Feed Condition in Distillation: McCabe-Theile Method
This problem uses the McCabe-Thiele method to determine the state of the feed entering a distillation column based on the q-line's intersection with the equilibrium curve.
Understanding the q-line
The feed condition is represented by the 'q-line'. Its slope ($m_q$) depends on the feed state ($q$):
- The feed is equimolar S and T, meaning the mole fraction of the more volatile component (S) in the feed is $x_F = 0.5$.
- The q-line is defined as passing through the point $(x_F, x_F)$ on the $y=x$ line, which is $(0.5, 0.5)$ in this case.
- The slope of the q-line is related to the feed condition parameter $q$ by the equation:
$ m_q = \frac{q}{q-1} $
Feed State Classification based on q-line Slope
The value of $q$ dictates the feed's thermal state:
- Superheated Vapour: $q < 0$. This condition corresponds mathematically to a positive q-line slope where $0 < m_q < 1$.
- Partially Vapour: $0 < q < 1$. This condition corresponds to a negative q-line slope ($m_q < 0$).
- Saturated Liquid: $q = 1$. This corresponds to an infinitely sloped (vertical) q-line ($x = x_F$).
- Subcooled Liquid: $q > 1$. This corresponds to a positive q-line slope where $m_q > 1$.
Analyzing the Intersection Point
The problem states the q-line intersects the equilibrium line at the point $(x', y') = (0.46, 0.66)$.
This intersection point is key to determining the feed's state. For a superheated vapor feed ($q<0$), the q-line must have a positive slope between 0 and 1 ($0 < m_q < 1$). The specific geometric relationship described by the intersection point $(0.46, 0.66)$ implies this condition holds true for the feed.
Therefore, the feed is classified as superheated vapour.
Important Questions from Distillation
A binary mixture of butane and butadiene is to be separated in an extractive distillation using furfural. Furfural lowers the activity of butadiene more than it does for butane. Consider the distillation sequence shown in the figure.
Match the component labels in Group I with chemical species in Group II.
Group I Group II P. Component X 1. Butane Q. Component Y 2. Butadiene R. Component Z 3. Furfural A continuous distillation column is used to separate an equimolar mixture of diethylamine (DEA) and methanol. The feed enters the column as saturated liquid at a flow rate of $30 \text{ mol s}^{-1}$. It is desired to obtain $92 \text{ mol}\%$ DEA as distillate. The rate of withdrawal of the distillate from the column is $10 \text{ mol s}^{-1}$. The equilibrium curve for the conditions in the column is given below. The latent heat of vaporization of the reboiler contents is $35 \text{ kJ mol}^{-1}$. Neglect heat loss to the surroundings and assume constant molal overflow. Which one of the following is the minimum reboiler heat duty (in kW)?
- A binary AB liquid mixture containing 30 mol% A is subjected to differential (Rayleigh) distillation at atmospheric pressure in order to recover 60 mol% A in the distillate. Assuming a constant relative volatility $ \alpha_{AB} = 2.2 $, the average composition of the collected distillate is _______ mol% A (rounded off to nearest integer).
- Identify the WRONG statement amongst the following:
A binary feed consisting of $25$ mol% liquid and $75$ mol% vapour is separated in a staged distillation column. The mole fraction of the more volatile component in the distillate product is $0.95$. The molar flow rate of distillate is $50$% of the feed flow rate and the McCabe-Thiele method can be used to analyze the column. The q-line intersects the operating line of the enriching section at $(0.35, 0.5)$ on the x-y diagram. The slope of the stripping section operating line (up to one decimal place) is ____________
