Question

The E-curve for a non-ideal reactor defines the fraction of fluid having age between t and t + dt:

• A. At the inlet
• B. At the outlet
• C. Inside the reactor
• D. In the bypass stream

Hint:

Age Distribution Functions Summary: - \(E(t) \cdot dt\): Fraction of fluid elements leaving the reactor with an age between \(t\) and \(t+dt\). Measured at the outlet. - \(I(t) \cdot dt\): Fraction of fluid elements present inside the reactor body with an age between \(t\) and \(t+dt\). - At the inlet, all entering fluid elements have an initial age of zero.

Answer 1

The Correct Option is B

Concept: The Residence Time Distribution (RTD) of fluid elements inside a chemical reactor vessel is characterized using the exit age distribution function, commonly referred to as the $E$-curve ($E(t)$).

Step 1: Defining the physical meaning of the E-curve.
The $E$-curve represents the distribution of times that different fluid elements spend inside the reactor system before exiting. Mathematically, the quantity $E(t) \cdot dt$ represents the fraction of fluid elements in the exiting stream that have spent an age (or residence time) between $t$ and $t + dt$ inside the reactor: \[ \int_{0}^{\infty} E(t) \cdot dt = 1 \]

Step 2: Identifying where the measurement is defined.
Let us analyze why the $E$-curve is defined specifically at the outlet stream location:
• Fluid elements entering the reactor at the inlet all have an initial residence time or age of exactly zero ($t = 0$). Therefore, statement (1) is incorrect.
• The distribution of fluid ages remaining *inside* the reactor vessel is characterized by a different distribution function, known as the internal age distribution function or $I$-curve ($I(t)$), rather than the $E$-curve. Therefore, statement (3) is incorrect.
• The $E$-curve is determined experimentally by injecting a tracer at the inlet and measuring the resulting tracer concentration profile over time exclusively at the outlet exit stream of the reactor. Thus, the $E$-curve specifically quantifies the age distribution of the fluid elements leaving the system at the outlet. This matches option (2) perfectly.