65 b
MIN
MAX
SET
référence (Pref)
Pt100
Sortie
EXPERIMENTAL SET-UP :
Source
réacteur (P)
dissociation
Régulation
PID
2 °C
SET
SET
formation
Spectrophotomètre
6100
2105
2130
Azote
Pref
Injecteur
liquide
haute
pression
Sortie
Semi-batch pressurized
and stirred reactor
• Isothermal (1°C)
• Isobaric [30-100 bars]  gas
consumption
•Turbidity sensor
C.D.P.
Pref
1
Pref
2
P
Méthane
Sortie
Cryostat
Turbidity
sensor
Parallel light
beam
Scattering events
Crystallization of methane
hydrate
Calculated granular data
Influence of
stirring rate
f(D) [cm-4 ]
P = 45 bar ; t # 250 s
6.0E+07
Population density
function
5.0E+07
Stirring rate
200 rpm
4.0E+07
300 rpm
3.0E+07
400 rpm
2.0E+07
1.0E+07
D [µm]
0.0E+00
0
20
40
60
80
100
120
-1.0E+07
Particle number
per unit volume
Np [cm-3]
1.4E+6
Particle mean D  1  D f ( D )dD
diameter
Np 0

Np   f ( D )dD
0
45 bar ; 0% PVP K30
D [µm]
15
200 tr/min
300 tr/min
400 tr/min
500 tr/min
1.2E+6
1.0E+6
45 bar ; 0% PVP K30
200 tr/min
300 tr/min
400 tr/min
500 tr/min
14
13
12
8.0E+5
11
6.0E+5
10
9
4.0E+5
8
2.0E+5
7
t-tL [s]
0.0E+0
0
200
400
600
800
1000
1200
1400
t-tL [s]
6
0
200
400
600
800
1000
1200
1400
In situ optical methods for
particle size determinations
Example of application of
turbidimetry : reaction between
two jets
In situ optical methods for particle size determinations
Example of application of turbidimetry : reaction between two jets
Effect of the jet velocity on the particle mean diameter
In situ optical methods for particle size determinations
Conclusions on spectral turbidimetry
Method easy to operate and relatively cheap
Possibility of in situ measurements even in difficult conditions
Reliable method however only in a restricted size range
(0.1 mm – 5 mm for most crystals)
Main drawback : limitation to highly dilute suspensions :
concentration less than 10-4 in volume in most cases
In situ optical methods for particle size determinations
Analysis of backscattered light


Ib
 f d p , , m
I0
with : Ib : backscattered intensity
I0 : incident intensity
dp : particle diameter
 : solids volume fraction
m : refractive indices ratio (solid/liquid)
L : reactor wall - sensor distance
In situ optical methods for particle size determinations
Analysis of backscattered light
Example : variation of backscattered intensity vs
volume fraction in solid
1,0E-1
TiO2 (0,35 µm)
Glass beads (56,9 µm)
Al2O3 (0,21 µm)
d
Al2O3 (1,79 µm)
Ib/I0
1,0E-2
z
q
1,0E-3
1,0E-4
1,0E-7 1,0E-6 1,0E-5 1,0E-4 1,0E-3 1,0E-2 1,0E-1 1,0E+0

In situ optical methods for particle size determinations
Analysis of backscattered light
Dimensionless diagramme
3,5E-2
SiO2 0,5 µm
SiO2 1,0 µm
SiO2 1,5 µm
TiO2
Al2O3 1µm
Al2O3 3µm
latex 0,46µm
glass beads
billes
de verre
3,0E-2
2,5E-2
Ib/I0
2,0E-2
1,5E-2
1,0E-2
5,0E-3
0,0E+0
1,0E-4
1,0E-3
1,0E-2
1,0E-1
1,0E+0
l *-1 (µm-1)

~
Relevant parameter : transport mean free path  *  N sca 1  m 

1
In situ optical methods for particle size determinations
Analysis of backscattered light
Models (1)
2
2
2
3
Ib/I0
1

1. single backscattering approximation
2. Monte Carlo simulation
3. radiative transfer theory : diffusion approximation
In situ optical methods for particle size determinations
Analysis of backscattered light
Models (2)
d
Single backscattering
z
Ib
 N b f ( N s , R, )
I0
Radiative transfer theory
N sca
   ,
 ,
 
 ,
s I (r , s )   I (r , s ) N sca 
p( s , s ') I (r , s )d '

4 4 
Ib
Approximation of diffusion
 5 2 f ( N ,  sca , m , R)
I0
In situ optical methods for particle size determinations
Analysis of backscattered light
Models (3) : agreement theory-measurements
In situ optical methods for particle size determinations
Analysis of backscattered light
Application to particle sizing (1)
4,0E-2
By using the universal curve
as calibration curve :
Ib/I0
Measured backscattered
intensity  transport mean
free path  mean diameter
2,0E-2
1,0E-2
1000
0,0E+0
1,0E-4
1,0E-2
m
= 1,087 (silica in water)
100
Measurement range :
moderate and high
concentrations in solid
measurements
mesures
3,0E-2
dp
(µm)
~ *-1
1,0E+0
-1
l water)
(µm )
m = 1,367 (alumina in
10
1
0,1
0,01
1,0E-5
1,0E-4
1,0E-3

1,0E-2
1,0E-1
1,0E+0
In situ optical methods for particle size determinations
Analysis of backscattered light
Application to particle sizing (2)
Comparison between the measurement size ranges of
turbidimetry and backscattering for 2 different values of the
solid phase refractive index
In situ optical methods for particle size determinations
Example of application of turbidimetry : monitoring of titanium
dioxide aggregation in water
0.025
3.5E-2
3.0E-2
5,00E-03
3,13E-04
0.023
2.5E-2
2.0E-2
Ib/I0
Ib/I0
0.021
0.019
1.5E-2
1.0E-2
5.0E-3
0.017
0.0E+0
1.0E-4
0.015
-50
0
50
100
150
200
250
1.0E-3
1.0E-2
~
l *-1 (µm-1)
t (s)
Two different behaviours according to the volume fraction in solid
1.0E-1
In situ optical methods for particle size determinations
Example of application of turbidimetry : monitoring of titanium
dioxide aggregation in water
0.025
0.02
Ib/I0
= 1500 rpm
= 1084 rpm
= 610 rpm
= 343 rpm
0.015
= 175 tr/min
0.01
-100
100
300
500
700
t (s)
Influence of stirring rate
900
1100
1300
In situ optical methods for particle size determinations
Conclusions on the use of light backscattering for particle sizing
Method easy to operate and relatively cheap
Possibility of in situ measurements
Possibility of characterization of contrated suspensions
For the moment only information on mean diameter