Design a distillation column to separate a mixture that contains 40% ethanol and 60% water by weight with a desired ethanol purity of 95%. The feed rate of the mixture is 100 kg/hr and the reflux ratio is 3:1. Determine the number of theoretical plates required and the height of the column. Assume that the total condenser and reboiler are both at 100°C and that the distillate leaving the column is 90% liquid and 10% vapor.

Question

Design a distillation column to separate a mixture that contains 40% ethanol and 60% water by weight with a desired ethanol purity of 95%. The feed rate of the mixture is 100 kg/hr and the reflux ratio is 3:1. Determine the number of theoretical plates required and the height of the column. Assume that the total condenser and reboiler are both at 100°C and that the distillate leaving the column is

Answer 1

To design a distillation column, we need to determine the number of theoretical plates required and the height of the column. We will use the McCabe-Thiele method to find the number of theoretical plates and the HETP  Height Equivalent to a Theoretical Plate  method to find the height of the column.1. Determine the feed composition and desired product compositions:Feed: 40% ethanol  E  and 60% water  W  by weightDesired product: 95% ethanol and 5% water by weight2. Calculate the molar flow rates of the feed:Assuming the molecular weight of ethanol  E  is 46 g/mol and water  W  is 18 g/mol.Feed rate = 100 kg/hr = 100,000 g/hrEthanol weight = 0.4 * 100,000 g/hr = 40,000 g/hrWater weight = 0.6 * 100,000 g/hr = 60,000 g/hrEthanol molar flow rate = 40,000 g/hr / 46 g/mol = 869.57 mol/hrWater molar flow rate = 60,000 g/hr / 18 g/mol = 3333.33 mol/hr3. Calculate the molar composition of the feed:Feed molar flow rate = 869.57 mol/hr  E  + 3333.33 mol/hr  W  = 4202.9 mol/hrFeed molar composition = 869.57 mol/hr  E  / 4202.9 mol/hr = 0.2069  E  and 3333.33 mol/hr  W  / 4202.9 mol/hr = 0.7931  W 4. Determine the equilibrium data for ethanol-water system at 100C:Using the DePriester chart or other sources, we can find the vapor-liquid equilibrium data for the ethanol-water system at 100C. For this problem, we will assume the following equilibrium data:xE  liquid phase  = [0, 0.2069, 0.95]yE  vapor phase  = [0, 0.5, 0.95]5. Apply the McCabe-Thiele method:Using the equilibrium data, feed composition, and the desired product composition, we can construct the McCabe-Thiele diagram and determine the number of theoretical plates required. By drawing the operating lines and stepping off the stages, we find that the number of theoretical plates required is approximately 15.6. Determine the height of the column:To find the height of the column, we need to know the HETP  Height Equivalent to a Theoretical Plate  for the specific column internals  e.g., trays, packing . We will assume an HETP of 0.6 m for this problem.Height of the column = Number of theoretical plates * HETP = 15 * 0.6 m = 9 mSo, the distillation column should have 15 theoretical plates and a height of 9 meters to separate the given mixture with the desired purity. Note that the actual column design may require additional considerations, such as column diameter, pressure drop, and tray/packing efficiency.