Reactor Design

Reactor design turns kinetics into equipment. Learn the general mole balance, design equations for batch, CSTR and PFR, space time and space velocity, Levenspiel plots, reactors in series, choosing reactor type for selectivity, and non-isothermal design basics.

Given a rate law and a production target, how big must the reactor be, and what type? The general mole balance, combined with idealised flow patterns, answers this for the three ideal reactors — the starting point for every real reactor design.

Reactor choice affects conversion, selectivity, heat management and cost.

An analogy

A CSTR is like a well-stirred soup pot where everything is instantly mixed; a PFR is like a conveyor belt where each slice travels through without mixing with the others.

The three ideal reactors

Batch: everything charged, reacts over time — flexible, used for small volumes and pharma. CSTR: continuous feed, perfectly mixed, outlet = contents — easy temperature control, liquids. PFR: no axial mixing, concentration falls along length — high conversion per volume, often tubes or packed beds.

Levenspiel plots

Plot F_A0/(−r_A) vs X. PFR volume = area under the curve; CSTR volume = rectangle (height at exit X). For positive-order reactions, PFRs need less volume than CSTRs for the same conversion — the gap grows at high conversion.

Reactors in series

Several CSTRs in series approach PFR performance. A CSTR followed by a PFR can be optimal for autocatalytic reactions. Levenspiel plots show which sequence minimises total volume.

Selectivity and non-isothermal operation

For parallel reactions, high concentration favours higher-order paths (use PFR/batch); low concentration favours lower-order (use CSTR). Energy balances couple temperature and conversion; adiabatic reactors, interstage cooling and multiple steady states (CSTR) complicate design. Real reactors deviate from ideal — residence-time distribution quantifies it.

Formulas

• General mole balance: F_A0 − F_A + ∫ r_A dV = dN_A/dt
• CSTR: V = F_A0 X / (−r_A)_exit
• PFR: V = F_A0 ∫₀^X dX / (−r_A)
• Batch: t = N_A0 ∫₀^X dX / (−r_A V)
• First order, isothermal: CSTR kτ = X/(1 − X); PFR kτ = −ln(1 − X)

Worked example: CSTR vs PFR volume

Given: First order, X = 0.9

Find: Volume ratio CSTR/PFR.

• CSTR kτ = 0.9/0.1 = 9
• PFR kτ = ln 10 = 2.30
• Ratio = 3.9

Answer: CSTR needs ≈ 3.9× more volume

Worked example: Space velocity

Given: Reactor 2 m³, feed 10 m³/h

Find: τ and SV.

• τ = 0.2 h = 12 min
• SV = 5 h⁻¹

Answer: 12 min, 5 h⁻¹

Common mistakes

• Wrong: Using inlet rate in a CSTR design equation. — Right: A CSTR operates at exit conditions — use exit rate.
• Wrong: Ignoring volume change in gas reactions. — Right: Include expansion factor ε when moles change.

Applications

• Petrochemicals: Tubular reactors for cracking; packed beds for catalytic reactions.
• Polymers: CSTR trains for polymerisation with good temperature control.
• Pharma & fine chemicals: Batch and emerging continuous-flow microreactors.

Key takeaways

• Batch, CSTR, PFR design equations from mole balances.
• CSTR at exit conditions; PFR integrates.
• Levenspiel plots compare volumes.
• Choose type for conversion, selectivity and heat control.

Going further

• Residence-time distribution: Tracer tests characterise non-ideal flow (dispersion, dead zones, bypass).
• Multiple steady states: CSTR heat generation vs removal curves can intersect at several points.
• Process intensification: Microreactors and reactive distillation combine steps.