Bioreactor Design Simulator: Stirred-Tank Geometry & Power Input

simulator intermediate ~10 min
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D = 0.86 m, P = 1.2 kW — standard geometry

A 1000 L vessel with H/D = 2 has a tank diameter of 0.86 m. Two Rushton turbines at 150 rpm provide adequate mixing with a Reynolds number well above 10,000 and a mixing time under 30 seconds.

Formula

D = (4V / (π × H/D))^(1/3)
P = Np × ρ × N³ × d⁵ (power input)
Re = ρ × N × d² / μ (Reynolds number)

The Workhorse of Biotechnology

The stirred-tank bioreactor is the most widely used vessel for industrial fermentation, from brewing beer to manufacturing monoclonal antibodies. Its conceptually simple design — a cylindrical vessel with mechanical agitation, gas sparging, and temperature control — conceals complex fluid dynamics that critically affect cell growth, product formation, and process economics.

Geometry and Scaling Rules

Standard bioreactor geometry follows well-established rules of thumb: impeller diameter d/D ≈ 1/3, liquid height H/D ≈ 2-3 for microbial processes, four equally spaced baffles of width D/10, and impeller clearance of D/3 from the bottom. These proportions ensure efficient mixing and gas dispersion. Deviating from standard geometry requires careful computational fluid dynamics analysis.

Power and Mixing

Power input determines mixing intensity, oxygen transfer, and heat generation. The dimensionless power number Np relates power to impeller speed and diameter. In turbulent flow (Re > 10,000), Np is constant — about 5.5 for Rushton turbines and 1.7 for pitched-blade turbines. Mixing time scales as the inverse cube root of specific power input, meaning doubling the mixing rate requires an eightfold increase in power.

Shear Considerations

While vigorous mixing benefits oxygen transfer and nutrient distribution, excessive shear stress damages cells. Mammalian cells are 100-1000× more shear-sensitive than bacteria. The maximum shear rate occurs at the impeller tip and scales with tip speed v = πNd. Keeping tip speed below 1.5 m/s for mammalian cells and below 7 m/s for bacteria is a common design guideline.

FAQ

What is a stirred-tank bioreactor?

A stirred-tank bioreactor (STR) is a cylindrical vessel equipped with mechanical impellers, baffles, and spargers for growing microorganisms or cells in liquid culture. It is the most common bioreactor type in the pharmaceutical, food, and biotechnology industries, with volumes ranging from 1 L bench-scale to 200,000 L production-scale.

What is the ideal H/D ratio for a bioreactor?

Standard microbial fermenters use H/D ratios of 2-3, which provides good oxygen transfer with multiple impellers. Mammalian cell bioreactors often use H/D closer to 1-1.5 to minimize hydrostatic pressure variations. The optimal ratio depends on the specific process requirements.

How do you calculate bioreactor power input?

Power input P = Np × ρ × N³ × d⁵, where Np is the dimensionless power number (5.5 for Rushton turbines in turbulent flow), ρ is fluid density, N is impeller speed in rev/s, and d is impeller diameter. Multiple impellers approximately multiply the single-impeller power.

What is the Reynolds number in bioreactors?

The impeller Reynolds number Re = ρNd²/μ determines the flow regime. Re < 10 is laminar (poor mixing), Re > 10,000 is fully turbulent (good mixing, constant power number). Most industrial fermentations operate well into the turbulent regime.

Sources

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