chem

Chemical Reaction Engineering: CSTR, PFR & RTD

Ideal reactor design equations, comparisons and residence time distribution — the classic conversion question in every process interview.

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Key formulas

τ = C_A0 · X / (−r_A) at exit
CSTR space time: Whole reactor at exit concentration — the key CSTR vs PFR difference.
dX/dV = (−r_A)/F_A0
PFR design equation: Integrate along the reactor; equivalent to batch time for constant density.
k = A·e^(−E/RT)
Arrhenius: Rate roughly doubles per 10 °C rise for typical activation energies.

Cheat sheet

▸Design equations (constant density, basis volume): Batch/PFR: τ = C_A0 ∫ dX/(−r_A); CSTR: τ = C_A0·X/(−r_A,exit) — the CSTR works at exit conditions, the PFR at every point along the path.
▸First-order: CSTR conversion X = kτ/(1 + kτ); PFR X = 1 − e^(−kτ). For the same τ, a PFR always beats a CSTR for positive-order kinetics.
▸Zero or negative order → CSTR may be better (CSTR works at low concentration where the rate is higher for negative order); autocatalytic needs a mixed strategy.
▸Parallel reactions: select the reactor concentration/temperature that maximises the desired reaction's rate relative to the undesired one (instantaneous vs rate-based selectivity).
▸RTD: E(t) curve from tracer tests. Ideal CSTR: E = (1/τ)e^(−t/τ); PFR: all fluid exits at exactly τ (a spike). Non-ideal reactors use the E-curve plus micromixing models (tanks-in-series, dispersion).
▸Temperature effects: Arrhenius k = A·e^(−E/RT); exothermic reactions need heat removal — runaway risk in CSTRs is a classic safety question.

CSTR vs PFR vs Batch

Aspect	CSTR	PFR	Batch
Mixing	Perfectly mixed, exit = reactor	No axial mixing, plug flow	Well mixed, no flow
Concentration profile	Uniform at exit (low)	Decreases along length	Decreases with time
First-order, same τ	Lower conversion	Highest conversion	Same as PFR
Control of T	Easy (jacket, uniform)	Harder along length	Jacketed vessel
Typical use	Continuous liquid, stirred	Tubular gas/liquid	Pharma, fine chemicals

Visual

Concentration profile (A → products):
 CA
 CA0 ─●─── PFR: exponential decay along reactor length
      \____
 CSTR ─ ─ ─ ─ ─ CA_exit (flat line — reactor at exit conc.)
      +---------+--------→ reactor length / time
 Note: CSTR does ALL reacting at the low exit concentration.

MCQ mastery quiz

1. In a CSTR the entire reactor operates at…

2. For first-order kinetics and equal space time, highest conversion is obtained in…

3. The E-curve of an ideal CSTR is…

4. If the desired reaction has higher activation energy than the undesired one, choose…