crystal morphology: measurement, modelling and closed-loop

XueXue Z WangZ Wang

Professor in Intelligent Measurement and ControlProfessor in Intelligent Measurement and Control

Institute of Particle Science and EngineeringInstitute of Particle Science and Engineering

[email protected]@leeds.ac.uk

Crystal Morphology: Measurement, Crystal Morphology: Measurement,

ModellingModelling and Closedand Closed--loop Controlloop Control

Crystal ShapeCrystal Shape

Of critical importance to the end-use properties of the final product e.g. bioavailability

Dictates other properties e.g. particle size

Affects downstream processing filtration, grinding, solid/liquid separations

47.40 C

Observation on ModellingObservation on ModellingCrystal morphology Crystal morphology prediction only for single prediction only for single crystals:crystals: HABIT,HABIT, CeriusCerius22 ....

Gap: single crystal Gap: single crystal morphology morphology −− crystal crystal population in a reactorpopulation in a reactor

Is there such a thing Is there such a thing ‘‘morphology for crystalmorphology for crystalpopulation in a reactor ?population in a reactor ?

HABIT SHAPE

Growth Growth BehaviourBehaviour of Crystal Population in a of Crystal Population in a Reactor: Reactor: Population Balance (PB) Population Balance (PB) ModellingModelling

PB modelling is Process Scale Modelling, Useful for Process Design, Optimisation and Control

Observation on Observation on ModellingModelling

PB Modelling: Evolution of Crystal Size Distribution with Time

Size Definition: Diameter of a Sphere Having the Same Volume as the Crystal

Shape distribution ?Shape distribution ?

Observation on Observation on MeasurementMeasurement

XRD, FTIR, Acoustic Spectroscopy, Raman, FBRM…Providing Little or Limited Shape Information

On-line Imaging: PVM, Perdix, GSK Imaging..Image Analysis as the Bottleneck

Observation on Observation on Morphology ControlMorphology ControlPrevious Work: Focused on CSD Control

Closed-loop Control of Shape Distribution: Perceived as too Challenging to Achieve

ObjectivesObjectives

1. “Morphological” PB Modelling the Growth Behaviour of All Crystals in a Reactor; Shape Distribution as well as Size Distribution

2. Demonstrate: Simple Closed-Loop Strategy for Morphology and CSD Control

3. 2D and 3D On-line Characterisation of Morphology of Growing Crystals: Imaging and Image Analysis

4. Future Work

Population Balance Population Balance ModellingModelling

Ln(L,t)G

ttLn

∂∂=

∂∂ - ),(

n(L,t) – the number of crystals of size L at time tG – crystal growth rate, m/s

Nucleation and GrowthNucleation and Growth

σ αkG =σα bkb

B =

B – No. crystals /(m3s) α = ccsat

satc −

Mass and Energy BalancesMass and Energy Balances

),,,,( hkGLfdtdC ρ= ),,,,,,,,,( JTTAUVHkGLf

dtdT Δ= ρ

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

10 20 50 100 200 5000.000

0.005

0.010

0.015

0.020

0.025

0.030

� ��0.24

� ��0.20

� ��0.16

� ��0.12

� ��0.08

��0.04

� ��0.024

� ��0.008

MultiMulti--dimensionaldimensional (two) PB (two) PB ModellingModelling

n(LL,LW ,t) – the number of crystals of length LL, width LW, at time t

GL,GW – crystal growth rates of length and width , m/s

0 )],,([)],,n([ ),( , =

∂∂+

∂∂+

∂∂

W

WLW

L

WLLWL

LtLLnG

LtLLG

ttLLn

Plate crystals: length L, Width W, thickness 0

{111}{110}

{100}

x1

MorphologicalMorphological PB PB ModellingModelling

Size definition of a face: distance from geometric centre

Assumption: symmetrical faces have identical growth behaviour

Potash alum crystal

26 faces: 8 { 111 }6 { 100 }12 { 110 }

Three independent facesx, y, z

Only Growth

),,(),,(),,(

)],,(),,([]),,([),,(1

tyxRtyxDtyxB

tyxGtyxx

vtyxt

tyx N

ii

irrrrrr

rrrrrrrrr

+−=∂∂+⋅∇+

∂∂ ∑

=

ψψψ

),()],(),([)(),([)(

11

txRtxGtxxt

tVtxtV

N

ii

i

T

T

rrrr

=∂∂+

∂∂ ∑

=

ψψ

MorphologicalMorphological PB PB ModellingModelling

With GRD Without GRD

x – {111} y – {110} z – {100}

Comparisons of crystal shape evolution: Magenta – without GRD Black –with GRD for growth rates of faces {100} and {110}

30 µm

Time (s)700 900 1100 1300500 1500 1700

100 µm

2100 2300 2700 2900 Time (s1900 2500 3100 3300

AIChEAIChE J. J. 54(9), 232154(9), 2321--2334(2008)2334(2008)

Evolution of individual face {100}

x – {111} y – {110} z – {100}

500s 3300

s

Evolution of face 110

x – {111} y – {110} z – {100}

AIChEAIChE J. J. 54(9), 232154(9), 2321--2334(2008)2334(2008)

Evolution of growth sector boundaries

Magenta, Green - without GRD

Red, Black - with GRD

500700

9001100

13001500

1700 3300 Time (s)

{111}

{111}

{111}

{111}

{110} {110}

{100}

{100}

AIChEAIChE J. J. 54(9), 232154(9), 2321--2334(2008)2334(2008)

Lacmann et al. (1999), Chem. Eng. Technol., 22:279-289

{100}{111}

{110}

{100}

{110}

{111}

{111}

{111}

80 µm

AIChEAIChE J. J. 54(9), 232154(9), 2321--2334(2008)2334(2008)

Hot-stage Imagesb1, b2 & b3 − 80, 100 & 120s (5oC/min)

c1, c2 & c3 − 200, 240 & 280s (3oC/min)

b1

abc d

ef

12

3

45 6

8

7

109

1112b2

a

bc

d

e

f

1

2

34

56

8

7

109

1112 b3a

b

cd

e

f

1

2

3

4

56

8

7

10

9

1112

c3

ab

c

de

f

12

3

4

5

6 87

10

9

11

12c2

ab

c

de

f

12

3

4

5

6 87

10

9

11

12c1

ab

c

de

f

12

3

4

5

6 87

10

9

11

12

a3

a'

b'

c' d'

e'

f'

1'

2'

3'4'

5' 6'

8'

7'

10'

9'

11'12'

25 µm

a2

a'

b'

c' d'

e'

f'

11'12'

1'

2'

3'

4'

6'5'

8'

7'

9'

10'

15 µm

a1

f'a'

b'

c' d'

e'

11',12'

1',2'

3',4'

5',6'

7',8'

9',10'

20 µm

Predicted Crystal shape (3oC/min)240s

Qualitative agreement between prediction with GRD

and experiment

Shape Optimisation and Control

MPB

Crystal Shape and Size Distributions

Cooling or SupersaturationProfile; Impurity;

Solvents. Parameters

Simulation

Desired Crystal Shape and Size Distributions

MPB

Optimum Cooling or Supersaturation

Profile

Optimisation

G1 = f1(σ, size)G2 = f2(σ, size)G3 = f3(σ, size)

Initial Shape Distribution

Faceted Growth Rate

Target ShapeDistribution

Morph

ologic

al PB M

odel

Optim

isatio

n Algo

rithm


Supersaturation ProfileLeading to Desired Shape

Distribution


Optimum T or σ Profile, Leading to Desired Shape and Size Distributions

While Tracking T or σ Profile can be easily achieved by manipulating cooling water flowrate – simple feedback PID closed-loop control

Optimum T profile

Optimum σ Profile


Tracking T or σ Profile cannot guarantee the desired shape and size distributions; real-time sensing and predictive control is needed

Optimum T profile

Optimum σ Profile

22D & 3D Imaging and Image AnalysisD & 3D Imaging and Image Analysis

Camera

Fibre optic light

Reactor

- Camera speed: up to 30 images/s

- Field of view from 105μmX140μm

- 0.5 L batch reactor

AIChEAIChE J J 5151, 1406, 1406--10651065 (2005)(2005)

Camera

Fibre optic light

Reactor

REAL-TIME MONITORING

Low threshold High thresholdOriginal ImageOriginal Image

Challenges to Image AnalysisChallenges to Image Analysis

Morphologicalclosing

Morphologicalopening

Edge detectionScale 1


Removesmall objects

Real-time image

Segmented image

Region-filling

Edge addition

Morphologicalclosing

Morphologicalopening



Removesmall objects

Real-time image

Segmented image

Region-filling

Edge addition

A Multi-scale Image Segmentation

Method Using Wavelets

Accuracy

Robustness

Speed

ChemChem Eng Eng SciSci 6060(4) 1053(4) 1053--1065 (2005)1065 (2005)

Scale 1 Scale 2

ChemChem Eng Eng SciSci 6060(4) 1053(4) 1053--1065 (2005)1065 (2005)

Scale 1 + 2

Morphological closing

Region filling

Morphological opening

Removal of objects with lessThan 200 pixels & add grey scale

(a) Original image(b) Edges at 1st scale

(c) Edges at the 2nd scale

(d) Combined edges (e) Morphological closing (f) Region-filling on image

J Process Control J Process Control 15(715(7) ) 785785--797 (2005)797 (2005)

(h) Segmented objects after removing those with less than 200 pixels

(i) Original grey scale intensity superimposed

(g) Morphological opening

J Process Control, 15(7), 785-797 (2005)

DescriptorsShape descriptors

Database retrievalusing shape features

33--D shape from 2D images: camera modelD shape from 2D images: camera model

AIChEAIChE J. 52(6) 2297J. 52(6) 2297--2305 (2006)2305 (2006)

StereoVisionStereoVision ImagingImaging

Stereo angle (θ)

Stereo DVM cameras

Crystal growth cell (temperaturecontrolled

X-Y stage

Interface box for control of stereo angles, focus,

synchronisation of camera snapshots and

light sources, and and image recording

PC with software for Image management, analysis,and 3D shape construction

Light source

Camera head

OnOn--line 3D Imagingline 3D Imaging

Image AnalysisImage Analysis

Shape RecognitionShape Recognition

Faceted Growth RatesFaceted Growth Rates& PB& PB

Morphology Morphology PredictionPrediction

MultiMulti--dimensional dimensional Population Population

Balance ModellingBalance Modelling

ComputationalComputationalFluid DynamicsFluid Dynamics

++++

++++

Model-based Morphology Control

++++

ChemChem Eng Eng SciSci 6363, 1173, 1173--1184 (2008)1184 (2008)

Optimum Supersaturation

Profile

200 Litre Reactor, 200 Litre Reactor, donated by donated by AstraZenacaAstraZenaca

Move to 200 Litre Reactor Move to 200 Litre Reactor

OnOn--going and Future Workgoing and Future Work1. Use of Impurity / Solvent for Shape and CSD ControlSeeded crystallization producing β form L-glutamic acid, L-

phenylalanine as habit modifying impurity

a. The initial shape and size distribution of beta-form L-glutamic acid

))C103.5(109.41(σ0257.0G

)σ22.2σ15.251.0(G2

16.3impurity

2794.1L

2W

×××−=

−+−=−

β Form L-glutamic acid

2. Future Project: Formulation of Habit Modifying

Impurities / Solvents and Design of Crystal

Morphology: Integrating High–throughput

Technology with Multi-scale Modelling

Crystal16 control PC

2D/3D imaging probe

Crystal16 system

Crystal charcterisation(XRD,TGA,DSC etc.)

Imaging PC

Data analysis, decision making

RS1000 rack

Crystal16 control PC

2D/3D imaging probe

Crystal16 system

Crystal charcterisation(XRD,TGA,DSC etc.)

Imaging PC

Data analysis, decision making

RS1000 rack

Courtesy of AvantiumTechnologies BV

AcknowledgementAcknowledgement

3M Health Care3M Health CareDr JDr J Calderon Calderon De De AndaAnda

Dr Dr CaiCai YunYun MaMa Dr Dr JianJian WanWan

Dr Dr RuifaRuifa LiLi

Professor Professor Kevin J Kevin J Roberts Roberts

Miss JulianParton

Shape Project, StereoVision Project

Contact: Prof. Xue Z Wang, [email protected]

http://www.astrazeneca.co.uk/

http://www.leeds.ac.uk/speme/ipse/intellisense/index.html

http://www.syngenta.co.uk/index.asp

crystal morphology: measurement, modelling and closed-loop

Documents