Enter the reaction rate, conversion, and molar flow rate into the calculator to determine the reactor volume. This calculator helps in designing and analyzing chemical reactors.

Reactor Volume Calculator

Enter any 3 values to calculate the missing variable

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Reactor Volume Formula

The following formula is commonly used to calculate the reactor volume for a continuous stirred-tank reactor (CSTR) using the reaction rate evaluated at the reactor (exit) conditions.

V_R = \frac{F_{A0} X}{-r_A}

Variables:

  • VR is the reactor volume (L)
  • FA0 is the molar flow rate of reactant A entering the reactor (mol/s)
  • X is the conversion of reactant A (dimensionless)
  • −rA is the rate of disappearance of reactant A per reactor volume (mol/(L·s)) (entered as a positive value)

To calculate the reactor volume, multiply the molar flow rate by the conversion, then divide by the rate of disappearance (−rA). If you only know volumetric flow rate v0 (e.g., L/s), you can convert to molar flow rate using FA0 = v0CA0.

What is Reactor Volume?

Reactor volume is the space within a chemical reactor where the reaction takes place. It is a critical parameter in the design and operation of a reactor, as it affects the residence time of reactants and the overall conversion of reactants to products. For a specified reactor type and kinetics, the required volume is determined based on the desired conversion, the feed rate, and the reaction rate under the relevant operating conditions. It is essential for ensuring that the reactor can achieve the required production rate and product quality.

How to Calculate Reactor Volume?

The following steps outline how to calculate the Reactor Volume.

  1. First, determine the molar flow rate of reactant entering the reactor (FA0) in mol/s.
  2. Next, determine the conversion (X), which is dimensionless.
  3. Next, determine the rate of disappearance of the reactant (−rA) in mol/(L·s) (use a positive value for −rA).
  4. Next, gather the formula from above = VR = (FA0 * X) / (−rA).
  5. Finally, calculate the Reactor Volume (VR) in liters.
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

molar flow rate (FA0) = 1.5 mol/s

conversion (X) = 0.85

rate of disappearance (−rA) = 0.02 mol/(L·s) (so VR = (1.5 × 0.85)/0.02 = 63.75 L)