Design a distillation column that can separate a mixture consisting of 40% acetone, 30% methanol, and 30% ethanol with a feed rate of 100 mol/h. The distillate should consist of at least 98% acetone, and the bottom product should contain no more than 1% acetone. You may assume that the column operates at a constant pressure and has 20 equilibrium stages. Determine the reflux ratio and the number of trays required to achieve this separation.

Question

Design a distillation column that can separate a mixture consisting of 40% acetone, 30% methanol, and 30% ethanol with a feed rate of 100 mol/h. The distillate should consist of at least 98% acetone, and the bottom product should contain no more than 1% acetone. You may assume that the column operates at a constant pressure and has 20 equilibrium stage

Answer 1

To design a distillation column for this separation, we will use the McCabe-Thiele method. First, we need to obtain the vapor-liquid equilibrium  VLE  data for the acetone-methanol-ethanol system. For simplicity, we will assume that the system behaves as an ideal mixture, and we will use the relative volatility    values for the binary pairs: Acetone-Methanol   2.5 Acetone-Ethanol   2.0 Methanol-Ethanol   1.25Since acetone is the most volatile component, it will be the top product. Methanol and ethanol will be the bottom products.Next, we need to determine the operating conditions for the column. We are given the following specifications:Feed rate  F  = 100 mol/hFeed composition: xF_Acetone = 0.4, xF_Methanol = 0.3, xF_Ethanol = 0.3Distillate composition: xD_Acetone  0.98Bottom product composition: xB_Acetone  0.01Using the mass balance equations, we can calculate the distillate  D  and bottom  B  product flow rates:D = F *  xF_Acetone - xB_Acetone  /  xD_Acetone - xB_Acetone  = 100 *  0.4 - 0.01  /  0.98 - 0.01   42.35 mol/hB = F - D = 100 - 42.35  57.65 mol/hNow, we will use the McCabe-Thiele method to determine the number of equilibrium stages and the reflux ratio  L/D . We will construct the operating lines for the rectifying and stripping sections of the column using the given feed and product compositions.Rectifying section operating line equation:y =  L/D  * x + xD_Acetone *  1 - L/D Stripping section operating line equation:y =  L/B  * x + xB_Acetone *  1 - L/B We will use the Fenske equation to estimate the minimum number of equilibrium stages  Nmin  required for the separation:Nmin = log[ xD_Acetone *  1 - xB_Acetone   /  xB_Acetone *  1 - xD_Acetone  ] / log    6.5Since the column has 20 equilibrium stages, we have enough stages for the separation. Now, we need to determine the minimum reflux ratio  Lmin/D  using the Underwood equation:Lmin/D =   - 1  /   - xD_Acetone   1.5To ensure a good separation, we will use a reflux ratio of 1.5 times the minimum reflux ratio:L/D = 1.5 * Lmin/D  2.25Now, we can use the operating lines and the equilibrium curve to determine the actual number of trays required for the separation. This can be done graphically using the McCabe-Thiele method or by using a simulation software. For this problem, we will assume that the actual number of trays required is close to the minimum number of equilibrium stages  Nmin .Therefore, the reflux ratio  L/D  is approximately 2.25, and the number of trays required for the separation is approximately 7.