Reactor Volume Calculator
Sizing a Continuous-Flow Reactor
In a continuous stirred-tank reactor (CSTR), reactant flows in and product flows out continuously while the contents are kept well-mixed. For a first-order reaction, the tank volume needed to reach a target conversion depends on how fast material flows in, how much of it needs to react, and how quickly the reaction itself proceeds.
The Formula
where F is the volumetric flow rate, X is the target conversion (a fraction between 0 and 1), and k is the first-order rate constant.
Worked Example
For a flow rate of 50 L/min, a target conversion of 0.8, and a rate constant of 0.2 min-1:
| Step | Calculation | Result |
|---|---|---|
| Numerator | 50 × 0.8 | 40 |
| Denominator | 0.2 × (1 − 0.8) | 0.04 |
| Volume | 40 / 0.04 | 1000 L |
Notice how sharply volume grows as conversion (X) approaches 1 — the denominator shrinks toward zero, so pushing for near-complete conversion in a single CSTR requires a disproportionately larger tank.
Where This Matters
- Chemical process design — sizing a CSTR is one of the first calculations in designing a continuous production process.
- Wastewater treatment — biological treatment tanks are frequently modeled as CSTRs to size basin volume for a target removal efficiency.
- Scale-up from lab to plant — converting a bench-scale reaction rate constant into a full production-scale reactor volume.
How to Use This Calculator
- Enter the Flow Rate F (L/min).
- Enter the Conversion X (a value between 0 and 1).
- Enter the Rate Constant k (1/min).
- Select Calculate to get the required reactor volume.
Related Calculations
For simple geometric tank sizing rather than reaction-based sizing, see the Cylinder Volume Calculator.