Chemical reactors are vessels or pipes where reactants are converted into products under controlled conditions. Two ideal reactor models used throughout chemical engineering are the continuous stirred-tank reactor, CSTR, and the plug-flow reactor, PFR. They matter because reactor choice affects conversion, selectivity, safety, cost, and product quality.
Comparing them helps engineers predict how real reactors will behave before building them.
A CSTR is modeled as perfectly mixed, so the outlet composition is the same as the composition everywhere inside the tank. A PFR is modeled as flow through a tube with no mixing along the flow direction, so concentration and reaction rate change continuously from inlet to outlet. Residence time describes how long fluid elements stay in the reactor, and it strongly influences conversion.
For many simple reactions, a PFR reaches higher conversion than a CSTR of the same volume, but a CSTR can be easier to control, cool, and operate with slurries or variable feeds.
Key Facts
- CSTR mole balance at steady state: F_A0 - F_A + r_A V = 0, where r_A is negative for reactant A consumption.
- CSTR design equation: V = F_A0 X / (-r_A) evaluated at the exit concentration.
- PFR design equation: dF_A/dV = r_A, or V = integral from 0 to X of F_A0 dX / (-r_A).
- Space time: tau = V / volumetric flow rate, for constant-density flow.
- For a first-order liquid reaction in a CSTR: X = k tau / (1 + k tau).
- For a first-order liquid reaction in a PFR: X = 1 - e^(-k tau).
Vocabulary
- Continuous stirred-tank reactor
- A reactor model in which feed enters continuously, products leave continuously, and the contents are assumed to be perfectly mixed.
- Plug-flow reactor
- A reactor model in which fluid moves through a tube like plugs, with mixing across the tube but no mixing along the flow direction.
- Conversion
- The fraction of a limiting reactant that has been consumed by the reaction.
- Residence time
- The average time a fluid element spends inside a reactor.
- Reaction rate
- The rate at which a reactant is consumed or a product is formed per unit reactor volume.
Common Mistakes to Avoid
- Using inlet concentration for the CSTR rate instead of outlet concentration. In a perfectly mixed CSTR, the tank concentration equals the exit concentration, so the rate must be evaluated at exit conditions.
- Assuming a PFR has the same concentration everywhere. In a PFR, concentration changes with position along the reactor length, so the rate usually changes continuously.
- Treating residence time as exactly the same for every molecule in a real CSTR. An ideal CSTR has a broad residence time distribution because some fluid leaves quickly and some stays longer.
- Comparing CSTR and PFR performance without checking the reaction rate law. The relative volume needed for a target conversion depends on how rate changes with concentration, temperature, and phase behavior.
Practice Questions
- 1 A first-order liquid reaction has k = 0.40 min^-1 and tau = 5.0 min. Calculate the conversion in a CSTR using X = k tau / (1 + k tau).
- 2 For the same first-order reaction with k = 0.40 min^-1 and tau = 5.0 min, calculate the conversion in a PFR using X = 1 - e^(-k tau).
- 3 A reaction is highly exothermic and requires tight temperature control with cooling coils and good mixing. Explain whether a CSTR or PFR would usually be easier to operate safely, and justify your choice.