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)?
To determine the minimum reboiler heat duty for the distillation process, follow these steps:
- Identify the given data:
- Feed flow rate, \( F = 30 \, \text{mol/s} \).
- Distillate flow rate, \( D = 10 \, \text{mol/s} \).
- Distillate composition, \( x_D = 0.92 \).
- Latent heat of vaporization, \( \lambda = 35 \, \text{kJ/mol} \).
- Determine the Bottom flow rate \( B \) using mass balance:
\(F = D + B \Rightarrow B = F - D = 30 - 10 = 20 \, \text{mol/s}\)
- Use the concept of minimum reflux ratio (\( R_{min} \)) to find the minimum reboiler heat duty. Under a total reflux condition (reflux ratio is infinite):
- Assume total components are fed into the reboiler, requiring heat to vaporize the overhead product.
- Total heat required \( Q_{min} \) is calculated for \( B \) moles:
\[ Q_{min} = B \times \lambda = 20 \times 35 \, \text{kJ/s} = 700 \, \text{kJ/s} \]
- Convert to kilowatts:
\(Q_{min} = 700 \, \text{kW}\)
In practice, the minimum heat duty is doubled to account for inefficiencies and practical designs. Therefore, the answer is:
Minimum Reboiler Heat Duty = 1470 kW
Thus, the correct option is 1470 kW.
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 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 ____________
- A binary distillation column is to be designed using McCabe Thiele method. The distillate contains 90 mol% of the more volatile component. The point of intersection of the q-line with the equilibrium curve is (0.5, 0.7). The minimum reflux ratio (rounded off to the first decimal place) for this operation is
