Modeling Approaches to Increase the Efficiency of Clear-Point- Based Solubility Characterization

Transcription

1 Modeling Approaches to Increase the Efficiency of Clear-Point- Based Solubility Characterization Paul Larsen, Dallin Whitaker Crop Protection Product Design & Process R&D OCTOBER 4, 2018 TECHNOBIS CRYSTALLI ZATI ON WORKSHOP

2 Who is Corteva? 2

3 Crystallization Background Image Analysis Statistical Estimation Population Balance Modeling PhD Thesis, UW-Madison 2007: 3

4 Crystallization Background Optimization of industrial crystallizers Solubility characterization Design and start-up of new, commercial-scale, continuous crystallizer Formulation product development 4

5 Early Stage Solvent Screening 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 5

6 Solubility Measurement: Analytical Method Analytical method (aka slurry equilibration) Add excess solids to solvent to create slurry Equilibrate at desired temperature Sample and analyze supernatant 6

7 Isothermal Clear-Point Method Loading [wt%] C 40 C 7

8 Polythermal Clear-Point Method Laser source Detector Clear point Cloud point Temperature Transmissivity 8

9 Polythermal Method: Crystal16 Figure courtesy of Technobis Crystallization Systems 9

10 Method Comparison Sample prep time Heating/mixing equipment time Analytical analysis time Impurity analysis Cloud point Accuracy Material Quantity Analytical method Isothermal Clear point Polythermal Clear point 10

11 Downsides of Polythermal Method Polythermal clear-point determination requires 1. a priori knowledge of the solubility in the various solvents of interest 2. 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. 11

12 A priori knowledge of solubility 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 12

13 COSMOtherm Approach polarization charge density (σ) calculation σ-profile generation Statistical Thermodynamics Phase equilibrium predictions VLE, SLE, LLE, DOW RESTRICTED 13

14 COSMOtherm Features 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 approaches 3. 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 14

15 COSMOtherm Accuracy Measured Mass Fraction Agrochemical Active Ingredient, Mw ~ 500 g/mol High solubility in many organic solvents Predicted Mass Fraction 15

16 COSMOtherm Accuracy Measured Mass Frac Agrochemical Active Ingredient, Mw ~ 400 g/mol High solubility in many organic solvents Predicted Mass Frac 16

17 Measured Mass Fraction COSMOtherm Accuracy Agrochemical Active Ingredient, Mw ~ 450 g/mol Low solubility in many organic solvents Predicted Mass Fraction 17

18 COSMOtherm Accuracy 1.0 Measured Mass Fraction Agrochemical Intermediate, Mw ~ 400 g/mol Hansen method ineffective (R 2 <0.3) Predicted Mass Fraction COSMOtherm is not perfect, but good enough to get in the right ballpark for polythermal solubility measurement 18

19 COSMOtherm and Solubility Workflow 19

20 Predicting solubility at specific temperature ln γγxx = HH ff RR 1 TT ff 1 TT Simplified Schroder-Van Laar cc = AA + BBBB + CCTT 2 Empirical ln xx = AA + BB TT + CC ln TT Semi-empirical and many other variations Recommend semi-empirical because Schroder-Van Laar often not adequate and empirical may produce non-physical results 20

21 Selecting a suitable ramp rate for polythermal clear-point method Factors that determine suitable temperature ramp rate: Intrinsic dissolution rate Initial particle size distribution (PSD) Solubility Particle size, [um] Approach: Use simulation to characterize impact of these factors on measurement accuracy 21

22 Characterizing measurement accuracy via simulation Type Equation Key Assumptions Population Balance D Size-independent dissolution rate Dissolution rate DD = kk dd CC CC Well-mixed, no mass transfer limitations Mass Balance D Constant slurry volume Transmittance (Beer-Lambert) Dilute slurry, single-scattering Model solution via method of characteristics and method of moments H. B. Matthews, Model Identification and Control of Batch Crystallization for an Industrial Chemical System, PhD thesis, University of Wisconsin-Madison, April

23 Example Simulation Output t = 0 min PSD t = 900 min t = 1150 min solubility Liquid phase conc. Particle size, [um] Time [min] start end of transition Time [min] 23

24 DOE: impact of variables on measurement accuracy 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] Particle Size Distribution Characteristic Length [µm] Design: full-factorial (64 simulations) 24

25 DOE: impact of variables on measurement accuracy 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] Particle Size Distribution Solubility Curve Characteristic Length [µm] Design: full-factorial (64 simulations) 25

26 DOE Results Mean particle size Dissolution rate constant Ramp rate Slope of solubility curve PSD shape Solubility at 0 C 26

27 Some Practical Questions 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? 27

28 Impact of Particle Size and Ramp Rate Mean size = 100 µm 50 µm Mean size = 100 µm 50 µm 10 µm 10 µm 28

29 Impact of Particle Size and Ramp Rate 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. 29

30 Impact of Particle Size and Ramp Rate Mean size = 100 µm 50 µm 10 µm Polythermal clear point method not recommended for systems with solubility < 1000ppm. 30

31 What determines the shape of the transmittance profile? narrow wide Transmittance time time Hypothesis: Measurement error correlates with transition width. Transition width = Temp at end Temp at start 31

32 Measurement error vs transition width Wide transition does not necessarily indicate low accuracy 32

33 Measurement error vs transition width Purple: low solubility Blue: medium solubility Yellow: high solubility Marker size: particle size Transition width depends on many factors Generally increases with decreasing solubility and increasing particle size 33

34 Measurement error vs transition width Purple: low dissolution rate constant Yellow: high dissolution rate constant Marker size: ramp rate Transition width also affected by Ramp rate and dissolution rate 34

35 Summary 1. Polythermal clear point method has many advantages for earlystage 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. 35