Model-Based Evaluation of Direct Nucleation Control Approaches for

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Model-based Evaluation of Direct Nucleation Control Approaches for the Continuous Cooling Crystallization of Paracetamol in a Mixed Suspension Mixed Product Removal System David Acevedo, Yang Yang, Daniel J. Warnke, and Zoltan K Nagy Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.7b00860 • Publication Date (Web): 13 Sep 2017 Downloaded from http://pubs.acs.org on September 20, 2017

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Crystal Growth & Design

Model-Based Evaluation of Direct Nucleation Control Approaches for the Continuous Cooling Crystallization of Paracetamol in a Mixed Suspension Mixed Product Removal System David Acevedo, Yang Yang, Daniel J. Warnke, Zoltan K. Nagy* Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN 47907

Direct Nucleation Control (DNC) is a model-free feedback control approach based on the measurement of particle number in crystallization process. The experimental implementation has demonstrated that this approach is efficient to produce large and uniform crystals in batch crystallization, or to reduce startup duration and suppress disturbance in continuous crystallization. In this work, five different DNC frameworks/strategies are proposed for a continuous MSMPR crystallization of paracetamol-water system and evaluated systematically using model-based approach. It is found that the Reverse DNC framework could provide the best control performance in terms of startup, set point change and disturbance suppression. In addition, an optimal heating/cooling rate of about 0.6

o

C/min was determined. These

observations are applicable for the model compound studied (paracetamol) and should be investigated for other systems. This study provides a general guidance of designing DNC framework with best control performance for continuous MSMPR crystallization.

Corresponding author: Prof. Zoltan K Nagy FRNY G027D Purdue University Davidson School of Chemical Engineering Forney Hall of Chemical Engineering 480 Stadium Mall Drive West Lafayette, IN 47907-2100 [email protected] (765) 494-0734 (office) (765) 494-0805 (fax)

ACS Paragon Plus Environment


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Model-Based Evaluation of Direct Nucleation Control Approaches for the Continuous Cooling Crystallization of Paracetamol in a Mixed Suspension Mixed Product Removal System David Acevedo, Yang Yang, Daniel J. Warnke, Zoltan K. Nagy* Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN 47907 Abstract Direct Nucleation Control (DNC) is a model-free feedback control approach based on the measurement of particle number in crystallization process. The experimental implementation has demonstrated that this approach is efficient to produce large and uniform crystals in batch crystallization, or to reduce startup duration and suppress disturbance in continuous crystallization. In this work, five different DNC frameworks/strategies are proposed for a continuous MSMPR crystallization of paracetamol-water system and evaluated systematically using model-based approach. It is found that the Reverse DNC framework could provide the best control performance in terms of startup, set point change and disturbance suppression. In addition, an optimal heating/cooling rate of about 0.6

o

C/min was determined. These

observations are applicable for the model compound studied (paracetamol) and should be investigated for other systems. This study provides a general guidance of designing DNC framework with best control performance for continuous MSMPR crystallization.

Keywords: Continuous Crystallization, MSMPR, Direct Nucleation Control, Model-free Control


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1. Introduction Crystallization is a common separation and purification operation in the pharmaceutical manufacturing where over 90% of the active pharmaceutical ingredients are crystals of small organic molecules.1,2 Operation and control of batch crystallizers has been widely studied in industry and academia due to the numerous advantages such as operating flexibility and short development time.3,4 Efficient control of crystal properties such as crystal size distribution (CSD), polymorphic form, and shape is critical for production functionality and operational efficiency;5-10 variations in these properties can affect downstream processes such as filtration, drying and milling. Moreover, batch-to-batch variability is an important issue on batch operations which can result significant loss of material that are out of specification. Continuous operation offers numerous advantages such as consistency on product quality, lower operation cost, and shorter down time.11-13 The pharmaceutical industry has been undergoing a shift from batch to continuous operation throughout the last decade.14-16 Part of this shift has been due to the initiative implemented by the U.S. Food and Drug Administration (FDA) on advancing pharmaceutical manufacturing.17 Minimum work on the development of commercial manufacturing line of drug substances is available in literature. One of the few available work discussed the continuous production of an active ingredient through reactive crystallization.18 However, significant work has been done in academia on the development, optimization and control of continuous crystallization platforms. Currently, there are two popular platforms for continuous crystallization, mixed suspension mixed product removal (MSMPR) and tubular crystallizers. Single or multi-stage MSMPR crystallizers are a series of continuous well-stirred tanks connected in series which are suitable for systems with slow growth kinetics.19-26 The other common continuous crystallization platform are tubular crystallizers;27-30 however, tubular crystallizers are prone to fouling, clogging, and settling issues among other disadvantages.31 Therefore, the development and control of continuous crystallization process in MSMPR system is of significant interest for the undergoing shift from batch to continuous operation, although it has some disadvantages such as broad residence time (RT) distribution and crystal size distribution. The implementation of a concentration control strategy on a continuous MSMPR system was evaluated.32 It was observed that the proposed continuous MSMPR operation achieves higher



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production capacity with shorter mean residence time and comparable product yield as in batch although smaller mean crystal size was achieved. Recent work demonstrated the implementation in a single stage and two-stage MSMPR operation a model-free control strategy well studied in batch systems.33 Direct Nucleation Control (DNC) is a Process Analytical Technology (PAT) based feedback control strategy which automatically switches between nucleation and fine dissolution by heating or cooling the system.34-37 It has been found that the implementation of DNC in batch operation improves the crystal product quality (i.e. average size and size distribution) while reducing the batch-to-batch variability. Nonetheless, it was found that the implementation of DNC in a continuous MSMPR system significantly reduces the startup duration, allows for controlled set-point changes, and quickly suppresses disturbances in the process.33 This was extended for a wet-milling based DNC approach in a continuous crystallization system.38 Similar impact with respect to disturbance rejection and control setpoint change during the continuous operation was observed. However, no improvement on the startup time was observed when DNC was implemented. The implementation of DNC on a continuous MSMPR system has been mainly studied experimentally. Therefore, further study is necessary in order to evaluate the implementation of a well-studied batch feedback control strategy to a continuous operation. This work focuses on the model based evaluation of multiple DNC approaches on a single stage MSMPR system. An optimal strategy for continuous operation in base of startup time and disturbance rejection is proposed. The cooling crystallization of an active pharmaceutical ingredient (API), paracetamol, is used as model compound through the multiple simulation case studies presented in this work.

2. Direct Nucleation Control Methodology The concept of DNC was initially studied via the optimization of batch crystallization process under multiple crystallization kinetics such as nucleation, growth, and dissolution.34 It has been observed that the dissolution of fines via temperature cycling promotes the growth of larger crystals while reducing the width of CSD. DNC is a model-free feedback control approach which uses a similar concept in which the number of counts present in the system is controlled by adaptive heating/cooling cycles. The use of a PAT tool that gives real-time quantitative or qualitative information regarding the number of particles in the system such as Focused Beam Reflectance Measurement (FBRM) tool is required for the implementations of DNC.39-41 Figure 1


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shows the conventional DNC control implementation and operating profile. The number of counts is obtained from the FBRM and sent to the controller which automatically alters from cooling to heating cycles to generate nucleation or trigger fines dissolution in order to maintain the number of counts per second at desired level. In the event of significant nucleation, where the number of counts per second exceeds the set point or upper limit, the temperature in the system raises until dissolution of fines occurs and the number of counts per second is reduced to the desired level.

Tjacket (t)

-

Tcryst(t)

Chiller

setpoint # per s

DNC

Concentration

counts # per s +

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


metastable limit

solubility curve

operating profile

Tsetpoint(t)

Temperature

+

Figure 1. General DNC control framework (left) and conventional operating profile in batch cooling crystallization processes with DNC (right).

The general DNC approach shown in Figure 1 shows that the number of counts per second is required for the implementation of this control strategy. In this work, the total number of particle is assumed to be the zeroth moment of the number density simulated via the solution of a population balance model (PBM). A perfect temperature control with a specific time lag was assumed in order to consider the actual performance of chiller controller and calculate the setpoint jacket temperature. Multiple DNC strategies can be formulated where a proportional type feedback controller was used for controlling the temperature. The main differences in the multiple DNC strategies is the use of limits and cooling/heating structure. The simplest DNC structure only considers the desired counts level as set-point. Figure 2 shows the DNC strategies that could be implemented in a continuous scenario. The DNC algorithm heats or cools the system in order to stabilize and reach the desired number of counts per second on the system. The system is considered stable when the number of particles reaches a similar



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value to the set-point and the minimum temperature set before starting the process are reached. A minimum or maximum temperature is usually given to the controller and fixed maximum heating/cooling rate are specified.33 This type of DNC strategy will be referred as simple DNC throughout this work.

Figure 2. Algorithm for multiple DNC strategies implemented in a continuous cooling crystallization process.

The simple DNC strategy could be modified in order to consider only upper and lower limits for the number of counts per second. This type of control strategy will switch between cooling and heating the system when the number of counts per seconds rises above the upper limit or decreases below the lower limit; controlling within an operational space should allow the system to stabilize quicker since no action would occur within the bounds. This type of DNC strategy will be referred as Bounds DNC throughout this work. Bounds DNC was the type of strategy implemented experimentally in previous works which showed to have significant impact on the startup time and disturbance rejection capability.33 Two more configurations could be designed from the integration of Simple and Bounds DNC. The first strategy would be referred as Predictive DNC where now the set-point and lower/upper limit are considered. In this strategy, the system reacts similarly as Bounds DNC when the number of counts per second are above or below the limits. However, slower cooling/heating rates are imposed when the number of particles are above or below the set-point. The decision between heating or cooling depends on the previous history of the number of counts per second: is it increasing or decreasing? The second structure, Reverse DNC, follows a similar concept. The structure of Reverse DNC within the upper and lower limits considers excess nucleation and rapid dissolution by implementing an opposite algorithm. Fast cooling is implemented while


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nucleation occurs below the lower limit; the system switches to slow heating until the upper limit is reached in this way the controller suppresses excess nucleation on the system. The last possible DNC strategy only considers the set-point and upper limit. This is the conventional DNC strategy proposed in previous work.35 This could be observed as a type of bound DNC. However, the system changes from slow heating or cooling from the history of the number of counts per second which facilitates the dissolution of fines. Also, the system is controlled until the number of counts per second reaches a similar value to the desired level and the system is stabilized which differs significantly for Bounds DNC. This type of DNC strategy will be referred as Basic DNC throughout this work. All the possible DNC structures shown in Figure 2 are evaluated throughout this work via model-based case studies to determine the optimal implementation for a continuous crystallization scenario. 3. Model Development The seeded continuous cooling crystallization of paracetamol in water in a single stage MSMPR was simulated in MATLAB®. The general form of the PBM describing a MSMPR cascade consisting of m stages and assuming no agglomeration or breakage can be written as డ௡೔ డ௧

=−

డ(ீ௡೔ ) డ௑

where ݊௜

+

ொ೔షభ ௡೔షభ ିொ೔ ௡೔ ௏೔

+ ܰ for i =1, …, m

(1)

is the number density in the ith stage, G is the overall growth rate, Qi is the

volumetric flowrate, and Vi is the volume of suspension and ܰ is the overall nucleation rate. Several assumptions were considered in order to arrive to Eq. (1) such as, well-mixed stages and the sums of the volumetric flowrates entering and leaving the cascade of MSMPR are equal. A size independent growth rate, and primary and secondary nucleation rates were considered following ‫݇ = ܩ‬௚ ܵ ௚

(2)

ܰூ = ݇௕ூ ܵ ௕

(3) ௝

ܰூூ = ݇௕ூூ ܵ ௕ூூ ‫ܯ‬௧

(4)

where ݇௚ and ݇௕ are the growth and nucleation rate constants, ݃ and ܾ are the growth and nucleation rate order, and ݆ is an experimentally determined constant which relates the impact of magma density, ‫ܯ‬௧ , to the nucleation rate. The nucleation and growth rate parameters were obtained from literature and used through this study since the goal is to understand the impact of



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various DNC strategies on the process dynamics and steady state product.42 The magma density can be calculated as ‫ܯ‬௧ = ߩ௖ ݇௩ ‫ ܺ݊ ׬‬ଷ ݀ܺ

(5)

with ߩ௖ being the crystal density and ݇௩ the shape factor. The relative supersaturation is expressed as ܵ=

஼ି஼ೄ (்)

(6)

஼ೄ (்)

where ‫ ܥ‬is the solute concentration and ‫ܥ‬ௌ (ܶ) is the equilibrium concentration at the operating temperature, T. The equilibrium concentration was estimated from the solubility curve obtained from literature.42 The PBM model was coupled with mass balance equations to evaluate the dynamic change of the solute concentration in the system which is given by డ஼೔ డ௧

= −ߩ௖ ݇௩ ‫݊ ׬‬௜ ܺ ଶ ݀ܺ +

ொ೔షభ ஼೔షభ ିொ೔ ஼೔ ௏೔

(7)

The first order dynamics of the temperature controller was simulated following ௗ் ௗ௧

=

்ೄು ି்

(8)

ఛ

with ܶௌ௉ being the temperature set-point and ߬ controller lag time which was assume to be 50 seconds. This number was approximated from observations from previous experimental data obtained from common lab scale experimental setup. The dissolution kinetics are considered to be similar to the growth kinetics with an order of 1. The model was solved using a high resolution finite volume method as described in previous work.31

4. Results and Discussion

The implementation of DNC on a continuous single stage MSMPR was evaluated via the simulation based study of the cooling crystallization of paracetamol. Previous work demonstrated that the implementation of DNC can reduce the startup time and disturbance rejection compared to normal continuous operation.33 Therefore, the impact of various DNC strategies on the startup time, process dynamics, and time to reach steady state after a disturbance was evaluated to determine the optimal framework for a continuous operation. The time to reach 95% of the steady state (or controlled state of operation) zeroth moment was determined throughout all the simulations performed. The time point when the system dynamics stabilize was defined as the startup time. The initial set points for all scenarios evaluated in this


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work were obtained from simulation results of the cooling crystallization of paracetamol in water without any DNC strategy implemented. The process conditions and simulation parameters are shown in Table 1.

Table 1. Process conditions and simulation parameters for cooling crystallization of paracetamol in MSMPR system for a 30 min residence time. Variable

Units -1

Value

Variable

Units

Value

0.02

‫݊ܮ‬௦௘௘ௗ௦

µm

54

‫ܥ‬଴

g g water

ܶ௦௔௧

°C

31

‫ܸܥ‬௦௘௘ௗ௦

%

25

ܸ

cm3

400

ܵ௦௘௘ௗ௦

%

2

ܶ௢௣௧

°C

25

߬

sec

50

ߩ௖

%

1.33

ܰ

N

100

݇௩

-

0.54

‫ݐ‬௙

min

1000

4.1.Set-point change and process dynamics

The impact of the various DNC strategies was evaluated by simulating all scenarios described in Figure 2. All the process conditions were fixed as described in Table 1. The DNC set point, cooling and heating rate were not varied between all the DNC strategies in order to determine mainly the influence of the framework on the dynamics and startup. The fast heating and cooling rates were fixed to 0.5°C per min. The slow heating and cooling rates were fixed to half of the fast heating and cooling rate throughout all the scenarios. The set point change magnitude was also fixed through the set point change model based evaluation studies. The change has fixed to 75% decrease in the initial number of particles calculated from the zeroth moment of the distribution. Figure 3 shows the process dynamics for the cooling crystallization of paracetamol when Basic, Simple, and Predictive DNC strategies were applied.



6

2.0x10 Process temperature (Basic DNC) Process temperature (Simple DNC) Process temperature (Predictive DNC) µ0 (Basic DNC)

1.8x10

40

µ0 (Simple DNC)

1.6x10

35

DNC set-point DNC lower bound DNC upper bound

6

6

µ0 (Predictive) 6

1.4x10

o

6

1.2x10

30

6

1.0x10

5

25

8.0x10

3

Temperature [ C]

45

µ0 [#/kg ]

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

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5

6.0x10

20

5

4.0x10

15

5

2.0x10

10

0.0

0

5

10

15

20

25

30

RT# [-]

Figure 3. Process temperature (black) and zeroth moment (blue) dynamics obtained for the cooling crystallization of paracetamol in a single stage MSMPR process controlled via Basic (solid), Simple (dashed), and Predictive (dotted) DNC strategies.

The startup procedure shows that the three scenarios follow similar dynamics. The initial decrease of the temperature produces high amount of crystals due to a primary nucleation event. Afterwards, the temperature is increased which reduces the number of particles below the lower limit of the control strategy. A periodic state of operation is achieved for all three DNC strategies. This could be due to fast dissolution and nucleation kinetics. The Basic and Simple strategies react after the system goes below the set point. This leads to significant dissolution of crystals before the system reacts and start cooling again. Similarly, this can be observed for the Predictive DNC strategy since the system will keep dissolving crystals until the number of crystals goes below the lower bound; significant amount of crystals is dissolved through this period. Therefore, a period behavior is expected since constant generation and destruction of crystal will occur due to the slow response of the DNC strategy. Nonetheless, previous work demonstrated advantages of period state operation of a continuous crystallization process; this type of operation was demonstrated as a feasible continuous crystallization method, without encountering operating problems such as encrustation, fouling or blockage of transfer units [43]. This type of periodic behavior was not obtained for the cooling crystallization of paracetamol when Bound or Reverse DNC is implemented as shown in Figure 4.


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40

6

2.0x10 Process temperature (Bound DNC) Process temperature (Reverse DNC) µ0 (Bound DNC)

35

6

1.8x10

µ0 (Reverse DNC)

6

1.6x10

6

1.4x10

30

o

6

1.2x10

25

6

1.0x10

5

8.0x10

20

3

Temperature [ C]


µ0 [#/kg ]

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


5

6.0x10

5

4.0x10

15

5

2.0x10

10

0.0

0

5

10

15

20

25

30

RT# [-]

Figure 4. Process temperature (black) and zeroth moment (blue) dynamics obtained for the cooling crystallization of paracetamol in a single stage MSMPR process controlled via Bound (solid) and Reverse(dashed) DNC strategies.

The Bound and Reverse DNC strategies shows that the system reaches steady state after the initial first order oscillations. The two control strategies shows similar dynamics. Nonetheless, Bound DNC takes longer time to reach a control state of operation since the control framework does not change the operating temperature until the total number of particles go beyond the bounds specified. Also, the counter reaction structure of Reverse DNC minimizes further nucleation or dissolution as soon as the total number of particles is within the bounds. The five DNC strategies are summarized and compared in Table 2 and 3 for both the start-up and set point change scenarios. It is clear that for these two scenarios, Reverse DNC requires least amount of time to reach steady state due to its ability to prevent overheating or overcooling. For example, when zeroth moment is decreasing from upper limit to set point, the nucleation rate is actually smaller than the MSMPR crystal washout speed which means the system should cool down in order to reach steady state, and vice versa. Bound DNC requires slightly longer time to reach steady state, whereas the other three can never reach true steady state.



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Table 2. Startup time and steady state conditions for base case study.

DNC

L43 (µ µm)

Yield (%)

Topt (°°C)

Predictive Basic Simple Bound Reverse

386.1 385.7 387.8 385.9 388.3

37.3 42.8 39.1 40.6 41.8

26.2 24.0 25.5 25.0 24.8

timess (#RT) 6.00 6.36 6.35 5.67 4.17

offset (#x104 /kg) -7.34 7.22 -2.39 1.31 1.05

State P P P S S

Table 3. Steady state conditions and time to reach steady state for set point change of 25%.

DNC

L43 (µ µm)

Yield (%)

Topt (°°C)


467.8 444.8 450.0 412.6 410.7

19.6 15.4 14.5 18.4 20.1

32.3 33.6 33.9 32.9 32.3

timess (#RT) 22.5 23.0 22.0 20.3 20.2

offset (#x104 /kg) 7.39 -1.97 -2.80 -1.46 2.14

State P P P S S

4.2.Disturbance rejection

The feedback nature of the DNC strategy should allow for efficient disturbance rejection during the continuous operation. Previous work demonstrated the performance of Bound DNC during the continuous crystallization of paracetamol.19 The performance of all possible DNC structures (refer to Figure 2) were evaluated by implementing a set of disturbance on the nucleation rate for a period of 0.25 residence times. The magnitude of the disturbance was 1x106 #/kg on the zeroth moment. For example, in practice this can occur from accidental seeding from an encrust layer that could form during the continuous operation. The disturbance was implemented after 16 residence times in order to assure a controlled state of operation before the disturbance. A base case study without DNC was evaluated in order to determine the time required to simply wash out the fine particles. It is found that a total of 13 RT was necessary for the system to reach a controlled state of operation after the disturbance without DNC. A shorter time to reach controlled state of operation could be expected when DNC is implemented since the system will automatically heat up the slurry to dissolve the fine particles introduced. This could be observed clearly from the dynamics shown in Figure 5.


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Process temperature (Basic DNC) Process temperature (Simple DNC) Process temperature (Predictive DNC) µ0 (Basic DNC)

45 40

µ0 (Simple DNC) µ0 (Predictive)

35 o


30 25

2.4x10

6

2.2x10

6

2.0x10

6

1.8x10

6

1.6x10

6

1.4x10

6

1.2x10

6

20

1.0x10

6

15

8.0x10

5

6.0x10

5

4.0x10

5

2.0x10

5

10 5 0

3

Temperature [ C]

(a)

µ0 [#/kg ]

0.0

0

5

10

15

20

25

RT# [-] 6

1.8x10

6

1.6x10

6

1.4x10

6

25

1.2x10

6

1.0x10

6

20

8.0x10

5

6.0x10

5

4.0x10

5

2.0x10

5

35

µ0 (Reverse DNC)


30 o

Temperature [ C]

(b)

15 10 5 0

3

2.0x10

40

Process temperature (Bound DNC) Process temperature (Reverse DNC) µ0 (Bound DNC)

µ0 [#/kg ]

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


0.0

0

5

10

15

20

25

RT# [-]

Figure 5. Temperature (black) and zeroth moment (blue) dynamics for continuous cooling crystallization of paracetamol in water under (a) Basic, Simple, Predictive, (b) Bound, and Reverse DNC strategies. The disturbance was introduced after 16 RT by adding 1x106 #/kg on the zeroth moment.

The dynamics observed for Basic, Simple and Predictive DNC follow similar tendency as demonstrated in the previous sections. The Basic, Simple, and Predictive DNC reach a periodic controlled state of operation (Figure 5a). Nonetheless, it can be observed that Basic and Predictive DNC allows for smaller disturbance effect since the zeroth moment reaches the control boundary faster compare to Simple DNC. No significant difference is observed in the time that takes the system to reach steady state as shown in Table 4. Also, minimum differences on the steady state product attributes and operating conditions are observed between the three scenarios. This demonstrates that the DNC framework used will not have significant effect on the product continuously manufactured.



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Table 4. Steady state conditions and time to reach steady state after disturbance on the number of crystals (1x106#/kg).

DNC

L43 (µ µm)

Yield (%)

Topt (°°C)


388 386 388 387 390

39 40 41 41 40

26.2 25.2 25.4 24.7 25.2

timess (#RT) 7.33 7.33 7.48 5.58 5.33

offset (#x104 /kg) -3.53 -1.58 1.82 1.72 -1.02

State P P P S S

The implementation of Reverse and Bound DNC allows for faster response as the disturbance occurs. A significant reduction on the time to reach controlled state of operation was achieved as shown in Table 4. Moreover, Reverse DNC reaches steady state faster than Bound DNC. This can be related to the same reason as described in previous section. Also, smaller offset from the set point can be achieved when Reverse DNC is implemented. The yield and volumetric mean size achieved is comparable to the base case, Predictive, Basic, and Simple DNC scenarios. Therefore, by implementing DNC less time and product is wasted when disturbances occur in the process.

4.3.Optimal scenario

Throughout the previous sections, the DNC conditions such as cooling and heating rates were fixed in order to understand the impact of the algorithm structure in the performance. However, further improvement on the DNC performance can be done via simulation base optimization. Reverse DNC was chosen as the optimal framework since it showed to have the best performance (shortest time to reach controlled state of operation) as shown in section 4.1 and 4.2. The impact of cooling/heating rate on the disturbance rejection performance of the Reverse DNC framework was studied in this section. Three cooling/heating rates were simulated which are commonly used in laboratory scale (0.1, 0.6, 1°C per minute). A pulse disturbance of 1.0×106 was implemented on the nucleation rate as a worst case scenario compared to the previous section. The dynamic profiles obtained for each case study is shown in Figure 6.


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6

2.4x10

60

µ0 (no DNC) µ0 (Reverse DNC, 0.1 Celsius/min) µ0 (Reverse DNC, 0.6 Celsius/min) µ0 (Reverse DNC, 1 Celsius/min) DNC set-point DNC lower bound DNC upper bound

(a)

6

2.0x10

Process temperature (no DNC) Process temperature (Reverse DNC, 0.1 Celsius/min) Process temperature (Reverse DNC, 0.6 Celsius/min) Process temperature (Reverse DNC, 1 Celsius/min)

(b)

55 50

Temperature [ C]

6

45

3

o

1.6x10

µ0 [#/kg ]

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


6

1.2x10

5

8.0x10

40 35 30 25

5

4.0x10

20 0.0 0

10

20

30

40

0

RT # [-]

10

20

30

40

RT# [-]

Figure 6. (a) zeroth moment and (b) temperature dynamics for the cooling crystallization of paracetamol in water under a pulse disturbance at 16 residence times (RT).

The implementation of Reverse DNC with a slow cooling/heating rate such as 0.1°C per minute shows slow dynamics. The system takes close to 20 residence times to reach steady state which would result in practice in significant waste of product. This slow dynamics are due to the magnitude of the disturbance which leads to the controller to take the temperature to the maximum allowed temperature (50°C). This leads to almost complete dissolution of crystals before the system reacts and starts decreasing slowly until nucleation occurs again. Therefore, slow cooling rates can result in negative effect as observe from the no DNC scenario. However, a similar CSD was achieved before and after the pulse disturbance took place as shown in Figure 7a. The base case study reaches steady state faster than the 0.1°C per minute; it takes 16 residence times to wash out the fine crystals.



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

(a)

(b)

(c)

Figure 7. Crystal size distribution pf seed crystals, before and after disturbance for the cooling crystallization of paracetamol under Reverse DNC strategy at (a) 0.1, (b) 0.6, and (c) 1°C per min.


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The fastest cooling/heating rate resulted in a similar time to reach steady state than the base case study. This occurred due to the fast nucleation and dissolution event that occur since the controller switches between cooling and heating at a fast rate; constant nucleation and dissolution event generates numerous oscillations during the continuous operation which result in significant amount of wasted material since most oscillations are out of the operating boundary. The impact of the numerous oscillations can be observed on the steady state CSD achieved after the pulse disturbance which is different to the distribution from the base case study. Therefore, the scenario at high rate is not optimal for the cooling crystallization of paracetamol in water. For this system, small amount of oscillations are observed for the scenario in which the heating and cooling rate was set to 0.6°C per minute. As observed in Figure 6a, the disturbance was suppressed after 3 oscillations, which demonstrates that there is an optimal cooling and heating rate which a balance between fast reaction and minimum oscillations can be achieved. Also, the steady state distribution after the extreme pulse disturbance implemented is similar to the one achieved after the startup procedure. This indicates that an optimal cooling and heating rate for the Reverse DNC framework is close to 0.6°C per minute for the scenarios studied in this work. But in practice, the optimal heating/cooling rate for Reverse DNC framework should be a strong function of API nucleation and growth kinetics, performance of temperature controller (e.g. time lag), and even the heat transfer efficiency of the experimental setup. Simulation shown in this section can provide a recommendation for optimal heating/cooling rate but some trial and error experiments are still necessary to determine the actual optimal value, which can highly influence the final performance of DNC.

Conclusion The simulation based analysis performed for the continuous cooling crystallization of paracetamol in water in a MSMPR system showed that the optimal DNC framework is Reverse DNC followed by Bound DNC. In addition, an optimal heating/cooling rate is critical in Reverse DNC framework, and too fast or too slow heating/cooling could end up with large oscillation or long reaction time. This Reverse DNC framework, which is optimal for continuous MSMPR, differ from the common optimal batch DNC strategy that has been demonstrated in literature such as Basic or Predictive DNC. This observation concludes that further analysis and optimization of batch model-free strategies should be performed when implementing in



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continuous systems. The difference is mainly because continuous crystallization has continuous wash out and removal of crystals whereas batch crystallization doesn’t have. Future work could be performed in which model-free supersaturation control strategies performed in batch operation can be analyzed and optimized for continuous systems. Furthermore, this type of model-based analysis facilitates the transfer of knowledge from batch to continuous by reducing the experimentation.

Acknowledgments This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant no. DGE-1333468. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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For Table of Contents Use Only

Model-Based Evaluation of Direct Nucleation Control Approaches for the Continuous Cooling Crystallization of Paracetamol in a Mixed Suspension Mixed Product Removal System David Acevedo, Yang Yang, Daniel J. Warnke, Zoltan K. Nagy* Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN 47907

counts

Tjacket (t)

+

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


-

SP Tcryst(t)

DNC

Chiller

+

TSP

A series of DNC strategies were investigated via simulation based scenarios of the cooling crystallization of paracetamol in a MSMPR system. The result showed that Reverse DNC is the most suitable strategy with respect to disturbance rejection and set-point changes. This study demonstrated the use of model-based study for designing better strategies for continuous crystallization systems.


Model-Based Evaluation of Direct Nucleation Control Approaches for

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