26.36 Mass Transfer (Optimum Reflux Ratio)

Transcription

1 26.36 Mass Transfer (Optimum Reflux Ratio) A sieve-plate distillation column is being designed to handle 700 lb mol of feed per hour. The unit is to operate continuously at a total pressure of 1 atm. The feed contains 45 mol% benzene and 55 mol% toluene, and the feed enters at its boiling temperature. The overhead product from the distillation tower must contain 92 mol% benzene, and the bottoms must contain 95 mol% toluene. Plant Design and Economics Ahmad and Associates

2 Determine the following: a) The optimum reflux ratio as moles liquid returned to tower per mole of distillate product drawn. b) The ratio of the optimum reflux ratio to the minimum reflux ratio. c) The percentage of the total variable cost due to steam consumption at the optimum conditions. Plant Design and Economics Ahmad and Associates

3 The following data apply: The molal heat capacity for liquid mixtures of benzene and toluene in all proportions may be assumed to be 40 Btu/(lb.mol.ºF). The molal heat of vaporization benzene and toluene may be taken as 13,700 Btu/lb.mol. Effect of change in temperature on heat capacity and heats of vaporization are negligible. Heat losses from the column are negligible. Effects of pressure drop over the column may be neglected. Plant Design and Economics Ahmad and Associates

4 The overall coefficient of heat transfer is 80 Btu/(hr.ft 2.ºF) in the reboiler and 100 Btu/(hr.ft 2.ºFnser) in the condenser. The boiling temperature is 201ºF for the fee, 179ºF for the distillate, and 227ºF for the bottoms. The temperaturedifference driving force in the reflux condenser may be based on an average cooling-water temperature 90ºF, and the change in cooling-water temperature is 50ºF for all cases. Saturated steam at 60 psi is used in the reboiler. At this pressure, the temperature of the condensing steam is 292ºF and the heat of condensation is Btu/lb. Plant Design and Economics Ahmad and Associates

5 The column diameter is to be based on a maximum allowable vapor velocity of 2.5 ft/s at the top of the column. The overall plate efficiency may be assumed to be 70 percent. The unit to operate 8500 h per year. Plant Design and Economics Ahmad and Associates

6 Steam = $ llll ; Cooling water = $ gggggg or $ llll The sum of costs for piping, insulation, and instrumentation can be estimated to be 60 percent of the cost for the installed equipment. Annual fixed charges amount to 15 percent of the total cost for installed equipment, piping, instrumentation, and insulation. Plant Design and Economics Ahmad and Associates

7 The following costs are for the installed equipment and include delivery and erection costs: Sieve-plate distillation columns Condenser tube-andshell heat exchanger Diameter $/plate Heat-transfer area $ Heattransfer area Reboiler tube-and shell heat exchanger , , , , , , , , , ,600 Plant Design and Economics Ahmad and Associates $

8 Sample calculation for reflux ratio = 1.5 Annual cost for distillation column. The slope of the enriching operating line = R = 1.5 = 0.6 RR The total number of theoretical stages required for the given separation is 12.1 stages. The actual number of stages = NN ttt 1 ηη = = 16. Plant Design and Economics Ahmad and Associates

9 The moles of distillate per hour (MM DD ) and the moles of bottoms per hour (MM BB ) may be determined by a benzene material balance as follows: MM FF xx FF = (MM DD ) xx FF +(MM FF MM DD ) xx WW = (MM DD 0.92)+(700 MM DD )(0.05) MM DD = 322 moles distillate /h MM BB = 378 moles bottoms /h Moles vapor per hour at top of column = MM DD RR + 1 = = 805 Plant Design and Economics Ahmad and Associates

10 Volumetric flow rate = nnnnnn pp = 1 = ft3 h = ft3 s Vapor velocity at top of tower = 2.5 ft s Cross-sectional area, AA = VV vv = ,5 = ft 2 Column diameter, DD = 4AA ππ = 4(41.72) ππ =7.3 ft Plant Design and Economics Ahmad and Associates

11 Cost per plate and vessel = $4290 Annual cost for distillation column = $16,470 Plant Design and Economics Ahmad and Associates

12 Annual cost for condenser Rate of heat transfer, qq MM VV λλ = 805 Heat transfer area, AA = Btu h qq = UU TT tt = = 1240 ft Cost per square foot = = $ Annual cost for condenser = = $6150 Plant Design and Economics Ahmad and Associates

13 Annual cost for reboiler: qq RR + qq FF = qq CC + qq DD qq FF = = Btu h qq DD = = Btu h qq RR = = 11,110,000 Btu h Plant Design and Economics Ahmad and Associates

14 Heat transfer area, AA qq = UU TT tt = = 2120 ft2 Cost per square foot = = $ Annual cost for condenser = = $13,020 Plant Design and Economics Ahmad and Associates

15 Annual cost for cooling water Btu ( h $ h) = (1.0 Btu = $20,220 lb. F 50 F lb) Annual cost for steam = $ h) (915.5 Btu = $155,100 lb 1000 lb) ( Btu h Plant Design and Economics Ahmad and Associates

16 Total annual variable cost at reflux ratio of 1.5 = $16,470 + $6,150 + $13,020 + $20,220 + $155,100 = $210,960 By repeating the preceding calculations for different reflux ratios R N D Col Cond Reb CW Steam Total , , , ,120 17, , , , ,390 18, , , , ,720 19, , ,690 Plant Design and Economics Ahmad and Associates

17 The minimum total cost per year occurs at a reflux ratio of For conditions of minimum reflux ratio, the slope of the enriching line RR mm RR mm + 1 = RR mm = 1.14 RR oooooo RR mm = = 1.1 At the optimum conditions: Annual steam cost = $139,500; Total annual variable cost = $198,000 Percentage of variable cost due to steam consumption = $139,500 $198, = 70% Plant Design and Economics Ahmad and Associates