Optical methods for in-situ particle sizing
-
Upload
valentine-raymond -
Category
Documents
-
view
24 -
download
4
description
Transcript of Optical methods for in-situ particle sizing
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
A sample of granular solid = a huge number of grains of different shape and size
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
Assumption : one size parameter – " mean " diameter D – of a crystal is characteristic of all its properties
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), visualizationIn situ : a few of the previous methods
Size range :
Introduction
Particle size distribution
0.001 0.01 1010.1 100001000100 D in m
SievingSettling
Microscopy
Laser beam scattering
Light scattering
- problem of sampling (off-line and on-line characterisations) :general problem of sample withdrawal (isokinetic character)hydrodynamic perturbationscrystal or aggregate fragility
- interest of in-situ characterizationsprocess controlbetter mastering of the product qualityunderstanding of the processes
- problem of sampling (off-line and on-line characterisations) :general problem of sample withdrawal (isokinetic character)hydrodynamic perturbationscrystal or aggregate fragility
- interest of in-situ characterizationsprocess controlbetter mastering of the product qualityunderstanding 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 particle size distribution determinations from optical measurements spectral turbidimetry ( pseudo-absorbance) for dilute suspensions analysis of backscattered light for concentrated suspensions
A difficult experimental problem
Introduction
How to monitor (continuously) a crystallization process ?How to monitor (continuously) a crystallization process ?
In situ optical methods for particle size determinations
Light scattering fundamentals
Scattering angle and and mean scattering angle Scattering angle and and mean scattering angle
i
Incident rayIncident ray
Scattered rayScattered ray
small particle dp < isotropic scatteringsmall particle dp < isotropic scattering large particle dp > anisotropic scatteringlarge particle dp > anisotropic scattering
0
2 sincos4
disca
0
2 sin4
diCsca
Anisotropy factor Scattering cross sectionAnisotropy factor Scattering cross section
scaC
ip 2
Phase functionPhase function
ALGORITHM
1 0
L
I
I L
ln
I0IL
LEXPERIMENTALS
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0,45
0,50
240 290 340 390 440 490 540 590 640 690 740
0,0
0,5
1,0
1,5
2,0
2,5
3,0
I0
IL
Intensity Turbidity
(nm)
I0
IL
[nm]
Intensity Turbidity
I0 IL
DTHEORY
0,00E+0
5,00E+7
1,00E+8
1,50E+8
2,00E+8
2,50E+8f (D)
D
Crystal population density function f (D)
D
DDfQsca d)(m)DD,,(4
2
0
In situ optical methods for particle size determinations
Spectral turbidimetry measurement principle
slurry
laser diode
holder
optical fiber bundle A bundle B
photodiode
bundle A + Breceiving fiber
emitting fiber
In situ optical methods for particle size determinations
Backscattering measurement principle
Suspension of monodisperse non-absorbing spherical particles Suspension of monodisperse non-absorbing spherical particles
INCdxdI
sca: Light intensity at abscissa x: Light intensity at abscissa x
: Particle number per unit volume [#/cm3]: Particle number per unit volume [#/cm3]
: Scattering area [cm2]: Scattering area [cm2]
IN
scaC
Scattering coefficient :Scattering coefficient :
géom
sca
C
CQ : area of particle cross-section: area of particle cross-sectiongéomC
for a spherical particlefor a spherical particle4
2DCgéom
In situ optical methods for particle size determinations
Fundamentals of spectral turbidimetry (1)
Case of a monodisperse suspension of non-absorbing spherical particles : Case of a monodisperse suspension of non-absorbing spherical particles :
24QND
dDDDQf
0
24
Case of a polydisperse suspension of non-absorbing spherical particles : Case of a polydisperse suspension of non-absorbing spherical particles :
In situ optical methods for particle size determinations
Fundamentals of spectral turbidimetry (2)
In situ optical methods for particle size determinations
Fundamentals of spectral turbidimetry (3)
index refractive medium dispersingindex refractive particlem
Determination of scattering coefficient Q : Mie theory Determination of scattering coefficient Q : Mie theory
Q : function of wavelength , particle diameter D, and mQ : function of wavelength , particle diameter D, and m
0
0,51
1,52
2,53
3,5
0 5 10 15 20
Dm 12
scaQ
Example : methane hydrate crystals in water
Example : methane hydrate crystals in water
1 : Rayleigh1 : Rayleigh
2 : Rayleigh-Debye (Gans)2 : Rayleigh-Debye (Gans)
2-3 : Anomalous diffraction2-3 : Anomalous diffraction
3 : Fraunhoffer scattering3 : Fraunhoffer scattering
4 : Total reflection4 : Total reflection
1-4 : Optical resonance1-4 : Optical resonance
Elsewhere : : MIE (no approximation)
Elsewhere : : MIE (no approximation)
Different possible approximationsDifferent possible approximations
MIEMIE
mm
00 11
11
22
44
33
D
1-41-4
2-32-3
dDDDfmDQ
0
2,,4
“Direct” calculation for a polydisperse suspension“Direct” calculation for a polydisperse suspension
t
MMT
,...,,
11 tNDfDfDf ,...,2,1f
fAMT withwith NDDDMDA ,...,1;,...,1mD,,Q 2
No particular difficulty in the “direct” problemNo particular difficulty in the “direct” problem
In situ optical methods for particle size determinations
Particle size distribution calculation from turbidity spectra (1)
Suspension water/polystyrene latex particles
mean diameter Dp=0.778 m ; nearly monodisperse
“Direct” calculation for a polydisperse suspension : example“Direct” calculation for a polydisperse suspension : example
In situ optical methods for particle size determinations
Particle size distribution calculation from turbidity spectra (2)
Experimental data : nm750350
“Turbidity vector” definition :
Discretization of the turbidity spectrum (M values)t
MMT
,...,,
11
Data to obtain : population density function
Restriction to size range
Df
Discretization of the diameter range (N values)
max,min DD
“Population density vector” definition
tNDfDfDf ,...,2,1f
The "inverse" problem The "inverse" problem
In situ optical methods for particle size determinations
Particle size distribution calculation from turbidity spectra (3)
An ill- conditioned problem : Matrix A nearly singularAn ill- conditioned problem : Matrix A nearly singular
The "inverse" problem : derivation of f from experimental TM The "inverse" problem : derivation of f from experimental TM
In situ optical methods for particle size determinations
Particle size distribution calculation from turbidity spectra (4)
TM = A.fTM = A.f
Constrained least-square method: Min( ||TM - Af||2 + q(f))
(Twomey, 1977; Eliçabe and Garcia Rubio, 1989)
Constrained least-square method: Min( ||TM - Af||2 + q(f))
(Twomey, 1977; Eliçabe and Garcia Rubio, 1989)
A solution…..A solution…..
1st method : simple inversion:1st method : simple inversion:
Mtt TAAA
1f̂
MTA 1f̂
Catastrophic !Catastrophic !
Small variation in TM large variation in f Small variation in TM large variation in f
2nd method : least square2nd method : least square
Crystallization of methane hydrate in pressurized reactor [30-100 bars]Methane + water Methane hydrate (gas) (liquid) (solid)
Crystallization of methane hydrate in pressurized reactor [30-100 bars]Methane + water Methane hydrate (gas) (liquid) (solid)
In situ optical methods for particle size determinations
Examples of application of turbidimetry
Crystallization of titanium oxide in a two-jet reactorTitanium chloride + water Titanium dioxide + HCl (gas) (gas) (solid)
Crystallization of titanium oxide in a two-jet reactorTitanium chloride + water Titanium dioxide + HCl (gas) (gas) (solid)
• Isothermal (1°C)
• Isobaric [30-100 bars] gas consumption
•Turbidity sensor
Pt10
0
Pref1
Pref2
Pref
C.D.P.
W EST 6100
2105
SET AT ALM2130 1
2
AL1AL2AL3 65 b
SET
MAXMIN
form ation dissociation
PRESSION TEM PERATURE
réacteur (P)
référence (Pref)
RégulationPID
AL1AL2AL3 65 b
SET
MAXMIN
AL1AL2AL3 2 °C
SET
MAXMIN
W EST 6100
2105
SET AT ALM2130 1
2
Sortie
Sortie
M éthane
Azote
Sortie
Spectrophotomètre
Analyseur Source
Injecteurliquidehautepression
Cryostat
P
EXPERIMENTAL SET-UP :
Semi-batch pressurizedand stirred reactor
In situ optical methods for particle size determinations
Example of application of turbidimetry : crystallization of
methane hydrate
Turbidity sensor
Turbidity sensor
Parallel light beam
Parallel light beam
Scattering eventsScattering events
Particle number per unit volume
Influence of stirring rate
0dD)D(fD
Np1D
0dD)D(fNp Particle mean
diameter
6.0E+07
P = 45 bar ; t # 250 sf(D) [cm-4]
-1.0E+07
0.0E+00
1.0E+07
2.0E+07
3.0E+07
4.0E+07
5.0E+07
0 20 40 60 80 100 120
200 rpm
300 rpm
400 rpm
D [µm]
Stirring rate
0.0E+0
2.0E+5
4.0E+5
6.0E+5
8.0E+5
1.0E+6
1.2E+6
1.4E+6
0 200 400 600 800 1000 1200 1400
200 tr/min
300 tr/min
400 tr/min
500 tr/min
45 bar ; 0% PVP K30Np [cm-3]
t-tL [s]6
7
8
9
10
11
12
13
14
15
0 200 400 600 800 1000 1200 1400
200 tr/min
300 tr/min
400 tr/min
500 tr/min
45 bar ; 0% PVP K30D [µm]
t-tL [s]
Population density function
Calculated granular data
Crystallization of methane hydrate
Crystallization of methane hydrate
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 diameterEffect of the jet velocity on the particle mean diameter
In situ optical methods for particle size determinations
Example of application of turbidimetry : reaction between two jets
Method easy to operate and relatively cheapMethod easy to operate and relatively cheap
Possibility of in situ measurements even in difficult conditionsPossibility of in situ measurements even in difficult conditions
Reliable method however only in a restricted size range (0.1 m – 5 m for most crystals)
Reliable method however only in a restricted size range (0.1 m – 5 m for most crystals)
In situ optical methods for particle size determinations
Conclusions on spectral turbidimetry
Main drawback : limitation to highly dilute suspensions : concentration less than 10-4 in volume in most cases
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
I
If d mb
p0
, ,
w i th : I b : b a c k s c a t t e r e d in t e n s i t yI 0 : i n c id e n t i n t e n s i t yd p : p a r t i c l e d i a m e te r : s o l i d s v o lu m e f r a c t i o nm : r e f r a c t i v e i n d i c e s r a t i o ( s o l id / l i q u id )L : r e a c to r w a l l - s e n s o r d i s t a n c e
In situ optical methods for particle size determinations
Analysis of backscattered lightExample : variation of backscattered intensity vs
volume fraction in solid
1,0E-4
1,0E-3
1,0E-2
1,0E-1
1,0E-7 1,0E-6 1,0E-3 1,0E-2 1,0E-1 1,0E+0
I b/I
0
TiO2 (0,35 µm)
Glass beads (56,9 µm)
Al2O3 (0,21 µm)
Al2O3 (1,79 µm)
1,0E-5 1,0E-4
z
d
0,0E+0
5,0E-3
1,0E-2
1,5E-2
2,0E-2
2,5E-2
3,0E-2
3,5E-2
1,0E-4 1,0E-3 1,0E-2 1,0E-1 1,0E+0
l *-1 (µm-1)
I b/I 0
SiO2 0,5 µmSiO2 1,0 µmSiO2 1,5 µmTiO2Al2O3 1µmAl2O3 3µmlatex 0,46µmbilles de verreglass beads
In situ optical methods for particle size determinations
Analysis of backscattered lightDimensionless diagramme
Relevant parameter : transport mean free pathRelevant parameter : transport mean free path ~*
N sca 11
1. single backscattering approximation2. Monte Carlo simulation3. radiative transfer theory : diffusion approximation
1. single backscattering approximation2. Monte Carlo simulation3. radiative transfer theory : diffusion approximation
I b/I
02 22 31
In situ optical methods for particle size determinations
Analysis of backscattered lightModels (1)
In situ optical methods for particle size determinations
Analysis of backscattered lightModels (2)
Single backscatteringSingle backscattering
z
d
I
IN f N Rb
b s0
( , , )
Radiative transfer theoryRadiative transfer theory
s I r s I r s N
Np s s I r s dsca
sca ( , ) ( , ) ( , ' ) ( , ) ', , ,
4 4
I
If N Rb
sca0
25 ( , , , )Approximation of diffusionApproximation of diffusion
1.0E-5
1.0E-4
1.0E-3
1.0E-2
1.0E-1
1.0E-6 1.0E-5 1.0E-4 1.0E-3 1.0E-2 1.0E-1 1.0E+0
mesure
simulation deMonte Carlo
approximation dediffusion
Presi 3µm
In situ optical methods for particle size determinations
Analysis of backscattered lightModels (3) : agreement theory-measurements
1.0E-5
1.0E-4
1.0E-3
1.0E-2
1.0E-1
1.0E-6 1.0E-5 1.0E-4 1.0E-3 1.0E-2 1.0E-1 1.0E+0
mesure
simulations deMonte Carlo
approximation dediffusion
Presi 1µm
0,0E+0
1,0E-2
2,0E-2
3,0E-2
4,0E-2
1,0E-4 1,0E-2 1,0E+0
l *-1 (µm-1)
I b/I
0
mesures
~
measurements
In situ optical methods for particle size determinations
Analysis of backscattered lightApplication to particle sizing (1)
By using the universal curve as calibration curve :
Measured backscattered intensity transport mean free path mean diameter
By using the universal curve as calibration curve :
Measured backscattered intensity transport mean free path mean diameter
0,01
0,1
1
10
100
1000
1,0E-5 1,0E-4 1,0E-3 1,0E-2 1,0E-1 1,0E+0
dp
(µm)
m = 1,087 (silica in water)
m = 1,367 (alumina in water)
Measurement range : moderate and high
concentrations in solid
Measurement range : moderate and high
concentrations in solid
In situ optical methods for particle size determinations
Analysis of backscattered lightApplication to particle sizing (2)
Comparison between the measurement size ranges of turbidimetry and backscattering for 2 different values of the
solid phase refractive index
Comparison between the measurement size ranges of turbidimetry and backscattering for 2 different values of the
solid phase refractive index
0.015
0.017
0.019
0.021
0.023
0.025
-50 0 50 100 150 200 250
t (s)
I b/I 0
5,00E-033,13E-04
In situ optical methods for particle size determinations
Example of application of turbidimetry : monitoring of titanium dioxide aggregation in water
0.0E+0
5.0E-3
1.0E-2
1.5E-2
2.0E-2
2.5E-2
3.0E-2
3.5E-2
1.0E-4 1.0E-3 1.0E-2 1.0E-1
l *-1 (µm-1)
I b/I
0~
Two different behaviours according to the volume fraction in solidTwo different behaviours according to the volume fraction in solid
0.01
0.015
0.02
0.025
-100 100 300 500 700 900 1100 1300
t (s)
I b/I 0
= 175 tr/min
= 343 rpm
= 1084 rpm= 610 rpm
= 1500 rpm
In situ optical methods for particle size determinations
Example of application of turbidimetry : monitoring of titanium dioxide aggregation in water
Influence of stirring rateInfluence of stirring rate
Method easy to operate and relatively cheapMethod easy to operate and relatively cheap
Possibility of in situ measurementsPossibility of in situ measurements
Possibility of characterization of contrated suspensionsPossibility of characterization of contrated suspensions
In situ optical methods for particle size determinationsConclusions on the use of light backscattering for particle sizing
For the moment only information on mean diameterFor the moment only information on mean diameter