Lecture 10

Question 1

The graphical method used in the last lecture to determine the number of equilibrium stages serves what function? What are the issues with it?

Answer 1

The graphical method of §6.3 for determining N has educational value because a graph provides a visual insight into the phenomena involved. However, the graphical method becomes tedious when the following occurs:
(1) problem specifications fix the number of stages rather than the percent recovery of solute
(2) more than one solute is absorbed or stripped
(3) the location of the equilibrium curve is unknown because the optimal operating T and P have not been established
(4) very low or very high concentrations of solute force the construction to the corners of the diagram so that multiple Y–X diagrams of varying scales are needed to achieve accuracy

Question 2

What can we then use instead of the graphical method?

Answer 2

When the graphical method is unsuitable, the analytical method of Kremser is useful for obtaining results that can be used to initialize rigorous methods in the process
simulators.

Question 3

What is the analytical method of Kremser?

Answer 3

Kremser introduced a group method that relates the number of equilibrium stages to the recovery of one key component in a single-section, countercurrent cascade used for multicomponent absorption or stripping. The procedure is called a group method because it only provides an overall
treatment of the group of stages in the cascade. The procedure does not consider detailed changes in temperature, pressure, phase compositions, and flow rates from stage to stage.

Question 4

What is the derivation for the fraction of species not absorbed using the analytical method of Kremser?

Answer 4

Absorber description (Shown in digital notes):

Consider a countercurrent absorber of N adiabatic, equilibrium stages, as shown in digital notes, with stages numbered from top to bottom. The absorbent is pure, and component molar flow rates are vi and li. In the vapor and liquid phases, respectively. The following derivation applies to any component in the vapor feed. Mole fractions are y and x, and total molar flow rates are V and L. Now go to the written notes for derivation

Stripper description (Shown in digital notes):

Assume the components stripped from the liquid are not present in the entering vapor, and ignore absorption of the stripping agent. Stages are numbered from bottom to top. Now go to the written notes for derivation

Question 5

Determining the Number of equilibrium stages using Murphy’s efficiency?

Answer 5

Digital notes