Contents Sample problems and eercises Distillation... 3 Sample problems... 3 Sample : Calculating vapor phase composition for immiscible liquids... 3 Sample 2: Calculating boiling point and vapor phase composition for immiscible liquids... 3 Sample 3: Continuous distillation / Flash distillation... 5 Sample 4: Batch distillation... 8 Sample 5: Distillation of a benzene toluene miture in a plate column... Sample 6: Distillation of a benzene toluene miture in a plate distillation column, with heat duty calculations... Sample 7: Distillation of an isopropanol propanol miture on a plate distillation column... 2 Sample 8: Distillation of a cycloheanol phenol miture... 2 Sample 9: Distillation of a benzene toluene miture on a plate column... 3 Sample : Distillation of a benzene toluene miture on a packed column... 3 Eercises... 3 Problem.... 3 Problem 2.... 3 Problem 3.... 4 Problem 4.... 4 Problem 5.... 4 Problem 6... 4 Problem 7... 4 Problem 8... 4 Problem 9... 5 Problem... 5 Problem... 5 Problem 2... 6 Problem 3... 6 Problem 4... 6 Problem 5... 6 Problem 6... 7 Problem 7... 7 Problem 8... 7 Problem 9... 8 Problem 2... 8 Problem 2... 8 Problem 22... 8
Problem 23... 9 Appendi... 9 Antoine constants... 9 Important properties of unordered packings... 22 2
Sample problems and eercises Distillation Sample problems Sample : Calculating vapor phase composition for immiscible liquids Calculate the equilibrium vapor phase composition of a liquid heane water miture at 5 C, assuming that heane and water are completely immiscible. The vapor pressures of the pure components can be described by the Antoine equation: B log p A. T C The constants A, B and C are given for p [torr] and T [ C]. Their values are as follows: Solution Heane A 6,8724 8,73 B 68,72 73,63 C 224,2 233,426 Water When there are more than one components in a miture, they are indeed according their volatility. The most volatile compound (owning the lowest boiling point at a given pressure) gets the inde. Thus in this problem heane is the compound, the less volatile water is the compound 2. In the case of a miture of only two components, indees are normally not used, but all concentrations are given for the more volatile compound, in this case heane. These two liquids are immiscible, thus the vapour pressure is the sum of the vapor pressures of the individual components, calculated by the Antoine equations: p B A T C 6,8724 68.72 5C 224. 2 45.6 torr p 2 B2 A2 T C 8,73 73.63 2 5C 233. 426 92.3 torr The sum of the tensions gives the total pressure (if the liquid miture is boiling): P p p2 45.6 torr 92.3 torr 497.9 torr 6638Pa 66 kpa. If we wish to change the torr to Pa: torr = Hgmm = 33.322 Pa, thus 76 torr = 325 Pa = atm. Molar fraction of heane in the vapor phase above the liquid miture can be calculated by the Dalton law: p 45.6 torr y.85. P 497.9 torr Molar fraction of the water in the vapor phase: y y.85.85. 2 Sample 2: Calculating boiling point and vapor phase composition for immiscible liquids Determine the boiling point and vapor phase composition of a water toluene miture at atmospheric pressure (P = 76 torr), assuming the complete immiscibility of the components! The Antoine constants of the pure components (given for p [torr] and T [ C]) are: 3
Solution Water A 8.73 7.5596 B 73.63 644.5 C 233.426 233.524 Toluene Water is the more volatile component, thus al molar compositions without indeing are given for the water content. These two liquids are immiscible, thus the vapour pressure is the sum of the tension of the individual components, calculated by the Antoine equations. The miture starts boiling, when the sum of the vapor pressures equals to the given (atmospheric) pressure. Let s calculate the vapor pressures of the individual components with the Antoine equations! We need to look for the temperature when the sum of the vapor pressures are eactly equal to the atmospheric pressure. It is the boiling temperature of the toluene water miture. It is easier to determine the eact temperature, if we calculate the values also for the (76-p ) formula at each temperatures, and plot the 76-p and p 2 values as functions of the temperature in a common diagram as shown in Fig.. Intersection of the two curves gives the temperature of boiling. T [ C] p [torr] p 2 [torr] p +p 2 [torr] 76-p [torr] 3 3.7 2.9 52.7 728.3 4 55.2 35.4 9.6 74.8 5 92.3 57.7 5. 667.7 6 49. 9.9 239.9 6. 7 233.2 39. 372.2 526.8 8 354.5 26.9 56.5 45.5 9 525.3 3.5 825.8 234.7 76. 426.8 86.9 -. 4
Fig.. Determination of the boiling temperature at the atmospheric distillation of two immiscible liquids. The boiling point read from the diagram is 87.7 C. At this temperature value the vapor pressures of the liquids are: 8.73 73.63 p 87.7C 233. 426 48.9 torr, 2 B A T C B2 A2 T C 7.5596 644.5 2 p 87.7C 233. 524 276.4 torr. Sum of the two values is almost equal to the atmospheric pressure: 2 p p 48.9 torr 276.4 torr 757.3 torr 76 torr. Molar fraction of water in the vapor phase according to Dalton s law: p 48.9 torr y.635. P 757.3 torr Molar fraction of toluene in the vapor phase: y y.635.365. 2 More eact results might be obtained by iteration or if we solve the equations numerically. Note, that the boiling point of a miture of water and another liquid immiscible with water is always at a lower temperature than C. This makes the steam distillation viable. Sample 3: Continuous distillation / Flash distillation Flash distillation is used to evaporate half of a 4 mole% benzene toluene miture. 5
a) What is the composition of the resulting distillate and residue? b) By changing the amount of evaporated miture, what is the maimum possible benzene content of the distillate? c) By changing the amount of evaporated miture, what is the maimum possible toluene content of the residue? Solution a) What is the composition of the resulting distillate and residue? Component balance: F F L V y. Since 5% of the feed is evaporated:.5 F = L = V. Let s substitute it into the component balance equation: F F L V y.5 F. 5 Fy, F.5. 5y. By taking into account that F =.4, we end up in an equation of a linear:.4.5. 5 y, F.8 y y. 8. We know, that the vapor and liquid products of a flash distillation are in equilibrium, thus the liquid composition and vapour composition y values correspond to the coordinates of one single point of the equilibrium curve. We also derived from the balance equations that y, 8. The intersection of this linear funcition and of the equilibrium curve gives the operation point of this flash disitillation as shown in Fig 2. The equilibrium curve was drawn using the method described in the Appendi. 6
Fig. 2.Determination of the vapor and liquid composition at a flash distillation Read from the diagram: y. 5, and. 29. b) By changing the amount of evaporated miture, what is the maimum possible benzene content of the distillate? Maimum possible benzene content of the distillate can be achived if minimum amount of vapor is evaporated. The yma value can be read from Fig. 3. y ma.62. 7
Fig. 3. Possible working intervals of a flash disitillation (sample 3. b, c) c) By changing the amount of evaporated miture, what is the maimum possible toluene content of the residue? Maimum toluene content is obtained in the liquid product when almost the total feed is evaporated.. The min value can be read from Fig. 3.: min.22, thus maimal toluene content is: -.22 =.78. Sample 4: Batch distillation kmol of a 6 mole% benzene toluene miture is subjected to batch distillation until a 3 mole% residue is obtained. How many kg of distillate is obtained, and what is its benzene content? (Also solve the problem using relative volatility, average α) Solution Mass balance: L L D. Component balance: L L D D. Rayleigh-equation: L ln L d. y 8
9 The Rayleigh-equation can be solved by numerical integration. We shall use the method of trapezoids. We read the corresponding and y values from the equilibrium curve, calculate the values of the f() function and perform the numerical integration. i [-] y [-] f()=/(y-) [-] Δ [-].6.79 5.263 2.55.75 5..5 3.5.7 4.762.5 4.45.67 4.545.5 5.4.62 4.545.5 6.35.57 4.545.5 7.3.5 4.762.5 Based on the data of the table y f ) ( function can be drawn (Fig 4.). Fig 4. Graphical integration of the Rayleighequation(sample 4.) Method of trapezoids: n i i i i n i i i i y y f f y d 2 2 2 2 ) ( ) (
d y y y 2 n n i2, y i d 5,263 4,762,5 5 4,762 4,545 4,545 4,545,42. y 2 L ln L.42, L kmol L 24.7 kmol..42.42 e e D L L kmol- 24.7 kmol 75.83 kmol. Average molar fraction of benzene in the distillate: L L kmol.6-24.7kmol.3 D.696. D 75.83kmol Mass of distillate: m D D D M D M M, D benzene D toluene kg kg m D 75.83kmol.696 78.696 92 6238kg. kmol kmol Solution using average relative volatility Relative volatility at the beginning of the distillation: y /.79/.6 2.52. ( y) /( ) (.79) /(.6) at the end of the distillation: y /.5/.3 2.44. ( y) /( ) (.5) /(.3) If we may consider the relative volatility as constant, the best estimation is to take the average of the calculated values α and α : 2.52 2.44 2 2 2.48 a more eact estimation may be achieved if we perform the same calculations for several point: i [-] y [-] α [-].6.79 2.44 2.55.75 2.45 3.5.7 2.47 4.45.67 2.48 5.4.62 2.49 6.35.57 2.5
7.3.5 2.52 Rayleigh-equation using constant relative volatility: L.6.3 ln ln ln ln 2.48 ln.4. L 2.48.3.6 Deviation of L ln value is less than %. L L kmol L 24.4 kmol,.4.4 e e D L L kmol- 24.4 kmol 75.59 kmol, L L kmol.6-24.4 kmol.3 D.697, D 75.59 kmol kg kg m D 75.84kmol.697 78.697 92 626kg. kmol kmol Sample 5: Distillation of a benzene toluene miture in a plate column 5 kmol/h of a 4 mole% benzene toluene is separated on a continuous distillation column operating at amospheric pressure to yield a 92 mole% distillate and 8 mole% bottoms product. Feed is a liquid vapor miture in : ratio, introduced optimally. a) What are the molar flows of the distillate and bottoms product? b) What is the minimally required number of theoretical plates? c) What is the minimal reflu ratio? d) How many theoretical plates must the column be equivalent to, and where should the feed be introduced if the operating reflu ratio is.5 times the minimum? (The column is fitted with a partial reboiler.) e) How many plates are required in a column with integrated reboiler to achieve the separation described in part d) if the average column efficiency is.7? f) What is the required height of the column if plate spacing is 3 cm? Sample 6: Distillation of a benzene toluene miture in a plate distillation column, with heat duty calculations 5 kmol/h of a 4 mole% benzene toluene is separated on a continuous distillation column operating at amospheric pressure to yield a 92 mole% distillate and 8 mole% bottoms product. The operating reflu ratio is 3. The column contains 5 plates. Feed is a : ratio liquid vapor miture, introduced optimally. Use the ideal gas law for calculations. a) What are the molar flows of the distillate and bottoms product? b) What is the value of the load factor at the top and bottom of the column, assuming a column diameter of. m and a plate pressure drop of 3 torr? c) What is the hourly requirement of heating steam (2.7 bar) and cooling water (c p,water = 4,8 kj/kgk), if the cooling water temperature can rise by no more than 5 C and assuming that the feed is a : ratio liquid vapor miture liquid at boiling point?
The enthalpy of vaporization for the miture is 3336 kj/kmol. Sample 7: Distillation of an isopropanol propanol miture on a plate distillation column 24 kg/h of a propanol isopropanol miture containing 45 mass% isopropanol is separated in a continuous distillation column, at atmospheric pressure to yield products containing 9 mass% isopropanol and 95 mass% propanol. The optimally introduced feed is a vapor liquid miture containing 5% vapor. The propanol isopropanol miture can be considered to be ideal. The average enthalpy of vaporization is 4.5 kj/mol. Both components have a molar mass of 6. g/mol. The Antoine constants are as follows (substitute pressure in Hgmm and temperature in C): Atmospheric boiling point A B C isopropanol 82,6 C 8,87829 2,33 252,636 propanol 97,2 C 7,757 44,63 98,85 a) What are the molar flows of the distillate and the bottoms product? b) What is the minimal number of plates? c) What is the minimal reflu ratio? d) How many theoretical plates must the column be equivalent to, and where should the feed be introduced if the operating reflu ratio is.3 times the minimum? e) How many plates are required in the column (fitted with a partial reboiler) if the average plate efficiency is.65? f) What is the height of the column if the plates are separated by 4 cm? g) What column diameter is required to maintain the load factor in the interval of,2,8 Pa /2? h) What is the hourly heat duty in the condenser and in the reboiler? Sample 8: Distillation of a cycloheanol phenol miture 38 kmol/h of a cycloheanol phenol miture containing 65 mole% cycloheanol is separated in a continuous distillation column operating at atmospheric pressure to yield a 95 mole% distillate and 2 mole% bottoms product. Feed temperature is 24 C. The operating reflu ratio is 3. The column contains 5 plates. The ideal gas law, as well as Dalton s and Raoult s laws can be used for calculations. The enthalpy of vaporization for the miture is 457 kj/kmol. The specific heat capacity of the liquid miture is approimately equal to that of cycloheanol (2 J/(mol K)). For the Antoine constants, see Appendi. atmospheric boiling point ( C) cycloheanol 6,7 94, M (g/mol) phenol 8,8,2 a) What are the molar flows of the distillate and bottoms product? b) What is the ratio between the operating and minimal reflu ratio (R/R min )? c) Given a column diameter of.4 m, what is the load factor at the top of the column? d) What is the hourly required amount of heating steam, if the heating steam temperature is 5 C above the reboiler temperature? 2
Sample 9: Distillation of a benzene toluene miture on a plate column kmol/h of a benzene toluene miture containing 45 mole% benzene is separated in a continuous distillation column operating at atmospheric pressure to yield a distillate containing 95 mole% benzene and a bottoms product containing 97 mole% toluene. The operating reflu ratio is 2. Feed is a 2 C liquid, introduced optimally. The enthalpy of vaporization for the miture is 3336 kj/kmol, its specific heat capacity is.844 kj/kgk. Use the ideal gas law for calculations. a) What are the molar flows of the distillate and the bottoms product? b) How many plates are required in the column fitted with an integral reboiler, given an average column efficiency of.75? c) What is the required diameter of the column if the allowable load factor at the bottom of the column is.3 Pa /2 and the pressure drop across the plates is 4 torr? Sample : Distillation of a benzene toluene miture on a packed column kmol/h of a 45 mole% benzene toluene miture is separated in a continuous packed distillation column to yield a distillate containing 95 mole% benzene and a bottoms product containing 97 mole% toluene. The operating reflu ratio is 5. Feed is a 2 C liquid, introduced optimally. The eperimentally determined mass transfer coefficient is.34 mol/m 2 s, the packing has a specific surface of 2 m 2 /m 3. The allowable load factor at the top of the column is.3 Pa /2. The enthalpy of evaporation for the miture is 3336 kj/kmol, its specific heat capacity is.844 kj/kgk. Use the ideal gas law for calculations. a) What are the molar flows of the distillate and bottoms product? b) Calculate the height of a transfer unit for the upper and lower sections! c) Calculate the nmber of transfer units for the upper and lower sections! d) Calculate the height of the column! Eercises Problem. Calculate the equilibrium vapor composition of a liquid miture containing 4 mole% benzene and 6 mole% toluene at 6 C. Raoult s law applies to this miture. What is the composition of the benzene toluene miture that boils at 9 C under 76 Hgmm pressure? Also determine the equilibrium vapor composition. (Answer: T = 6 C, p = 39.5 torr, p 2 = 39 torr, P = 24 torr, y =.6525, T = 9 C, p = 2 torr, p 2 = 46.7 torr, =.575, y =.772) Problem 2. Calculate the equilibrium phase compositions of a benzene toluene miture at 76 torr and plot the boiling point curve and the equilibrium curve based on the Raoult Dalton law. Based on the diagrams, determine the boiling point of a miture containing 55 mole% benzene, and the corresponding vapor composition. (Answer: T bp = 9.5 C, y =.75) 3
Problem 3. The flash distillation of a kmol/h,.5 mole fraction benzene toluene miture yields a.4 mole fraction residue. What is the composition of the distillate, and what are the flowrates of the distillate and residue? (Answer: y =.62, L = 54.55 kmol/h, V = 45.45 kmol/h) Problem 4. A 7 kmol/h methanol water miture containing 42 mole% methanol is continuously distilled at atmospheric pressure to yield a residue of 27 mole%. What is the composition of the distillate, and what are the flowrates of the distillate and residue? (Answer: D,metanol =.58, V = 33.87 kmol/h, L = 36.3 kmol/h) By changing the amount evaporated miture, what is the maimum possible methanol content of the distillate? (Answer: y ma =.735) Problem 5. An 8 kmol/h phenol metacresol miture containing 49 mole% phenol is separated by flash distillation at atmospheric pressure and 93 C. a) What are the compositions and molar flow rates of the distillate and residue? b) By changing the amount of the evaporated miture, what is the maimal metacresol content of the residue? (Answer: a) D,phenol =.53, W,phenol =.4, V = 2.46 kmol/h, L = 5.54 kmol/h. b) D,metacresol.ma =.375) Problem 6 In a flash distillation, 4% of a pentane heane miture containing 35 mole% heane is evaporated at atmospheric pressure. What is the composition of the resulting distillate and residue? (Answer: D,pentane =.79, W,pentane =.56) Problem 7 Using batch distillation to separate kmol of a 5 mole% benzene toluene miture, a residue with 5 mole% benzene content is obtained. Calculate the amount of material (in moles) that must be evaporated, the masses of the distillate and residue, and the composition of the distillate. (Answer: ln(l /L ) = 2.8, L =.6 kmol, D = 9.4 kmol, m = 54.8 kg, m D = 795 kg, Problem 8 D =.529) A benzene toluene miture containing 6 mole% toluene is batch distilled at atmospheric pressure until 93.2 kg residue having 2 mole% benzene content is obtained. What is the mass and the composition of the resulting distillate? (Answer: L = kmol, L = 44.8 kmol, D = 34.8 kmol, D =.48, m D = 2968 kg) 4
Problem 9 65 kmol of a phenol metacresol miture containing 55 mole% phenol is batch distilled at atmospheric pressure until a residue with 75 mole% metacresol is obtained. What is the amount and composition of the distillate? (Answer: L = 6.52 kmol, D = 58.48 kmol, D =.58) Problem A 5 mole% methanol water miture is separated at atmospheric pressure in a continuous distillation column yielding a distillate containing 95 mole% methanol and a bottoms product containing 95 mole% water. Feed is liquid at boiling point. a) Determine the minimal reflu ratio. b) Use the McCabe Thiele method to determine the minimal number of plates. c) How many theoretical plates are necessary to carry out the separation with reflu ratio R =? At which theoretical plate should the feed be introduced? (Answer: a) D /(R min +) =.62, R min =.53, b) N min = 5, c) N theoretical = 8; N feed = 5) Problem 85 kg/h of a 5 mole% benzene toluene must be separated on a continuous distillation column into a bottoms product with.5 mole fraction benzene and a distillate with.95 mole fraction. The reflu ratio is R = 3. The enthalpy of vaporization for the miture is 3336 kj/kmol, its specific heat capacity is.844 kj/kgk. a) What are the mass flows of the distillate and the bottoms product? b) How many theoretical plates are necessary, and where should the feed be introduced, assuming the feed is liquid at boiling point, liquid at 2 C, vapor liquid miture containing 3% vapor? c) How many real plates are required if the feed is a 2 C liquid and the average plate efficiency is 75%? d) What diameter column is required if feed is 2 C liquid, average plate efficiency is 66%, the pressure drop across a real plate is 4 torr and the allowable load factor at the bottom of the column is.4 Pa /2? e) What are the hourly requirements of heating steam and cooling water, assuming a heating steam pressure of 2.25 bars, cooling water entering at 2 C and heating up by no more than 2 C, and the feed being a : ratio liquid vapor miture? (Answer: a) F = kmol/h, W = 5 kmol/h, D = 5 kmol/h, m W = 4565 kg/h, D = 3935 kg/h, b) q (bp) =, N theo (bp) = 9, q (2 C) =.372, N theo(2 C) = 9, q (3%) =.3, N theo(3%) =, c) N val =.66, d) T reb = 8 C, P reb = 79 Pa, V = 2 kmol/h, V = 237.3 kmol/h, ρ G,lower = 3.9 kg/m 3, v lower =,8 m/s, D column =.76 m, e) V = 2 kmol/h, Q cond = 685 kw, m water = 72.6 t/h, V = 5 kmol/h, Q reboiler = 264 kw, r G = 29.37 kj/kg, m steam = 2.8 t/h) m 5
Problem 2 A 5 mole% benzene toluene miture is separated on a continuous distillation column. Requirements of the distillation: D = 95 mole% benzene, M = 7 mole% benzene. The following data about the operation of the column are available: reflu ratio R = 3, feed is liquid at boiling point. Reflu is the result of total condensation. a) Assuming kmol/h feed, what are the mass flows of the distillate and bottoms product? b) How many theoretical plates are required to achieve the separation? c) To which plate must the feed be introduced? (Answer: D = 48.86 kmol/h = 353 kg/h, W = 5.4 kmol/h = 4655 kg/h, N theo = 9; N feed = 5) Problem 3 8 kmol/h of a 47 mole% methanol water is separated in a continuous distillation column to yield a 9 mole% distillate and a 7 mole% bottoms product. Feed is a 6% vapor liquid miture. The column contains 8 plates and an integrated reboiler, column diameter is.5 m, operating reflu ratio is R = 4. a) What are the mass flows and mass percent compositions of the products? b) What is the ratio between the operational and minimal reflu ratio (R/R min )? c) What is the average column efficiency? d) What is the load factor F at the top and bottom of the column, if the pressure drop across the plates is negligible? Use the ideal gas law in the calculations. (Answer: a) D = 38.55 kmol/h, md 8 kg / h, W = 4.45 kmol/h, mw 787 kg / h, D,mehtanol = 94 m/m%, W,methanol = 2 m/m%, b) R min =.73, R/R min = 5.47, c) N theo = 5 (reboiler is theoretical plate), efficiency =.5, d) V = 92.75 kmol/h, T reb = 95.5 C, v G,reb =.764 m/s, ρ G,reb =.628 kg/m 3, F reb =.65 Pa /2, V = 6.75 kmol/h, T top = 66.6 C, v G,top =.844 m/s, ρ G,top =.98 kg/m 3 ; F top =.885 Pa /2 ) Problem 4 A 6 kmol/h pentane heane miture is to be separated. The miture contains 4 mole% pentane. In a continuous distillation column, 9% of the pentane must be recovered in 96 mole% purity. a) What are the molar flows of the products? b) What is the minimal number of plates? c) Working with.5 times the minimal reflu ratio, how many theoretical plates must the column be equivalent to and where should the feed (liquid at boiling point) be introduced? (Answer: a) D = 22.5 kmol/h, W = 37.5 kmol/h, b) N min = 6, c) R min =.3, R =.7; N theo =, N feed = 6) Problem 5 75 mol/h of a 62 mole% methanol water miture is separated on a continuous distillation column. A 92 mole% purity distillate and 5 mole% purity bottoms product is required. Feed is liquid at 29 C. Reflu ratio is 2.5. The average enthalpy of vaporization of the miture is 3732 kj/kmol, its specific heat capacity si 3.5 kj/kgk. Use the ideal gas law for calculations. a) What is the required height of the column if the average plate efficiency is.75 and plates are spaced cm apart? 6
b) What diameter column is required if the allowable load factor value at the top of the column is Pa /2? (Answer: a) N theo = 5, N real = 6, H column = 6 cm, b) T bp,top = 66 C, ρ G,top =. kg/m 3, v G,top =.95 m/s, A column,top =.373 m 2, D column,top =.69 m) Problem 6 2 kmol/h of a pentane heane miture containing 52 mole% heane is separated on a continuous distillation column. The disstillate must contain no more than 5% heane, the bottoms product must contain no more than 6% pentane. Feed is liquid at 29 C. Reflu ratio is.7. The average enthalpy of vaporization for the miture is 3732 kj/kmol, its specific heat capacity is 2,36 kj/kgk. Use the ideal gas law for calculations. a) What are the molar flows of the products? b) What is the minimal number of plates? c) What is the load factor at the top and bottom, if the column diameter is.9 m? d) How much cooling water and atmospheric pressure heating steam is required if the cooling water can be heated up by no more than 5 C? (Answer: a) D = 35.39 kmol/h, W = 39.6 kmol/h, b) N min = 6, c) q =., T bp,top = 49 C, ρ G,top = 2.86 kg/m 3, V = 95.56 kmol/h =.675 m 3 /s, v G,top =.6 m/s, F top = Pa /2, T bp,bottom = 66 C, ρ G,bottom = 3.6 kg/m 3, V = 3.6 kmol/h =.796 m 3 /s, v G,bottom =.8 m/s, F bottom =.4 Pa /2, d) Q condenser = 3.55 6 kj/h, r G = 2256.685 kj/kg, m steam =.57 t/h, Q reboiler = 3.83 6 kj/h, m water Problem 7 = 6. t/h) By separating 5 kmol/h of a phenol metacresol miture containing 4 mole% phenol, products of 6 mole% purity must be obtained. Feed into the continuous distillation column is a : ratio liquid vapor miture, reflu ratio is 6.5. Use the ideal gas law for calculations. a) What are the mass flows and mass percent phenol contents of the products? b) How many theoretical plates are required for the separation and at which plate should the feed be introduced? c) How many real plates are required if the average plate efficiency is.8? d) What is the required height of the column, if the plates are 35 cm apart? e) What is the required diameter of the column, if the maimum allowable load factor value at the bottom of the column is. Pa /2? (Answer: a) D =.93 kmol/h = 83 kg/h, W = 3.7 kmol/h = 329 kg/h, D,phenol = 93.7 m/m%, W,phenol = 5.26 m/m%, N theo = 5, N feed = 9, N real = 8, H column = 6.3 m, T bp,bottom = 2 C, ρ G,bottom = 2.44 kg/m 3, v G,bottom =.74 m/s, A column,bottom =.84 m 2, D column,bottom =.484 m) Problem 8 2 kmol/h of a 5 mole% benzene toluene miture is separated on a continuous distillation column. Feed is liquid at 2 C, reflu ratio is 3.2. The distillate must contain at least 96 mole% benzene, the bottoms product must contain at least 95 mole% toluene. The average enthalpy of vaporization for the miture is 326 kj/kmol, its specific heat capacity is,8 kj/kgk. Use the ideal gas law for calculations. a) What are the molar flows of the products? b) What is the plate efficiency if the column contains real plates? 7
c) How much cooling water and.7 bar (above atmospheric pressure) heating steam is required, if the cooling water can be heated up by no more than 2 C? (Answer: a) D = 59.34 kmol/h, W = 6.66 kmol/h, b) q =.34, N theo = 9, η =.7, c) V = 249.23 kmol/h, Q condenser = 8 6 kj/h, r G = 274.25 kj/kg, m steam = 3.68 t/h, V = 29.3 kmol/h, Q reboiler = 9.3 6 kj/h, m water = t/h) Problem 9 9 kmol/h of a methanol water miture containing 6 mole% water is to be separated. Using a continuous distillation column, 95% of the methanol must be recovered in 9 mole% purity. Feed is a liquid vapor miture containing 6% liquid. Reflu ratio is 3. The average enthalpy of vaporization of the miture is 3644 kj/kmol. Use the ideal gas law for calculations. a) What is the minimal number of plates? b) How much cooling water and 2 C heating steam is required if the cooling water can be heated up by no more than 5 C? c) What is the required column diameter, if the maimum allowable load factor at the top of the column is.2 Pa /2? (Answer: a) N min = 4, b) D = 38 kmol/h, W = 52 kmol/h, w,methanol = 3.46 mol%, V = 29.56 kmol/h, Q condenser = 8 6 kj/h, r G = 222.675 kj/kg, m steam = 3.63 t/h, V = 67.56 kmol/h, Q reboiler = 6. 6 kj/h, m water = 97.4 t/h, c) T bp,top = 67 C, ρ G,top =. kg/m 3, v G,top =.4 m/s, A column,top =.3 m 2, D column,top =.45 m) Problem 2 In a packed column, kmol/h of a phenol metacresol miture containing 4 mole% phenol must be separated into 9 mole% phenol and 92 mole% cresol. Reflu ratio is 7. Feed is an 8% liquid vapor miture, introduced optimally. The eperimentally determined mass transfer coefficient is.59 mol/m 2 s. Column diameter is 23.4 cm, specific surface area of the packing is 2 m 2 /m 3. The allowable load factor at the top of the column is.2 Pa /2. Calculate the number and height of transfer units in the upper and lower sections! What is the required height of the column? (Answer: D =.39 kmol/h, V =.87 mol/s, T top = 83.5 C, ρ G,upper = 2.55 kg/m 3, v upper =.75 m/s, A column =.43 m 2, HTU y,upper =.7 m, V =.8 mol/s, HTU y,lower =.6 m, NTU y,upper = 6.928, NTU y,lower = 5.66, H upper =. m, H lower =.79 m, H =.89 m) Problem 2 5 kmol/h of a methanol water miture containing 45 mol% water is separated in a packed column. Both the distillate and the bottoms product must have 95 mole% purity. Reflu ratio is 6, feed is at boiling point. Column diameter is.4 m, specific surface area of the packing is 2 m 2 /m 3. Mass transfer coefficient is eperimentally determined to be.43 mol/m 2 s. a) Calculate the number and height of transfer units in the lower and upper sections! b) Calculate the height of the column! (Answer: a) NTU upper = 4.36, NTU lower =.86, D = 2.22 kmol/h, V = 5.56 kmol/h, HTU upper =.4 m, V = 5.56 kmol/h, HTU lower =.4 m, b) H column,upper =.74 m, H column,lower =.74 m, H column = 2.48 m) Problem 22 2 kmol/h of a pentane heane miture containing 4 mole% heane is to be separated by continuous distillation on a packed column. Distillate heane content is 5 mole%, bottoms product heane content 8
is 9 mole%. Reflu ratio is 5.8, feed is a : ratio vapor liquid miture. Column diameter is.3 m, specific surface area of the packing is 2 m 2 /m 3. The eperimentally determined mass transfer coefficient is.4 mol/m 2 s. a) Calculate the number and height of transfer units in the lower and upper sections! b) Calculate the height of the column! (Answer: a) NTU upper = 3.59, NTU lower = 2.32, D =.8 kmol/h, V = 8 kmol/h, HTU upper =.4 m, V = 7 kmol/h, HTU lower =.34 m, b) H column,upper =.4 m, H column,lower =.94 m, H column = 2.32 m) Problem 23 By continuous distillation in a packed column, 4 mol/h of a5 mole% phenol metacresol miture is separated. Phenol content in the distillate is 9 mole%, phenol content in the bottoms product is 5 mole%. Reflu ratio is 5, feed is liquid at boiling point. Column diameter is 5 cm, specific surface area of the packing is 2 m 2 /m 3. Column height is.7 m, feed is introduced m from the bottom. Calculate the height of transfer units in the upper and lower sections! (Answer: NTU upper = 6.78, NTU lower = 8.7, D = 2.22 kmol/h, HTU upper =. m, HTU lower =. m) Appendi Antoine constants The constants in the Antoine equation are determined by phase equilibrium measurements. When creating equilibrium diagrams using the Antoine equation and applying Raoult s and Dalton s laws, always consider the following: Raoult s and Dalton s laws can only be applied to ideal mitures. While during distillation, the gas phase can usually be considered ideal (Dalton s law is applicable), the liquid phase is often non-ideal (Raoult s law is not necessarily applicable). Thus, the method of calculation cannot be used to construct the equilibrium diagram of non-ideal mitures. Mitures with an azeotropic point are eamples of highly non-ideal mitures. The calculation method detailed below can be used for nearly ideal solutions: Using the Antoine equation, calculate the vapor pressures of the pure components at different temperatures, distributed evenly in the interval between the boiling points of the pure components. The boiling point of a pure component at a given pressure can also be calculated from the Antoine equation: p B A T C. Assuming that the vapor space contains only the vapors of the two components, the given total pressure can be epressed as the sum of the partial pressures: P p p2. If Raoult s law is applicable, then there is an eplicit relationship between partial pressure and the liquid phase mole fraction (inde refers to the more volatile component): p and p2 p 2. p From these equations, for a given total pressure, the mole fraction of the more volatile compound can P p2 be epressed at each chosen temperature:. p p Dalton s law also applies, thus the vapor phase mole fraction of the more volatile compound can be p p epressed: y. P P 2 9
The Antoine constants of pure components, found in databases and in literature describe the relationship between vapor pressure and temperature only in a certain pressure and temperature interval. Outside this interval, they cannot be used, or yield unreliable results. The Antoine constants have no dimensions themselves, but the units in which temperature must be substituted (K, C, F) and the units in which the calculated pressure is obtained (torr, Pa, bar stb.) is always specified. Antoine constants specified for different units can be converted among each other, based on the conversion factors of different units of pressure: pascal (Pa N/m 2 ) or bar (bar) technical atmosphere (at or kp/cm 2 ) physical atmosphere (atm) (torr) and (Hgmm) pounds square (psi) Pa 5.97 6 9.8692 6 7.56 3 45.4 6 bar.97.98692 75.6 4.54 at 98 66.5.98665.96784 735.56 4.223 atm 325.325.332 76 4.696 torr 33.322.3332-3.3595-3.358-3 9.337 3 psi 6.89476 68.948-3 7.37-3 68.46-3 5.75 lbf/in² per inch The following eample demonstrates converting Antoine constants specified in Hgmm and C into Antoine constants specified in Pa and K: p BHgmm, C AHgmm, C T C CHgmm, C Hgmm p Pa /33,322 Pa Hgmm A Hgmm, C A A Hgmm, C Hgmm, C B T C C log log Hgmm, C Hgmm, C 33,322 33,322 log p Pa/33,322 log p Pa B T K 273,5K thus: A 33,322 B Hgmm, C Hgmm, C C Hgmm, C log 33,322 log A p Pa/33,322 log p Pa Pa,K Pa,K T K 273,5K CHgmm, C T K CPa, K A Pa, K Hgmm, C log, B Pa, K BHgmm, C és C Pa, K CHgmm, C 273,5K. The following table lists the Antoine constants of some pure components near atmospheric pressure, as well as their atmospheric boiling points and molar masses. Pressure is specified in Hgmm. temperature is specified in C. A Hgmm,C B Hgmm, C Hgmm, C B C M (g/mol) T bp ( C) benzene 6.9565 2.3 22.79 78. 8. cycloheane 6.95333 343.94 29.38 92..6 cycloheanol 5.95583 777.36 9. 94. 6.7 ethanol 7.687 332.4 99.2 46. 78.3 ethylbenzene 6.94994 42.32 22.6 6.2 36.4 phenol 7.294 59.68 74.2.2 8.8 heptane 6.9338 268.64 26.95.2 98.4 heane 6.87772 7.53 224.37 86.2 68.7 2
i-butane 7.236 32. -274.7 58. -2. i-propanol 8.87829 2.33 252.64 6. 82.6 i-octane 6.885 257.84 22.74 4.3 99.2 methanol 8.897 582.27 239.73 32. 64.5 m-cresol (3-methyl-phenol) 6.7647 355.92 46.73 8 22.7 n-butane 6.7258 99.65 237. 58. -.4 octane 6.92373 355.3 29.52 4.3 25.7 pentane 6.87632 75.78 233.25 72. 36 propanol 7.757 44.63 98.85 6. 97.2 toluene 6.95464 344.8 29.48 92..6 water 8.73 73.63 233.43 8.. 2
Important properties of unordered packings Packing Material Specific weight (kg/m 3 ) Size (mm mm) Specific surface area (m 2 /m 3 ) Void volume (m 3 /m 3 ) F t factor (-) Raschigring Ceramic 795 65 2 2,8 25 25 3 36 95,67,73 58 55 57 35 35 4 4,76 95 535 5 5 5 98,77 65 575 7 7 7 72,77 37 Raschigring Metal 2,5 2,5 25 25 4 37 5 5 57 75 75 32 Berlsaddle Ceramic 78 64 2,5 2,5 25 25 545 26,65,68 24 Pall-ring Polypropylene 8 25 25 22,9 52 65 35 35 6,93 4 65 5 5,93 25 53 9 9 86,94 6 Pall-ring Metal 46 25 25 25,94 48 39 38 38 35,95 28 38 5 5 5,95 2 36 78,96 6 HY-PAKring Metal 34 224 25 25 5 5,96,97 42 8 28 75 75,97 5 Intalosaddle Ceramic 74 672 2,5 2,5 25 25 625 255,7,73 2 98 625 38 38 95,76 52 6 5 5 8,76 4 58 76 76 92,79 22 Super- Intalo Polypropylene 8 56,4 25 2,5,2 5 25,5 288 25,85,96 33 2 59,2 76 38 2,6 2,97 6 Super- Intalo Ceramic 625 595 25 2,5 5 25,79,8 6 3 22
Tellerett Poliprolilén 28 25 9,5 2 269,82 488 47 9 3 3 285,88 27 3 5 9 3 3 28,89 255 2 59 9 3 3 25,92 23 2 73 28 3 4 27,89 8 88 95 37 3 6 94,9 29 47 45 48 3 6 65,95 76 23