# A Semi-Mechanistic Prediction of Residence Time Metrics in Twin Screw Granulation

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Twin Screw Wet Granulation

#### 1.2. Objectives

## 2. Materials and Methods

**FR**), processing screw speed (

**RPM**), liquid-to-solid percentage (

**LS**), screw configuration described by number of kneading elements (

**NK**) and stagger angle (

**SA**) between them. The table also lists the available number of points sourced from each study.

## 3. Theory and Metrics

#### 3.1. Theory behind Equation Development

#### 3.2. Formulation of the Equations for the Metrics

#### 3.3. Algorithm Development

- i
- Comparison between main effects plot of the experiments and that of the model
- ii
- Satisfactory parity plots, realistic narrow upper and lower bounds were set, and the model’s performance was determined based on how many predicted points fell between these limits; in addition the root mean square of errors $RMSE$ too was evaluated as a statistical measure for goodness of fit
- (iii)
- Wherever possible, the values of the tuning parameters in the model when trained on different datasets were compared, and physical interpretation was made for their ranges

## 4. Results and Discussion

#### 4.1. Qualitative Analysis- Main Effects Plots

**FR**), number of kneading elements (

**# KEs**) in the configuration, stagger angle between the kneading elements (

**SA**) and the rotational speed of the shafts of the extruder (

**RPM**) have been shown on the experimental MRT and on the model predicted MRT in Figure 4 for the Kumar et al. 2015 dataset. From the figures, it can be seen that the MRT of the TSG showed an increasing trend with respect to the increasing powder feed rate range from 10 kg/h to 25 kg/h and number of kneading elements from 2 to 12. On the other hand, the MRT decreased with respect to increasing screw speed from $500\phantom{\rule{0.277778em}{0ex}}RPM$ to $900\phantom{\rule{0.277778em}{0ex}}RPM$. These observations are in line with the equations formulated in Section 3.2. However, it can be seen that the average MRT increased and then subsequently decreased as the stagger angle was increased from first 30${}^{\circ}$ to 60${}^{\circ}$ and then 90${}^{\circ}$. Additionally, it was reported by Kumar et al. 2015 [21], that several experimental data points were missing for run cases of 90${}^{\circ}$ SA due to the jamming of the equipment. This lack of comparable data points is the reason for a low average MRT value at high stagger angle.

**FR**(indicated by the first sub-figure in blue), it can be seen that the model (solid curve) predicted a much steeper increase and wider range of MRT values compared to the experimental runs (individual points). The average model predictions were closer for powder feed rate values of 25 kg/h at higher MRT values. A similar observation is made from the second sub-figure (red curve, main-effects of

**# KEs**) whereby, the average model prediction was lower compared to the experimental values at two kneading elements configurations yielding low MRT values. On the other hand, from the fourth sub-figure (yellow curve, main effects of

**RPM**), the average MRTs predicted were lower at lower screw speeds corresponding to larger MRT settings. Lastly, it can be seen from the third sub-figure (green curve, main effects of

**SA**) that MRTs were under-predicted at settings corresponding to lower experimental MRT (30${}^{\circ}$ & 90${}^{\circ}$

**SA**values), and were over-predicting for the intermediate setting of 60${}^{\circ}$.

**FR**,

**# KEs**,

**SA**and

**RPM**), there is an addiotional factor

**LS**along which the effects have been in plotted too as indicated by the pink line and points. From the figures, it is seen that the MRT of the TSG showed an increasing trend with respect to the increasing powder feed rate range from 10 kg/h to 25 kg/h. On the other hand, the MRT decreased with respect to increasing screw speed from $500\phantom{\rule{0.277778em}{0ex}}RPM$ to $900\phantom{\rule{0.277778em}{0ex}}RPM$. Similar to the results for the Kumar et al. 2015 dataset, these observations are in line with the equations developed. Comparing the main effects of the kneading elements, it can be seen that the model predicted average MRT values were lower than the experimental average values for 4 and 6 kneading elements in the screw configuration. The plausible reason for this observation may be that the granules formed had occupied more space in the kneading zone than what was calculated theoretically, thereby increasing the holdup and consequently the MRT. On the other hand, the mean experimental MRT showed no observable change upon increasing the stagger angle from 30${}^{\circ}$ to 60${}^{\circ}$. Similar to the effects of low number of kneading elements, the granules formed at 30${}^{\circ}$ stagger angle might have plausibly occupied more space than estimated leading to higher experimental MRT values. Despite these unexpected observations, the model equations were not changed to fit the predictions/main effects trends better as doing so would have removed the generalizable nature of the model which has been the goal of this study all along.

#### 4.2. Quantitative Analysis- Parity Plots

**LS**% ages were varied from 6 to $8\%$ for the Kumar et al. 2016 dataset. One plausible reason for the poor prediction using the combined Training set may be that the main effects of

**FR**have been contrary for the Kumar et al. 2015 and Kumar et al. 2016 experimental datasets respectively as seen in Section 4.1. Additionally, from the parity plots in Figure 10c,d, it is seen that the properly predicted, under- and over-predicted points were distributed in equal proportion across the training, validation and test datasets. This gives further indication to the veracity of the modelling approach.

#### 4.3. Quantitative Analysis- Comparing Model Parameters

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**(

**a**): Schematic of a typical continuous wet granulation process and; (

**b**): a TSE used for continuous wet granulation process.

**Figure 2.**Schematic showing (

**a**) kneading block of 7 elements each with thickness 3 units and

**SA**60${}^{\circ}$; (

**b**) kneading block of 21 elements each with thickness 1 unit and

**SA**18${}^{\circ}$; and (

**c**) conveying section of length 21 units and full turn angle 360${}^{\circ}$.

**Figure 3.**Schematic for algorithm adopted to train and validate mean residence time (MRT) and variance models on datasets.

**Figure 4.**Experimental results vs. Model predictions: Main effects of varied parameters on MRT for the Kumar et al. 2015 [21] dataset.

**Figure 5.**Experimental results vs. Model predictions: Main effects of varied parameters on MRT for the Kumar et al. 2016 [26] dataset.

**Figure 6.**Experimental results vs. Model predictions: Main effects of varied parameters on variance for the Kumar et al. 2015 [21] dataset.

**Figure 7.**Experimental results vs. Model predictions: Main effects of varied parameters on variance for the Kumar et al. 2016 [26] dataset.

**Figure 8.**Experimental observations (X) vs. predicted model responses (Y) when trained on the Kumar et al. 2015 [21] dataset.

**Figure 9.**Experimental observations (X) vs. predicted model responses (Y) when trained on the Kumar et al. 2016 [26] dataset.

**Figure 11.**Experimental MRT observations (X) vs. predicted model MRT responses (Y) when trained on the Ismail et al. 2019 [14] dataset.

**Table 1.**Summary of the twin screw wet granulation residence time distribution (RTD) available and collected from the literature.

Data Source | Equipment Name | Process Material | Varied Parameters | Number of Points |
---|---|---|---|---|

Kumar et al. 2015 [21] | ConsiGma-25 | $\alpha $-Lactose MH | FR, RPM, NK & SA | 66 |

Kumar et al. 2016 [26] | ConsiGma-25 | $\alpha $-Lactose MH | FR, RPM, LS, NK & SA | 51 |

Ismail et al. 2019 [14] | Three-Tec | Avicel PH-101 | FR, RPM, LS & NK | 24 |

Total: 141 |

Parameter | Kumar et al. 2015 | Kumar et al. 2015 + 2016 | Kumar et al. 2016 | Ismail et al. 2019 |
---|---|---|---|---|

${b}_{1}$ | 0.33 | 0.46 | 0.53 | 1.67 |

${b}_{2}$ | 0.99 | 1.24 | 0.33 | 0.96 |

${b}_{3}$ | 0.65 | 1.09 | 0.24 | 1.32 |

${b}_{4}$ | 1.33 | 1.15 | 1.08 | 0.63 |

${b}_{5}$ | 5.35 | 2.29 | 1.16 | - |

${b}_{6}$ | 1.99 | 2.24 | 1.33 | - |

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**MDPI and ACS Style**

Muddu, S.V.; Kotamarthy, L.; Ramachandran, R.
A Semi-Mechanistic Prediction of Residence Time Metrics in Twin Screw Granulation. *Pharmaceutics* **2021**, *13*, 393.
https://doi.org/10.3390/pharmaceutics13030393

**AMA Style**

Muddu SV, Kotamarthy L, Ramachandran R.
A Semi-Mechanistic Prediction of Residence Time Metrics in Twin Screw Granulation. *Pharmaceutics*. 2021; 13(3):393.
https://doi.org/10.3390/pharmaceutics13030393

**Chicago/Turabian Style**

Muddu, Shashank Venkat, Lalith Kotamarthy, and Rohit Ramachandran.
2021. "A Semi-Mechanistic Prediction of Residence Time Metrics in Twin Screw Granulation" *Pharmaceutics* 13, no. 3: 393.
https://doi.org/10.3390/pharmaceutics13030393