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Autonomous Liquid–Liquid Extraction Operation in Biologics Manufacturing with Aid of a Digital Twin including Process Analytical Technology^{ †}

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

#### 1.1. Liquid–Liquid Extraction and Aqueous Two-Phase Systems for Biologics

#### 1.2. Quality by Design and Digital Twins

## 2. Review of Physiochemical Fundamentals for Scalable Digital Twin Modelling of Mixer–Settlers for Liquid–Liquid Extraction Process

#### 2.1. Fluid Dynamics

#### 2.2. Continuous Settler Equipment

#### 2.3. Settler Models

#### 2.3.1. Modelling Depth

#### 2.3.2. Henschke Model

- The vertical velocity in the film is neglected because the change in film thickness is very small compared to distance from the center of the film.
- The continuous phase is treated in the dispersion as an incompressible Newtonian fluid with constant viscosity.
- Gravity is negligible compared to the pressure due to the droplet packing.
- The film is considered to be two-dimensional.
- The spherical curvature of the film is neglected in the coalescence.

#### 2.3.3. Computational Fluid Dynamics

#### 2.3.4. Distributed Plug Flow Model

- There is no concentration or velocity gradient in the radial direction.
- The model is one-dimensional.
- The convective transport is superimposed by a dispersive one.
- In the axial direction, material values, axial dispersion coefficient, and the geometric dimensions are assumed to be constant.
- A transient mass transport can be represented.

## 3. Material and Methods

#### 3.1. Process Analytical Technologies

#### 3.2. Experimental Setup

#### 3.2.1. Batch Settling Experiments

#### 3.2.2. Continuous Horizontal Settler

#### 3.2.3. Alkaline Lysis and ATPE

#### 3.3. Continous Settler Process Model

## 4. Results

#### 4.1. Implementation of the Digital Twin

#### 4.2. Model Parameter Determination

#### 4.3. Validation of the Process Model

#### 4.3.1. Plausibility

#### 4.3.2. Sensitivity

#### 4.3.3. Precision

#### 4.3.4. Accuracy and Validation

#### 4.4. Risk Analysis

#### 4.5. Experimental Feasibility by Autonomous Operation Study

## 5. Conclusions and Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Presentation of the risk analysis and regulation within the framework of the QbD [13].

**Figure 2.**Schematic and qualitive illustration of the development path from a stationary model to a digital twin with the example of the mixer–settler [9].

**Figure 3.**Schematic representation of the coalescence of a droplet with the phase boundary [25].

**Figure 4.**Schematic representation of the settling behavior of a water/oil system (

**a**) and the sedimentation and coalescence curve over time (

**b**) [26].

**Figure 5.**Schematic drawing of a mixer–separator [28].

**Figure 7.**Schematic representation of the radial concentration distribution of ideal and real plug flow [48].

**Figure 13.**Schematic representation of the model validation workflow [55].

**Figure 16.**Illustration of the regression quality of the OLS regression (

**a**) and parameter sensitivities of the MFAT simulations (

**b**).

**Figure 17.**Plot of model quality of fit (

**a**) and correlation loading plot of PLS analysis from MFAT results (

**b**).

**Figure 18.**Illustration of the design spaces for density continuous phase (

**a**), hold-up (

**b**), coalescence parameter (

**c**), interface tension (

**d**), viscosity disperse phase (

**e**), and droplet diameter (

**f**) from the OLS analysis of the MFAT simulation study.

**Figure 19.**Representation of wedge length from experiments and simulations from ATPE (

**a**), n-butanol/water, water/cyclohexanone, water/n-hexanes, and cyclohexane/water material systems (

**b**).

**Figure 22.**Representation of the effects and relative probability of the studied disturbances of the process.

**Figure 23.**Plot of measured volumetric flow rate (

**a**), density (

**b**), Sauter diameter (

**c**), and simulated and measured wedge length from aqueous ATPE experiment (

**d**).

**Figure 24.**Acquisition of the droplets (

**left**) and evaluation of the image (

**right**) by the SOPAT-PA probe and the SOPAT algorithm.

**Figure 25.**Histogram of Sauter diameters (

**a**) and cumulative distribution (

**b**) of all images from the SOPAT probe of the biomass experiment.

**Figure 26.**Plot of measured volumetric flow rate (

**a**), density (

**b**), Sauter diameter (

**c**), and simulated and measured dispersion wedge length (

**d**) from the biomass igneous ATPE test.

**Table 1.**Representation of dimensionless ratios from simulations of a horizontal continuous settler.

Characteristic Number | Region | Lowest Value | Highest Value |
---|---|---|---|

Reynolds number | Inlet | 3.26 × 10^{2} | 7.99 × 10^{3} |

Settler | 3.03 × 10^{−3} | 6.18 × 10^{−1} | |

Weber number | Inlet | 1.25 × 10^{−4} | 4.40 × 10^{−2} |

Settler | 1.61 × 10^{−4} | 9.28 × 10^{−2} | |

Bond number | Inlet | 1.03 × 10^{−2} | 8.93 × 10^{−1} |

Settler | 1.48 × 10^{−2} | 3.50 × 10^{0} | |

Archimedes number | Inlet | 7.34 × 10^{1} | 2.46 × 10^{3} |

Settler | 1.17 × 10^{2} | 7.26 × 10^{3} |

Parameter | Unit | Lower Boundary | Upper Boundary |
---|---|---|---|

Flow rate | [m³/s] | $5\times {10}^{-6}$ | $2.5\times {10}^{-5}$ |

Density continuous phase | [kg/m³] | 1086 | 1126 |

Density disperse phase | [kg/m³] | 1172 | 1212 |

Viscosity continuous phase | [Pa s] | 0.007 | 0.009 |

Viscosity disperse phase | [Pa s] | 0.003 | 0.005 |

Initial droplet diameter | [µm] | 418 | 1045 |

Interface tension | [N/m] | $3.5\times {10}^{-4}$ | $1.05\times {10}^{-3}$ |

Hold-Up | [-] | 0.40 | 0.85 |

Coalescence parameter | [-] | 0.08 | 0.12 |

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**MDPI and ACS Style**

Uhl, A.; Schmidt, A.; Hlawitschka, M.W.; Strube, J.
Autonomous Liquid–Liquid Extraction Operation in Biologics Manufacturing with Aid of a Digital Twin including Process Analytical Technology. *Processes* **2023**, *11*, 553.
https://doi.org/10.3390/pr11020553

**AMA Style**

Uhl A, Schmidt A, Hlawitschka MW, Strube J.
Autonomous Liquid–Liquid Extraction Operation in Biologics Manufacturing with Aid of a Digital Twin including Process Analytical Technology. *Processes*. 2023; 11(2):553.
https://doi.org/10.3390/pr11020553

**Chicago/Turabian Style**

Uhl, Alexander, Axel Schmidt, Mark W. Hlawitschka, and Jochen Strube.
2023. "Autonomous Liquid–Liquid Extraction Operation in Biologics Manufacturing with Aid of a Digital Twin including Process Analytical Technology" *Processes* 11, no. 2: 553.
https://doi.org/10.3390/pr11020553