Question

Design a distillation column to separate a mixture of ethanol and water using McCabe-Thiele Method. The feed contains 50 mol% ethanol and the distillate should have a purity of at least 95 mol% ethanol. The reflux ratio is 2.5 and the boil-up ratio is 1.5. The column must have 10 theoretical plates. Determine the number of trays above the feed and below the feed and the corresponding compositions of the distillate and bottoms.

Answer 1

To design a distillation column using the McCabe-Thiele method, we need to follow these steps:1. Obtain the vapor-liquid equilibrium  VLE  data for the ethanol-water system. For simplicity, we will use the following equilibrium data:x  mol% ethanol in liquid   : 0.0, 10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 70.0, 80.0, 90.0, 100.0y  mol% ethanol in vapor    : 0.0, 18.0, 35.0, 50.0, 63.0, 74.0, 82.0, 88.0, 93.0, 97.0, 100.02. Determine the feed condition  q-line . Since the feed is a saturated liquid, q = 1. The slope of the q-line is q/ q-1  = 1/ 1-1  = , which means the q-line is vertical.3. Determine the rectifying and stripping operating lines. The reflux ratio  R  is 2.5, so the slope of the rectifying line is  R+1 /R = 3.5/2.5 = 1.4. The boil-up ratio  V/B  is 1.5, so the slope of the stripping line is  V/B+1 / V/B  = 2.5/1.5 = 1.67.4. Draw the operating lines and the q-line on the x-y diagram. The intersection of the rectifying line and the q-line gives the feed tray composition  x_F = 50 mol% ethanol . The intersection of the stripping line and the q-line gives the bottom composition  x_B .5. Perform a McCabe-Thiele graphical construction to determine the number of theoretical trays. Start from the distillate composition  x_D = 95 mol% ethanol  and step off the stages using the VLE data and operating lines. The column must have 10 theoretical plates, so adjust the stripping line to meet this requirement.6. After completing the McCabe-Thiele construction, count the number of trays above and below the feed tray. Let's assume there are N_above trays above the feed and N_below trays below the feed.7. Determine the corresponding compositions of the distillate and bottoms. The distillate composition is already given  x_D = 95 mol% ethanol . The bottom composition can be obtained from the intersection of the stripping line and the q-line  x_B .Please note that the actual design of a distillation column requires more accurate VLE data and more detailed calculations. The above procedure is a simplified version to demonstrate the McCabe-Thiele method.