Flow modeling and reactor comparison: Identify the incorrect statement about vessel dispersion, space time, and ideal flow patterns.

Introduction / Context:
Ideal reactor models help engineers estimate sizes and performance. Plug flow and complete mixing are two extremes, characterized by dispersion and mixing behavior. Recognizing correct statements avoids design errors.

Given Data / Assumptions:

• D is axial dispersion coefficient, U is superficial velocity, L is reactor length.
• Constant density system for space time equivalence with residence time.
• Positive overall reaction order.

Concept / Approach:
Plug flow implies no axial mixing, which mathematically yields a vessel dispersion number approaching zero. A CSTR is totally mixed, analogous to infinite axial dispersion. For positive orders, PFR requires less volume than a CSTR at the same conversion, not the other way around.

Step-by-Step Solution:
Evaluate statement a: correct limit behavior for dispersion number.Evaluate b: with constant density, space time = V/Q equals residence time; correct.Evaluate d: ideal tubular reactor has radial mixing only; correct by definition.Therefore c is the incorrect claim.

Verification / Alternative check:
Levenspiel plot method shows area for CSTR is larger than PFR for positive orders, meaning a larger volume is needed for the CSTR to reach the same conversion.

Why Other Options Are Wrong:
They are not wrong; they state standard truths about dispersion, space time, and ideal tubular flow.

Common Pitfalls:
Applying the CSTR advantage in negative order or autocatalytic systems to all kinetics; the comparison reverses depending on order and selectivity goals.

Final Answer:
For positive reaction orders, a mixed (CSTR) is always smaller than a plug flow reactor for the same duty.