Non-ideal Flow Models Questions and Answers

Answer: A

Correct answer: a Peclet number on particle diameter

In a packed bed the mixing length is set by the particles rather than by the vessel, so the dispersion correlations are written in terms of a Peclet number based on particle diameter - and that group settles at a value of about two for liquids in turbulent flow over a wide range of conditions. The vessel Peclet number is then obtained from it and the bed geometry, as the next item shows.

Answer: B

Correct answer: 800

The two Peclet numbers differ by the ratio of the lengths involved: \[ Pe_{vessel} = Pe_{particle} \times \frac{L}{d_p} = 2 \times \frac{2}{0.005} = 2 \times 400 = 800. \] A vessel Peclet number of 800 means dispersion is very small compared with convection, so this bed is close to plug flow - which is the usual finding for a long bed of small particles.

Answer: C

Both are true and the reason gives the arithmetic: even a modest particle Peclet number becomes a very large vessel value once multiplied by several hundred particle diameters. Packed beds are close to plug flow in practice.

Answer: D

The parameter cannot be fitted before the moments are known, and conversion is the last step because it needs the model as well as the kinetics. Skipping the moments loses the connection to the data. Each step depends on the one before.

Answer: A

Correct answer: cannot distinguish the causes of a spread

A single parameter fitted to a tracer curve reproduces the width of the distribution and nothing more. Bypassing, dead volume, channelling and genuine axial mixing can give similar variances by quite different mechanisms, and the model cannot tell them apart - so it may predict conversion adequately while pointing at the wrong fault, and the shape of the curve must be examined as well as its variance.

Answer: B

Correct answer: 1 and 2 only

Statements 1 and 2 give the usual basis of the choice: the dispersion model suits tubular vessels departing slightly from plug flow, and tanks in series suits vessels with substantial back mixing, where a small \( N \) describes the behaviour naturally. Statement 3 is wrong - the two models give different conversions for the same variance, and the difference grows as the deviation from plug flow increases.

Answer: C

Both are calibrated to the same variance and the linearity of the rate makes the details of the mixing unimportant. The choice becomes significant for higher orders and for series reactions. Both models match the same variance.