Question

A chemical engineering company has a mixture of ethanol and water with a concentration of 30% ethanol to separate using a distillation column. The company needs to obtain a concentration of 80% ethanol in the distillate at a reflux ratio of 3. Calculate the number of theoretical plates required in the column for the separation, assuming no vapor or liquid bypass, and that the minimum vapor velocity is maintained.

Answer 1

To calculate the number of theoretical plates required in the distillation column, we can use the Fenske-Underwood-Gilliland  FUG  method. This method involves three steps:1. Calculate the minimum number of theoretical plates  Nmin  using the Fenske equation.2. Calculate the minimum reflux ratio  Rmin  using the Underwood equation.3. Calculate the actual number of theoretical plates  N  using the Gilliland correlation.Step 1: Fenske EquationNmin =  log  xD 1 - xB  / xB 1 - xD     /  log   Where:- xD is the mole fraction of ethanol in the distillate  0.8 - xB is the mole fraction of ethanol in the bottoms  0.3 -  is the relative volatility of ethanol to water  assumed to be 2.3 for ethanol-water system Nmin =  log  0.8 1 - 0.3  / 0.3 1 - 0.8     /  log 2.3  Nmin  2.45Step 2: Underwood EquationRmin =   /   - 1  Where:-  is the parameter calculated using the Underwood equation:  =  xD - xF  /   - 1 xF is the mole fraction of ethanol in the feed  0.3  =  2.3 * 0.8 - 0.3  /  2.3 - 1   1.15Rmin =  1.15 /  1.15 - 1  Rmin  11.5Step 3: Gilliland CorrelationN = Nmin *  1 +  R / Rmin ^0.5 Where:- R is the actual reflux ratio  3 N = 2.45 *  1 +  3 / 11.5 ^0.5 N  4.07Since the number of theoretical plates must be a whole number, we can round up to the nearest whole number:N  5Therefore, the distillation column requires approximately 5 theoretical plates for the separation of ethanol and water at a reflux ratio of 3 to obtain a concentration of 80% ethanol in the distillate.