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Calcimator

Process Scale-Up Calculator

Scale reactor agitation from lab to production using constant tip speed, constant P/V, or constant Reynolds number criteria.

About this calculator

This calculator scales bench-scale agitation up to production using the three classical mixing scale-up criteria from chemical engineering practice, all built on the geometric-similarity assumption that Impeller Diameter follows a fixed diameter-ratio rule (impeller roughly 0.35x the tank diameter, within the commonly cited 0.3-0.4 range often loosely called the "T/3 rule") at both scales. Because of that assumption, Impeller Diameter algebraically reduces to depending on Production Reactor Volume ALONE -- Lab Reactor Volume cancels out of the formula entirely, along with Lab Agitator Speed, Lab Agitator Power, and Scale-Up Criterion, none of which move it at all. Scale-Up Criterion changes how Production Agitator Speed and Production Power are derived from the volume ratio: Constant Tip Speed (N2 = N1 x D1/D2) keeps the impeller tip's linear velocity fixed, protecting shear-sensitive materials from being torn apart at larger scale; Constant P/V (N2 derived so that power per unit volume, P/V, stays fixed) preserves mass-transfer intensity, the usual priority for fermentation and gas-liquid mixing; Constant Reynolds Number (N2·D2^2 = N1·D1^2) preserves the mixing FLOW PATTERN, the priority when turbulence structure matters more than raw power or shear.

Under every one of these three criteria, however, Production Agitator Speed always falls as Production Reactor Volume grows -- larger impellers need to spin more slowly to hit the same tip speed, power density, or Reynolds number -- even though the exact rate of that decline differs criterion by criterion. Estimated Mixing Time applies the simplified t ∝ 1/N relationship (specifically, the rotational period at Production Agitator Speed) as a rough floor estimate, not a validated blend-time correlation from mixing literature, which would additionally depend on vessel geometry, baffling, and fluid viscosity.

Inputs

gal
gal
RPM
W

Results

Volume Scale Ratio

1,000×

Production Agitator Speed

30 RPM

Production Power500 W
Impeller Diameter0.6 m
Estimated Mixing Time2 s
How to Use This Calculator
  1. Enter the Lab Reactor Volume in liters and the target Production Reactor Volume in liters — the ratio defines the scale-up factor.
  2. Enter the Lab Agitator Speed in RPM and Lab Agitator Power in watts from bench-scale testing.
  3. Select the Scale-Up Criterion: 1 = constant tip speed (good for shear-sensitive processes), 2 = constant power per volume (good for mass transfer), 3 = constant Reynolds number (preserves mixing pattern).
  4. Review the Production Agitator Speed in RPM and Production Power in watts to specify the production agitator motor.
  5. Note the Impeller Diameter in meters to specify the production vessel and agitator geometry.
  6. Use the Estimated Mixing Time in seconds to assess blend time and ensure homogeneity at production scale.

How the result changes with Lab Reactor Volume

Lab Reactor VolumeVolume Scale RatioProduction Agitator Speed
2.52,000×23.81 RPM
3.751,333.33×27.26 RPM
7.5666.67×34.34 RPM
13384.62×41.25 RPM

What each input means

Lab Reactor Volume
Volume of the laboratory reactor in liters.
Production Reactor Volume
Volume of the production-scale reactor in liters.
Lab Agitator Speed
Rotational speed of the lab impeller in revolutions per minute.
Lab Agitator Power
Power consumption of the lab agitator in watts.
Scale-Up Criterion
Constant tip speed suits shear-sensitive processes; constant P/V suits mass transfer; constant Reynolds number preserves the mixing pattern.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    5 parameters
    Lab Reactor Volume = 5, Production Reactor Volume = 5000, Lab Agitator Speed = 300, Lab Agitator Power = 5, Scale-Up Criterion = 1 = 5 input(s) provided
  2. Calculate Volume Scale Ratio
    Volume Scale Ratio
    1000 = 1000
  3. Calculate Production Agitator Speed
    Production Agitator Speed (from Scale-Up Criterion and diameter ratio)
    30 = 30
  4. Calculate Production Power
    Production Power (P ∝ N³D⁵, from Scale-Up Criterion)
    500 = 500
  5. Calculate Impeller Diameter
    Impeller Diameter
    0.5985 = 0.5985

Engine last updated . Checked against 3 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Why doesn't Lab Reactor Volume affect Impeller Diameter at all?

Impeller Diameter combines the lab tank's geometry with the volume SCALE RATIO between lab and production, and under the fixed 0.35 impeller-to-tank diameter-ratio geometric-similarity rule this calculator uses, Lab Reactor Volume algebraically cancels out of that combination -- Impeller Diameter ends up depending on Production Reactor Volume alone. This is a direct consequence of assuming both vessels share the same impeller-to-tank diameter ratio, not a coincidence or an unused input.

Why does Production Agitator Speed always drop as Production Reactor Volume grows, no matter which Scale-Up Criterion I pick?

All three criteria -- Constant Tip Speed, Constant P/V, and Constant Reynolds Number -- relate agitator speed to impeller diameter with a NEGATIVE exponent, so a larger production impeller (which follows from a larger Production Reactor Volume under the fixed 0.35 diameter-ratio rule) always calls for a slower speed to hold that criterion's quantity fixed. Only the exact rate of the decline differs between the three criteria, not its direction.

Which Scale-Up Criterion should I use for a shear-sensitive process like a cell culture?

Constant Tip Speed is the standard choice for shear-sensitive materials, since it directly controls the impeller blade's linear velocity -- the quantity most closely tied to shear stress on fragile particles, cells, or crystals. Constant P/V and Constant Reynolds Number instead prioritize mass-transfer intensity and flow-pattern similarity respectively, which can allow higher local shear at production scale even while satisfying their own criterion.

Is Estimated Mixing Time a real blend-time prediction I can rely on?

Treat it as a rough floor estimate, not a validated number -- it applies a simplified inverse relationship to Production Agitator Speed (roughly, the time for one impeller rotation) rather than a full mixing-time correlation from the literature. Real blend-time correlations additionally depend on vessel geometry, baffle configuration, and fluid viscosity, none of which this calculator collects as inputs.

Why does Production Power depend on Lab Agitator Power in a straight proportional way?

Under all three scale-up criteria, once the speed ratio between lab and production is fixed by the criterion you chose, the power scaling law P proportional to N^3 D^5 reduces to a fixed multiplier applied directly to Lab Agitator Power -- so doubling Lab Agitator Power always doubles Production Power for the same Scale-Up Criterion and the same two reactor volumes, whichever criterion is selected.

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