modeling approaches to increase the efficiency of clear ......2018/10/04  · (dynochem), nrtl -sac...

Modeling Approaches to Increase the Efficiency of Clear-Point-Based Solubility CharacterizationPaul Larsen, Dallin WhitakerCrop Protection Product Design & Process R&D

OCTOBER 4, 2018

TECHNO BIS CRYSTALLI Z ATI O N WORKSHOP

Agriculture Division of DowDuPont

Who is Corteva?

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Crystallization Background

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• Image Analysis

• Population Balance Modeling

• Statistical Estimation

PhD Thesis, UW-Madison 2007:http://jbrwww.che.wisc.edu/theses/larsen.pdf

Crystallization Background

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• Optimization of industrial crystallizers• Solubility characterization• Design and start-up of new, commercial-scale,

continuous crystallizer• Formulation product development

Early Stage Solvent Screening

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• Objective:• Identify promising solvents for crystallization and/or formulation

• Constraints:• Material availability• Time

• Considerations• Solvency for active ingredient• Solvent physical properties• Impact on product performance• Regulatory considerations• Cost/availability

Analytical method (aka slurry equilibration)• Add excess solids to solvent to create slurry• Equilibrate at desired temperature • Sample and analyze supernatant

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Solubility Measurement: Analytical Method

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Isothermal Clear-Point MethodLoading [wt%]

2 4 6 8 10 12 14 16

20 °C

40 °C

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Transmissivity

Temperature

Clear point

Cloud point

Lasersource

Detector

Polythermal Clear-Point Method

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Figure courtesy of Technobis Crystallization Systems

Polythermal Method: Crystal16

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Analytical method

Isothermal Clear point

Polythermal Clear point

Sample prep timeHeating/mixing equipment timeAnalytical analysis timeImpurity analysisCloud pointAccuracyMaterial Quantity

Method Comparison

Downsides of Polythermal Method

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Polythermal clear-point determination requires 1. a priori knowledge of the solubility in the various solvents of

interest2. a method to extrapolate the measured results to a specific

temperature of interest, 3. understanding of suitable temperature ramp rates for

adequate accuracy

Each of these challenges can be addressed by modeling.

A priori knowledge of solubility

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Options for solubility range-finding:1. Experimental 2. Semi-empirical

• Determine model parameters by regressing data in 4+ different solvents

• Examples: Hansen (HSPiP), Regressed UNIFAC (Dynochem), NRTL-SAC (AspenTech)

3. Quantum chemistry, ab initio• Determine solubility based on molecular structure,

quantum chemistry, and statistical thermodynamics• Examples: COSMO-RS (COSMOtherm), COSMO-SAC

hansen-solubility.com

AspenTech

COSMOtherm Approach

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StatisticalThermodynamics

polarization charge density (σ) calculation

σ-profilegeneration

Phase equilibrium predictionsVLE, SLE, LLE,

COSMOtherm Features

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1. Accuracy• Reasonably accurate relative solubility prediction based on molecular

structure alone – no data required• Sufficiently accurate absolute solubility prediction based on solubility data in

single solvent – even for complex molecules (Mw < 600 g/mol)

2. Less material usage and experimental effort than other approaches3. Useful for other applications (e.g. cocrystal screening, partition ratios)4. Speed

• May require days for quantum calcs for new molecule• Solubility prediction takes only minutes – hundreds/day

5. Ease-of-use• Software easy to use (but learning curve is steeper than other approaches)• Software designed for scripting and batch processing

COSMOtherm Accuracy

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0

0.2

0.4

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0 0.2 0.4 0.6 0.8

Mea

sure

d M

ass F

ract

ion

Predicted Mass Fraction

Agrochemical Active Ingredient, Mw ~ 500 g/molHigh solubility in many organic solvents

COSMOtherm Accuracy

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0

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0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Mea

sure

d M

ass

Frac

Predicted Mass Frac

Agrochemical Active Ingredient, Mw ~ 400 g/molHigh solubility in many organic solvents

COSMOtherm Accuracy

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Agrochemical Active Ingredient, Mw ~ 450 g/molLow solubility in many organic solvents

0

0.1

0.2

0.3

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Mea

sure

d M

ass F

ract

ion

Predicted Mass Fraction

COSMOtherm Accuracy

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Agrochemical Intermediate, Mw ~ 400 g/molHansen method ineffective (R2<0.3)

0.0

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1.0

0.0 0.25 0.5 0.75 1.0

Mea

sure

d M

ass F

ract

ion

Predicted Mass Fraction

COSMOtherm is not perfect, but good enough to get in the right ballpark for polythermal solubility measurement

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COSMOtherm and Solubility Workflow

Predicting solubility at specific temperature

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ln 𝛾𝛾𝑥𝑥 =∆𝐻𝐻𝑓𝑓𝑅𝑅

1𝑇𝑇𝑓𝑓−

1𝑇𝑇

𝑐𝑐 = 𝐴𝐴 + 𝐵𝐵𝑇𝑇 + 𝐶𝐶𝑇𝑇2

ln 𝑥𝑥 = 𝐴𝐴 +𝐵𝐵𝑇𝑇 + 𝐶𝐶 ln𝑇𝑇

…and many other variations

Recommend semi-empirical because Schroder-Van Laar often not adequate and empirical may produce non-physical results

Simplified Schroder-Van Laar

Empirical

Semi-empirical

Selecting a suitable ramp rate for polythermal clear-point method

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Factors that determine suitable temperature ramp rate:• Intrinsic dissolution rate• Initial particle size distribution (PSD)• Solubility

Approach: Use simulation to characterize impact of these factors on measurement accuracy

Particle size, [um]

Characterizing measurement accuracy via simulation

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Type Equation Key Assumptions

Population Balance

Size-independent dissolution rate

Dissolution rate

Well-mixed, no mass transfer limitations

Mass Balance Constant slurry volume

Transmittance(Beer-Lambert)

Dilute slurry, single-scattering

Model solution via method of characteristics and method of moments

D

D

𝐷𝐷 = 𝑘𝑘𝑑𝑑 �̂�𝐶 − �̂�𝐶∗

H. B. Matthews, Model Identification and Control of Batch Crystallization for an Industrial Chemical System, PhD thesis, University of Wisconsin-Madison, April 1997.

Example Simulation Output

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t = 0 min

t = 900 min

t = 1150 min

Particle size, [um]

PSD

Time [min]

Time [min]

solubility

Liquid phase conc.

end of transitionstart end

DOE: impact of variables on measurement accuracy

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Objective: Determine relative significance of variables impacting accuracy of polythermal clear-point-based solubility measurement

Factors:1. Ramp rate [C/min]2. Mean particle size [um]3. PSD shape [unitless]4. Dissolution rate constant [cm/min]5. Solubility at 0 C [mass fraction]6. Slope of solubility curve [1/C]

Design: full-factorial (64 simulations)

Characteristic Length [µm]

Particle Size Distribution

DOE: impact of variables on measurement accuracy

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Objective: Determine relative significance of variables impacting accuracy of polythermal clear-point-based solubility measurement

Factors:1. Ramp rate [C/min]2. Mean particle size [um]3. PSD shape [unitless]4. Dissolution rate constant [cm/min]5. Solubility at 0 C [mass fraction]6. Slope of solubility curve [1/C]

Design: full-factorial (64 simulations)

Characteristic Length [µm]

Particle Size Distribution

Solubility Curve

DOE Results

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Mean particle sizeDissolution rate constantRamp rateSlope of solubility curvePSD shape

Solubility at 0 C

Some Practical Questions

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1. What systems are suitable for clear-point-based measurement?2. How small should particles be to obtain accurate

measurement?3. What ramp rate is needed for worst-case scenario (low

solubility, low dissolution rate)?4. What can we learn from the shape of the transmittance

profile?

Impact of Particle Size and Ramp Rate

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Mean size = 100 µm

50 µm

10 µm

Mean size = 100 µm

50 µm

10 µm

Impact of Particle Size and Ramp Rate

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Mean size = 100 µm

50 µm

10 µm

Mean size = 100 µm

50 µm

10 µm

For systems with solubility <1 wt%, it is recommended to use particles with size ~10um.

Impact of Particle Size and Ramp Rate

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Mean size = 100 µm

50 µm

10 µm

Polythermal clear point method not recommended for systems with solubility < 1000ppm.

What determines the shape of the transmittance profile?

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narrow wide

Tran

smitt

ance

time time

Hypothesis: Measurement error correlates with transition width.

Transition width = Temp at end – Temp at start

Measurement error vs transition width

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Wide transition does not necessarily indicate low accuracy

Measurement error vs transition width

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Purple: low solubilityBlue: medium solubilityYellow: high solubilityMarker size: particle size

Transition width depends on many factors Generally increases with decreasing solubility and increasing particle size

Measurement error vs transition width

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Purple: low dissolution rate constantYellow: high dissolution rate constantMarker size: ramp rate

Transition width also affected by Ramp rate and dissolution rate

Summary

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1. Polythermal clear point method has many advantages for early-stage solvent screening.

2. Predictive tools such as COSMOtherm increase the experimental efficiency of clear point methods.

3. Measurement accuracy depends not only on ramp rate but also on initial PSD, intrinsic dissolution rate, and solubility curve.

4. Keep ramp rate and initial particle size as small as feasible to increase accuracy.