# A Comparative Study of Coupled Preferential Crystallizers for the Efficient Resolution of Conglomerate-Forming Enantiomers

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## Abstract

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## 1. Introduction

## 2. Coupled Preferential Crystallizer Configurations

#### 2.1. CPC-MSMPR Configuration

#### 2.2. CPC Configuration

#### 2.3. CPC-D Configuration

## 3. Model of the Coupled Crystallization Process

## 4. Results and Discussion

#### 4.1. DL-threonine/H_{2}O as Model System

_{2}O is chosen as a model system for these studies [11]. The kinetic parameters for DL-threonine are identical for both the enantiomers. For the CPC-MSMPR configuration, two MSMPR vessels of volume $V=0.45$ L are connected together with exchange of liquid phase. The vessels contain racemic liquid phase at $36{\phantom{\rule{3.33333pt}{0ex}}}^{\circ}$C (${T}_{sat}=45{\phantom{\rule{3.33333pt}{0ex}}}^{\circ}$C) with homochiral solid phase. The feed streams with the same conditions are fed to each vessel. In order to the keep slurry volume constant, the same amount of slurry as the feed stream is taken out of the vessels as the product stream. The results obtained from CPC-MSMPR are compared with the conventional CPC and CPC-D configurations. The condition for CPC configuration is similar to CPC-MSMPR except that there are no feed and product streams. For CPC-D, the condition for the crystallization vessel (Tank 1) is same as CPC. However, the dissolution vessel (Tank 2) is at saturation temperature ${T}_{sat}=45{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$C and it contains a racemic solid phase. The process conditions are summarized in Table 1.

#### 4.2. Liquid and Solid Phase Mass Evolution

#### 4.3. Effect of Feed Flow Rate on CPC-MSMPR Productivity and Yield

#### 4.4. Effect of Liquid Phase Exchange Rate on CPC-MSMPR Productivity and Yield

#### 4.5. Effect of Seed Mass on CPC-MSMPR Productivity and Yield

#### 4.6. Productivity and Yield of CPC and CPC-D Configurations

#### 4.7. Comparison of Productivities and Yields for Various Configurations

#### 4.8. Effect of Nucleation Kinetics on the Performances of Various Configurations

_{2}O system were used in the simulation results. Here we investigate how the nucleation kinetic parameters affect the performance of the various configurations. The secondary and primary nucleation rates for this system are given by Equations (19) and (21), respectively. A scaling factor $\alpha $ is used to scale the parameters ${k}_{b,sec}^{\left(j\right)}$ and ${k}_{nuc}$ appearing in those equations. For instance, when $\alpha =1$, we have the original values of the parameters as shown in Table A1 and when $\alpha =10$, these two parameters are increased ten-fold. This essentially means that with $\alpha =10$ the primary and secondary nucleation rates are increased ten-fold in the same process condition. Such a study will be useful in predicting process performance for systems with higher nucleation rates. The simulation results using various values of $\alpha $ for the CPC-MSMPR configuration are shown in Figure 11a where the process parameters used are seed mass 1 g, feed rate 80 mL min${}^{-1}$, and liquid phase exchange 80 mL min${}^{-1}$. As can be seen, the productivities plummet to zero between 1 h and 3 h for $\alpha =10,100,500$ as it significantly increases the nucleation rate for both the preferred and counter enantiomers, resulting in the product purity dropping below the cut-off purity of $e{e}_{S}=99\%$. The higher the nucleation rate, the sooner the purity falls below the cut-off value. The simulation results for CPC and CPC-D configurations are shown in Figure 11b where the following process parameters used, seed mass 1 g, liquid phase exchange 80 mL min${}^{-1}$, racemate mass 70 g. As can be seen, similar trends (i.e., drop in productivity) are found with high values of $\alpha $ for the CPC and CPC-D configurations. The harvesting period for the CPC-D configuration has also reduced significantly. However, it is to be noted that a higher value of $\alpha =100$ is used for the CPC configuration in order to demonstrate the effect of nucleation parameter, as $\alpha =10$ did not have any noticeable effect . This is because the supersatuation plays an important role in nucleation rate, and in the CPC configuration there are no provisions for the continuous supply of feed slurry or selective dissolution of racemate to compensate for the consumed supersaturation for which both the growth and nucleation rate processes compete. Thus, the effect of the increased value of nucleation kinetic parameters is less prominent for the CPC configuration. For a crystallization system with high nucleation rate, a larger seed mass can be useful in promoting growth and suppressing nucleation.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A. Model Parameters

Parameter | Symbol | Value | Units |
---|---|---|---|

constant for density | ${K}_{1}$ | $1.00023\times {10}^{-3}$ | ${\mathrm{m}}^{3}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{kg}}^{-1}$ |

constant for density | ${K}_{2}$ | $4.68\times {10}^{-9}$ | ${\mathrm{m}}^{3}\phantom{\rule{3.33333pt}{0ex}}{\left(\mathrm{kg}{\phantom{\rule{3.33333pt}{0ex}}}^{\circ}\mathrm{C}\right)}^{-1}$ |

constant for density | ${K}_{3}$ | $0.3652\times {10}^{-3}$ | ${\mathrm{m}}^{3}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{kg}}^{-1}$ |

volume shape factor | ${k}_{v}$ | 0.1222 | - |

density of solid threonine | ${\rho}_{s}$ | 1250 | ${\mathrm{kg}\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}}^{-3}$ |

ideal gas constant | ${R}_{g}$ | 8.314 | J (K mol)${}^{-1}$ |

activation energy for growth | ${E}_{A,g}$ | $7.55\times {10}^{4}$ | J mol${}^{-1}$ |

activation energy for secondary nucleation | ${E}_{A,bsec}$ | $6.38\times {10}^{4}$ | J mol${}^{-1}$ |

dissolution rate constant | ${k}_{diss}$ | $3\times {10}^{-5}$ | m s${}^{-1}$ |

growth rate constant | ${k}_{g,eff}$ | $1.24\times {10}^{7}$ | m s${}^{-1}$ |

growth exponent | g | $1.19$ | - |

growth parameter (size-dependent term) | ${a}_{ASL}$ | $2\times {10}^{4}$ | m${}^{-1}$ |

growth exponent (size-dependent term) | $\gamma $ | −0.4 | - |

secondary nucleation rate constant | ${k}_{bsec,eff}$ | $3.97\times {10}^{24}$ | m${}^{-3}$ s${}^{-1}$ |

exponent for third moment | ${n}_{\mu 3}$ | 3.0258 | - |

secondary nucleation exponent | ${b}_{sec}$ | $4.8$ | - |

primary nucleation rate constant | ${k}_{nuc}$ | 1000 | s${}^{-1}$ |

primary nucleation exponent | ${b}_{nuc}$ | 1 | - |

nucleation induction time | ${t}_{ind}$ | 7200 | s |

slope of sigmoidal function | $\varphi $ | 0.01 | - |

solubility parameter | ${m}_{sol}$ | $1.2\times {10}^{-3}$ | ${}^{\circ}$C |

solubility parameter | ${b}_{sol}$ | $0.059013$ | - |

solubility parameter | ${a}_{1sol}$ | $-0.0780$ | - |

solubility parameter | ${a}_{2sol}$ | $-0.1043$ | - |

mean seed size of enantiomer ${E}_{1}$ (L-threonine) | ${L}_{mean,{E}_{1}}$ | 27,95 | $\mathsf{\mu}\mathrm{m}$ |

standard deviation of seed CSD | ${\sigma}_{ln,{E}_{1}}$ | 0.3, 0.34 | - |

mean size of racemate | ${L}_{mean,rac}$ | 9 | $\mathsf{\mu}\mathrm{m}$ |

standard deviation of racemate CSD | ${\sigma}_{ln,rac}$ | 0.5 | - |

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**Figure 1.**(

**a**) Coupled preferential crystallization in MSMPR crystallizers (CPC-MSMPR), where each vessel initially containing supersaturated racemic solution is continuously fed with a slurry containing the seed of the specific enatiomorph. Exchange of liquid phase makes use of the depletion of the counter enantiomer in the other vessel; (

**b**) The coupled preferential crystallizer (CPC) configuration, which is similar to CPC-MSMPR except that there is no continuous feed and product removal; (

**c**) The coupled preferential crystallization-dissolution (CPC-D) configuration, which is similar to CPC except that Tank 2 (seeded with racemic solid) is maintained at saturation temperature so that dissolution of counter enantiomorph ${E}_{1}$ takes place.

**Figure 2.**Evolution of mass in liquid and solid phases for the coupled preferential crystallization in MSMPR crystallizers (CPC-MSMPR).

**Figure 3.**Evolution of mass in liquid and solid phases for the coupled preferential crystallization (CPC) configuration.

**Figure 4.**Evolution of mass in liquid and solid phases for the coupled preferential crystallization-dissolution (CPC-D) configuration.

**Figure 5.**Simulation results showing effect feed flow rate on the productivity and yield for the coupled preferential crystallization in MSMPR crystallizers (CPC-MSMPR) (seed mass 2 g, liquid phase exchange rate 80 mL min${}^{-1}$). (

**a**) Increase in feed flow rate up to 80 mL min${}^{-1}$ causes an increase in production to a certain level, beyond which no significant improvement in production is achieved; (

**b**) Yield of the process decreases while feed flow rate increases, as increase of feed flow rate reduces the residence time of the solution (for legend please refer to (

**a**)).

**Figure 6.**Simulation results showing the effect of the liquid phase exchange rate on the productivity and yield of the coupled preferential crystallization in MSMPR crystallizers (CPC-MSMPR) (feed flow rate 80 mL min${}^{-1}$, seed mass 2 g). (

**a**) Increase of liquid phase exchange increases productivity; (

**b**) Yield of the processes decreases while the feed flow rate increases, as an increase of the feed flow rate reduces the residence time of the solution.

**Figure 7.**Simulation results showing the effect of seed mass on the productivity and yield of the coupled preferential crystallization in MSMPR crystallizers (CPC-MSMPR) (feed flow rate 80 mL min${}^{-1}$, exchange rate 80 mL min${}^{-1}$). (

**a**) Productivity increases with seed mass; (

**b**) Yield increases with seed mass (for legend please refer to (

**a**)).

**Figure 8.**Simulation results showing the effect of seed mass on the productivity and yield of the coupled preferential crystallization (CPC) configuration (exchange rate 80 mL min${}^{-1}$). Final productivity and yield are not affected by seed mass. (

**a**) Productivity evolution; (

**b**) Yield evolution.

**Figure 9.**Simulation results showing effect of racemate mass on the productivity and yield of coupled preferential crystallization-dissolution (CPC-D) configuration (seed mass 2 g, exchange rate 80 mL min${}^{-1}$). (

**a**) Productivity for Tank 1 and Tank 2; (

**b**) Yield for Tank 1 and Tank 2.

**Figure 10.**(

**a**) Comparison of productivities for various process configurations. Process parameters used are seed mass 8 g, feed flow rate rate 80 mL min${}^{-1}$, exchange rate 80 mL min${}^{-1}$, and racemate mass 70 g. The productivity for coupled preferential crystallization in MSMPR crystallizers (CPC-MSMPR) is found to be the highest. The sudden rise and fall of productivities for the coupled preferential crystallization-dissolution (CPC-D) configuration is due to the use of cut-off purity of $e{e}_{S}=99\%$; (

**b**) Curves showing comparison of yields. The yield of CPC-MSMPR is the lowest. The relatively high yield of CPC-D configuration in Tank 2 is due to the use large amount of racemic solid.

**Figure 11.**Simulation results showing the effect of nucleation kinetic parameters on productivity in Tank 1 for various configurations. (

**a**) Results for the coupled preferential crystallization in MSMPR crystallizers (CPC-MSMPR) with incremental values of $\alpha $; (

**b**) results for coupled preferential crystallization (CPC) and coupled preferential crystallization-dissolution (CPC-D) configurations. The scaling factor $\alpha $ is used to modify the kinetic parameters. With higher nucleation rate (i.e., higher value of $\alpha $), the purity of the product can go below the cut-off purity of $e{e}_{S}=99\%$ earlier, thus affecting the productivity.

**Table 1.**Process conditions used in simulation studies for coupled preferential crystallization in MSMPR crystallizers (CPC-MSMPR), coupled preferential crystallization (CPC) in batch mode and coupled preferential crystallization-dissolution (CPC-D) in batch mode.

CPC-MSMPR | CPC | CPC-D | |||||
---|---|---|---|---|---|---|---|

Variable | Tank 1 | Tank 2 | Tank 1 | Tank 2 | Tank 1 | Tank 2 | |

Liquid phase | ${m}_{\mathrm{rac},\mathrm{L}}$ | $97.48$ g | $97.48$ g | $97.48$ g | $97.48$ g | $97.48$ g | $97.48$ g |

${m}_{\mathrm{H}{}_{2}\mathrm{O}}$ | $369.83$ g | $369.83$ g | $369.83$ g | $369.83$ g | $369.83$ g | $369.83$ g | |

Solid phase | ${m}_{\mathrm{E}1,\mathrm{S}}$ (L-threonine) | $2.00$ g | − | $2.00$ g | − | $2.00$ g | $35.00$ g |

${m}_{\mathrm{E}2,\mathrm{S}}$ (D-threonine) | − | $2.00$ g | − | $2.00$ g | − | $35.00$ g | |

Temperatures | ${T}_{cryst}^{\left({T}_{1}\right)};{T}_{cryst}^{\left({T}_{2}\right)}$ | $36{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ | $36{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ | $36{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ | $36{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ | $36{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ | $45{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ |

Exchange rate | ${F}_{ex}$ | 80 mL min${}^{-1}$ | 80 mL min${}^{-1}$ | 80 mL min${}^{-1}$ | |||

Feed rate | q | 80 mL min${}^{-1}$ | 80 mL min${}^{-1}$ | − | − | − | − |

Removal rate | q | 80 mL min${}^{-1}$ | 80 mL min${}^{-1}$ | − | − | − | − |

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**MDPI and ACS Style**

Majumder, A.; Nagy, Z.K.
A Comparative Study of Coupled Preferential Crystallizers for the Efficient Resolution of Conglomerate-Forming Enantiomers. *Pharmaceutics* **2017**, *9*, 55.
https://doi.org/10.3390/pharmaceutics9040055

**AMA Style**

Majumder A, Nagy ZK.
A Comparative Study of Coupled Preferential Crystallizers for the Efficient Resolution of Conglomerate-Forming Enantiomers. *Pharmaceutics*. 2017; 9(4):55.
https://doi.org/10.3390/pharmaceutics9040055

**Chicago/Turabian Style**

Majumder, Aniruddha, and Zoltan K. Nagy.
2017. "A Comparative Study of Coupled Preferential Crystallizers for the Efficient Resolution of Conglomerate-Forming Enantiomers" *Pharmaceutics* 9, no. 4: 55.
https://doi.org/10.3390/pharmaceutics9040055