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An Experimental and Computational Approach to Development of Mixing Processes for Miscible Liquids in Unbaffled Tanks

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Abstract

Purpose

Mixing of liquids is a critical unit operation in the biopharmaceutical drug product manufacturing. It commonly consists of mixing miscible liquids to dilute bulk drug substance (DS) or pool multiple lots of drug substance. In the past, at-scale mixing studies have been conducted to determine the mixing parameters, namely mixing speed, and mixing time. At-scale studies have historically been utilized to overcome the challenges associated with geometric dissimilarity of mixing systems found when scaling up. In addition, such studies are quite costly, as they often use actual DS to overcome a lack of representativeness associated with simple salt trace models often employed. As a result, there is a significant need for alternative cost-effective methods that can predict mixing parameters with close agreement to actual experiments and operations.

Method

At-scale mixing experiments were conducted using full-sized tanks and surrogate solutions. Several computational fluid dynamic (CFD) simulation methods were conducted and compared with the experiments to determine the most reliable computational techniques.

Results

The experiments demonstrate that surrogate solutions can be used reliably to determine mixing parameters in at-scale studies instead of the valuable drug products. Studying different CFD methods also showed that transient simulations that use a large eddy simulation (LES) viscous model and a sliding mesh can correctly predict the mixing parameters.

Conclusion

Results of this study establish a practical and reliable methodology to perform mixing studies for miscible liquids with different kinematic viscosities. The methods discussed herein greatly reduce the routine mixing study costs in the biopharmaceutical industry and increase efficiency and accuracy of the results, allowing proactive scale-up of mixing operations.

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Abbreviations

a :

Hypotenuse of the right triangle with legs h and c, which is used to calculate dv in the mixing tank, cm

b :

Height of the air-liquid interface from the base of the top flange at the center of the mixing tank, cm

c :

Distance between wall and top flange of the mixing tank, cm

C 0 :

Initial concentration, mg/mL

C ∞ :

Final concentration, mg/mL

C i :

Instantaneous concentration, mg/mL

C i ′ :

Normalized concentration, dimensionless

D :

Impeller diameter, m

DDB :

Diffusion coefficient of DS to buffer, m2/s

D l :

Impeller diameter in large tank, m

D s :

Impeller diameter in small tank, m

d v :

Vortex depth defined as vertical distance between air-liquid interface at vessel axis and elevation of the same interface at vessel wall, cm

h :

Height of the air-liquid interface from the base of the top flange at the mixing tank wall, cm

N :

Impeller speed, rps or rpm

N l,max :

Maximum impeller speed in large tank, rps or rpm

N s,max :

Maximum impeller speed in small tank, rps or rpm

ρ:

Density, kg/m3

t 95 :

Time to reach and remain at 95% homogeneity, min

t 95 , exp :

Experimentally determined t95, min

t 95 , sim :

t95 Determined by simulations, min

u :

Fluid velocity, m/s

ν:

Kinematic viscosity, m2/s

V tip :

Impeller tip speed, m/s

v y :

Fluid velocity along y-axis, m/s

x :

Position of a given point on the impeller surface, m

x 0 :

Initial mass fraction, dimensionless

x ∞ :

Final mass fraction, dimensionless

x i :

Instantaneous mass fraction, dimensionless

X i :

Position of the rotation axis, m

x i ' :

Normalized mass fraction, dimensionless

μ:

Dynamic viscosity, Pa·s

μ B :

Compounding buffer viscosity, kg/m·s

τ xy :

y-Component of stress tensor τx, Pa

τ xz :

z-Component of stress tensor τx, Pa

τ zy :

y-Component of stress tensor τz, Pa

ω i :

Angular velocity of the impeller, rad/s

References

  1. Bee JS, Stevenson JL, Mehta B, Svitel J, Pollastrini J, Platz R, et al. Response of a concentrated monoclonal antibody formulation to high shear. Biotechnol Bioeng. 2009;103(5):936–43.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  2. Grenville RK. Blending of viscous Newtonian and pseudo-plastic fluids. Cranfield: Cranfield Institute of Technology; 1992.

    Google Scholar 

  3. Rieger F, Ditl P, Novák V. Vortex depth in mixed unbaffled vessels. Chem Eng Sci. 1979;34(3):397–403.

    Article  CAS  Google Scholar 

  4. Desai KG, Li L, Palmer M, Rosamonte M, Schofield P, Pongwa L, et al. Mixing of a mAb formulation in a new magnetically coupled single-use mixing system: key learnings of preliminary experimental and computational evaluation. J Pharm Sci. 2019;108(12):3932–7.

    Article  PubMed  Google Scholar 

  5. Yu Z, Finch BA, Hale DA. Mixing of stratified miscible liquids in an unbaffled tank with application in high concentration protein drug product manufacturing. Ind Eng Chem Res. 2018;57(9):3397–409.

    Article  CAS  Google Scholar 

  6. Thomas J, Sinha K, Shivkumar G, Cao L, Funck M, Shang S, et al. A CFD digital twin to understand miscible fluid blending. AAPS PharmSciTech. 2021;22(3):91.

    Article  PubMed  Google Scholar 

  7. Kuschel M, Fitschen J, Hoffmann M, von Kameke A, Schluter M, Wucherpfennig T. Validation of novel Lattice Boltzmann Large Eddy Simulations (LB LES) for equipment characterization in biopharma. Processes. 2021;9(6):950.

    Article  CAS  Google Scholar 

  8. Zadghaffari R, Moghaddasa JS, Revstedt J. A mixing study in a double-Rushton stirred tank. Comput Chem Eng, Publication in Lund University Research Portal. 2009;33(7):1240–6.

    CAS  Google Scholar 

  9. Corsini A, Delibra G, Sheard AG. A critical review of computational methods and their application in industrial fan design. ISRN Mech Eng. 2013;2013:1–20.

    Article  Google Scholar 

  10. Kresta SM, Etchells AW, Dickey DS, Atiemo-Obeng VA. Advances in industrial mixing: a companion to the handbook of industrial mixing. Hoboken: Wiley; 2015.

    Google Scholar 

  11. Olofsson C, Sundell E. CFD simulations of mixing using a magnetically driven impeller - method development and validation study. Chalmers University of Technology: Department of Mechanics and Maritime Sciences; 2019.

  12. Torotwa I, Ji C. A study of the mixing performance of different impeller designs in stirred vessels using computational fluid dynamics. Designs. 2018;2(1):10.

    Article  Google Scholar 

  13. Som S, Senecal PK, Pomraning E. Comparison of RANS and LES turbulence models against constant volume diesel experiments; 2012.

  14. Saltzman WM, Radomsky ML, Whaley KJ, Cone RA. Antibody diffusion in human cervical mucus. Biophys J. 1994;66(2 Pt 1):508–15.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  15. Paul EL, Atiemo-Obeng VA, Kresta SM. Handbook of industrial mixing: Science and practice. Hoboken: Wiley; 2004.

    Google Scholar 

  16. ANSYS. ANSYS fluent user guide. Canonsburg: ANSYS Inc; 2020.

    Google Scholar 

  17. Bird RB, Stewart WE, Lightfoot EN. Transport phenomena, Revised 2nd Edition. New York: Wiley; 2002.

  18. Haringa C, Vandewijer R, Mudde RF. Inter-compartment interaction in multi-impeller mixing. Part II. Experiments, sliding mesh and large Eddy simulations. Chem Eng Res Des. 2018;136:886–99.

    Article  CAS  Google Scholar 

  19. Barrue H, Bertrand J, Cristol B, Xuereb C. Eulerian simulation of dense solid-liquid suspension in multi-stage stirred vessel. J Chem Eng Jpn. 2001;34(5):585–94.

    Article  CAS  Google Scholar 

  20. Oshinowo LM, Bakker AJ. CFD Modeling of solids suspensions in stirred tanks. TMS Annual Meeting; 2002.

  21. Jahoda M, Moštĕk M, Kukuková A, Machoň V. CFD modelling of liquid homogenization in stirred tanks with one and two impellers using large Eddy simulation. Chem Eng Res Des. 2007;85(5):616–25.

    Article  CAS  Google Scholar 

  22. ANSYS. ANSYS fluent theory guide. Canonsburg: ANSYS, Inc.; 2020.

    Google Scholar 

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Acknowledgements

The authors would like to acknowledge the help of Adam Sokolnicki, Gayathri Raja, and Matthew Turiano from MilliporeSigma M LabTM in Burlington, MA for using the mixing tanks in the lab and for their help and support during the experiments.

Funding

The authors received no external funding for the completion of this work. Work described within was executed through routine Biogen drug product process development activity. All authors were employed by Biogen at the time of the studies conducted to support this work.

Author information

Authors and Affiliations

  1. Biologics & Advanced Therapy Medicinal Products, Biogen Inc., Cambridge, MA, USA

    Mehrrad Saadatmand, Matthew Lau & Bashir Siddique

  2. Drug Product Development, Moderna, Inc., Norwood, MA, USA

    Mehak Mehta & Jason E. Fernandez

  3. Purification and Drug Product Sciences, Oxford Biomedica Solutions LLC, Bedford, MA, USA

    Kelly Walsh

Authors
  1. Mehrrad Saadatmand
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  2. Mehak Mehta
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  3. Kelly Walsh
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  5. Bashir Siddique
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Corresponding author

Correspondence to Mehrrad Saadatmand.

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Appendix

Appendix

Some of the tables and methods were moved to Appendix for brevity and coherence of the main text. Table V shows results of the mixing stress study for mAb B. Tables VI and VII show the ANSYS Fluent solver setups for the simulations performed in this paper. These tables are reported here to help the interested reader to reproduce simulations similar to those in this work. Briefly, the steps needed to reproduce such simulations are as follows:

  1. 1.

    Generate the mesh based on the mesh type and cell numbers provided in the “Computational Mesh and Time Step” section.

  2. 2.

    Decide about the simulation methods and use the information about the parameters and mixing conditions in the “Simulation Setup” to define the simulation setup.

  3. 3.

    Using the information provided in “CFD Approach for Developing At-Scale Mixing Parameters” section along with Tables VI and VII, set up the ANSYS Fluent solver settings.

  4. 4.

    Use the recommended time steps discussed in the “Computational Mesh and Time Step” section and run the simulation.

Table V Analytical Data Obtained from Mixing Stress Study for mAb B
Full size table
Table VI Solver Setup for TR Simulations
Full size table
Table VII Solver Setup for SSTa k-ω, and Reynolds Stress with Viscous Models Quadratic Pressure-Strain
Full size table

Determination of Vortex Depth in Stainless Steel Tank

To experimentally determine the vortex depth, lengths a and b (Fig. 9) were measured before and after starting the impeller’s rotation using a metal tape measure. Length c = 118.45 mm is constant and depends on the tank geometry. Lengths b and h are equal before starting the electromotor (Fig. 9a). Upon starting the impeller’s rotation, b is increased and h and a are decreased (Fig. 9b). The vortex depth, dv, is defined as

$$d_v=b-h$$
(9)

which from geometry is calculated as:

$$d_v=b-\sqrt{a^2-c^2}$$
(10)
Fig. 9
figure 9

Measuring vortex depth (a) before and (b) after the start of the impeller’s rotation.

Full size image

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Saadatmand, M., Mehta, M., Walsh, K. et al. An Experimental and Computational Approach to Development of Mixing Processes for Miscible Liquids in Unbaffled Tanks. Pharm Res 40, 2087–2101 (2023). https://doi.org/10.1007/s11095-023-03579-w

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