Non-ideal flow modeling: Which is the classic single-parameter model proposed to describe deviations from plug flow and perfect mixing?

Introduction / Context:
Real reactors rarely exhibit ideal plug flow or ideal mixing. Non-ideal behavior is captured using RTD-based models. Two widely used conceptual models are the dispersion model and the tanks-in-series model.

Given Data / Assumptions:

• Goal: represent axial mixing and spreading around plug flow.
• Prefer minimal parameterization for tractable fitting.

Concept / Approach:
The dispersion model augments the convective plug-flow equation with a single axial dispersion coefficient. In nondimensional form, the behavior depends on one parameter, the dispersion number (Dax / uL), which quantifies deviation from plug flow. The tanks-in-series model uses an integer or real-valued number of perfectly mixed CSTRs in series; while often treated as a single parameter N, it is conceptually different and sometimes regarded as having a discrete nature.

Step-by-Step Solution:
Identify single-parameter formulation → dispersion number controls E(t).Fit RTD → obtain Dax/uL from experimental E(t) or F(t).Use parameter to predict conversion and scale-up impacts.

Verification / Alternative check:
Limiting cases: dispersion number → 0 gives ideal plug flow; very large values approach mixed-flow behavior, matching expected trends.

Why Other Options Are Wrong:

• Tanks-in-series: commonly used but often treated as semi-empirical with N; the historically termed single-parameter "proposed" model is the dispersion model.
• Neither / two-parameter models: contradict common practice in RTD modeling.

Common Pitfalls:
Assuming a unique mapping between the two models; while they can be approximately related (N ≈ 1/dispersion number for some ranges), they are not identical.

Final Answer:
Dispersion model