Equivalence of plug flow reactors (PFRs): N PFRs in series with a total volume V provide the same conversion as a single PFR of volume V for reactions of which order?

Introduction / Context:
Understanding reactor equivalences aids in debottlenecking and scale-up. Plug flow reactors placed in series are often encountered in tubular bundles, coil reactors, or staged packed beds.

Given Data / Assumptions:

• All reactors behave ideally as PFRs (no axial dispersion, uniform velocity profile).
• Total reactor volume V is fixed; N reactors in series partition V but maintain PFR behavior in each segment.

Concept / Approach:
For a PFR, the design equation is ∫ dX/(-rA) = V/F_A0. Since the integrand depends only on conversion and kinetics, and not on how the volume is partitioned, splitting V into segments and placing them in series yields the same overall integral as a single PFR with the same total volume, regardless of reaction order.

Step-by-Step Solution:
Write PFR design equation: V = F_A0 ∫₀^X dX / (-r_A).Partition V into V1 + V2 + ... + VN with corresponding conversion increments.The sum of integrals over segments equals the single integral to the final conversion.Therefore, equivalence holds for any order.

Verification / Alternative check:
Contrast with CSTRs, where N CSTRs in series approach PFR behavior as N increases; here all are already PFRs, so exact equivalence holds.

Why Other Options Are Wrong:
Limiting the statement to specific orders (first/second/third) is unnecessary; the integral argument is general.

Common Pitfalls:
Confusing PFRs in series with CSTRs in series; only the latter changes behavior with N dramatically.

Final Answer:
Any reaction order