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Design a distillation column for the separation of a binary mixture of ethanol and water, with a feed consisting of 50 weight percent ethanol and 50 weight percent water. The column should be able to produce a distillate product containing at least 90 weight percent ethanol, with a recovery of at least 95 weight percent of the ethanol i

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To design a distillation column for the separation of a binary mixture of ethanol and water, we will use the McCabe-Thiele method. This method involves constructing a graphical representation of the equilibrium stages and operating lines to determine the number of theoretical trays required for the desired separation.1. Feed composition and flow rate:Feed composition: 50 wt% ethanol and 50 wt% waterFeed flow rate: 1000 kg/hr2. Distillate and bottom product specifications:Distillate composition: at least 90 wt% ethanolRecovery of ethanol in the feed: at least 95 wt%3. Determine the relative volatility    of ethanol to water:For ethanol-water mixtures, the relative volatility is approximately 2.3.4. Construct the equilibrium curve:Using the relative volatility and vapor-liquid equilibrium data for ethanol-water mixtures, plot the equilibrium curve on an x-y diagram  x = liquid phase mole fraction of ethanol, y = vapor phase mole fraction of ethanol .5. Determine the feed condition:Since the feed is a 50/50 mixture of ethanol and water, it is a saturated liquid. Therefore, the feed line will have a slope of +1.6. Determine the operating lines:For the rectifying section  above the feed tray , the operating line equation is y = R/ R+1  * x + xD/ R+1 , where R is the reflux ratio and xD is the distillate composition.For the stripping section  below the feed tray , the operating line equation is y = L'/V' * x + xB *  1 - L'/V' , where L' and V' are the liquid and vapor flow rates in the stripping section, and xB is the bottom product composition.7. Optimize the reflux ratio  R :To minimize the number of trays and energy consumption, we can use the Fenske-Underwood-Gilliland method to determine the optimal reflux ratio. The minimum reflux ratio  Rmin  can be found using the Underwood equation, and the optimal reflux ratio is typically 1.2 to 1.5 times the minimum reflux ratio.8. Determine the number of theoretical trays:Using the McCabe-Thiele method, step off the equilibrium stages between the rectifying and stripping operating lines, starting from the distillate composition  xD  and ending at the bottom product composition  xB . The number of stages intersected is the number of theoretical trays required for the desired separation.9. Calculate the heat load required for the operation of the column:The heat load for the reboiler  Qr  can be calculated using the equation Qr = L' *  hL - hB , where hL and hB are the enthalpies of the liquid leaving the reboiler and the bottom product, respectively.The heat load for the condenser  Qc  can be calculated using the equation Qc = V *  hV - hD , where hV and hD are the enthalpies of the vapor leaving the top tray and the distillate product, respectively.By following these steps, you can design a distillation column for the separation of a binary mixture of ethanol and water, determine the number of theoretical trays required, and calculate the heat load required for the operation of the column.

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