CSTR & PFR Reactor Sizing

CSTR vs PFR — when to use which

For positive-order kinetics (rate increases with concentration), PFR is more efficient — it operates at high concentration most of the way, only experiencing the slow tail at the outlet. CSTR operates everywhere at the outlet concentration (slow). Hence the volume penalty.

The volume ratio grows with conversion target:

• X = 0.5: CSTR/PFR ratio ≈ 1.4 for 1st order
• X = 0.8: ratio ≈ 2.5
• X = 0.9: ratio ≈ 3.9
• X = 0.99: ratio ≈ 22
• X = 0.999: ratio ≈ 145

For very high conversion, PFR is dramatically more efficient. CSTRs in series approach PFR behavior — 3 CSTRs in series gives ~70% of PFR efficiency at X = 0.9.

Why pick CSTR anyway

Despite the volume penalty, CSTRs are popular for several reasons:

• Heat transfer: well-mixed, easy to add cooling jackets or coils. PFR has long residence time at high temperature in the back end — runaway risk.
• Catalyst handling: slurry catalysts are easy in CSTRs (mixed); fixed-bed PFRs need pellets.
• Multiphase: gas-liquid, liquid-liquid mixing is easy in CSTRs.
• Operations: easy to start up, shut down, change setpoints. PFRs have transient behavior that takes hours to settle.
• Series staging: 3-5 CSTRs in series gives PFR-like efficiency with CSTR operability.
• Negative order or autocatalytic: CSTR is sometimes more efficient when rate decreases with concentration.

Beyond simple kinetics

This calculator handles single irreversible 1st- or 2nd-order reactions with constant volumetric flow. Real chemistry has:

• Reversible reactions: −r = k(C_A − C_A,eq); volume needs to be larger near equilibrium.
• Multiple reactions: parallel and series networks; selectivity matters as much as conversion.
• Variable density: gas-phase reactions where moles change; ε ≠ 0 corrections needed.
• Non-isothermal: rate depends on T (Arrhenius), and T depends on conversion (heat of reaction). Coupled energy balance required.
• Catalyst deactivation: rate drops over time; reactor must be sized for end-of-cycle.

For these, use Aspen Plus, gPROMS, COMSOL, or solve the design ODEs numerically (Fogler ch. 8–14).

Liquid-phase, constant-density assumption

For most liquid-phase reactions in dilute solution, the volumetric flow doesn't change with conversion (ε = 0). For gas-phase, especially at high conversion of a reactant that produces multiple moles of product, ε can be 0.5 or higher and changes the design equation. PFR with ε ≠ 0:

V = v₀/k × ∫(1 + εX)/(1 − X) dX (1st order, gas)

This calculator uses ε = 0; for gas-phase, multiply CSTR volume by (1 + εX) and PFR volume by an integration correction factor.

Reference: Fogler, H.S. (2016). Elements of Chemical Reaction Engineering, 5th ed., Pearson, ch. 1–4. Smith, J.M. (1981). Chemical Engineering Kinetics, 3rd ed., McGraw-Hill.