Axial dispersion model and reactor contacting: what flow idealization is represented by a Peclet number approaching infinity (Pe → ∞)?

Introduction / Context:The Peclet number (Pe) measures the ratio of convective transport to axial dispersion (mixing). It appears in the axial dispersion model for tubular reactors, packed beds, and mass transfer equipment. Recognizing the limiting behaviors helps link real devices to ideal reactors used in design calculations.

Given Data / Assumptions:

• Pe = u * L / D_ax, where u is superficial velocity, L is characteristic length, and D_ax is axial dispersion coefficient.
• Steady operation; constant properties along the device.
• Comparisons with idealized flow models: Plug Flow Reactor (PFR) vs. Continuous Stirred Tank Reactor (CSTR).

Concept / Approach:As Pe → ∞, axial dispersion D_ax → 0 relative to convection, meaning material moves axially with negligible back-mixing. This is the essence of plug flow: concentration and temperature vary only along the axis, not radially/axially due to mixing. Conversely, Pe → 0 represents dominant dispersion and approaches complete back-mixing (CSTR-like behavior).

Step-by-Step Solution:Define Peclet number: Pe = convective transport / dispersive transport.Take limit Pe → ∞: dispersion vanishes → profiles are sharp → behavior tends to PFR.Map to reactor idealizations: PFR corresponds to zero axial mixing.

Verification / Alternative check:Solutions of the axial dispersion model show that dimensionless exit age distributions narrow as Pe increases; in the limit, the distribution collapses to a delta function—characteristic of plug flow.

Why Other Options Are Wrong:(a) and (b) imply strong back-mixing (low Pe). (d) mentions zero eddy diffusivity but equivocates; the ideal limit is indeed plug flow. (e) is unrelated to Peclet characterization.

Common Pitfalls:Confusing laminar velocity profiles with axial mixing; laminar flow can still approach plug-flow behavior at very high Pe if dispersion is negligible compared with convection.

Final Answer:Plug flow (negligible axial mixing)