Question

In a solvent regeneration process, a gas is used to strip a solute from a liquid in a countercurrent packed tower operating under isothermal condition. Pure gas is used in this stripping operation. All solutions are dilute and Henry's law, $y^ = mx$, is applicable. Here, $y^$ is the mole fraction of the solute in the gas phase in equilibrium with the liquid phase of solute mole fraction $x$, and $m$ is the Henry's law constant. Let $x_1$ be the mole fraction of the solute in the leaving liquid, and $x_2$ be the mole fraction of solute in the entering liquid. When the value of the ratio of the liquid-to-gas molar flow rates is equal to $m$, the overall liquid phase Number of Transfer Units, NTU$_{OL$, is given by}

• A. $\frac{x_2 - x_1}{x_1}$
• B. $\frac{x_2 + x_1}{x_2 - x_1}$
• C. $\ln \left( \frac{x_2}{x_1} \right)$
• D. $\ln \left( \frac{x_2 + x_1}{x_2 - x_1} \right)$

Hint:

For solvent regeneration processes, use Henry's law for solute partitioning and apply mass balance for NTU calculations.

Answer 1

The Correct Option is A

For this stripping process, the Number of Transfer Units for the liquid phase can be determined by the relationship: \[ NTU_{OL} = \frac{x_2 - x_1}{x_1} \] This is derived from the equilibrium relation and the concept of mass transfer in packed bed columns. Therefore, (A) is correct.
[6pt] Another commonly used relationship for NTU in such systems involves logarithmic expressions. Hence, (C), $\ln \left( \frac{x_2}{x_1} \right)$ is also a correct representation.