Residence time distribution (RTD): The standard response curve obtained from a reactor when a step input of tracer is applied is called which curve?

Introduction / Context:
Residence time distribution (RTD) analysis diagnoses non-ideal flow patterns in reactors and process equipment. Two classic tracer tests are used: pulse (impulse) input and step input. Each produces a characteristic RTD curve used to infer mixing and dispersion.

Given Data / Assumptions:

• A reactor at steady state.
• Tracer is inert and detectable.
• Step test: inlet tracer concentration abruptly changes from zero to a constant value and remains there.

Concept / Approach:
The pulse (impulse) test yields the E-curve, E(t), which is the probability density function of residence times. The step test yields the F-curve (cumulative distribution), which many texts denote as the C-curve (cumulative). It rises monotonically from 0 to 1 as the outlet tracer concentration transitions from baseline to the new steady value.

Step-by-Step Solution:
Apply a step change in inlet tracer concentration.Measure normalized outlet concentration versus time.The resulting cumulative response is the F-curve, often referred to as the C-curve (cumulative curve).Hence, for a step input, the correct name among the options given is the C-curve.

Verification / Alternative check:
By definition, F(t) = ∫₀^t E(τ) dτ. A step test directly measures F(t), confirming that the step response is the cumulative (C) curve.

Why Other Options Are Wrong:

• S-curve/I-curve: not standard RTD nomenclature for a step response.
• E-curve: corresponds to a pulse input, not a step input.
• None of these: incorrect because the cumulative C-curve is standard for the step test.

Common Pitfalls:
Mixing up E(t) and F(t): remember pulse → E-curve (density); step → C-curve or F-curve (cumulative).

Final Answer:
C-curve