Chemical Engineering Volume 2: Coulson and Richardson’s

Nội dung text: Chemical Engineering Volume 2: Coulson and Richardson’s

1. PROBLEMS 1173 The ketone enters at the rate of 0.0022 m3/s m2 of tower cross-section. It contains no acetic acid, and leaves with a concentration of 0.21 kmol/m3. The aqueous phase flows at the rate of 0.0013 m3/s m2 of tower cross-section, and enters containing 0.68 kmol acid/m3. Calculate the overall extraction coefficient based on the driving force in the ketone phase. What is the corresponding value of the overall HTU, based on the ketone phase? Using units of kmol/m3, the equilibrium relationship under these conditions may be taken as: (Concentration of acid in the ketone phase) = 0.548 (concentration in the aqueous phase.) 13.3. Propionic acid is extracted with water from a dilute solution in benzene, by bubbling the benzene phase into the bottom of a tower to which water is fed at the top. The tower is 1.2 m high and 0.14 m2 in area, the 3 drop volume is 0.12 cm , and the velocity of rise is 12 cm/s. From laboratory tests, the value of Kw for forming −5 2 3 −5 2 3 drops is 7.6 × 10 kmol/s m (kmol/m ) and for rising drops Kw = 4.2 × 10 kmol/s m (kmol/m ). 3 3 What is the value of Kwa for the tower in kmol/sm (kmol/m )? 13.4. A 50 per cent solution of solute C in solvent A is extracted with a second solvent B in a countercurrent multiple contact extraction unit. The mass of B is 25 per cent that of the feed solution, and the equilibrium data are: 100% B 100% C 100% A Determine the number of ideal stages required, and the mass and concentration of the first extract if the final raffinate contains 15 per cent of solute C. 13.5. A solution of 5 per cent acetaldehyde in toluene is to be extracted with water in a five stage co-current unit. If 25 kg water/100 kg feed is used, what is the mass of acetaldehyde extracted and the final concentration? The equilibrium relation is given by: (kg acetaldehyde/kg water) = 2.20(kg acetaldehyde/kg toluene) 13.6. If a drop is formed in an immiscible liquid, show that the average surface available during formation of the drop is 12πr2/5, where r is the radius of the drop, and that the average time of exposure of the interface is 3tf /5, where tf is the time of formation of the drop. 13.7. In the extraction of acetic acid from an aqueous solution in benzene in a packed column of height 1.4 m and cross-sectional area 0.0045 m2, the concentrations measured at the inlet and outlet of the column are: 3 acid concentration in the inlet water phase, Cw2 = 0.69 kmol/m 3 acid concentration in the outlet water phase, Cw1 = 0.685 kmol/m − flowrate of benzene phase = 5.7 × 10−6 m3/s = 1.27 × 10 3 m3/m2s 3 inlet benzene phase concentration, CB1 = 0.0040 kmol/m 3 outlet benzene phase concentration, CB2 = 0.0115 kmol/m The equilibrium relationship for this system is: ∗ ∗ = CB /Cw 0.247. Determine the overall transfer coefficient and the height of the transfer unit.
2. PROBLEMS 1175 The equilibrium relationship is given by: (kg acid/kg isopropyl ether) = 0.3 (kg acid/kg water). 13.12. It is proposed to recover material A from an aqueous effluent by washing it with a solvent S and separating the resulting two phases. The light product phase will contain A and the solvent S and the heavy phase will contain A and water. Show that the most economical solvent rate, W (kg/s) is given by: 2 0.5 W = [(F ax0)/mb)] − F/m where the feedrate is F kg/s water containing x0 kg A/kg water, the value of A in the solvent product phase = £a/kg A, the cost of solvent S = £b/kg S and the equilibrium data are given by: = (kg A/kg S)product phase m(kg A/kg water)water phase where a, b and m are constants. 14.1. A single-effect evaporator is used to concentrate 7 kg/s of a solution from 10 to 50 per cent of solids. Steam is available at 205 kN/m2 and evaporation takes place at 13.5 kN/m2. If the overall heat transfer coeffi- cient is 3 kW/m2 K, calculate the heating surface required and the amount of steam used if the feed to the evaporator is at 294 K and the condensate leaves the heating space at 352.7 K. The specific heat capacity of a 10 per cent solution is 3.76 kJ/kg K, the specific heat capacity of a 50 per cent solution is 3.14 kJ/kg K. 14.2. A solution containing 10 per cent of caustic soda has to be concentrated to a 35 per cent solution at the rate of 180,000 kg/day during a year of 300 working days. A suitable single-effect evaporator for this purpose, neglecting the condensing plant, costs £1600 and for a multiple-effect evaporator the cost may be taken as £1600 N,whereN is the number of effects. Boiler steam may be purchased at £0.2/1000 kg and the vapour produced may be assumed to be 0.85 N kg/kg of boiler steam. Assuming that interest on capital, depreciation, and other fixed charges amount to 45 per cent of the capital involved per annum, and that the cost of labour is constant and independent of the number of effects employed, determine the number of effects which, based on the data given, will give the maximum economy. 14.3. Saturated steam leaves an evaporator at atmospheric pressure and is compressed by means of saturated steam at 1135 kN/m2 in a steam jet to a pressure of 135 kN/m2. If 1 kg of the high pressure steam compresses 1.6 kg of the evaporated atmospheric steam, what is the efficiency of the compressor? 14.4. A single-effect evaporator operates at 13 kN/m2. What will be the heating surface necessary to concen- trate 1.25 kg/s of 10 per cent caustic soda to 41 per cent, assuming a value of the overall heat transfer coefficient U of 1.25 kW/m2 K, using steam at 390 K? The heating surface is 1.2 m below the liquid level. The boiling-point rise of solution is 30 deg K, the feed temperature is 291 K, the specific heat capacity of the feed is 4.0 kJ/kg K, the specific heat capacity of the product is 3.26 kJ/kg K and the density of the boiling liquid is 1390 kg/m3. 14.5. Distilled water is produced from sea-water by evaporation in a single-effect evaporator, working on the vapour compression system. The vapour produced is compressed by a mechanical compressor of 50 per cent efficiency, and then returned to the calandria of the evaporator. Extra steam, dry and saturated at 650 kN/m2, is bled into the steam space through a throttling valve. The distilled water is withdrawn as condensate from the steam space. 50 per cent of the sea-water is evaporated in the plant. The energy supplied in addition to that necessary to compress the vapour may be assumed to appear as superheat in the vapour. Using the following data, calculate the quantity of extra steam required in kg/s. The production rate of distillate is 0.125 kg/s, the pressure in the vapour space is 101.3 kN/m2,thetemper- ature difference from steam to liquor is 8 deg K, the boiling point rise of sea-water is 1.1 deg K and the specific heat capacity of sea-water is 4.18 kJ/kg K. The sea water enters the evaporator at 344 K through an external heater. 14.6. It is claimed that a jet booster requires 0.06 kg/s of dry and saturated steam at 700 kN/m2 to compress 0.125 kg/s of dry and saturated vapour from 3.5 kN/m2 to 14.0 kN/m2. Is this claim reasonable?
3. PROBLEMS 1177 range in the system. The overall heat transfer coefficients may be taken as 2.5, 2.0 and 1.6 kW/m2 Kinthe first, second and third effects, respectively. 14.13. A triple-effect evaporator concentrates a liquid with no appreciable elevation of boiling point. If the temperature of the steam to the first effect is 395 K, and vacuum is applied to the third effect so that the boiling point is 325 K, what are the approximate boiling points in the three effects? The overall heat transfer coefficients may be taken as 3.1, 2.3, 1.3 kW/m2 K in the three effects, respectively. 14.14. A three-stage evaporator is fed with 1.25 kg/s of a liquor which is concentrated from 10 to 40 per cent solids by mass. The heat transfer coefficients may be taken as 3.1, 2.5 and 1.7 kW/m2 K, respectively, in each effect. Calculate the steam flow at 170 kN/m2 and the temperature distribution in the three effects, if: (a) the feed is at 294 K, and (b) the feed is at 355 K. Forward feed is used in each case and the values of U are the same for the two systems. The boiling point in the third effect is 325 K and the liquor has no boiling point rise. 14.15. An evaporator operating on the thermo-recompression principle employs a steam ejector to maintain atmospheric pressure over the boiling liquid. The ejector uses 0.14 kg/s of steam at 650 kN/m2, and superheated by 100 deg K, and produces a pressure in the steam chest of 205 kN/m2. A condenser removes surplus vapour from the atmospheric pressure line. What is the capacity and economy of the system, and how could the economy be improved? The feed enters the evaporator at 293 K and the concentrated liquor is withdrawn at the rate of 0.025 kg/s. The concentrated liquor exhibits a boiling point rise of 10 deg K. Heat losses to the surroundings are negligible. For the ejector, the nozzle efficiency is 0.95, the efficiency of momentum transfer is 0.80 and the efficiency of compression is 0.90. 14.16. A single-effect evaporator is used to concentrate 0.075 kg/s of a 10 per cent caustic soda liquor to 30 per cent. The unit employs forced circulation in which the liquor is pumped through the vertical tubes of the calandria which are 32 mm o.d. by 28 mm i.d., and 1.2 m long. Steam is supplied at 394 K, dry and saturated, and the boiling point rise of the 30 per cent solution is 15 deg K. If the overall heat transfer coefficient is 1.75 kW/m2 K, how many tubes should be used, and what material of construction would be specified for the evaporator? The latent heat of vaporisation under these conditions is 2270 kJ/kg. 14.17. A steam-jet booster compresses 0.1 kg/s of dry and saturated vapour from 3.4 kN/m2 to 13.4 kN/m2. High pressure steam consumption is 0.05 kg/s at 700 kN/m2. (a) What must be the condition of the high pressure steam for the booster discharge to be superheated through 20 deg K? (b) What is the overall efficiency of the booster if the compression efficiency is 100 per cent? 14.18. A triple-effect backward-feed evaporator concentrates 5 kg/s of liquor from 10 per cent to 50 per cent solids. Steam is available at 375 kN/m2 and the condenser operates at 13.5 kN/m2. What is the area required in each effect, assumed equal, and the economy of the unit? The specific heat capacity is 4.18 kJ/kg K at all concentrations and there is no boiling-point rise. The overall heat transfer coefficients are 2.3, 2.0 and 1.7 kW/m2 K respectively in the three effects, and the feed enters the third effect at 300 K. 14.19. A double-effect climbing film evaporator is connected so that the feed passes through two preheaters, one heated by vapour from the first effect and the other by vapour from the second effect. The condensate from the first effect is passed into the steam space of the second. The temperature of the feed is initially 289 K, 348 K after the first heater and 383 K and after the second heater. The vapour temperature in the first effect is 398 K and in the second 373 K. The flowrate of feed is 0.25 kg/s and the steam is dry and saturated at 413 K. What is the economy of the unit if the evaporation rate is 0.125 kg/s?
4. PROBLEMS 1179 should be the pressure of the steam? The surface in each effect is 50 m2 and the coefficients for heat transfer in the first and second effects are 2.8 and 1.7 kW/m2 K, respectively. It may be assumed that the concentrated solution exhibits a boiling-point rise of 5 deg K, that the latent heat has a constant value of 2260 kJ/kg and that the specific heat capacity of the liquid stream is constant at 3.75 kJ/kg K. 14.26. A salt solution at 293 K is fed at the rate of 6.3 kg/s to a forward-feed triple-effect evaporator and is concentrated from 2 per cent to 10 per cent of solids. Saturated steam at 170 kN/m2 is introduced into the calandria of the first effect and a pressure of 34 kN/m2 is maintained in the last effect. If the heat transfer coefficients in the three effects are 1.7, 1.4 and 1.1 kW/m2 K, respectively, and the specific heat capacity of the liquid is approximately 4 kJ/kg K, what area is required if each effect is identical? Condensate may be assumed to leave at the vapour temperature at each stage, and the effects of boiling point rise may be neglected. The latent heat of vaporisation may be taken as constant throughout. 14.27. A single-effect evaporator with a heating surface area of 10 m2 is used to concentrate NaOH solution at 0.38 kg/s from 10 per cent to 33.33 per cent by mass. The feed enters at 338 K and its specific heat capacity is 3.2 kJ/kg K. The pressure in the vapour space is 13.5 kN/m2 and 0.3 kg/s of steam is used from a supply at 375 K. Calculate: (a) The apparent overall heat transfer coefficient. (b) The coefficient corrected for boiling point rise of dissolved solids. (c) The corrected coefficient if the depth of liquid is 1.5 m. 14.28. An evaporator, working at atmospheric pressure, is to concentrate a solution from 5 per cent to 20 per cent solids at the rate of 1.25 kg/s. The solution, which has a specific heat capacity of 4.18 kJ/kg K, is fed to the evaporator at 295 K and boils at 380 K. Dry saturated steam at 240 kN/m2 is fed to the calandria, and the condensate leaves at the temperature of the condensing stream. If the heat transfer coefficient is 2.3 kW/m2 K, what is the required area of heat transfer surface and how much steam is required? The latent heat of vaporisation of the solution may be taken as being equal to that of water. 15.1. A saturated solution containing 1500 kg of potassium chloride at 360 K is cooled in an open tank to 290 K. If the density of the solution is 1200 kg/m3, the solubility of potassium chloride is 53.55 kg/100 kg water at 360 K and 34.5 at 290 K calculate: (a) the capacity of the tank required, and (b) the mass of crystals obtained, neglecting loss of water by evaporation. 15.2. Explain how fractional crystallisation may be applied to a mixture of sodium chloride and sodium nitrate, given the following data. At 293 K, the solubility of sodium chloride is 36 kg/100 kg water and of sodium nitrate 88 kg/100 kg water. Whilst at this temperature, a saturated solution comprising both salts will contain 25 kg sodium chloride and 59 kg sodium nitrate/100 kg of water. At 373 K these values, again per 100 kg of water, are 40 and 176, and 17 and 160 kg respectively. 15.3. 10 Mg (10 tonne) of a solution containing 0.3 kg Na2CO3/kg solution is cooled slowly to 293 K to form crystals of Na2CO3.10H2O. What is the yield of crystals if the solubility of Na2CO3 at 293 K is 21.5 kg/100 kg water and during cooling 3 per cent of the original solution is lost by evaporation? 15.4. The heat required when 1 kmol of MgSo4.7H2O is absorbed isothermally at 291 K in a large mass of water is 13.3 MJ. What is the heat of crystallisation per unit mass of the salt? 15.5. A solution of 500 kg of Na2SO4 in 2500 kg water is cooled from 333 K to 283 K in an agitated mild steel vessel of mass 750 kg. At 283 K, the solubility of the anhydrous salt is 8.9 kg/100 kg water and the stable crystalline phase is Na2SO4.10H2O. At 291 K, the heat of solution is −78.5 MJ/kmol and the heat capacities of the solution and mild steel are 3.6 and 0.5 kJ/kg deg K respectively. If, during cooling, 2 per cent of the water initially present is lost by evaporation, estimate the heat which must be removed.
5. PROBLEMS 1181 16.5. A 100 kg batch of granular solids containing 30 per cent of moisture is to be dried in a tray dryer to 15.5 per cent of moisture by passing a current of air at 350 K tangentially across its surface at the velocity of 1.8 m/s. If the constant rate of drying under these conditions is 0.7 g/s m2 and the critical moisture content is 15 per cent, calculate the approximate drying time. It may be assumed that the area of the drying surface is 0.03 m2/kg dry mass. 16.6. A flow of 0.35 kg/s of a solid is to be dried from 15 per cent to 0.5 per cent moisture based on a dry basis. The mean heat capacity of the solids is 2.2 kJ/kg deg K. It is proposed that a co-current adiabatic dryer should be used with the solids entering at 300 K and, because of the heat sensitive nature of the solids, leaving at 325 K. Hot air is available at 400 K with a humidity of 0.01 kg/kg dry air, and the maximum allowable mass velocity of the air is 0.95 kg/m2s. What diameter and length should be specified for the proposed dryer? 16.7. 0.126 kg/s of a product containing 4 per cent water is produced in a dryer from a wet feed containing 42 per cent water on a wet basis. Ambient air at 294 K and 40 per cent relative humidity is heated to 366 K in a preheater before entering the dryer which it leaves at 60 per cent relative humidity. Assuming that the dryer operates adiabatically, what is the amount of air supplied to the preheater and the heat required in the preheater? How will these values be affected if the air enters the dryer at 340 K and sufficient heat is supplied within the dryer so that the air leaves also at 340 K and again with a relative humidity of 60 per cent? 16.8. A wet solid is dried from 40 to 8 per cent moisture in 20 ks. If the critical and the equilibrium moisture contents are 15 and 4 per cent respectively, how long will it take to dry the solid to 5 per cent moisture under the same conditions? All moisture contents are on a dry basis. 16.9. A solid is to be dried from 1 kg water/kg dry solids to 0.01 kg water/kg dry solids in a tray dryer consisting of a single tier of 50 trays, each 0.02 m deep and 0.7 m square completely filled with wet material. The mean air temperature is 305 K and the relative humidity across the trays may be taken as constant at 10 per cent. The mean air velocity is 2.0 m/s and the convective coefficient of heat transfer is given by: 0.8 2 hc = 14.3G W/m deg K where G is the mass velocity of the air in kg/m2s. The critical and equilibrium moisture contents of the solid are 0.3 and 0 kg water/kg dry solids respectively and the density of the solid is 6000 kg/m3. Assuming that the drying is by convection from the top surface of the trays only, what is the drying time? 16.10. Skeins of a synthetic fibre are dried from 46 per cent to 8.5 per cent moisture on a wet basis in a 10 m long tunnel dryer by a countercurrent flow of hot air. The air mass velocity, G, is 1.36 kg/m2sandthe inlet conditions are 355 K and a humidity of 0.03 kg moisture/kg dry air. The air temperature is maintained at 355 K throughout the dryer by internal heating and, at the outlet, the humidity of the air is 0.08 kg moisture/kg dry air. The equilibrium moisture content is given by: we = 0.25 (per cent relative humidity) and the drying rate by: −4 1.47 R = 1.34 × 10 G (w − wc)(Hw − H ) kg/s kg dry fibres where H is the humidity of the dry air and Hw the saturation humidity at the wet bulb temperature. Data relating w, H and Hw are as follows: w HHw relative humidity (kg/kg dry fibre) (kg/kg dry air) (hg/hg dry air) (per cent) 0.852 0.080 0.095 22.4 0.80 0.0767 0.092 21.5 0.60 0.0635 0.079 18.2 0.40 0.0503 0.068 14.6 0.20 0.0371 0.055 11.1 0.093 0.030 0.049 9.0
6. PROBLEMS 1183 chromatography, the complete separation of a mixture containing more than a few components is likely to involve two or three columns for optimum economic performance. Why is this?  =  = = = 19.3. By using the chromatogram in Figure 19.3, show that k1 3.65, k2 4.83, α 1.32, Rs 1.26 and N = 500. Show also that, if ε = 0.8andL = 1.0m,thenK1 = 14.6, K2 = 19.3andH = 2.0 mm, where R is the retention ratio, Rs is the resolution, d is the obstruction factor, H is the plate height, K1 and K2 are   the distribution coefficients, k1 and k2 are the capacity factors, ε is the packing voidage, L is the length of the column, and N is the number of theoretical plates. Calculate the ratio of plate height to particle diameter to confirm that the column is inefficient, as might be anticipated from the wide bands in Figure 19.3. It may be assumed that the particle size is that of a typical GC column as given in Table 19.3. 19.4. Suggest one or more types of chromatography to separate each of the following mixtures: (a) α-andβ-pinenes (b) blood serum proteins (c) hexane isomers (d) purification of cefonicid, a synthetic β-lactam antibiotic.