Design a distillation column that separates a mixture of ethanol and water with a 95% ethanol purity and a production rate of 1000 liters per hour. The mixture contains 50% ethanol and 50% water by volume. The distillation column should operate at a pressure of 1 atm and a temperature range of 78-85°C. Assume that the feed enters the column as a saturated liquid and that the overhead product is 90% ethanol, while the bottom product is 5% ethanol. Determine the number of stages required and the reflux ratio for this system.

Question

Design a distillation column that separates a mixture of ethanol and water with a 95% ethanol purity and a production rate of 1000 liters per hour. The mixture contains 50% ethanol and 50% water by volume. The distillation column should operate at a pressure of 1 atm and a temperature range of 78-85°C. Assume that the feed enters the column as a saturated liquid a

Answer 1

To design a distillation column, we need to determine the number of stages required and the reflux ratio. We will use the McCabe-Thiele method to determine the number of stages and the Fenske equation to determine the minimum number of stages. We will also use the Underwood equations to determine the minimum reflux ratio and the Gilliland correlation to determine the actual reflux ratio.1. Determine the relative volatility    of ethanol and water at 1 atm and 78-85C:At 1 atm, the boiling points of ethanol and water are 78.37C and 100C, respectively. The vapor pressures of ethanol and water at these temperatures can be found using the Antoine equation:P_ethanol = 10^8.04494 -  1554.3 /  78.37 + 273.15 + 220.64    = 1.199 atmP_water = 10^8.07131 -  1730.63 /  100 + 273.15 + 233.426    = 0.946 atmThe relative volatility    is the ratio of the vapor pressures: = P_ethanol / P_water = 1.199 / 0.946 = 1.2672. Determine the minimum number of stages  Nmin  using the Fenske equation:Nmin = log  xD *  1 - xF   /  xF *  1 - xD    / log   = log  0.9 *  1 - 0.5   /  0.5 *  1 - 0.9    / log 1.267  = 3.47Since the number of stages must be an integer, we round up to get Nmin = 4.3. Determine the minimum reflux ratio  Rmin  using the Underwood equations:q = 1  saturated liquid feed  =   - 1  /   *  q - 1  + 1  =  1.267 - 1  /  1.267 *  1 - 1  + 1  = 0.267Rmin =  xD *   /  1 - xD  =  0.9 * 0.267  /  1 - 0.9  = 2.3974. Determine the actual reflux ratio  R  using the Gilliland correlation:R = Rmin *  1.5 - 0.5  + 0.5 = 2.397 * 1 + 0.5 = 2.8975. Determine the number of stages  N  using the McCabe-Thiele method:Since we have the actual reflux ratio  R  and the minimum number of stages  Nmin , we can use the McCabe-Thiele method to determine the number of stages  N . However, this method requires a graphical representation of the equilibrium curve and operating line, which cannot be done here. Instead, we can estimate that the actual number of stages  N  will be slightly higher than the minimum number of stages  Nmin  due to the increased reflux ratio:N  Nmin + 1 = 4 + 1 = 5In conclusion, the distillation column should have approximately 5 stages and a reflux ratio of 2.897 to separate the ethanol-water mixture with the desired purity and production rate.