Non-ideal flow in reactors: The deviation from ideal plug flow caused by axial mixing within the flowing fluid is most appropriately described by which mathematical model?

Introduction / Context:
Real chemical and biochemical reactors rarely behave as perfect plug flow reactors (PFRs). Small-scale backmixing along the flow direction—called axial mixing—causes dispersion of solute concentration profiles and broadens residence-time distributions (RTDs). The standard way to quantify this non-ideality is the dispersion model, which adds a Fickian-like axial dispersion term to the convective material balance.

Given Data / Assumptions:

• Steady, incompressible flow in a tubular reactor.
• Axial gradients exist; radial gradients are negligible (fully developed flow/adequate mixing across radius).
• Isothermal and single, nonreactive tracer for RTD interpretation (concept extends to reactive cases).

Concept / Approach:
The dispersion model assumes that deviations from plug flow arise from an effective axial dispersion coefficient, D_ax, analogous to molecular diffusion but representing hydrodynamic mixing. The governing species balance combines convection and dispersion with reaction if present.

Step-by-Step Solution:
Write axial species balance for a tracer: v * dC/dx = D_ax * d^2C/dx^2 − r(C).Recognize that D_ax captures backmixing; when D_ax → 0, the model reduces to ideal PFR.Relate to RTD: the dimensionless group Pe = v * L / D_ax (Péclet number) measures approach to plug flow (Pe → ∞).Conclude that the proper framework for axial mixing is the dispersion model.

Verification / Alternative check:
Tracer tests (e.g., pulse input) yield outlet curves that are fit using the dispersion model to estimate D_ax or Pe. Good agreement across flow rates supports the model for many laminar-to-turbulent transitional regimes in packed beds and empty tubes with mild mixing.

Why Other Options Are Wrong:
Langmuir model describes adsorption isotherms, not reactor hydrodynamics.

Friedlander model and Pasceri model are not standard frameworks for axial dispersion in reactors.

Common Pitfalls:

• Confusing dispersion with complete backmixing (CSTR model). Dispersion lies between ideal plug flow and ideal mixing.
• Ignoring wall effects or radial gradients when Pe is low; assumptions must be checked.

Final Answer:
Dispersion model