Residence Time Distribution Questions and Answers

Answer: A

It is a property of the flow pattern alone and says nothing directly about the chemistry. Two reactors with the same distribution can still give different conversions if the kinetics are not linear. It is a property of the flow alone.

Answer: B

Correct answer: a pulse tracer injection at the inlet

Injecting a sharp pulse of inert tracer and recording its concentration at the outlet gives the age distribution directly: every tracer molecule entered at the same instant, so the outlet concentration against time, normalised to unit area, is \( E(t) \). A step input gives the cumulative \( F \) curve instead, from which \( E \) must be obtained by differentiating.

Answer: C

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason is the mathematics. \[ F(t) = \int_0^{t} E(s)\,\mathrm{d}s, \] and the relation holds because the system is linear in the tracer: a step is the integral of a pulse, so its response is the integral of the pulse response. That is why either experiment will do, and why the step test is often preferred in practice - integration is far kinder to noisy data than differentiation.

Answer: D

The two experiments are equivalent in principle and the choice is practical. A step is easier to carry out while a pulse gives the curve of interest directly. The two carry the same information. The choice between them is practical.

Answer: A

The first two are correct and define how the curve is used. The third confuses a flow property with a chemical one, since the curve says nothing about what reacted while the fluid was inside. Its area is normalised to unity.

Answer: B

The mean is the area weighted average of time, which for a skewed distribution differs from the peak. For a well behaved reactor it should equal the volume divided by the volumetric flow. A shortfall points to dead volume.

Answer: C

Both are true and the reason gives the diagnosis: part of the vessel is not participating, so the active volume is smaller than the geometric one and the fluid moves through it faster. The shortfall measures the inactive fraction.

Answer: D

A narrow distribution has a small variance and approaches plug flow, while a broad one approaches a stirred tank. The variance is what feeds into the dispersion and tanks in series models. A narrow curve means near plug flow.

Answer: A

For an ideal stirred tank the variance equals the square of the mean, which is the widest spread of any single vessel. A plug flow reactor at the other extreme has a variance of zero. The stirred tank is the widest single vessel.

Answer: B

The distribution is the fingerprint of the flow pattern, and comparing a measured curve against these four is how a real reactor is diagnosed. The laminar case is the one most often overlooked. Each pattern has its own signature.