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How a good numerical modelling strategy can help scale-up of single-use bioreactors

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Background:

Scale-up relationships between different sized wave-mixed bioreactors are not fully understood. Computational Fluid Dynamics (CFD) offers the ability to understand the flow dynamics and shear environment at large scale (50 L) during the mixing of a surfactant and product. The same environment can then be generated at small scale (500 mL) and the impact of mixing tested on high value product. Model validation was performed by comparing the numerical and experimental mixing times. 

Geometry of wave bioreactors

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 Computational domains for wave bioreactors:

• 50 L (large scale) and 500 mL (small scale) geometries created in DesignModeler

• Variable amount of air in each wave bioreactor

• Fully inflated and deflated cases investigated

• Axis of symmetry through centre of bag used to reduce the computational time required

Mesh of computational domains

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Computational domains are divided into minute volumes, or elements, to create a ‘mesh’

• Elements must be small enough to capture the main features of the process being modelled

• Refined in area of interest/ potential turbulence (close to walls)

• Conservation equations of transport phenomena are then applied and solved for each element

Shear rate in 50 L wave bioreactor

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Profile the hydrodynamic environment generated in the 50 L wave bioreactor

• Fully inflated – worst-case scenario for shear rate

• 15 rpm rocking speed•10 degree rocking angle

• Maximum and average shear rate distributions calculated

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Shear rate in 500 mL wave bioreactor

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Profile the hydrodynamic environment generated in the 500 mL and compare to the 50 L wave bioreactor

• Fully inflated, 15 rpm, 9 degrees 

• Shear rates peak when bag was at maximum angle of 9 degrees

• 500 mL generates both higher maximum and average shear rates

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Distribution of shear between scales

Actual volume experiencing elevated levels of shear between the scales

• Higher percentage of the liquid experienced elevated levels of shear (> 30s-1) in the 500 mL bag

• Using a rocking speed of 15 rpm and angle of 9 degrees will generate higher levels of shear compared to the 50 L bag (15 rpm, 10 degrees).

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Comparison of shear across the scales

Divide the shear rate into bands of 5 s-1 to allow specific ranges of shear experienced to be compared:

• 0.7 % of the volume in 50 L - > 50 s-1

• 9 % of the volume in 500 mL > 50 s-1

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Mixing times in 500 mL wave bioreactor

CFD used to simulate the mixing times for deflated and inflated 500 mL mixing bags. Difference for surfactant to be equal at vertical and side locations in bags calculated.

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Qualitative validation

Inject tracer mixed with surfactant to bag and record dispersal

• Data presented for deflated bag (worse-case mixing time)

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Quantitative validation

Take samples at separate locations at a series of time points

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Measure absorbance of dye in a UV spectrophotometer

• Performed across two separate days with two replicates each day

• Surfactant (containing tracer) well mixed by 600 s

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Conclusions

• Maintaining similar operating conditions of rocking, speed and angle on scale-up would generate lower shear rates in the large scale bag.

• Higher surface area to volume ratio results in a greater percentage of the liquid volume being in contact with the bag walls causing higher shear rates at small scale.