Nucleation & Growth Kinetics: A Comparison of FBRM … · The sample then returns to ......

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Nucleation & Growth Kinetics:

A Comparison of FBRM and Laser Diffraction

Paul Barrett & Brian Glennon([email protected] & [email protected])

Department of Chemical Engineering,University College Dublin,Ireland

As presented at Lasentec Users’ Forum 2000Orlando, Florida

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FBRM & Laser Diffraction : A Comparison

Experimental Design

• Aluminium Potassium Sulphate K2SO4.Al2(SO4)3.24H2O

• Well researched system

• Regular octahedra formed

• Low aspect ratio

• Solubility has high temperature dependence

• Reported size dependent growth kinetics

The crystallisation system under examination was potash alum in water, a well-researched system with much independent- literature kinetic information available. In water, the crystals formed are regular octahedra, making them suitable for laser diffraction measurement.

The solubility of the potash alum in water has a high temperature dependence. So by manipulating the saturation temperature, a wide variety of solids concentrations can easily be examined. There is reported size-dependent growth for the system. We felt it would be interesting to examine the FBRM’s response to such a system.

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Experimental Conditions

• Unbaffled, jacketed vessel, working volume 400 mL

• Pitched blade impeller

• Seeded, isothermal & controlled cooling batches

• FBRM & Laser Diffraction utilised to monitor crystallisation

FBRM (in- line) and laser diffraction (on-line) were used to simultaneously monitor the crystallization. This allowed for a real- time comparison of data recorded from both measurements.

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Photograph of apparatus: Slurry from the crystallizer is fed dir ectly to the laser diffraction measurement cell via a peristaltic pump. The sample then returns to the crystallizer. A wide variety of validation experiments were performed to ensure that the peristaltic pump did not damage the crystals. There was also an issue with the refractive index of a crystal and its saturated solution being very close. The saturated temperature was chosen to ensure that the ratio of the refractive index was great enough that it did not significantly influence the laser diffraction calculations.

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Experimental Conditions

• Seed loading versus obscuration

• Low Concentrations (0.02-2.5 wt. %)

• FBRM - M400LF - 38 logarithmic channels 1-1000 µm

• Laser Diffraction (Malvern Mastersizer Micro)

100 logarithmic channels 0.3 - 300 µm

• 5 seconds measurement duration

For the conditions examined in these experiments, the laser diffraction unit requires a solids concentration less than 1.5 wt %. Above this concentration, the laser obscuration would be too high for a successful measurement. Therefore, a seed loading was selected that allowed operation in this low concentration region. Kinetic information for these seeded batches will be extracted using both FBRM and laser diffraction.

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Close-up photograph of the crystallizer: A sample for the laser diffraction system is removed near the FBRM window and returned sub-surface.

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Isothermal Batch

• Batch is saturated at 30oC

• Seeding at 27.9oC

• Initial supersaturation level 0.0115 kg hydrate/kg solution

• Seeds: 0.081 g of 38-45 µm sieve fraction

• Regular single octahedra

• Concentration range 0.02 - 0.5 wt %

• In-line conductivity measurement

• Supersaturation via a simple mass balance

3

2

1

2

1

LL

MM

=

An SOP was developed for seed preparation. The seeds used for the batches presented here were obtained from the 38- to 45-µm sieve fraction. Microscopic analysis confirmed them to be regular single octahedra.

An in- line conductivity probe was initially evaluated for monitoring the supersaturation. However, it was deemed unsuitable as the small changes in supersaturation encountered in the isothermal batch were of the same order of magnitude as the error on the probe. The supersaturation was estimated via a simple mass balance.

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Particle Size Profile (measured via laser diffraction)

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0 500 1000 1500 2000 2500

Time (s)

Par

ticl

e D

iam

eter

( µm

)

Mean DiameterStandard Deviation

Particle size data measured via laser diffraction for the isothermal batch: The spherical equivalent volume-based diameter, as measured by the laser diffraction unit, is increasing over time, indicating an increase in crystal dimension. The standard deviation remains relatively constant indicating, for the conditions examined here, that growth is independent of size.

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• Simulations: 1: G = fn (L, ∆C), 2: G = fn (L)

Experimental Size Data & Literature Kinetics Simulations

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Time (s)

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eter

(m

)

Mean DiameterSimulation 1Simulation 2

With knowledge of the initial seed loading and seed temperature, the growth rate of these seeds was predicted using literature kinetic values. To simply solve the population, it was assumed there was no nucleation – a valid assumption due to the low supersaturation conditions employed.

Simulation 1 estimated the growth rate as a function of the particle size and supersaturation. The initial supersaturation and seed loading are known, so by a simple iterative technique, the growth rate (and hence particle diameter at any instant in time) is estimated for the entire batch. Simulation 2 estimates the growth rate as a function of size only. Again, with knowledge of the initial seed size, the predicted growth rate and size throughout the batch can be calculated.

Plotting the measured experimental laser diffraction volume based mean diameter data and the “simulations,” one can see that the simulations compare reasonably well to the experimental data.

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Isothermal Chord Count Profile

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45

0 500 1000 1500 2000 2500

Time(s)

Co

un

ts (

#/s)

12.7-22.022.0-31.631.6-45.545.5-65.465.4-94.194.1-135.4135.4-162.4

Seed Point

Channel count ranges

FRBM count data (#/s) in selected size ranges is plotted for the duration of the isothermal batch. This shows that after seeding, there is a steady increase in counts across all channels.

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Mean Particle Size vs. Mean Chord Length

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16 17 18 19 20 21 22 23 24

Lasentec Mean Chord Length (number-based) (µm)

Las

er D

iffr

acti

on

Mea

n (

volu

me-

bas

ed)

(m

)

The FBRM mean chord length is compared in real time to the laser diffraction volume based mean for the duration of the isothermal batch. Plotting this data, a linear relationship is obtained, indicating that both measurement techniques have done well in tracking the growth in isothermal crystallisation.

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Controlled Cool Batch

• Batch is saturated at 30oC

• Seeding at 27.9oC

• Seeds: 0.11 g of 38-45 µm sieve fraction

• Concentration range 0.02 - 2.5 wt %

• Cooling profile selected to minimise potential for nucleation

The seed loading and cooling profile were carefully selected to minimize the potential for nucleation.

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Time (s)

Tem

per

atu

re (o

C)

1.5

ff0

0

t

t

TT

TT

=

−

−

An exponential cooling profile is employed for the controlled cooling batch.

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0

10

20

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50

60

0 500 1000 1500 2000 2500

Time (s)

Co

un

ts (

#/s)

12.7-22.022.0-31.631.6-45.545.5-65.465.4-94.194.1-135.4135.4-162.4

Seed Point

FRBM count data (#/s) in selected size ranges is plotted for the duration of the controlled cooling batch. Again this shows that after seeding, there is a steady increase in counts

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Comparison of Measured & Simulated Particle Diameters

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Time (s)

Par

ticl

e D

iam

eter

(vo

lum

e-b

ased

) (

m)

Measured Mean DiameterSimulation 1Simulation 2

The duration of the controlled cooling batch was 2500 seconds, but laser diffraction measurements were only available for the first 900 seconds. After this point, the laser obscuration was too high. Plotted here is the experimentally measured laser diffraction volume based mean for 900 seconds. Also, the simulated diameters calculated using literature kinetic values, as discussed on slide 9, are plotted. The “simulations” are extrapolated for the entire batch. The simulated size data for the batch again agrees well with the laser diffraction mean diameter data.

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Comparison of Measured & Simulated Particle Diameters

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0 500 1000 1500 2000 2500 3000Time (s)

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ticl

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iam

eter

(m

)

Measured Mean DiameterSimulation 1Simulation 2FBRM Prediction

FBRM data was available for the duration of the entire batch. Using the linear relationship developed from the isothermal batch between the FBRM mean chord and laser diffraction mean (slide 11), the laser diffraction mean is estimated from the FBRM mean chord length for the entire batch. This prediction compares very well with the actual measured laser diffraction mean and with the simulations. Again, this is more evidence that FBRM did very well in tracking the growth of the crystals.

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Preliminary Data Analysis: Nucleation?

• Laser diffraction - no evidence of fines generation

• Source of FBRM fine chords counts:

Small particles, larger particles or combination of both?

• Relationship between midsize and fine chords

• Fine chords (1-12.7 µm) vs. Mid range chords (31.7-135.3 µm)

From the laser diffraction data there is no evidence of fines generation. However, as this is a volume-based measurement, it may not have the resolution on the fines side in the presence of coarse material to fully confirm this. A comprehensive review of the FBRM data is performed to fully determine if nucleation is taking place.

As a particle grows, we will get bigger chords, but we will still have fine chords, too. It is proposed that for the conditions examined here, there is a direct relationship between the number of fine chords and the number of midrange chords for a particle that is growing. In other words, for these low concentration experiments, all fine chords are measured from larger growing crystals.

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Fine Counts vs. Mid Range Counts

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Mid range counts (31.7-135.3 µm) (#/s)

Fin

es c

ou

nts

(1-

12.7

µm

) (#

/s)

IsothermalControl Cool

The fines versus midrange FBRM count data for the isothermal batch is shown. It is very unlikely that any nucleation is occurring here due to the experimental conditions used. The control cooling batch count data also follows the same trajectory, indicating that no nucleation is occurring. In other words, for these batches, all fine chord counts are coming from growing crystals.

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Fine Counts vs. Mid Range Counts

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Mid Range Counts (31.6-135.3 µm) (#/s)

Fin

es C

ou

nts

(1-

12.7

m

) (#

/s)

IsothermalControl Cool.Unseeded Crash Cool

Fines versus midrange FBRM count data for an unseeded crash cool is plotted here. It deviates greatly from the trajectory of the pervious two batches, indicting, as one would expect, nucleation.

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Isothermal & Controlled Cool Batches

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Time (s)

Dia

met

er(v

olu

me

-bas

ed)

(m

))

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Tota

l Cou

nts

(#/s

)

IsothermalControl CoolIsothermal CountsControl Cool Counts

Graphical summary of data collected for the isothermal and controlled cool batches.

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Mid Range Counts vs. Projected Area

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0.0E+00 1.0E+04 2.0E+04 3.0E+04 4.0E+04 5.0E+04

D2 (µm2)

Mid

Ran

ge C

ount

s (3

1.6-

135.

3 µ

m)

(#/s

)

IsothermalControl CoolControl Cool - adjusted

This is the mid-range FBRM count data versus the projected area, which will be a function of the spherical equivalent diameter squared. The projected area is estimated from the laser diffraction data. The projected area of the particle is essentially what the laser sees as it scans across. Due to the higher seed loading, there are initially about 30% more particles in the control cool batch than the isothermal batch. The controlled cool data is “adjusted” to contain the same number of particles as the isothermal batch. The adjusted data closely follows the isothermal data. Again, this is a sign that the number of particles has remained the same, indicating there is no nucleation.

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Conclusions

• Potential for predicting growth rates

• Calibrate for a particular system

• Careful experimental design to fully characterise system

• FBRM used to indicate nucleation

• Decipher fine chord counts to quantify nucleation rate

• Extend range of results- concentration and scale

• Possibility for control

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Questions and Answers

Q: On slide 16, I know you said that was circumstantial evidence for no nucleation, but could you just go over that again?

PB: It was essentially a comparison between the two. If you have a sphere, and the projected area is a circle, then the theoreticalprobability of getting chord length (y) from a particle of diameter (r) is equa l to y over 2r squared. As the circle increases in dimension, the probability of getting fine chords decreases, but the overall count rate will increase due to the increase in projected area.

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Q: Are you saying that with the controlled cooling, that makes sense?

PB: Exactly, because with the controlled cooling you follow the same objectives. We assume that again there is no nucleation. The laser diffraction correlates with this as well.

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Q: Where, exactly, was your probe in relation to the impeller? In abatch crystallization system, you can often easily exclude the coarser particles so you are effectively sampling from the finer particles, which is a problem when you do a mass balance.

PB: The FBRM probe is against the glass window and the probe is pointed down above the tip of the impeller. The line for the laser diffraction unit is attached to the side of the probe. Many background trials were done with silicate particles of various sizes. From these initial experiments, it was deemed that the sampling position would sample the whole population, not just the fines.

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Q: When you correlated the data from the Lasentec and the Malvern, what was the quality in the chord length between the mean chord and the volume-based diagram?

PB: It was a similar relationship, so we can effectively say that either one would correlate.

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Q: You said that each one was run at about 2,500 seconds. Was it an open system or did you have a top cover?

PB: This was an open system.

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Q: Did you take into account evaporation?

PB: With the lower temperature we used, it was not deemed a significant effect.

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Q: Have you done an experiment where you knew you had significant nucleation that you could see with the laser diffraction? A lot of times laser diffraction will miss fines.

PB: Yes, because there are bigger particles present. I did not detect it here, but on some of the batches you could see the fines.

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Q: What was the origin of the seeds and did you use the same batch of seeds for every experiment?

PB: The seeds were braised for 40 hours. They were in a high-solids concentration at 48% for 40 hours, and then we got nice, regular crystals. And, yes, we developed a protocol and used the same batch of seeds for every experiment.

RB: Just one comment. These results are for one particular system, the potash system. This particular material does not backscatter very well, which is another factor on the point of when you detect nucleation. In other words, with better backscattering you can detect earlier.

My point is that backscatter is material-dependent. The quality of these results is dependent on the material you run. I think the results are great. Don’t get me wrong. Somebody could come up with worse material and expect those results and not get them. But somebody could come up with better materia l and get even better results.

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