Page 221 - Separation process principles 2

186 Chapter 5 Cascades and Hybrid Systems

5.5 For Example 5.1, involving the separation of sodium carbon- (c) Two countercurrent stages are used?
ate from an insoluble oxide, compute the minimum solvent feed rate (d) An infinite number of crosscurrent stages is used?
in pounds per hour. What is the ratio of actual solvent rate to the min- (e) An infinite number of countercurrent stages is used?
imum solvent rate? Determine and plot the percent recovery of sol-
5.10 The uranyl nitrate (UN) in 2 kg of a 20 wt% aqueous solu-
uble solids with a cascade of five countercurrent equilibrium stages
tion is to be extracted with 500 g of tributyl phosphate. Using the
for solvent flow rates from 1.5 to 7.5 times the minimum value.
equilibrium data in Exercise 5.9, calculate and compare the per-
5.6 Aluminum sulfate, commonly called alum, is produced as a
centage recoveries for the following alternative procedures:
concentrated aqueous solution from bauxite ore by reaction with
(a) A single-stage batch extraction
aqueous sulfuric acid, followed by a three-stage, countercurrent
(b) Three batch extractions with one-third of the total solvent used
washing operation to separate soluble aluminum sulfate from the
in each batch (the solvent is withdrawn after contacting the entire
insoluble content of the bauxite ore, followed by evaporation. In a
typical process, 40,000 kglday of solid bauxite ore containing UN phase)
50 wt% A1203 and 50% inert is crushed and fed together with the (c) A two-stage cocurrent extraction
stoichiometric amount of 50 wt% aqueous sulfuric acid to a reactor, (d) A three-stage countercurrent extraction
where the A1203 is reacted completely to alum by the reaction (e) An infinite-stage countercurrent extraction
(f) An infinite-stage crosscurrent extraction
The slurry effluent from the reactor (digester), consisting of solid 5.11 One thousand kilograms of a 30 wt% dioxane in water solu-
inert material from the ore and an aqueous solution of aluminum tion is to be treated with benzene at 25OC to remove 95% of the
sulfate is then fed to a three-stage, countercurrent washing unit to dioxane. The benzene is dioxane-free, and the equilibrium data of
separate the aqueous aluminum sulfate from the inert material. If Example 5.2 can be used. Calculate the solvent requirements for:
the solvent is 240,000 kglday of water and the underflow from each (a) A single batch extraction
washing stage is 50 wt% water on a solute-free basis, compute the (b) Two crosscurrent stages using equal amounts of benzene
flow rates in kilograms per day of aluminum sulfate, water, and
(c) Two countercurrent stages
inert solid in each of the two product streams leaving the cascade.
(d) An infinite number of crosscurrent stages
What is the percent recovery of the aluminum sulfate? Would the
addition of one more stage be worthwhile? (e) An infinite number of countercurrent stages
5.7 (a) When rinsing clothes with a given amount of water, 5.12 Chloroform is to be used to extract benzoic acid from waste-
would one find it more efficient to divide the water and rinse sev- water effluent. The benzoic acid is present at a concentration
eral times; or should one use all the water in one rinse? Explain. of 0.05 mollliter in the effluent, which is discharged at a rate of
1,000 literth. The distribution coefficient for benzoic acid at
(b) Devise a clothes-washing machine that gives the most efficient
rinse cycle for a fixed amount of water. process conditions is given by
c1 = KEc"
Section 5.3
where K; = 4.2, c' = molar concentration of solute in solvent,
5.8 An aqueous acetic-acid solution containing 6.0 moles of acid and c" = molar concentration of solute in water. Chloroform and
per liter is to be extracted in the laboratory with chloroform at 25°C water may be assumed immiscible. If 500 literslh of chloroform is
to recover the acid (B) from chloroform-insoluble impurities pre- to be used, compare the fraction benzoic acid removed in
sent in the water. The water (A) and chloroform (C) are essentially
(a) A single equilibrium contact
immiscible. If 10 liters of solution are to be extracted at 25OC, cal-
culate the percent extraction of acid obtained with 10 liters of chlo- (b) Three crosscurrent contacts with equal portions of chloroform
roform under the following conditions: (c) Three countercurrent contacts
(a) Using the entire quantity of solvent in a single batch extraction 5.13 Repeat Example 5.2 with a solvent for which E = 0.90. Dis-
(b) Using three batch extractions with one-third of the total solvent play your results in a plot like Figure 5.7. Does countercurrent flow
used in each batch still have a marked advantage over crosscurrent flow? Is it desirable
to choose the solvent and solvent rate so that E > l? Explain.
(c) Using three batch extractions with 5 liters of solvent in the first,
3 liters in the second, and 2 liters in the third batch Section 5.4 i
Assume that the volumetric amounts of the feed and solvent do not 5.14 Repeat Example 5.3 for N = 1,3, 10, and 30 stages. Plot the
change during extraction. Also, assume the distribution coefficient percent absorption of each of the five hydrocarbons and the total
for the acid, KgB = (c~)~/(cB)~ = 2.8, where (CB)~ = concen- feed gas, as well as the percent stripping of the oil versus the num-
tration of acid in chloroform and (cB)~ = concentration of acid in ber of stages, N. What can you conclude about the effect of the
water, both in moles per liter. number of stages on each component?
5.9 A 20 wt% solution of uranyl nitrate (UN) in water is to be 5.15 Solve Example 5.3 for an absorbent flow rate of 330 lbmolih i
treated with tributyl phosphate (TBP) to remove 90% of the uranyl and three theoretical stages. Compare your results to the results of
nitrate. All operations are to be batchwise equilibrium contacts. As- Example 5.3 and discuss the effect of trading stages for absorbent
suming that water and TBP are mutually insoluble, how much TBP flow.
is required for 100 g of solution if at equilibrium (g UNlg TBP) = 5.16 Estimate the rninimum absorbent flow rate required for
5.5(g UNIg HzO) and: j
the separation calculated in Example 5.3 assuming that the key
(a) All the TBP is used at once in one stage? component is propane, whose flow rate in the exit vapor is to be 4 4
(b) Half is used in each of two consecutive stages? 155.4 Ibmolh.