nucleation and growth kinetics for combined cooling and … · 2018-10-15 · jennifer m. schall....

Jennifer M. SchallCo-authors: Dr. Jasdeep Mandur, Prof. Richard D. Braatz, Prof. Allan S. MyersonOctober 3rd, 2018

Nucleation and Growth Kinetics for Combined Cooling and Antisolvent Crystallizationin an MSMPR System: Estimating Solvent Dependency

Pharmaceutical companies are evaluating continuous processing to decrease costs and increase control.

SafetyEconomics Control

API C

once

ntra

tion

Antisolvent Fraction

Outlet

InletHow do we design robust continuous crystallization processes quickly, using minimal API?

2

MSMPR Advantages:

Robust, steady-state operation

Consistent final product and quality

Take advantage of operating conditions with beneficial kinetics

Can select configuration to control polymorphism, purity, morphology

MSMPR crystallizers offer many advantages over batch crystallizers.

MSMPR ≡ Mixed-suspension, mixed-product reactor3

API C

once

ntra

tion

Temperature

Outlet

Inlet

Model assumptions:

1. Well-mixed

2. Negligible agglomeration and breakage

3. No growth dispersion

4. Nucleate from size zero

Model equations:

1. Material balance

2. Population balance

3. Growth expression

4. Nucleation expression

SS MSMPR models are readily expanded for multi-stage SS MSMPR cascade design.

4

1−=+ iii

ii nndLdnGτ

( )∫ −== − iiivsiT CCdLnLkM 13ρ

,,

lnig

ii g i

s i

CG kC

=

2/3,

,

lnib

ii b i T

s i

CB k MC

=

Growth

𝐺𝐺 = 𝑘𝑘𝑔𝑔 𝑙𝑙𝑙𝑙𝐶𝐶𝐶𝐶𝑠𝑠

𝑔𝑔

Nucleation

𝐵𝐵 = 𝑘𝑘𝑏𝑏 𝑙𝑙𝑙𝑙𝐶𝐶𝐶𝐶𝑠𝑠

𝑏𝑏

𝑀𝑀𝑇𝑇2/3

Growth and nucleation parameters can be regressed simultaneously from SS MSMPR experimental data.

Parameter Regression

min𝜃𝜃

Φ 𝜃𝜃 = �0

𝐿𝐿𝑚𝑚𝑚𝑚𝑚𝑚

𝑙𝑙𝑒𝑒𝑒𝑒𝑒𝑒 − 𝑙𝑙𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐(𝐿𝐿) 2

subject to SS MSMPR Model equations

where 𝜃𝜃 = 𝑘𝑘𝑔𝑔,𝑔𝑔,𝑘𝑘𝑏𝑏 , 𝑏𝑏

5

Crystallization kinetic parameters can have both temperature and solvent dependence…

… so models of antisolvent crystallization processes must account for the role of solvent composition.

1. Improve protocol for designing continuous antisolvent crystallizations.2. Decrease the number of experiments required for process design.

KineticsThermodynamics

𝐺𝐺 = 𝑘𝑘𝑔𝑔(𝑇𝑇, 𝑥𝑥𝑠𝑠)𝜎𝜎𝑔𝑔(𝑒𝑒𝑠𝑠)

𝐵𝐵 = 𝑘𝑘𝑏𝑏(𝑇𝑇, 𝑥𝑥𝑠𝑠)𝜎𝜎𝑏𝑏(𝑒𝑒𝑠𝑠)𝑀𝑀𝑇𝑇2/3

API C

once

ntra

tion

Solvent Volume Fraction

6

𝐶𝐶 = 𝑓𝑓(𝑇𝑇, 𝑥𝑥𝑠𝑠)

We use a four-step process to evaluate solvent-dependent kinetics for continuous crystallizer design.

Obtain single-stage MSMPR kinetic data.Experiment

Determine the nucleation and growth parameters through regression.Regress

Evaluate changes in kinetic parameters as functions of solvent composition.Evaluate

Construct and validate continuous crystallization model using kinetic expressions

for nucleation and growth. Model

7

Our ultimate goal is to develop a continuous crystallization process for a commercial API.

Process Constraints

• < 8 stages• Combined cooling

+ antisolvent

Crystallization System

• Confidential API• Solvent mixture:

92 v% EtOH / 8 v% THF

• Antisolvent: Water

Final Product Characteristics

• Maximize yield (>90%)

• x50 > 40 μm• x90 < 250 μm

8







9

Single-stage MSMPR experiments are used to obtain kinetic data.

Cryst. Growth Des. 18, 3, 1560-157010

Single-stage MSMPR experiments are used to obtain kinetic data.

MSMPR Experimental Operating Conditions

Crystallizer Volume 80 mL

Feed Temp. 55°C

Crystallizer Temp. 10 - 30°C

Residence Time (RT) 1 - 3 hours

Solvent Volume Fractions 44 – 66%

Product Withdrawal Intermittent (1/10 RT)

11

Online, FBRM CLDs are used to track the transition to steady state. Steady-state operation is confirmed offline using HPLC and IR data.

0.3

0.5

0.7

0 300 600 900 1200 1500

Solvent VolumeFraction, xs(unitless)

Time, t (min)

0

5

10

15

20

25

0 300 600 900 1200 1500

Crystallizer Temperature, T

(°C)

Time, t (min)

0.0

0.5

1.0

1.5

2.0

2.5

0 300 600 900 1200 1500

Mother Liquor Concentration, C

(g API/kg solution)

Time, t (min)

0100020003000400050006000700080009000

10000

0 300 600 900 1200 1500

Particle Count Frequency

(#/s)

Time, t (min)

< 10 micron10 - 50 micron50 - 150 micron150 - 300 micron

Cryst. Growth Des. 18, 3, 1560-157012

Six steady-state continuous MSMPR experiments were used to map the operating space.

Experimental Conditions for Single-Stage MSMPR Kinetic Experiments

Steady-State Average

RunMSMPR Exp. #

TemperatureResidence

Time


Feed Concentration*

°C min unitless g API / kg solution

11 10 90 0.44 17.4312 20 90 0.44 17.431

23 10 180 0.66 27.1834 30 180 0.66 27.183

35 10 90 0.48 19.2206 30 90 0.48 19.220

4 7 20 90 0.47 20.154

* Adjusted for antisolvent addition

13

Both cooling and antisolvent addition affect solubility and crystallization kinetics, which affect yield.


RunMSMPR Exp. #


Time


Supersaturation Concentration Yield

°C min unitless unitless g API / kg solutionmass

%% of equil.

11 10 90 0.44 1.19 1.17 93.29 95.22 20 90 0.44 1.05 1.34 92.31 94.9

23 10 180 0.66 1.26 10.24 62.34 69.84 30 180 0.66 1.05 15.11 44.40 55.1

35 10 90 0.48 1.75 2.92 84.80 87.16 30 90 0.48 1.27 3.23 83.19 87.3

4 7 20 90 0.47 1.32 2.29 88.64 91.4

Experimental Results for Single-Stage MSMPR Kinetic Experiments

14







15

Before regressing kinetic parameters, we must first establish the solubility and approximate the CSD.

Equations for Regression

Operating Conditions

Outlet API concentration

Solubility

CLD

Supersaturation

CSD

Material balance

Population balance

Growth

Nucleation

Experimental Data

16

Solubility is required to predict supersaturation, and kinetics are very sensitive to errors in thermodynamic estimates.

03100.5

3000.6

10

Temperature, T (K)

Solvent Fraction, Xs

2900.7

2800.8

20

Sol

ubili

ty, S

(g/k

g of

sol

utio

n)

2700.9

30

40

Se x p

Sp re d

𝐺𝐺 = 𝑘𝑘𝑔𝑔 ln𝐶𝐶𝐶𝐶𝑠𝑠𝑠𝑠𝑐𝑐

𝑔𝑔

𝐵𝐵 = 𝑘𝑘𝑏𝑏 ln𝐶𝐶𝐶𝐶𝑠𝑠𝑠𝑠𝑐𝑐

𝑏𝑏

𝜌𝜌𝑘𝑘𝑣𝑣𝜇𝜇323

17

We evaluate solubility as a function of temperature and solvent composition.

1. Model temperature dependence using Apelblat equation.

2. Expand parameters to account for solvent composition.

ln 𝐶𝐶𝑠𝑠𝑠𝑠𝑐𝑐,𝑖𝑖 = 𝛽𝛽1𝑖𝑖 +𝛽𝛽2𝑖𝑖𝑇𝑇 + 𝛽𝛽3𝑖𝑖 ln 𝑇𝑇

𝛽𝛽𝑘𝑘 = 𝛼𝛼𝑘𝑘1 + 𝛼𝛼𝑘𝑘2𝑥𝑥𝑠𝑠 +𝛼𝛼𝑘𝑘3𝑥𝑥𝑠𝑠

+ 𝛼𝛼𝑘𝑘4 ln 𝑥𝑥𝑠𝑠

275 280 285 290 295 300 305 310

Temperature, K

0

5

10

15

20

25

30

35

Sol

ubili

ty, g

/kg

of s

olut

ion

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9

Solvent Composition, (v/v)

0

5

10

15

20

25

30

35

Sol

ubili

ty, g

/kg

of s

olut

ion

Decreasing solvent composition

Decreasing temperature

Cryst. Growth Des. 18, 3, 1560-157018

The volume-weighted CSD is approximated by the L4-weighted CLD from FBRM.

19

0

0.01

0.02

0.03

0.04

0.05

0.06

0 200 400 600

Volu

me-

base

d CS

D

Length, L (microns)

normalized CLD, L3normalized cubed PSD

0

0.01

0.02

0.03

0.04

0.05

0.06

0 200 400 600

Volu

me-

base

d CS

D

Length, L (microns)

normalized CLD, L4normalized cubed PSD

Cryst. Growth Des. 18, 3, 1560-1570

Kinetic parameters are determined through least-squares regression.

Steady-state parameter estimation:

min𝑘𝑘𝑔𝑔 ,𝑘𝑘𝑏𝑏

𝑤𝑤1 𝐶𝐶𝑒𝑒𝑝𝑝𝑒𝑒𝑝𝑝 − 𝐶𝐶𝑒𝑒𝑒𝑒𝑒𝑒2 + 𝑤𝑤2�

𝐿𝐿

𝑉𝑉𝑉𝑉𝑙𝑙𝐶𝐶𝐶𝐶𝐷𝐷𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝(𝐿𝐿)− 𝑉𝑉𝑉𝑉𝑙𝑙𝐶𝐶𝐶𝐶𝐷𝐷𝑝𝑝𝑚𝑚𝑝𝑝(𝐿𝐿)2

s.t.

𝑙𝑙 𝐿𝐿 =𝐵𝐵𝐺𝐺 exp −

𝐿𝐿𝜏𝜏𝐺𝐺

𝑉𝑉𝑉𝑉𝑙𝑙𝐶𝐶𝐶𝐶𝐷𝐷 =∫𝐿𝐿𝑖𝑖𝐿𝐿𝑖𝑖+1 𝑙𝑙 𝐿𝐿 𝐿𝐿3𝑑𝑑𝐿𝐿

∫𝐿𝐿0𝐿𝐿𝑓𝑓 𝑙𝑙 𝐿𝐿 𝐿𝐿3𝑑𝑑𝐿𝐿

𝐶𝐶𝑖𝑖𝑖𝑖 − 𝐶𝐶 − 6𝜌𝜌𝑘𝑘𝑣𝑣𝐵𝐵𝐺𝐺3𝜏𝜏4 = 0𝜇𝜇3 − 6𝐵𝐵𝐺𝐺3𝜏𝜏4 = 0

𝐺𝐺 = 𝑘𝑘𝑔𝑔 ln𝐶𝐶𝐶𝐶𝑠𝑠𝑠𝑠𝑐𝑐

𝑔𝑔

𝐵𝐵 = 𝑘𝑘𝑏𝑏 ln𝐶𝐶𝐶𝐶𝑠𝑠𝑠𝑠𝑐𝑐

𝑏𝑏 𝜇𝜇33𝐺𝐺𝜏𝜏

𝑔𝑔 = 1𝑏𝑏 = 2

20







21

Growth and nucleation rate coefficients increase with antisolvent fraction.

kbkg

0

0.1

0.2

0.3

0.4

0.5

0.4 0.5 0.6 0.7

Grow

th ra

te co

effic

ient

[kg]

(μm

/min

x 10

6 )

Solvent volume fraction [xs] (unitless)

0

1

2

3

4

5

0.4 0.5 0.6 0.7

Nuc

leat

ion

rate

coef

ficie

nt[k

b] (#

/min

/kg

solu

tion

x 10-6

)


Cryst. Growth Des. 18, 3, 1560-157022

Growth coefficients follow an Arrhenius temperature relationship, while nucleation coefficients show mild temperature sensitivity.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.4 0.5 0.6 0.7

Grow

th ra

te co

effic

ient

[k

g] (μ

m/m

in x

106 )

Solvent volume fraction [xs](unitless)

0

1

2

3

4

5

0.4 0.5 0.6 0.7

Aver

age

nucl

eatio

n ra

te co

effic

ient

[k

b] (#

/min

/kg

solu

tion

x 10-6

)


Cryst. Growth Des. 18, 3, 1560-157023

kbkg

Regressed kinetic parameters are used to reconstruct steady-state PSDs and concentrations.

MSMPR Exp. # Temperature (°C) Residence Time (min) Solvent Fraction (unitless)3 10 180 0.664 30 180 0.66

0 500 1000 1500 2000 2500 3000 3500

Time, (min)

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

AP

I Con

cent

ratio

n (g

/g)

Measured conc; Xs=66%; T=10C


predicted conc; Xs=66%; T=10C


0 100 200 300 400 500 600 700 800 900 1000

Length, L (microns)

0

0.01

0.02

0.03

0.04

0.05

0.06

Vol

ume

base

d di

strib

utio

n

L 4 weighted CLD; Xs=66%; T=10C

Predicted vol PSD; Xs=66%; T=10C



Cryst. Growth Des. 18, 3, 1560-157024







25

Data from MSMPR Experiment 7 were used to validate the kinetic parameter model.

2000 2500 3000 3500

Time, (min)

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

AP

I Con

cent

ratio

n (g

/g)

10-3



0 200 400 600 800 1000

Length, L (microns)

0

0.01

0.02

0.03

0.04

0.05

0.06

Vol

ume

base

d di

strib

utio

n



Cryst. Growth Des. 18, 3, 1560-157026

If we neglect solvent dependence in kinetics, crystallizer performance will not be acceptably predicted.

Kinetic parameters regressed from Experiments 5 & 6 (xs = 0.48) were used to predict data from Experiments 3 & 4 (xs = 0.66).

0 500 1000 1500 2000 2500 3000 35000.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

Time (min)

AP

I Con

cent

ratio

n (g

AP

I/g s

olve

nt)

Measured conc; xs=66%; T=10°C


predicted conc; xs=66%; T=10°C


0 200 400 600 800 10000

0.01

0.02

0.03

0.04

0.05

0.06

Length, L (microns)

Vol

ume-

base

d di

strib

utio

n fra

ctio

n (u

nitle

ss)

L4 weighted CLD; xs=66%; T=10°C

Predicted vol PSD; xs=66%; T=10°C



Cryst. Growth Des. 18, 3, 1560-157027

SS prediction with solvent-dependent kinetics

Crystallizer performance may not be acceptably predicted even at similar solvent compositions.

Kinetic parameters regressed from Experiments 5 & 6 (xs = 0.48) were used to predict data from Experiments 1 & 2 (xs = 0.44).

0 200 400 600 800 10000

0.01

0.02

0.03

0.04

0.05

0.06

Length, L (microns)

Vol

ume-

base

d di

strib

utio

n fra

ctio

n (u

nitle

ss)





0 500 1000 1500

0.5

1

1.5

2

x 10-3

Time (min)

API C

once

ntra

tion

(g A

PI/g

sol

vent

)





Cryst. Growth Des. 18, 3, 1560-157028

SS prediction with solvent-dependent kinetics

Small changes in solvent composition can have large yield impacts, arising from changing kinetics.


RunMSMPR Exp. #


TimeSolvent Volume

FractionYield

°C min unitless mass % % of equil.

35 10 90 0.48 84.80 87.16 30 90 0.48 83.19 87.3

4 7 20 90 0.47 88.64 91.4

Results for 90 min RT Single-Stage MSMPR Kinetic Experiments

29







30

Once we know the functionality of kinetic parameters, we can predict crystallizer performance in MSMPR cascades.

31

Thermodynamics & kinetics depend on operating conditions in each stage

Ti, xs,i kg,i, gi, kb,i, bi

Can now estimate attainable region & optimize cascade performance

AS

…AS ASAS

T1, xs,1 T2, xs,2 Ti-1, xs,i-1 Ti, xs,i

Product

In the simplest case, we can predict performance in a single crystallizer.

32

ASFeed

Ti, xs,i

Product

Optimization ProblemMaximize yield (Y) subject to:

60min 180mintotτ< <

10 55iC T C° ≤ ≤ °

,0.44 0.90s ix≤ ≤

50 40d mµ>

90 250d mµ<

70 g/kgfeedC =

Optimized Operating Conditions Product Constraints Met?

Case Feed Concentration

Residence Time

Temp. Solvent Fraction

Yield Yield > 90%? x50 > 40 μm x90 < 240 μm

g API / kg soln min °C unitless mass%Neglecting solvent effects on kinetics. 70 71.4 10.0 0.55 79.5% X

Kinetics are solvent-dependent. 70 104.9 10.0 0.47 95.4%

Final product specifications can be met in a single MSMPR crystallizer!

In the future, we will predict crystallization performance in multi-stage antisolvent MSMPR cascades.

This method requires 6+ steady-state experiments; fewer for transient experiments.Method

Growth and nucleation kinetic parameters are functions of solvent composition.Functionality

To acceptably model crystallizer performance, we should include solvent composition effects in kinetic expressions.

Modeling

Simulate and validate a multi-stage MSMPR crystallization cascade.Future Work

33

Acknowledgements

Prof. Allan Myerson

Prof. Bernhardt Trout

Prof. Richard Braatz

Myerson & Trout group members

Dr. Jasdeep Mandur

UROPs Tony Elian & Zach Schmitz

34

Supplemental Slides

At steady-state, particles are not appreciably agglomerated.

Experimental Conditions (6): 48% (EtOH/THF)/52% Water (v/v), 90 min RT, 30°C

36

Heavy fouling prevented online IR analysis and influenced start-up procedure.

37

Model for Multistage MSMPR

( )∫ −== − iiivsiT CCdLnLkM 13ρ

g

s

sg C

CCkG

−=

2/3b

sb T

s

C CB k MC

−=

Population Balance: Conservation equation for the number of crystals in a population

Mass Balance

Crystal Growth

Nucleation

ni: population density at stage iτi: residence time at stage iL: crystal sizeGi: crystal growth rate at stage iB: nucleation rate

MT i: Suspension density at stage iC: steady state solute concentrationρs: crystal densitykv : volume shape factor

Cs: equilibrium concentrationkg, g, kb, b: model parameters to

be estimated

1−=+ iii

ii nndLdnGτ (1)

(2)

(3)

(4)

nucleation and growth kinetics for combined cooling and … · 2018-10-15 · jennifer m. schall....

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