Distillation Design: Minimum Reflux Ratio
This solution outlines the calculation for the minimum reflux ratio (Rmin) using the McCabe Thiele method based on the provided parameters for a binary distillation column.
Given Parameters
- Distillate Composition (xD): 0.90 mol% more volatile component
- Intersection Point (q-line and Equilibrium curve): (x = 0.5, y = 0.7)
- Target: Calculate Minimum Reflux Ratio (Rmin)
McCabe Thiele Method for Minimum Reflux
The minimum reflux ratio (Rmin) in the McCabe Thiele method occurs when the operating line passes through the distillate composition point (xD, xD) and is tangent to the equilibrium curve, typically at the feed stage intersection. The line connecting (xD, xD) and the given intersection point (x, y) = (0.5, 0.7) defines the condition for minimum reflux.
Calculating Minimum Reflux Ratio (Rmin)
The slope of the operating line at minimum reflux can be calculated using the two points: (xD, xD) and (x, y).
$ \text{Slope} = \frac{y - x_D}{x - x_D} $
Substitute the given values:
$ \text{Slope} = \frac{0.7 - 0.90}{0.5 - 0.90} = \frac{-0.20}{-0.40} = 0.5 $
The slope of the operating line is also related to the minimum reflux ratio by the equation:
$ \text{Slope} = \frac{R_{min}}{R_{min} + 1} $
Equating the two expressions for the slope:
$ \frac{R_{min}}{R_{min} + 1} = 0.5 $
Solve for Rmin:
$ R_{min} = 0.5 \times (R_{min} + 1) $
$ R_{min} = 0.5 R_{min} + 0.5 $
$ 0.5 R_{min} = 0.5 $
$ R_{min} = 1.0 $
The calculated minimum reflux ratio is 1.0. This value falls within the acceptable range of 0.98 to 1.02.
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 ____________
