Library / Chemical / CHE-06
Chemical
Stirred-tank reactor volume
Volume of a continuous stirred-tank reactor for a target conversion.
- Ref
- CHE-06
- Rev
- v1
- Field
- Chemical
- Result
- V [m³]
FA0 feed molar flow in mol/s, X conversion (0 to 1) and −rA the consumption rate in mol/(m³·s), evaluated at the exit conditions. Steady ideal stirred tank with one feed and one outlet.
A well-stirred tank behaves as if the whole contents are at the exit composition. The volume needed is the amount converted per second divided by how fast that exit mixture reacts.
Calculator
- Molar flow converted1.2 mol/s
- Volume in litres3,000 L
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- A stirred tank runs at the low exit rate throughout, so it is larger than a plug-flow reactor for the same conversion.
- High conversion requires a large volume because the exit rate is low.
- Several stirred tanks in series approach plug-flow performance.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m³) | Local step | Change in result |
|---|---|---|---|---|---|---|
| FA0 Feed molar flow | 0.1 to 100 mol/s | 0.15 | 150 | 149.8 | +10% | +10 % |
| −rA Exit consumption rate | 0.01 to 10 mol/(m³·s) | 0.12 | 120 | 119.9 | +10% | −9.09 % |
| X Conversion | 0.1 to 0.95 | 0.5 | 4.75 | 4.25 | +undefined% | — |
Sweep of Conversion
| Conversion | Reactor volume (m³) |
|---|---|
| 0.1 | 0.5 |
| 0.2062 | 1.031 |
| 0.3125 | 1.563 |
| 0.4187 | 2.094 |
| 0.525 | 2.625 |
| 0.6312 | 3.156 |
| 0.7375 | 3.687 |
| 0.8438 | 4.219 |
| 0.95 | 4.75 |
Sweep one variable
Variables and how each one contributes
Reactor volume
What the equation gives you. Everything else feeds it.
Feed molar flow
Molar flow of reactant A into the reactor. Directly proportional.
Conversion
Fraction of A reacted. Strong: pushing conversion higher also lowers the rate, so volume rises faster than linearly if the rate falls.
Exit consumption rate
Rate of consumption of A at the exit composition. Inversely proportional.
Worked example with the values above
- Moles converted per second: FA0X = 2 × 0.6 = 1.2 mol/s.
- Divide by the exit rate: 1.2 / 0.4.
- V = 3 m³.
Assumptions and limits
- Steady, perfectly mixed tank, one feed and one outlet.
- Rate evaluated at the exit composition and temperature.
- Constant volumetric properties.
Common mistakes
- Using the feed rate instead of the exit rate.
- Entering conversion as a percentage.
- Using it for a plug-flow reactor, which needs an integral.
Statistics and uncertainty
The rate constant behind −rA is typically uncertain by 10–20%, and the volume carries that uncertainty directly. Designers usually add a safety margin of 10–25% to the calculated volume.
Where it is used
- Sizing reactors for fuel, propellant and decontamination processes.
- Estimating residence time.
- Comparing reactor types.
Maths you need
- Conversion: fraction reacted
- Reaction rate: mol per m³ per second