EXAMPLE 21.2. A continuous fractionating column is to be designed to separate30,000 kg/h of a mixture of 40 percent benzene and 60 percent toluene into an overheadproduct containing 97 percent benzene and a bottom product containing 98 percenttoluene. These percentages are by weight. A reflux ratio of 3.5 mol to 1 mol of product isto be used. The molal latent heats of benzene and toluene are 7,360 and 7,960 cal/g mol,respectively. Benzene and toluene form a nearly ideal system with a relative volatility ofabout 2.5; the equilibrium curve is shown in Fig. 21.14. The feed has a boiling point of95°C at a pressure of 1 atm. (a) Calculate the moles of overhead product and bottomproduct per hour. (b) Determine the number of ideal plates and the position of the feedplate (i) if the feed is liquid and at its boiling point; (ii) if the feed is liquid and at 20°C(specific heat 0.44 cal/g. °C); (iii) if the feed is a mixture of two-thirds vapor and one-third liquid. (c) If steam at 20 lb/in.² (1.36 atm) gauge is used for heating, how muchsteam is required per hour for each of the above three cases, neglecting heat losses andassuming the reflux is a saturated liquid? (d) If cooling water enters the condenser at25°C and leaves at 40°C, how much cooling water is required, in cubic meters per hour?Solution(a) The molecular weight of benzene is 78, and that of toluene is 92. The concen-trations of feed, overhead, and bottoms in mole fraction of benzene are0.216XF=11XB10|407840 6078 92FIGURE 21 14+9= 0.440XB =878XFXXD =977897785+ 3/2= 0.0235Feed line= 0.974XDThe average molecular weight of the feed is1006040+507892= 85.8The average heat of vaporization of the feed isλ = 0.44(7,360) +0.56(7,960) = 7,696 cal/g molThe feed rate F is 30,000/85.8= 350 kg mol/h. By an overall benzene balance, usingEq. (21.8),D = 3500.440 0.02350.974 -0.0235= 153.4 kg mol/hB = 350 153.4 = 196.6 kg mol/h(b) Next we determine the number of ideal plates and position of the feed plate.(i) The first step is to plot the equilibrium diagram and on it erect verticals at Xp, Xand xp. These should be extended to the diagonal of the diagram. Refer to Fig. 21.14The second step is to draw the feed line. Here f = 0, and the feed line is vertical and isa continuation of line x = xF. The third step is to plot the operating lines. The interceptof the rectifying line on the y axis is, from Eq. (21.22), 0.974/(3.5+ 1) = 0.216. Thispoint is connected with the point x, on the yx reference line. From the intersection of therectifying operating line and the feed line, the stripping line is drawn.The fourth step is to draw the rectangular steps between the two operating lines andthe equilibrium curve. In drawing the steps, the transfer from the rectifying line to thestripping line is at the seventh step. By counting steps it is found that, besides thereboiler, 11 ideal plates are needed and feed should be introduced on the seventh platefrom the top.is 7,696/85.8= 89.7 cal/g. Sub-(ii) The latent heat of vaporization of the feedstitution in Eq. (21.27) givesq=1+0.44(95-20)89.7= 1.37From Eq. (21.34) the slope of the feed line is -1.37/(1-1.37) = 3.70. When stepsare drawn for this case, as shown in Fig. 21.15, it is found that a reboiler and 10 idealplates are needed and that the feed should be introduced on the sixth plate.(iii) From the definition of q it follows that for this case q = and the slope of thefeed line is -0.5. The solution is shown in Fig. 21.16. It calls for a reboiler and12 plates, with the feed entering on the seventh plate.More plates are needed when the feed is largely vapor, partly because the feed lineIslants to the left and a few more plates are required in the rectifying section. The majorreason, however, is that partially vaporized feed contributes less liquid to the strippingsection than does a totally liquid feed, and the reflux ratio in the stripping section isreduced.To fulfill the conditions of the problem literally, the last step, which represents the reboiler, shouldreach the concentration XB exactly. This is nearly true in Fig. 21.14. Usually, xg does not correspond toan integral number of steps. An arbitrary choice of the four quantities Xp, X, X, and R, is not necessar-ily consistent with an integral number of steps. An integral number can be obtained by a slight adjust-the actual number of plates is established there is little reason for making this adjustment.ment of one of the four quantities, but in view of the fact that a plate efficiency must be applied before0.21610.0.216XBFIGURE 21.15Example 21.2, part (b)(ii).XB8.10Feed line981FIGURE 21.16Example 21 2. part (b)(iii).XFXFX-Feed line33XD11XD Repeat Example 21.2 parts a) and b) (MSH (textbook) p. 683-685) with the following changes:For part a)Vapor Composition, Mole Fraction BENZENE10.90.80.70.60.50.40.30.20.10For part b)0feed has 49.1 mol % benzene and overhead product has 96.6 mol % benzene(bottoms product concentration remains unchanged at 2.35 mol %)feed rate F is 352.4 kg mol/hri) remains unchanged - feed is liquid at boiling pointii) feed is liquid at 25 °Ciii) feed is a mixture with 3/5 vapor and 2/5 liquidX-Y Plot for BENZENE and TOLUENE (Thermo = UNIF01,P = 1.0000 atm)0.20.40.6Liquid Composition, Mole Fraction BENZENE0.81-x=yEquilibrium curve

Question

Accepted Answer

Composition of the feed is,
Benzene = 0.491
Composition of benzene in the overhead product = 0.966…