PFR Design — Plug Flow Reactor Sizing (Isothermal)

Reaction & Feed Parameters

Molar Feed Rate (F_A0)mol/s

Rate Constant (k)s⁻¹

Initial Concentration (C_A0)mol/m³

Target Conversion (X_target)—

Space Time (τ) relative to 1/k--

τ << 1/kτ ≈ 1/kτ >> 1/k

Awaiting Input

Reactor Volume (V)

--m³

Mean Residence Time (τ)

--s

Volumetric Flow (v₀)

--m³/s

Design Equation Check

V = F_A0∫dX/(-r_A)

For first‑order: –r_A = k·C_A = k·C_A0(1‑X)

PFR design: V = F_A0 ∫₀^X dX / (–r_A)

∴ V = (F_A0/(k·C_A0))·ln(1/(1‑X))

τ = V / v₀ = V·C_A0/F_A0

Fogler, Elements of Chemical Reaction Engineering, 4th Ed.

X vs. Reactor Length (z/L)

Levenspiel Plot (1/‑r_A vs. X)

Volumetric Sizing Chart