basic principles of FBRM

Particle ScienceTheory and Practice

Ian Haley

Outline of Modules 1

The Basics Part 1 - What is Particle Size

Part 2 - Presentation Method and Weighting

Part 3 – The Importance of Shape

Part 4 – Count-based Measurement

Instrumentation for Particle Characterisation Part 5 – FBRM and The Chord Length Distribution

Part 6 – Chord Length and Particle Shape

Part 7 - An Outline of Different Particle Characterisation Methods and the

Effect of Particle Shape

Outline of Modules

Statistics and Data Handling Part 8 - Understanding the Mean, Median and Mode of a Particle System

Part 9 – Precision and Accuracy

Part 10 – Correlating FBRM to Other Data

Part 11 - Channel Grouping and Statistics

Part 12 – Signal Aliasing

Practical Aspects of Using FBRM Part 13 - Probe Location and Orientation

Part 14 – Standard Procedures

Part 1: What is Particle Size?

Ian Haley

Particle Size

Particle “size” = 326 µmBut how was it calculated?And what does this tell us about the particle and others like it?

Many particles are complexThree-dimensional objects.Yet we want to represent their‘size’ by just one number.

What is the size of this particle?

But what is the size of this particle?

50 microns?

10 microns?

30 microns?

Some other number?

What is particle size?

“There is no single definition of particle size… In this (document), particle size is defined as the diameter of a sphere having the same physical properties; this is known as the spherical equivalent diameter.” (Source: International Standards Organization (ISO 9276-1:1998))

By volume By surface area

By settling

velocityBy sieve analysis

Part 2: Presentation Method and Weighting

Ian Haley

Particle Size and Physical Property

“There is no single definition of particle size… In this (document), particle size is defined as the diameter of a sphere having the same physical property; this is known as the spherical equivalent diameter.” (Source: International Standards Organization (ISO 9276-1:1998))

By volume By surface area

By settling

velocityBy sieve analysis

The physical property we use has a major effect on the way in which ”particle size” is calculated.

Using a Physical Property to Calculate Mean Size

What is the average size of this two-particle system?

In other words, “What does my PSA lab tell me?”

Diameter: 10µm Diameter: 100µm

Surface area: 314µm2

Volume: 524µm3

Surface area: 31,400µm2

Volume: 524,000µm3

Mean size: calculated statistics for a two-particle system

These numbers are all the “correct” average size.

There are a large number of other methods of calculation that would be correct as well.

Diameter: 10µm Diameter: 100µm

Mean diameter

Number-based dist. = 55.0 µm

Area-based dist. = 99.1 µm

Volume-based dist. = 99.9 µm

Mean size for equal volumes of 100 µm and 10 µm particles

Equal Volumes

Number-based dist. = 10.1 µm

Area-based dist. = 18.2 µm

Volume-based dist. = 55.0 µm

Comparing different physical properties

One 100 µm particle (A) contains the same quantity of material as one-thousand 10 µm particles (B)

Total number 1 particle 1000 particles

Diameter 100 µm 10 µm

Surface area 31,400 µm2 314,000 µm2

Total volume 524,000 µm3 524,000 µm3

10µm Diameter: 100µm

Number and Volume Distributions

10µm Diameter: 100µm

Sensitivity of Each Distribution to Fines

Insensitive to change fines!

Sensitive to change in fines!

Coarse in the presence of fines

100µm

Adding one coarse particle

100µm 100µm

Detecting breakage in a particle system

Breakage of 1 large particle into 1000 small particles

Initial particle system

After breakage of one particle

Relative change

Total number 27 particles 1026 particles 3700% increase

Total surface area 847,000 µm2 1,161,800 µm3 37% increase

Total volume 14,140,000 µm3 14,140,000 µm3 0%

Number mean diameter 100.0 µm 12.3 µm 87.7% decrease

Volume moment mean diameter 100.0 µm 96.7 µm 3.3% decrease

Why is the particle distribution range important?

All three distributions have the same mean but significantly different distributions!

Particle dimension (µm)

Defining Number and Square Weighting

What is the mean of this distribution?

Weighted vs. Unweighted Distributions, Part I

Example: A Population of Cubes

The size distribution is presented as: a) Total number

b) Total length (based on projected area)c) Total surface area d) Total volume of particles within each size classification

Mean = 7.1 µm Mean = 9.2 µm

Which distribution is the most sensitive in your application?

Number, Length, Area, Volume Distributions

Presentation method determines sensitivity to different regions of the population. (Example: Population of Cubes)

Number Distribution

Area Distribution

Length Distribution

Volume Distribution

Data presentation of cube distribution

The statistic choice/presentation method determines the sensitivity to different regions of the population.

Sq Weighted vs. Unweighted Distributions

Example: A population of cubes

FBRM®

No Weight

FBRM®

Square Weight

Emphasizes changes to the fine (small) end of the distribution

Emphasizes changes to the coarse (large)

end of the distribution

Square weighted Distribution

Weighted vs. Unweighted Distributions (1)

On Left: No Weighted FBRM distributions at 3 time points show a decrease in count and an increase in dimension

Unweighted distribution is sensitive to fine particles population

No Weighted Distribution

Time=0 min

Time=90 min

Time=180 min

On Right: Square Weighted FBRM distribution for same 3 time points show enhanced resolution to growth in coarse particle dimension

Square weighted distributions is sensitive to coarse particle dimension

Time=0 min

Time=90 min

Time=180 min

FBRM Distributions and Trended Statistics

Unweighted Distribution

#/s <50 µm

#/s 50-1000 µm

Square Weighted Distribution

Time=0 min

Time=90 min

Time=180 min

Time=0 min

Time=90 min

Time=180 min

Mean0 = 75µm

Mean180 = 141µm

Mean90 = 82µm

Weighted vs. Unweighted Distributions, (1)

Distribution weighting (by number, length, area, or volume) can significantly enhance or reduce the resolution to change.

Selecting the appropriate weighting function will enhance the changes that directly relate to the application goal.

In this example, the square-weighted distribution does not detect small changes in the concentration of fine material.

However, the unweighted distribution is very sensitive to the amount of fine material present.

Weighted vs. Unweighted Distributions, (2)

Distribution weighting (by number, length, area, or volume) can significantly enhance or reduce the resolution to change.

Selecting the appropriate weighting function will enhance the changes that directly relate to the application goal.

However, the square-weighted distribution is very sensitive to the amount of coarse material.

In this example, the unweighted distribution does not detect small changes in the concentration of coarse material.

Definitions: Fines vs. Coarse

Our descriptions of “fine” and “coarse” material are relative

Terms are used to describe the smallest and largest particles in a given system

Definitions are system specific

Fines Coarse

When talking particles, “size” is a generic term

Reporting of particle size must include definitions of:

The physical property selected to characterize size of the particles, for example:- Diameter- Chord length- Projected area- Surface area- Volume- Settling rate- Response of electrical, optical, or acoustical field

Statistical calculations and display, for example:- Number-based distribution- Length-based distribution- Area-based distribution- Volume-based distribution- Scale (log vs. linear)- Channel grouping- Count vs. normalized

Assumptions, for example:- Shape- Refractive index- Coincidence effects

Sensitivity to a given particle system trait depends on the chosen statistic

Distribution mean depends on both the property measured and the calculation used to characterize the particle distribution.

- Property Sphere having the same settling rate Sphere fitting through the same-size sieve aperture Sphere producing a similar diffraction pattern No shape assumption - Chord length distribution

- Calculation Number Length Area Volume

Different techniques use different properties to calculate size. None are fundamentally wrong, they just measure different properties of the particles.

Part 3: The Importance of Shape

Ian Haley

The Volume Spherical Equivalent Diameter (VSED)

The surface area of the needle is 60% greater than that of the sphere.

100 µm

10 µm

Calculate the diameter of a sphere with the same volume as a ‘needle’

24.7 µm

Why do we assume all particles are spherical?

Simplicity: A sphere is the only shape that can be described by one unique number (the diameter), regardless of the particle’s orientation.

How can particle size be calculated for non-spheres?

18 µm

Calculate the diameter of a sphere with the same volume as the cylinder

50 µm

How does the VSED relate to the length and width of this particle?

The surface area of the cylinder is 73% greater than the sphere!

A needle will handle and flow differently to a sphere!

A spherical equivalent diameter based on volume

(VSED)

How can particle size be calculated for non-spheres?

Calculate the diameter of a sphere with the same volume as the cylinder

100 µm

24 µm

The cylinder has doubled in length; but the diameter of the equivalent sphere has only increased by 33%

A spherical equivalent diameter based on volume

(VSED)

Is the Spherical Equivalent Diameter practical?

Can the SED help improve a process?

Very different morphologies for three batches of the same process

Would a SED provide meaningful information about the process?

Could it help improve the process?

Even if a true spherical equivalent diameter was measured…

In a chemical process, do spherical and non-spherical particles behave the same way?

Can spheres be used to model the behavior of non-spherical particles?

- They do not have the same surface area or flow properties.

Shape: If particles are not spherical, what happens?

Most instruments will assume that the signal is derived from a spherical particle, and in turn derive a spherical equivalent diameter based on this incorrect assumption.

At this point, there are no successful correction factors in commercial software (excluding some image analysis packages) that account for non-spherical shapes. Most will generally track growth or reduction of shaped particles, but not in an absolute sense.

The further particle shape moves away from a sphere, the less accurate instruments based on a spherical equivalent model become.

Part 4: Count-based Measurement

Ian Haley

Count-Based Particle Size Measurement

Instruments and techniques used to measure particle size fall into

two key groups:

A measurement is made on a ‘cloud’ or ‘ensemble’ of particles simultaneously.

Particles are not measured individually

The distribution is expressed as size vs percentage or ‘distribution density’

These are normalised techniques

Conversely….

Some instruments derive their data by measuring particles individually

The data is sensitive to changes in population

The distribution is expressed as size vs number

These are count-based techniques

Normalized vs. Count-Based Distributions, Part 1

Count-based distributions display changes in particle dimension and/or changes in the number-based particle concentration.

Normalization removes particle population information from the data.

In this example, particle dimension is held constant as the concentration of the dispersed phase increases.

While the number of measured chords increases, the normalized distribution shows that the size and shape of the particles remain relatively unchanged.

Normalized vs. Count-Based Distributions, Part 2

Each channel in a count-based distribution is independent of change occurring in other ranges of the distribution.

Each channel in a normalized distribution is dependent on changes occurring in other regions of the distribution.

The normalized, unweighted distribution indicates dramatic relative change in this size region.

The count-based distribution shows that the actual number of particles measured in this range did not change.

Count-Based Particle Size Measurement

Allows you to measure particle population

You can track changes in particle concentration

Track absolute changes in isolated size regions, independent of other

size regions

But, normalized techniques:

Hide the effect of concentration

Only relative changes in concentration can be tracked

Part 5: FBRM and The Chord Length Distribution

Ian Haley

How does FBRM work?

FBRM® Probe TubeFBRM® Probe Tube

SapphireWindowSapphireWindow

Beam splitterBeam splitter

Rotating opticsRotating optics

FBRM® Probe TubeFBRM® Probe Tube

Laser source fiberLaser source fiber

Focused beamFocused beamFBRM® Probe TubeFBRM® Probe Tube

Detection fiberDetection fiber

Laser source fiberLaser source fiber

Focused beamFocused beamFBRM Probe TubeFBRM Probe Tube

Cutaway view of FBRM In-process Probe

PVM® image illustrating the view from the FBRM Probe Window

Probe installed in process stream

What is FBRM® Technology?PVM® image illustrating the view from the FBRM® Probe Window

Enlarged view

Probe detects pulses of Backscattered light

And records measured Chord Lengths

Path of Focused Beam

This core patented technology is called Focused Beam Reflectance Measurement [FBRM®]

FBRM® Method of Measurement

What is FBRM® Technology ?

Path of Focused Beam

Enlarged view

Thousands of Chord Lengths are measured each second to produce the FBRM® Chord Length Distribution :

Typical FBRM applications include:-Crystallization-Formulations-Precipitation-Polymerization -Emulsification-Microencapsulation -Dissolution and disintegration-Flocculation-Fermentation

FBRM Instrument Configuration – Standard Focal Position

Standard Focal Position--0.02 mm (20µm inside the window) measured from outside surface of probe window.

Advantages-In majority of cases, provides excellent sensitivity to real-time change in count and dimensions of particle population.

-Minimizes noise from properties of the system that are not under investigation. Process flow

direction

Sapphire Window

Focused Beam

Rotating Lens

What Happens if the Focal Point is Outside the Window?

Outbound:

Intensity of focused beam is degraded by

- Absorption by the carrying fluid.

- Attenuation due to particles in front of the measuring zone.

Return:

Return signal is also degraded by- Absorption by the carrying fluid.

- Attenuation due to particles between the window and measuring zone.

Note: Particles between the window and the measuring zone will reflect light that will be detected as background signal. This will significantly degrade the signal-to-noise ratio.

Chords are Measured from every AspectChords are Measured from every Aspect

Chord Lengths from a Sphere

Chord length Probability: A Graphical Approach

1234567891 0

1 2 3 4 5 6 7 8 9 10C

C hordlength [a.u.]

Part 6: Chord Length and Particle Shape

Ian Haley

Chords are Measured from every AspectChords are Measured from every Aspect

Chord Lengths Measurements, FBRM

FBRM Particle Shape

A chord length distribution is a function of average shape and dimension of particles and particle structures as they actually exist in process.

- No shape is assumed.

- Affect of shape on FBRM measurement is known.

- In most cases the affect of shape on measurement can be filtered out or enhanced to track the change.

Sphere

Needle

Platelet

Sphere

Platelet

Needle

Monodispersed Distribution of Spheres, SED 500 µm

Normal Distribution of Spheres, Mean SED 200 µm, Std Dev 25 µm

Normal Distribution of Needles AR 2:1, Mean SED 200 µm, Std Dev 25 µm

Normal Distribution of Needles AR 4:1, Mean SED 200 µm, Std Dev 25 µm

growth of a needle

Modelling Chord Length Distributions 1

Ruf, A., Worlitschek, J, Mazzotti, M. Modeling and Experimental Analysis of PSD Measurements through FBRM. Part & Part Syst Characterization. 17 (4), 167-179, 2001.

growth of a needle

Distributions

How do we define a collection of particles of differing size and/or shape?

Number, Length, Area, Volume Distributions

Presentation method determines sensitivity to different regions of the population. (Example: Population of Cubes)

Which statistics are sensitive to length or width?

Square Wt

100000000

200000000

300000000

400000000

500000000

600000000

700000000

1 2 3 4 5 6 7 8

Dimension

1 3 5 7 15 25 40 65

Dimension

Part 7: An Outline of Different Particle Characterisation Methods

and the Effect of Particle Shape

Ian Haley

PVM® TechnologyParticle Video Microscope

Microscope quality images, in-process and in real time

Characterize particle systems from 2μm to 1mm

FBRM® TechnologyFocused Beam Reflectance Measurement

Track real-time changes in particles and droplets as they naturally exist in the process

Characterize particle systems from 0.5μm to 3mm

In-Situ Particle Characterization Tools

10 µm droplets

Imaging and Image Analysis METTLER TOLEDO PVM enables qualitative and quantitative particle

system characterization

9 chords

1 long chord

8 fine chords

The following schematic represents the change in morphology.

Long Needles

Short cubic/diamond crystals

Tracking the shape change with FBRM

5 chords

5 medium chords

PVM® Shows Seed Morphology

t=10mins

PVM® images show metastable seeds are long needle shaped crystals

PVM ® and FBRM ® Identify Habit Shift (Form Conversion)

t=25mins

At 25mins - polymorphic transformation occurs

The habit shifts from needles to blocks

FBRM ® and PVM ® Identify When Conversion is Complete

t=45mins

After 45mins the transformation is complete

The FBRM® distribution is narrower and tighter

How Laser Diffraction Works

Dilute sample (0.01% wt or lower) of particles added to Laser Diffraction bench top system

They are circulated to the measurement zone (particles can break, dissolve, etc during this step)

Particles are illuminated by a laser beam in transmission.

The particles scatter this light in all direction, the light scatter on the detector is collected (diffraction pattern)

A mathematical model (Mie and/or Fraunhofer theory) is used to fit a diffraction pattern of spheres with the measured diffraction pattern

Dilute Particles DetectorLaser

For Internal Use Only

What does the Laser Diffraction size data look like?

Volume Based Distribution

Normalized distribution

Distribution Assuming all particles are spheres

Sample 1: Bimodal distribution of Glass Spheres

Laser Diffraction

Image Analysis

Electro Sensing Zone

Sample 3: Needle like crystals

Laser Diffraction

Image Analysis

Electro Sensing Zone

Sieving will ‘size’ based on the 2nd largest particle dimension

Impact of Particle Shape on Sieving

Particles of the same ‘width’ will be ‘sized’ the same

Particles of different shapes but the same width will be ‘sized’ the same

Determining the appropriate method of measurement

What is the process or product parameter of concern? Critical parameters may include:

- Downstream processing efficiency Filtration Milling Drying Flow properties

- Product yield and purity

- Bulk Product quality properties Dissolution Bulk density Formulation properties

What region of the particle population directly affects the critical parameters?

What instrument permits us to monitor this critical parameter?

Is sampling or safety an issue?

Part 8:Understanding the Mean, Median and Mode

of a Particle System

Objective for this Module

Understand how the mean, median and mode are calculated

Study how particle system changes impact the mean and median

Understand the best statistic to choose for a given objective

Mean = 28µm (9+25+25+32+50)/5

Median = 25µm (50% greater than this size; 50% smaller than this size)

Mode = 25µm (most common occurrence)

A sample distribution of particles…

What happens when we add two coarse particles?

50µm25µm

Mean = 49µm (9+25+25+34+50+80+120)/7

Median = 32µm (50% greater than this size;50% smaller than this size)

What happens when we add 4 fine particles?

50µm25µm

Mean = 18µm (5+5+5+5+9+25+25+34+50)/9

Median = 9µm (50% greater this size;50% smaller than this size)

5µm5µm

The best stat depends on your region of interest

Mean: +75%Median: +22%

Mean: -35%

Median: -64%

Tracking Real Particle Attrition

Mean: -40%

Median: -67%

Tracking Real Particle Attrition

Mean: -40%

Median: -67%

Particle Count >20µm: + 185%

Conclusions

The mean, median and mode are all averages used to characterize particle systems

The mean is sensitive to outliers – a small number of very large (or very small) particles; for example large boulders during milling

The median is sensitive to changes in particle number; especially at the fine end of the distribution; for example secondary nucleation

Particle count in certain size classes is also a powerful statistic to study

Part 9: Precision and Accuracy

Ian Haley

Precision & Accuracy Defined

Precision- The ability of the instrument to yield the same

response to repeated measurements of the same unchanging sample.

Accuracy- The ability of an instrument to yield results that are as

close as possible to the absolute properties possessed by a sample.

- The ability of an instrument to yield results that are as close as possible to a recognized Reference or Standard Method

Accuracy

When discussing accuracy it is important to specify:

- The absolute property in question. (e.g. absolute chord length, true diameter, etc)

- The ‘reference’ technique by which that absolute property is independently determined.

Precision and Accuracy Explained

A. Both Precise and Accurate.

B. Measurement capable of monitoring and control: Precise measurement with a consistent offset (bias). Good sensitivity to change.

C. Poor measurement for process monitoring and control. Poor sensitivity to change. Average (x) of all measurements will approach the true value.

D. Measurement with both random error and offset.

Precision and Accuracy Explained (2)

Two goals of FBRM instrument design:

1)To ensure high instrument to instrument repeatability, so instruments are repeatable and can be validated across sites and during scale up (lab to plant).

2)To ensure high repeatability instrument to itself, so measurements of the same system will always measure the same distribution and provide opportunity for control, quality by design, and process optimization.

High Precision and High Accuracy

Case A (Ideal):

Accurate and Precise

True Mean = 4.0

Measured Mean = 4.0

95% Confidence Interval = +/-5.0%

0.0 1.0 2.0 3.0 4.0 5.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Poor Precision and High Accuracy

Case C: Accurate Measurement, poor precision

True Mean = 4.0

Measured Mean = 4.0

95% Confidence Interval = +/-50%

0.0 1.0 2.0 3.0 4.0 5.0

Time (minutes)

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

High Precision and Poor Accuracy

Case B: Precise Measurement with an Offset

True Mean = 4.0

Measured Mean = 6.0

95% Confidence Interval = +/-5.0%

0.0 1.0 2.0 3.0 4.0 5.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Precision Depends on the Selected Statistic

Why is this true?

Any given statistic is primarily the function some specific region of the chord length distribution.

Some regions may have more or less counts depending on the particle system.

Sensitivity Defined

The ability to of the instrument to respond to a real change in the process parameter of interest.

The higher the sensitivity, the smaller the real change in process the instrument is able to detect.

Precision and Sensitivity to Change

Is this noise?

Or is there insufficient information to provide a signal of sufficient stability (precision)?

0.0 1.0 2.0 3.0 4.0 5.0

Precision and Sensitivity to Change

A 0.1% increase in the solids concentration resulted in a corresponding 0.1% increase in the output signal.

Precision and Measurement Duration

Increasing single measurement duration improves measurement precision.

Elapsed Time (hr:min)

5 min.

1 min.

10 sec.

5 sec.

2 sec.

Precision and the Effect of Averaging

Increasing number of measurements to average (navg) improves measurement precision.

Elapsed Time (hr:min)

Precision vs Response Time

0.1 1 10 100 1000

Single Measurement Duration (tm) [sec]

Measurement Duration and Sensitivity to Change

Increasing the Measurement Duration (with no averaging) provides more stable data, but will increase the minimum response time.

-1.0 0.0 1.0 2.0 3.0 4.0

Elapsed Time (min)

+ 1.0 % by weight, SMD = 1 secStep Change in Concentration

-1.0 0.0 1.0 2.0 3.0 4.0

Elapsed Time (min)

-1.0 0.0 1.0 2.0 3.0 4.0

Elapsed Time (min)

-1.0 0.0 1.0 2.0 3.0 4.0Elapsed Time (min)

Effect of Averaging on Response Time

Increasing the number of measurements to average (navg) improves precision. However, response is dampened with increased averaging.

-1.0 0.0 1.0 2.0 3.0 4.0

Elapsed Time (min)

+ 1.0 % by weight, Average = 10Step Change in Concentration

-1.0 0.0 1.0 2.0 3.0 4.0

Elapsed Time (min)

-1.0 0.0 1.0 2.0 3.0 4.0

Elapsed Time (min)

-1.0 0.0 1.0 2.0 3.0 4.0

Elapsed Time (min)

Goal of Successful Instrument Implementation

Provide a precise measurement that reflects the smallest change of interest to the process or product parameter of concern.

Precision is of greater concern than Accuracy

Part 10: Correlating FBRM to Other Data

Ian Haley

Nucleation & Growth Kinetics:

A Comparison of FBRM and Laser Diffraction

Paul Barrett & Brian Glennon

Department of Chemical Engineering,

University College Dublin,

Ireland

FBRM vs. Laser Diffraction

50 70 90 110 130 150

FBRM Mean Chord Sqr. Wt. (Microns)

Isothermal Batch: FBRM,PVM,LD & FBRM Prediction

0 200 400 600 800 1000 1200 1400 1600 1800

Time (s)

LD Mean

FBRM Mean Sqr. Wt.

LD Extrapolation

PVM Dimension

Extrapolating LD data

Sieve Correlation with FBRM®

Sieve and Coulter Counter Correlation with FBRM®

Correlation to downstream product quality or process efficiency

Bruce A. Keiser, Ph.D.Nalco Chemical Company

How close does the FBRM instrument response come to the measurement of product quality or process efficiency

1) A correlation is made between specific cake resistance (filterability) and both the dimension and number of particles

2) One can measuring the in-situ particle dimension and count with FBRM® and predict downstream filtration rates.

3) FBRM® is highly successful in predicting filtration because of its high sensitivity to changes in the number of fine particles

Optimization of Pharmaceutical Batch Crystallization for Filtration and scale-upBrian K. Johnson, Carol Szeto, Omar Davidson and Art AndrewsAIChE Annual Meeting, Los Angeles, CA, November 1997

Optimizing Filtration and Scale-up

AJ Parker CRC forHydrometallurgy

Relating settling rate to chord length

0 100 200 300 400 500

Mean square-weighted chord length (µm)

200 rpm

t tlin

100 rpm

The Use of FBRM in the Study of Flocculation ProcessesPhil Fawell, CSIRO

Correlating biomass & ethanol production with FBRM

SPSC 01 (Ge et al 2004)

Correlation between first FBRM peak (flocs) biomass

Correlation between second FBRM peak (bubbles) and ethanol production

Part 11: Channel Grouping and Statistics

Ian Haley

Channel Grouping*

How to Choose the Right Channel Grouping for Your Work & the Affect of the Chosen Grouping on Statistics

Channel – A Definition

A bin with a specific upper and lower limit in microns. Counts with a chord length measured between those limits are put in that specific channel.

Hardware & Channel Grouping

The FBRM hardware is based on 4096 linear 0.25 micron channels, so the primary x-axis is this linear scale.

Software display provides user with options to group the distribution channels.

FBRM logarithmic scales are calculated from the linear scale channel data.

The choice between linear and log scales will change your statistics

Many other particle size instruments use hardware based on a log scale. They do not provide statistics based on a linear scale.

Logarithmic Grouping

Each channel width is progressively wider than the preceding channel width.

The distance between channel midpoints is proportionate to their logarithms.

High resolution is provided on the small-particle side of the distribution.

Significantly lower resolution (progressively wider channels) is provided on the large-particle side of the distribution.

Linear Grouping

All channels have equal width.

The distance between the channel midpoints is also equal.

Equal resolution is provided throughout the distribution.

Each channel has an equal probability of a count being placed in it.

Logarithmic Grouping

100-Channel Log Grouping (same data set as linear):

Linear Grouping

100-Channel Linear Grouping (same data set as log):

Grouping Effect on Statistics

Comparison of statistics (linear vs. logarithmic channel grouping for the same data set):

Statistic 100 Linear, 0-1000 µm

100 Log, 1-1000 µm

% Difference

#/sec 501,000 500,998 0.0004%

#/meas 1,002,000 1,001,996 0.0004%

Median 500.00 µm 499.96 µm 0.008%

Mean 500.00 µm 500.12 µm 0.024%

Mode 495.00 µm 520.79 µm 5.21%

10th Percentile 223.28 µm 223.17 µm 0.05%

12.525th Percentile 250.00 µm 249.96 µm 0.016%

%<250 µm 12.525% 12.53% 0.04%

%>=250 µm 87.475% 87.47% 0.006%

StdDev 204.35 µm 204.72 µm 0.18%

Choosing Channel Grouping

The more counts per channel, the better the statistical stability. The fewer channels chosen, the more counts there will be per channel.

The more channels chosen, the higher the potential resolution of change and the more counts required for statistical stability.

The fewer channels chosen, the lower the potential resolution of change and the less counts required for statistical stability.

Channel Grouping

Rules of Thumb:

Select the smallest channel range possible that encompasses all the data.

Use/explore linear and log channel groupings.

Internal usage only

Log v. Linear – Mostly fine particles

In this example most of the particle counts are less than 100µm – with an increase in the number of particles in this range over time

Using a linear scale – one-tenth of the channels are for particles less than 100µm – not very sensitive to change in this region

Using a logarithmic scale two-thirds of the channels are for particles less than 100µm – much more sensitive to change in this region*

Alternatively, zoom in on the linear channel

134*NOTE: The caveat is for channels narrower than the actual data (0.25 um), the data is interpolated

Internal usage only

Log v. Linear – Mostly coarse particles

In this example most of the particle counts are greater than 100µm – with an increase in the number of particles in this range over time

Using a linear scale – nine-tenths of the channels are for particles greater than 100µm –very sensitive to change in this region

Using a logarithmic scale one-third of the channels are for particles greater than 100µm – much less sensitive to change in this region

Internal usage only

Log scale

Internal usage only

Linear scale

Isolate region of change easily when looking at a linear scale

Internal usage only

Linear scale

Isolate region of change easily when looking at a linear scale

Part 12: Signal Aliasing

Ian Haley

Signal Aliasing

If a process shows periodic oscillations, the issue of ‘aliasing’ can be important.

Under certain conditions a combination of the process oscillation time, instrument response time, data lag and averaging can conspire to present a misleading result

The following slides explain….

Considering Signal Aliasing

Case A (measurement interval = 30 sec)

Ideal.

The output signal closely approximates the process variable.

a) Measurement Interval = 30 sec

Process Variable Measured Data Points Instrument Output Reconstructed Signal

Time (minutes)

Measurement Precision without Aliasing

Case B (30sec MD 5 measurement average= 150 sec)

Process dynamics are maintained, but the time lag is increased and the amplitude of the oscillations is dampened.

Time (minutes)

b) Averaging = 5 measurements

Case C (measurement interval = 120 sec)

Process dynamics are maintained, but the time lag is increased and the amplitude of the oscillations is dampened.

Time (minutes)

b) Measurement Duration = 120 sec

Case D (measurement interval = 240 sec)

Aliasing.

Process dynamics are misrepresented for a measurement interval greater than 175 seconds (half the period of the process oscillations).

c) Measurement Interval = 240 sec

0.0 5.0 10.0 15.0 20.0 25.0 30.0

Time (minutes)

Measurement Precision without Aliasing

Case C (30sec MD 10 measurement average = 300 sec)

Aliasing does not occur, even as the total measurement duration approaches the period of the process.

Note: At TMD = 350 seconds, the measured signal shows no dynamics.

c) Averaging = 10 measurements

10.0 15.0 20.0 25.0 30.0 35.0 40.0

Time (minutes)

Part 13: Practical Aspects of Using FBRM: Probe Location and Orientation

Ian Haley

The “Typical” FBRM® System

LENGTH

375MM14.75IN

FLANGE WELDEDTO DIP PIPE

BY CUSTOMER

EXHAUSTTUBE

RETAININGFLANGES

REACTOR TOP

ADAPTER WELDED TODIP PIPEBY CUSTOMER

Why is Probe Location and Orientation Important?

FBRM is a ‘point’ measurement

Particles passing that ‘point’ must be sufficiently representative of the process for process changes to be tracked.

The instrument can only measure what it can see.

Choosing a probe location

Probe insertion: 30-60° angle to the flow

- Presents probe tip with fresh slurry

- Maintains a clean probe window

Probe Orientation

Probe orientation becomes more important with:

- Extremes in individual particle density (very low or very high in relation to the carrying solution).

- Lower solids concentration.

- Lower carrying solution viscosity.

- A larger median particle size.

- A wider particle size distribution.

- Greater particle shape deviation from a sphere.

Probe Orientation

More flexibility in probe location is allowed by:- Smaller differences between particle density

and carrying solution density.

- Higher solids concentration (dispersed-phase liquid).

- A smaller median particle size.

- A narrower particle size distribution.

- Smaller differences between average particle shape and a sphere.

Ideal Probe Location in a Pipeline

Probe installed in a vertical, up-flow pipe, three to five pipe diameters from the top of the last elbow:

- Provides an ideal length of obstruction-free pipe upstream of the probe

- Offers the most uniformly random and representative presentation of the dispersed phase to the measurement zone

- Keeps the probe window residue-free

Typical Pipeline Installation: FBRM® D600S

Mounting in Stirrer Vessels

The goal is to provide a well-mixed, representative sample to the probe

Choose a mounting location that will present the material of interest to the probe tip

Mounting in Stirred Vessels

Avoid areas that are not completely homogeneous

If the probe is inserted from the top of the reactor, locate it near the leading side of the baffle

Avoid the trailing side of the baffle, as this is where there are dead areas and eddies where particles may settle or segregate

Down- vs. up-flow impeller

Location of the probe within the vessel must take into account the vertical direction of the flow. (Is the flow upward or downward at the vessel wall?)

For example, if the probe is inserted from the top of the vessel, the probe must be installed in a location where the flow is in a generally upward direction.

Part 14: Standard Procedures

Ian Haley

D600L Performance Verification

Instrument Repeatability Assurance Assessment of instrument measurement performance

Initial instrument OQ Uses PVC Reference Standard & Fixed Beaker Stand

Unique PVC Standard prepared and measured on new instrument in

Lasentec factory

Standard delivered with instrument to customer

Standard measured and compared with factory reference data

Continued instrument PQ Uses PVC Reference Standard & Fixed Beaker Stand

Measure Standard at regular intervals and compare with factory reference

Calibration Verification through Measurement of the PVC Reference Standard

PVC Measurement:

at the Factory

at startup (IQ/OQ)

after 3 months (PQ)

D600 Window Reference Procedure

Correct focus position of the laser is important Reproducibility

Best quality data

Window Reference Position is on the window surface Minimises effect of light scattering or refractive difference changes on quality of data

Over time, window position may drift Procedure for locating correct Window Reference Position

Precision micrometer used to adjust focus position

basic principles of FBRM

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