Design a distillation column to separate a mixture of ethanol and water with an initial composition of 40% ethanol and 60% water. The column should achieve a separation of at least 95% ethanol in the distillate product. The available packing materials are Pall rings with a diameter of 1.5 inches and a height of 2 inches. The column inlet flow rate is 1000 kg/hr with a pressure of 1 atm and a temperature of 80°C. The column should have 25 theoretical plates and operate at reflux ratios ranging from 1.5 to 3.0. Additionally, the column diameter should not exceed 3 feet. Provide the design calculations and specifications for the distillation column.

Question

Design a distillation column to separate a mixture of ethanol and water with a

Answer 1

To design the distillation column, we will follow these steps:1. Determine the vapor-liquid equilibrium  VLE  data for ethanol-water mixture.2. Calculate the minimum reflux ratio  Rmin  and select an operating reflux ratio  R .3. Determine the number of actual plates using the Height Equivalent to a Theoretical Plate  HETP  method.4. Calculate the column diameter.5. Calculate the column height.Step 1: VLE DataFor ethanol-water mixture, we can use the following Antoine equations to determine the vapor pressures of ethanol  A  and water  B  at the given temperature  80C :ln P_A  = 16.678 - 3640.2 /  T + 219.61 ln P_B  = 16.262 - 3799.89 /  T + 226.35 Where P_A and P_B are the vapor pressures of ethanol and water, respectively, and T is the temperature in Celsius.At 80C:P_A = 44.31 kPaP_B = 47.39 kPaUsing Raoult's Law, we can determine the equilibrium compositions of ethanol  x_A  and water  x_B  in the vapor phase:y_A =  x_A * P_A  / Py_B =  x_B * P_B  / PWhere P is the total pressure  1 atm = 101.325 kPa , and y_A and y_B are the vapor phase compositions of ethanol and water, respectively.Step 2: Reflux RatioUsing the Fenske equation, we can determine the minimum reflux ratio  Rmin  for the given separation:Rmin =  ^N+1  - 1  /   - 1 Where  is the relative volatility of ethanol to water, and N is the number of theoretical plates  25 . The relative volatility can be calculated as: =  y_A *  1 - x_B   /  y_B *  1 - x_A  For the given feed composition  40% ethanol and 60% water , we can calculate  as 2.1. Using the Fenske equation, we get:Rmin = 1.3We will choose an operating reflux ratio  R  of 2.0, which is within the specified range  1.5 to 3.0 .Step 3: Number of Actual PlatesUsing the HETP method, we can determine the number of actual plates required for the given packing material  Pall rings :HETP = 0.5 *  diameter + height  = 0.5 *  1.5 + 2  = 1.75 inchesNumber of actual plates =  25 theoretical plates  *  HETP  = 43.75  44 platesStep 4: Column DiameterUsing the flooding velocity method, we can estimate the column diameter:D =  4 * F  /   * _L * V_f Where D is the column diameter, F is the inlet flow rate  1000 kg/hr , _L is the liquid density  assumed to be 950 kg/m for the ethanol-water mixture , and V_f is the flooding velocity  assumed to be 0.15 m/s for the Pall rings .D = 0.91 m  3 feetThe column diameter is within the specified limit.Step 5: Column HeightThe column height can be calculated as:H = Number of actual plates * Packing height = 44 * 2 = 88 inches  7.3 feetDistillation Column Specifications:- Column diameter: 3 feet- Column height: 7.3 feet- Number of actual plates: 44- Packing material: Pall rings  1.5-inch diameter, 2-inch height - Operating reflux ratio: 2.0