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Internal Column Balances Feed tray V L V L F Feed Equation: y = -{(L - L)/(V - V)}x + Fzf/(V-V) y = -(Lf/Vf)x + (F/Vf)zf y = {q/(q-1)}x + zf/(1-q) q = (L-L)/F = (H-hf)/(H-h) Example 19: Find the value of q and draw the feed line for a feed containing 0.4 pentane and 0.6 toluene: (a) the feed is a saturated liquid, (b) the feed contains 0.5 fraction of vapor, (c) the feed was superheated so that each mole of feed vaporizes 10 moles of liquid, (d) the feed was subcooled so that each mole of feed condenses 2 moles of vapor. Example 19: Find the value of q and draw the feed line for a feed containing 0.4 pentane and 0.6 toluene: (a) the feed is a saturated liquid, (b) the feed contains 0.5 fraction of vapor, (c) the feed was superheated so that each mole of feed vaporizes 10 moles of liquid, (d) the feed was subcooled so that each mole of feed condenses 2 moles of vapor. Example 20: The distillation column shown in the figure below was used for the separation of 0.4 mole fraction pentane in toluene. The desired distillate and bottom products are 0.1 and 0.9, respectively. The feed enters the column as a superheated vapor that vaporizes 2 moles of liquid per mole of feed. Condenser QC D, xD= 0.9, hD Reflux ratio = L0/D = 3 Rmin Q=0 (a) What is q-value of the feed? Plot the F, z, hf 10 Kmole/min, 0.4 superheated vapor (n) feed line. (b) What is the minimum reflux ratio for the separation? (c) If the column reflux was operated at 3 Rmin, where is the optimum feed-plate location? Reboiler QR B, xB= 0.1, hB Boilup ratio = Vn+1/D (d) What is the boil-up ratio needed for the separation? (e) How many equilibrium stages is needed to accomplish the desired separation? (f) How much distillate and bottom are produced if the feed rate is 10 kmole/min? (g) What is the minimum number of trays needed for achieve the desired separation? Example 21: The distillation column shown in the figure below was used for the separation of 0.25 mole pentane from heptane. The desired distillate and bottom products are 0.05 and 0.95, respectively. The vapor flowrate in the enriching and stripping sections of the column are 2 D and 3B, respectively. Condenser QC D, yD= 0.95, hD Reflux ratio = L0/D Q=0 (a) What are the flowrates of distillate and F, z, hf 1 Kmole/min, 0.25 (n) bottom? (b) What is the (L/V)enriching and plot the top operating line? (c) Express the the operation reflux ratio, R as n Rmin Reboiler QR B, xB= 0.05, hB Boilup ratio = Vn+1/D (d) What is the boil-up ratio? Plot the bottom operating line. (e) Is the feed subcooled, saturated liquid, mixture, saturated vapor or superheated vapor? (f) How many equilibrium stages is needed to accomplish the desired separation? (g) Where is the optimum location of the feed plate? Example 22: A stripping column shown in the figure below was used to remove oil from contaminated water. The water leaving the bottom must be at least 99.7 % pure. The VLE data is plotted in the figure below. D, yD= 0.6, hD F, z, hf 15 Kmole/min, 0.10 Q=0 (a) Derive the top and bottom operating equation for the stripping column. (b) Plot the top and bottom operating line (c) Plot the feed line and determine the qvalue of the feed. (n) Reboiler QR B, xB= 0.003, hB Boilup ratio = Vn+1/D = 4 (d) What are the allowable feed in a stripping section i.e., subcooled, saturated liquid, mixture, saturated vapor and superheated vapor? and why? (e) Determine the number of stages needed for the separation. (f) What is the minimum reflux ratio for this separation column? Example 23: Crude oil could be extracted from sand found in Canadian province of Saskatchewan. Steam is used in the extraction process and the oil-water mixture is send through a series of distillation column. The final column known as the dehydrating column is employed for removing the final traces of water from the crude to meet the industrial maximum tolerance level of 0.01 mole fraction water. Instead of a condenser saturated liquid water was used directly as coolant. This arrangement has the added benefit of diluting the oil that remains in the water recovered at the distillate. The water from the distillate is then sent to settling tank to remove the final traces of oil before discharge. D, yD= 0.8, hD C, xc, hc (a) Derive the top operating equation for dehydration column. (b) Derive the bottom operating equation Q=0 (c) Derive the feed equation (d) Plot the respective top and bottom operating line as well as the feedline F, z, hf 75 Kmole/min, 0.20, 25 % vapor (n) Reboiler QR B, xB= 0.01, hB Boilup ratio = Vn+1/D = 3 (e) Determine the number of stages needed for the separation and the optimum feed plate location if the total tray efficiency is 0.25. Example 24: The distillation column shown in the figure below was used for the separation of 0.5 mole fraction methanol-water solution. The desired distillate and bottom products are 0.10 and 0.95, respectively. The feed enters the column as a superheated vapor that vaporizes 2 moles of liquid per mole of feed. Condenser QC D, xD= 0.9, hD Reflux ratio = L0/D = 2 Rmin Q=0 (a) What is q-value of the feed? Plot the F, z, hf 10 Kmole/min, 0.4 superheated vapor feed line. (b) What will happen if the feed condition changes from superheated to sat. vapor to sat. liquid and subcooled liquid. (n) Reboiler QR B, xB= 0.1, hB Boilup ratio = Vn+1/D (c) What is the minimum reflux ratio? (d) What is the minimum number of plates? Column Efficiency Overall Column Efficiency Eo = Nequil/Nactual Murphree Efficiency EMV = actual change in vapor change in vapor for equilibrium stage = yj - yj+1 yj* - yj+1