Question

For an ideal plug flow reactor, which of the following statements is/are true?

• A. It can be approximated by a large number of ideal continuous stirred tank reactors connected in series
• B. It has significant back mixing
• C. It has significant axial mixing
• D. It has a uniform velocity profile across any cross section

Hint:

List the defining assumptions of an ideal PFR (no axial mixing, no back mixing, flat velocity profile) and match each option against them.

Answer 1

The Correct Option is A, D

Step 1: Recall the defining assumptions of an ideal plug flow reactor (PFR).
In an ideal PFR, fluid moves through the reactor as a series of thin plugs, each plug moving at the same velocity with no mixing between one plug and the plug ahead of or behind it along the flow direction.
This means there is no axial mixing at all, every element of fluid spends exactly the same time in the reactor, and at any cross section, velocity, concentration and temperature are assumed uniform across the radius, with no radial variation.

Step 2: Check option (A), approximation by CSTRs in series.
A single ideal CSTR mixes everything instantly and has a spread-out residence time distribution. But connecting a large number, \(N\), of small ideal CSTRs in series, with the same total volume divided among them, narrows the overall residence time distribution more and more as \(N\) increases.
In the limit \(N \to \infty\), the tanks-in-series model's residence time distribution collapses to a single sharp spike, exactly matching plug flow behavior. So a PFR can indeed be approximated by a large number of ideal CSTRs in series. Option (A) is true.

Step 3: Check option (B), significant back mixing.
Back mixing is fluid moving backward against the main flow direction, mixing fluid that entered later with fluid that entered earlier.
This is the defining feature of a CSTR, not a PFR. An ideal PFR is defined by having no back mixing, so option (B) is false.

Step 4: Check option (C), significant axial mixing.
Axial mixing is mixing along the direction of flow, which would smear out the sharp residence time and blur the plug-flow assumption.
Real tubular reactors show some axial dispersion, but an ideal plug flow reactor is specifically defined as having zero axial mixing, that is the whole point of the plug idealization. So option (C) is false for an ideal PFR.

Step 5: Check option (D), uniform velocity profile.
The plug flow idealization assumes the fluid moves as a flat plug, meaning every point across a given cross section, at the center and near the wall alike, moves at the same velocity, with no radial velocity gradient.
This uniform, flat velocity profile is one of the core assumptions of the ideal PFR model, so option (D) is true.

Final Answer:
An ideal PFR has zero axial mixing and zero back mixing, but a uniform velocity profile across any cross section, and it is well approximated in the limit by a very large number of CSTRs in series.
\[ \boxed{\text{(A) Approximated by CSTRs in series, and (D) Uniform velocity profile}} \]