Process development in the QbD paradigm: mechanistic modeling of

Subscriber access provided by University of Glasgow Library

Process development in the QbD paradigm: mechanistic modeling of antisolvent crystallization for production of pharmaceuticals Manu Garg, Milan Roy, Paresh P. Chokshi, and Anurag S. Rathore Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/ acs.cgd.8b00055 • Publication Date (Web): 25 Apr 2018 Downloaded from http://pubs.acs.org on April 27, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

Crystal Growth & Design

Process development in the QbD paradigm: mechanistic modeling of antisolvent crystallization for production of pharmaceuticals Manu Garg, Milan Roy, Paresh P. Chokshi and Anurag S. Rathore Indian Institute of Technology Delhi, Hauz Khas, New Delhi-111016, INDIA ABSTRACT: Thorough process understanding is a pre-requisite for implementing quality by design during development of a pharmaceutical crystallization process. Identification of the critical process parameters and raw material attributes and creation of mechanistic models that can correlate these to the product quality attributes are the first steps in this approach. In this paper, a mechanistic model of antisolvent crystallization has been proposed. The model considers dependence of crystal growth rate on crystal mean size. A risk assessment was performed using Failure Mode and Effects Analysis to identify critical process parameter for designing experimentation. Crystal morphological data required for development of this model has been obtained using focused beam reflectance measurement. MATLAB has been used to identify optimal growth and nucleation parameters. The proposed model compares favorably to other similar models with respect to the accuracy of prediction of crystal size, surface area and volume, even at varying feedrate profiles of anti-solvent during crystallization. The average residual value obtained in given model is of the order th of 1/10 of the previous models. The superlative performance likely originates from the fact that most models ignore the size dependence of crystal growth rate. We expect the proposed model to be a useful tool in the arsenal of those involved in development of pharmaceutical crystallization.

ACS Paragon Plus Environment

1

Crystal Growth & Design 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

Page 2 of 17

1. INTRODUCTION Crystallization is a separation and purification technique that is commonly used in the pharmaceutical industry for manufacturing of pharmaceutical products. It involves a phase change such that a crystalline product is obtained from the solution. Supersaturation, a zone where concentration of the compound is above the saturation concentration, is the driving force for crystallization. There are four ways of achieving supersaturation, namely temperature change, solvent evaporation, chemical reaction, and salting out. Of these four, cooling and solvent evaporation has been the method of choice for crystallization for production of pharmaceutical products. However, last couples of decades have witnessed a rising interest in salting out (antisolvent crystallization). This shift has been fueled by the advantages that antisolvent crystallization offers in cases when the solute is highly soluble or unstable at high temperature. Many researchers have explored the nucleation and growth kinetics of antisolvent crystallization. Mydlarz et al. (1993) proposed a three-parameter 1 exponential size-dependent crystal growth rate function. Correlation between rates of nucleation and supersaturation have also been proposed by Takiyama et al. (1998) based on analysis of the effect of different concentrations of aqueous 2 and antisolvent solutions on final crystal shape and distribution. A comparison between model-based and direct design approach for controlling 3 anti-solvent and cooling crystallization was provided by Nagy et al. (2007). Nowee et al. (2008) proposed a model for antisolvent crystallization where crystal growth rate was assumed to be independent of crystal size and agglomeration, 4 and attrition phenomena were neglected. In a separate publication, Nowee et al. (2008) presented a model for seeded cooling crystallization, identified the kinetic 5 parameters, and validated the model using experiments. Gimbun et al. (2009) proposed differential algebraic equation framework for 6 solving a general population balance equation. Samad et al. (2011) provided a generic multi-dimensional model-based system for batch cooling crystallization 7 processes. Use of focused beam reflectance measurement (FBRM) for optimizing crystallization of needle shaped particles that can deliver a product of required 8 quality attributes has been presented by Leyssens et al. (2011). Recent advances include model-based systematic design and analysis approach for unseeded combined cooling and antisolvent crystallization (CCAC) systems by 9 Yang et al. (2014). Apart from these, other researchers have attempted to solve 10-18 the population balance equation or relate growth function to crystal size. However, to the best of our knowledge, a comprehensive model for antisolvent crystallization incorporating mass balance, volume conservation, saturation, nucleation, and size dependent crystal growth rate is yet to be proposed. In this work, we propose a model for antisolvent crystallization in which the crystal growth rate is correlated to crystal size. The parameters in the model have been obtained from the experiments and the proposed model is used to predict the mean crystal size, area, and volume during antisolvent crystallization. Optimization of the model has been performed using MATLAB to calculate the growth and nucleation rate parameters. The proposed model has been validated experimentally. It has been demonstrated that the proposed model offers a significantly more accurate prediction when compared with other models that ignore size dependence of crystal growth rate. We expect the proposed model to


2

Page 3 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57


be a useful tool in the arsenal of those involved in development of pharmaceutical crystallization.

2. MATHEMATICAL MODEL The population balance equation (PBE) for the transient of crystal size distribution (CSD) in the absence of crystal breakage and agglomeration can be 19 written as: (,)

=

( ()(,))

+ ( , )

(1)

Where ( , ) is the number density of crystals of size at any time t, ( ) is the size dependent crystal growth rate, and is the nucleation rate. Here, δ is the Dirac delta function and is the critical nucleus size. The moment transformation can be applied to the population balance equation for th simplification. The k moment of the crystal size distribution is given by:

= ( , )

(2)

The first four moments have physical significance. While the represents the total number of particles, represents the total length of the crystals, represents total crystal surface area, and represents total volume occupied by the crystals. These moments are based on per unit volume of total suspension. The moment transformation of equation (1) yields the following governing equations for the moments of the CSD:

= ( )( , ) + (0, )

(3)

It is not possible to solve the above equations since the growth term integral cannot be expressed in terms of moments. Hence, the quadrature method of moments (QMOM) was applied to equation (3) by approximating the moments as a set of abscissas and weights, resulting in the following equation:

= ∑$ ( # ) + (0, ) #% "# #

(4)

Here, "# are the weights, # are the abscissas, and N denotes the number of quadrature points. The governing equations for the moments (2)-(4) have been adopted from Marchisio et al. (2003) after neglecting agglomeration and 19 attrition. The governing equations for the moments can now be solved using the 19-20 standard PD algorithm . The mass fraction of the components is defined as '(

&# = ∑

'

,

(5)

Where, i represents the component in the crystallization system, and ) , ) and ) represent the mass of solvent, solute, and antisolvent in the solution, respectively. Similarly, & , & and & represent the mass fraction of solvent,


3


Page 4 of 17

solute and antisolvent, respectively. The mass balance for the dissolved solute in terms of third moment can be derived from mass balance equation for solute 4 accumulation , volume conservation equation and moment definition, and can be stated as: '*

=

+ , - . /

(6)

(+ / )

Where, α is the crystal volume shape factor coefficient, ρ is the crystal density, and 0 is the liquid phase volume of the suspension. Value of α has been taken 21 4 as 10 for needle-like crystals . The suspension volume V is given by

=

- .

+

- 1

(7)

Where, 0 2 is the solid phase suspension volume and is given by 0 2 = 0 × α ×

(8)

Concentration of solute is given as 5 =

'*

(9)

-. 22

The nucleation rate used in this study is given by = 67 (∆5)7

(10)

Here, 67 and b are the nucleation parameters and ∆5 denotes the degree of supersaturation. The crystal growth rate dependent on crystal size as proposed in this study is given by = × (1 −

'

)

(11)

Where, ) is a constant and captures the dependence of the growth rate on 4 the concentration of the antisolvent as given by the expression: ∆=

= ( + ; + ; ) ∗ ( ∗ )(>?@>A B/) =

(12)

*

Where, C is the equilibrium solubility of solute in mixture, , , , C , and C are growth constants, and ; is mass fraction of antisolvent in solute free mixture. The above mentioned equations are solved using ODE45 solver of MATLAB and optimization of parameters is achieved by making an objective function and solving it using the FMINSEARCH function of MATLAB. The parameter matrix was estimated as [7 , D, , , , C , C , )]. The objective function, which is minimized by FMINSEARCH, is represented by the following equation # # ε = ∑$ #%(F' − FG )

(13)


4

Page 5 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57


Where, F'# is the model predicted value of a measurable quantity, e.g. average crystal size at a particular time and FG# is the experimentally obtained value of the same quantity at the same time. An initial guess is given for which the model is solved and the predicted values are compared with experimental values by evaluating the square of the total error ε (objective function). FMINSEARCH returns an optimum set of parameters for which the objective function is minimized. The model for which the crystal growth rate is given by equation (11) is termed the ‘Dependent model’. Further, for comparison purpose we also examine the kinetics of crystallization in which the crystal growth rate is considered independent of the crystal size. Such a model is termed ‘Independent model’. The equations for mass balance of solute, concentration of solute, liquid and solid phase of suspension volume and nucleation remain same as that of ‘Dependent model’. The growth rate for the size independent model is given by =

(14)

Where, is same as that used in ‘Dependent model’. For the ‘Independent model’ the use of QMOM and PD algorithm is not required as equation (3) can be 19 written in form of moments in the following manner : ? A * /

=

(15)

=

(16)

=

(17)

=

(18)

Equations (15)-(18), along with the governing equations for mass, volume, and concentration are solved using ODE45 solver of MATLAB and parameter optimization is achieved following the same approach as in ‘Dependent model’. Parameter matrix in this case changes to [7 , D, , , , C , C ].


5


Page 6 of 17

1 2 3 3. EXPERIMENTAL SECTION 4 5 A quality risk assessment was performed using Failure Mode and Effects 6 Analysis (FMEA) of the given process parameters labelled as potential failure 7 modes (Table I). The values for severity, occurrence and detection were chosen using a 10 point scale and existing process controls at plant scale were taken 8 into consideration. The RPN number for ‘antisolvent flowrate’ was found to be 4 9 times more than RPN number of second process parameter. Hence, ‘antisolvent 10 flow rate’ was chosen as sole variable in experimentation design. 11 12 Table I. Risk assessment (FMEA approach) 13 Current 14 Potential Potential failure Severity Causes Occurrence process Detection 15 effect mode controls 16 Wrong Impact on 17 Improper Calibrated dip quantity of API 8 1 6 18 measuring rod solvent quality/yield 19 Wrong Impact on 20 Improper Calibrated dip quantity of API 8 1 6 21 measuring rod anti-solvent quality/yield 22 Wrong 23 Calibrated quantity of Impact on Improper 3 1 weighing 6 24 ammonium API quality weighing balance 25 carbonate 26 Improper Digital 27 Low reactor Partial utility 8 3 temperature 5 28 temperature dissolution applied/utility indicator 29 not working 30 Digital API Improper 31 High reactor 8 3 temperature 5 utility applied 32 temperature degradation indicator 33 No calibration Valve 34 Wrong rate Impact on on addition of antisolvent 6 8 controlled 10 35 API quality vessel/human addition manually 36 error 37 Manual entries Wrong 38 Delay in in production stirring time batch time 1 Human error 8 record with 6 39 before AS cycle centralized 40 addition digital clock 41 Manual entries 42 Wrong in production 43 stirring time Impact on 3 Human error 8 record with 6 44 after AS yield centralized 45 addition digital clock 46 Impact on VFD not 47 Inappropriate 3 1 VFD functional 5 Kla API quality working 48 49 50 51 52 6 53 54 ACS Paragon Plus Environment 55 56 57

RPN

48

48

18

120

120

480

48

144

15

Page 7 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57


For estimation of kinetic and growth parameters, experiments were performed 23 at different antisolvent flowrates to generate moments data using FBRM. Figure 1 shows the schematic of apparatus and instrumentation used in the study. A ternary system was used for performing antisolvent crystallization with the components being Dexlansoprazole as solute, n-heptane as antisolvent, and methyl-ethyl ketone as solvent. Next, n-heptane was added to a 25% concentrated solution of Dexlansoprazole in methyl-ethyl ketone in the automated lab reactor (ALR). A linear profile for anti-solvent addition was followed with the help of calibrated digital dosing pump. Anchor agitator was used to stir the slurry at constant 300 rpm. A temperature control system consisting of a Pt1000 temperature sensor and heating/cooling circulator (Huber, Germany) was used to maintain the temperature at 25°C. Focused beam reflectance measurement (FBRM) probe (Mettler Toledo Lasentec Products, USA) was used to track particle chord length every 10 seconds. The FBRM signal was converted to digital signal using a PCB. This was then connected to the FBRM PC for data monitoring.

Figure 1. Schematic diagram of the experimental set-up (A: Automated Lab Reactor, B: Temperature Control System, C: Pt1000 temperature sensor, D: FBRM PC, E: Dosing pump, F: Flask for anti-solvent, G: FBRM Probe) Experiment 1 was performed to obtain data required for parameter estimation for both ‘Dependent’ and ‘Independent’ models. Experiments 2-4 were performed at different flowrates of anti-solvent in order to analyze its effect on characteristics of crystallization. These data are then used for model validation and for comparison between ‘Dependent model’ and ‘Independent model’. The following table contains the experimentation details.

7 ACS Paragon Plus Environment


Page 8 of 17

Table II. Listing of experimental conditions for experiments 1-4. Experiment Experiment Experiment Parameter 1 2 3

Experiment 4

Solute (API)

1T

1T

1T

1T

Solvent quantity

4T

4T

4T

4T

Antisolvent quantity

10 T

10 T

10 T

10 T

Antisolvent flowrate (ml/hour)

500

125

250

166.67

Addition temperature (°C)

25-30

25-30

25-30

25-30

Agitator type

Anchor

Anchor

Anchor

Anchor

Agitator RPM

300

300

300

300

4. RESULTS AND DISCUSSION Optimization of parameters was performed using the conditions of experiment 1. Table III contains the crystallization parameters estimated for the ‘Dependent model’. Table III. Optimized growth and nucleation parameters for size dependent model. Parameter

#

Value

Unit #

-1

3

-1

7

11.7

No (g/ml) (ml s)

0.044

µm/s

1.8e-04

µm/s

-1.4e-04

µm/s

D

0.86

Dimensionless

C

8.9e-05

Dimensionless

C

-7e-06

Dimensionless

m 20.9 No refers to number of particles

-1

(µm)

A similar process of optimization was followed using the conditions of experiment 1 for ‘Independent model’ and the resulting parameters are listed in Table IV.


Page 9 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57


Table IV. Optimized growth and nucleation parameters for size independent model. Parameter Value Unit -1

3

-1

67

4.8

No(g/ml) (ml s)

0.11

µm/s

-0.001

µm/s

-0.004

µm/s

b

0.47

Dimensionless

C

0.0044

Dimensionless

C

0.0011

Dimensionless

The model estimates the transients of the moments of the crystal size distribution from which the average properties of the distribution can be obtained. In particular, the average size of the crystal, defined as / , the mean area of the crystals, defined as / , and the mean volume of the crystals, defined as / were calculated. These average quantities were selected as these are readily obtained from the experimental data for comparison. The time evolution of these average properties of the CSD is shown in Figures 2-4 for Experiment 1. Experimental and simulation results for both models are plotted together for comparison.

Figure 2. Mean crystal size (experiment 1)

Figure 3. Mean crystal area (experiment 1)

It is evident from Figure 2 that both the models over-predict the mean crystal size. The mean size increases till a certain time after which it decreases and becomes constant. Since the amount of anti-solvent added is quite significant in Experiment 1, the rate crystal growth is very high. The fast crystallization in a short time tends to decrease the solute concentration in the slurry leading to decrease in the degree of super-saturation, ∆I. The reduction in driving force for crystallization suppresses the growth, however the nuclei continues to form. Therefore, the peak in mean crystal dimension is followed by a drop. The time for



Page 10 of 17

achieving the peak value is predicted correctly by both the models. While the ‘Dependent model’ predicts the final mean size very accurately, the ‘Independent model’ fails to do so. It can be inferred from Figure 3 that the nature of the curve for the ‘Dependent’ model is very similar to the experimental data. Not only is the peak shape quite similar but the final value of mean area in crystal size distribution is also correctly predicted. In the case of mean size, the predicted peak is above the actual peak, whereas the predicted peak is lower than the actual peak in case of mean area. This is likely due to the fact that finer particles have larger surface area. In case of mean area, the ‘Independent model’ again fails to match the experimental data as depicted in Figure 3.

Figure 4. Mean crystal volume (experiment 1) Figure 4 represents the mean crystal volume and further confirms our findings. The ‘Dependent model’ predicts the actual data accurately including the peak and the final mean crystal volume. As in the case of ‘mean crystal area’, the ‘Independent model’ severely under-predicts the peak volume. It is evident from Figures 2-4 that while the peak value of number average crystal size predicted by the ‘Dependent model’ is lower than that found in the experiment, the model prediction of the peak values of the mean crystal surface area and volume are lower than those in the experiment. This observation suggests that the crystal size distribution (CSD) in the experiment is relatively broader than that predicted by the model. Also, the total number of crystals, and hence the rate of nucleation is believed to be higher in the experimental crystallization than that predicted by the optimized model parameters. Similar comparison can be made for the results from the ‘Dependent’ and ‘Independent’ models. The higher mean crystal size and lower mean crystal volume predicted by the ‘Independent model’ in comparison to that predicted by the ‘Dependent model’ suggests that the CSD in the ‘Independent model’ is narrower than in the ‘Dependent model’. This is expected as it is well known that the size dependent growth rate tends to broaden the distribution. The results clearly demonstrate the importance of considering dependence of the growth rate on the crystal size. As soon as nucleation occurs, the crystals attain a certain mean size. Hence, the model receives the initial mean size as an input instead of its starting value of zero. Figures 5-7 represent the mean crystal size, area, and volume obtained for


Page 11 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57


th

the experiment 2 for which case the flowrate is kept 1/4 to that in experiment 1. The three plots have similar characteristics with respect to the nature of curves and the behavior of ‘Dependent’ and ‘Independent’ models. For all three average quantities, the ‘Dependent model’ reaches the actual value after only around 800 seconds after which the model predictions are in close quantitative agreement with the experimental values. Unlike transients in Experiment 1, the curves for the mean quantities in Experiment 2 do not exhibit a peak value. Further, the mean crystal dimension at the end of Experiment 2 is around 25 µm, taking a time of around 3000 s, whereas that in the Experiment 1 is above 30 µm, requiring only 1000 s to attain, exhibiting a peak value of around 50 µm. This is attributed to the lower rate of crystallization in Experiment 2 due to the decreased amount of anti-solvent present in the system. It is important to note that the ‘Independent model’ over-predicts the final mean size and under-predicts the final mean area and volume. As mentioned earlier, this observation implies that the predicted distribution in the ‘Independent model’ is narrower than that in the ‘Dependent model’. The size dependent growth model appropriately captures the broadness of CSD as found in the experiment.



Figure 7. Mean crystal volume (experiment 2)

Figures 8-10 represent the mean crystal size, area and volume obtained for experiment 3 which was performed with antisolvent flowrate of 250 ml/hr. Figures



Page 12 of 17

11-13 represent the mean crystal size, area and volume obtained for experiment 4 which was performed with antisolvent flowrate of 166.67 ml/hr.



Figure 10. Mean crystal volume (experiment 3) It is evident from Figures 8 and 11 that the ‘Independent model’ over-predicts mean size while the ‘Dependent model’ accurately predicts not only the final mean size but also the nature of increase of mean size barring the first 5 minutes. The discrepancy in early crystallization kinetics is due to the unavailability of appropriate initial conditions for the model. Notwithstanding this initial discrepancy, the model predictions for the various mean quantities are in close quantitative agreement with the experimental findings for all flowrates of antisolvent examined. In comparison to experiment 2, the antisolvent flowrate is kept higher in Experiments 3 & 4. The higher antisolvent concentration results in higher growth rate (refer to equation (12)). Thus, the mean crystal size attains the peak value of around 20 m in around 1000 s in experiment 3 and around 1500 s in experiment 4. The slow crystallization due to reduced antisolvent concentration in experiment 2 requires around 3000 s to attain the final mean size of around 25 m. We can also observe from Figures 10 and 13 that in both the experiments, the ‘Independent model’ under-predicts the mean crystal volume, same as the case with experiment 2. The under prediction of mean size and over prediction of surface area and volume is an indication of narrow crystal size distribution when size independent


Page 13 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57


growth rate is considered. Importantly, the ‘Dependent model’ correctly predicts the mean crystal volume for both the experiments as shown in Figures 10 and 13. Thus, size dependent growth rate model is necessary to describe the broad crystal size distribution in antisolvent crystallization.



Figure 13. Mean crystal volume (experiment 4)

Hence, the ‘Dependent model’ correctly predicts the mean crystal size, area, and volume. Robustness of the model is thus proved by testing the model at different flowrates and comparing the model predictions with the experimental data. The proposed model performs satisfactorily except in the initial period.

5. CONCLUSIONS A mechanistic model for the kinetics of antisolvent crystallization has been proposed. The model considers the dependence of crystal growth rate on crystal size. It has been demonstrated that the ‘dependent growth model’ is superior in accuracy compared to the ‘independent growth model’ with respect to the prediction of the crystal characteristics such as mean crystal size, surface area and volume. The model has been validated using the experimental findings



Page 14 of 17

under different process conditions. The size dependent growth model captures the broadness in crystal size distribution, as inferred from the various moments of the distribution, in close agreement with the experimental findings. The role of antisolvent concentration in the slurry is examined by varying its flowrate. The increase in antisolvent concentration leads to faster crystallization. The results clearly elucidate the necessity of considering dependence of crystal growth rate on crystal size. The proposed model will be a useful tool to control the crystal size distribution in pharmaceutical crystallization processes.

ACKNOWLEDGEMENTS Experimental work was carried out at Research & Development Center, Sun Pharmaceutical Industries Ltd (Gurugram, India) with the support of Chemical Engineering Department of Indian Institute of Technology, Delhi (New Delhi, India). Authors acknowledge funding from the Department of Biotechnology, Ministry of Science and Technology (Centre of Excellence for Biopharmaceutical Technology grant BT/COE/34/ SP15097/2015).

REFERENCES (1) Mydlarz, J.; Jones, A.G. On the estimation of size-dependent crystal growth rate functions in MSMPR crystallizers. Chem. Eng. J. and Biochem. Eng. J. 1993, 53, 125-135. (2) Takiyama H.; Otsuhata T.; Matsuoka M. Morphology of NaCl crystals in drowning-out precipitation operation. Chem. Eng. Res. Des. 1998, 76, 809-814. (3) Nagy Z. K.; Fujiwara M.; Braatz R. D. Recent advances in the modelling and control of cooling and antisolvent crystallization of pharmaceuticals. IFAC Proceeding Volumes 2007, 40, 29-38. (4) Nowee S. M.; Abbas A.; Romagnoli J. A. Antisolvent crystallization: Model identification, experimental validation and dynamic simulation. Chem. Eng. Sci. 2008, 63, 5457 – 5467. (5) Nowee S. M.; Abbas A.; Romagnoli J. A. Optimization in seeded cooling crystallization: A parameter estimation and dynamic optimization study. Chem. Eng.Process. 2007, 46, 1096-1106. (6) Gimbun, J.; Nagy, Z. K.; Rielly C. D. Simultaneous quadrature method of moments for the solution of population balance equations, using a differential algebraic equation framework. Ind. Eng. Chem. Res. 2009, 48, 7798–7812. (7) Samad N. A. F. A.; Singh R.; Sin G.; Gernaey K. V.; Gani R. A generic multi-dimensional model-based system for batch cooling crystallization processes. Comput. Chem. Eng. 2011, 35, 828–843.


Page 15 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57


(8) Leyssens T.; Baudry C.; Hernandez M. L. E. Optimization of a crystallization by online FBRM analysis of needle-shaped crystals. Org. Process Res. Dev. 2011, 15, 413-426. (9) Yang Y.; Nagy Z. K. Model-based systematic design and analysis approach for unseeded combined cooling and antisolvent crystallization (CCAC) systems. Cryst. Growth Des. 2014, 14, 687−698. (10) Mydlarz J.; Jones A. G. On modelling the size dependent growth rate of potassium sulphate in an MSMPR crystallizer. Chem. Eng. Commun. 1990, 90, 47-56. (11) Rawlings J. B.; Miller S. M.; Witkowski W. R. Model identification and control of solution crystallization processes: a review. Ind. Eng. Chem. Res. 1993, 32, 1275-1296 (12) Miller S. M.; Rawlings J. B. Model identification and control strategies for batch cooling crystallizers. AIChE J. 1994, 40, 1312-1327. (13) Hu Q.; Rohani S.; Wang D. X.; Jutan A. Nonlinear kinetic parameter estimation for batch cooling seeded crystallization. AIChE J. 2004, 50, 17861794. (14) Nowee S. M.; Abbas A.; Romagnoli J. A. Model-based optimal strategies for controlling particle size in antisolvent crystallization operations. Cryst. Growth Des. 2008, 8, 2698-2706. (15) Nagy Z. K.; Fujiwara M.; Braatz R. D. Modelling and control of combined cooling and antisolvent crystallization processes. J. Process Control 2008, 18, 856–864. (16) Nagy Z. K. Model based robust control approach for batch crystallization product design. Comput. Chem. Eng. 2009, 33, 1685–1691. (17) Lindenberg C.; Krattli M.; Cornel J.; Mazzotti M. Design and optimization of a combined cooling/antisolvent crystallization process. Cryst. Growth Des. 2009, 9, 1124-1136. (18) Ciardha C. T. O.; Hutton K. W.; Mitchell N. A.; Frawley P. J. Simultaneous parameter estimation and optimization of a seeded antisolvent crystallization. Cryst. Growth Des. 2012, 12, 5247−5261. (19) Marchisio D. L.; Pikturna J. T.; Fox R. O.; Vigil R. D.; Barresi A. A. Quadrature method of moments for population balance equations. AIChE J. 2003, 49, 1266-1276. (20) Marchisio D. L.; Fox R. O. Solution of population balance equations using the direct quadrature method of moments. J. Aerosol Sci. 2005, 36, 43–73. (21) Myerson A. S. Handb. Ind. Cryst.(2nd Ed.).



Page 16 of 17

(22) Woo X. Y.; Tan R. B. H.; Chow P. S.; Braatz R. D. Simulation of mixing effects in antisolvent crystallization using a coupled CFD-PDF-PBE approach. Cryst. Growth Des. 2006, 6, 1291-1303. (23) Ruf A.; Worlitschek J.; Mazzotti M. Modeling and experimental analysis of PSD measurements through FBRM. Part. Part. Syst. Charact. 2000, 17, 167179.


Page 17 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


“For Table of Contents Use Only”

Manuscript title: Process development in the QbD paradigm: mechanistic modeling of antisolvent crystallization for production of pharmaceuticals Author list: Manu Garg, Milan Roy, Paresh P. Chokshi and Anurag S. Rathore TOC Graphic:

Synopsis: A mechanistic model of antisolvent crystallization has been proposed considering dependence of crystal growth rate on crystal mean size. Critical process parameter were identified by risk assessment for performing experimentation and generating crystal morphological data using focused beam reflectance measurement (FBRM). MATLAB was used to identify optimal growth and nucleation parameters for proposed model, which compares favorably to other similar models with respect to the accuracy of prediction of crystal size, surface area and volume, even at varying feedrate profiles of anti-solvent during crystallization.


Process development in the QbD paradigm: mechanistic modeling of

Recommend Documents