Greek letters
(2-70) This vapor velocity is the maximum for this existing drum, since it will give a linear vapor velocity equal
9. Use existing flash drums for a new separation problem
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Homework
A. Discussion Problems
A1. In Figure 2-9 the feed plots as a two-phase mixture, whereas it is a liquid before introduction to the flash chamber. Explain why. Why can’t the feed location be plotted directly from known
values of TF and z? In other words, why does hF have to be calculated separately from an equation such as Eq. (2-9b)?
A2. Can weight units be used in the flash calculations instead of molar units?
A3. Explain why a sequential solution procedure cannot be used when Tfeed is specified for a flash drum.
A4. In the flash distillation of salt water, the salt is totally nonvolatile (this is the equilibrium
statement). Show a McCabe-Thiele diagram for a feed water containing 3.5 wt % salt. Be sure to plot weight fraction of more volatile component.
A5. Develop your own key relations chart for this chapter. That is, on one page summarize everything you would want to know to solve problems in flash distillation. Include sketches, equations, and key words.
A6. In a flash drum separating a multicomponent mixture, raising the pressure will:
a. increase the drum diameter and increase the relative volatilities.
b. increase the drum diameter and cause no change to the relative volatilities.
c. increase the drum diameter and decrease the relative volatilities.
d. not change the drum diameter but increase the relative volatilities.
e. not change the drum diameter and not change the relative volatilities.
f. not change the drum diameter but decrease the relative volatilities.
g. decrease the drum diameter and increase the relative volatilities.
h. decrease the drum diameter and not change to the relative volatilities.
i. decrease the drum diameter and decrease the relative volatilities.
A7.
a. What would Figure 2-2 look like if we plotted y2 vs. x2 (i.e., plot less volatile component mole fractions)?
b. What would Figure 2-3 look like if we plotted T vs. x2 or y2 (less volatile component)?
c. What would Figure 2-4 look like if we plotted H or h vs. y2 or x2 (less volatile component)?
A8. For a typical straight-chain hydrocarbon, does:
a. K increase, decrease, or stay the same when temperature is increased?
b. K increase, decrease, or stay the same when pressure is increased?
c. K increase, decrease, or stay the same when mole fraction in the liquid phase is increased?
d. K increase, decrease, or stay the same when the molecular weight of the hydrocarbon is increased within a homologous series?
Note: It will help to visualize the DePreister chart in answering this question.
A9. In the vapor-liquid equilibrium data for methanol-water, if the methanol vapor mole fraction is 0.60, what is the methanol liquid mole fraction?
A10. Is there an azeotrope in the methanol-water system at a pressure of 1.0 atmospheres?
A11. The equilibrium K value is usually defined as
a. K = y/x, where y and x are weight fractions of the component in the vapor and liquid phases, respectively.
b. K = x/y, where x and y are weight fractions of the component in the liquid and vapor phases, respectively.
c. K = y/x, where y and x are mole fractions of the component in the vapor and liquid phases,
respectively.
d. K = x/y, where x and y are mole fractions of the component in the liquid and vapor phases, respectively.
A12. In a sequential solution procedure for flash distillation,
a. the mass balances, equilibrium relationships, and energy balances are solved simultaneously.
b. the mass balances and equilibrium relationships are solved first, and then the energy balance is solved.
c. the energy balance is solved first, and then the mass balances and equilibrium relationship are solved.
A13. Calculations are simpler for multicomponent flash distillation if the feed flow rate and mole fractions of the feed are specified plus
a. the drum pressure and feed temperature.
b. the drum temperature and feed temperature.
c. the drum temperature and the drum pressure.
d. the feed temperature and feed pressure.
e. all of the above; they are all equally difficult.
A14. The Rachford-Rice equation,
a. has excellent convergence properties for flash distillation.
b. was derived from the mass balances, equilibrium relationships, and energy balances.
c. is only useful for binary flash distillation.
d. all of the above.
e. none of the above.
A15. Use the DePriester chart:
a. What is the K value of propane at 240 kPa and 25°C?
b. What is the normal boiling point of n-pentane?
A16. Flash distillation is usually operated adiabatically. Where does the energy to vaporize part of the feed come from?
B. Generation of Alternatives
B1. Think of all the ways a binary flash distillation problem can be specified. For example, we have usually specified F, z, Tdrum, pdrum. What other combinations of variables can be used? (I have over 20.) Then consider how you would solve the resulting problems.
B2. An existing flash drum is available. The vertical drum has a demister and is 4 ft in diameter and 12 ft tall. The feed is 30 mol% methanol and 70 mol% water. A vapor product that is 58 mol%
methanol is desired. We have a feed rate of 25,000 lbmol/h. Operation is at 1 atm pressure. Since this feed rate is too high for the existing drum, what can be done to produce a vapor of the desired composition? Design the new equipment for your new scheme. You should devise at least three alternatives. Data are given in Problem 2.D1.
B3. In principle, measuring VLE data is straightforward. In practice, actual measurement may be very difficult. Think of how you might do this. How would you take samples without perturbing the system? How would you analyze for the concentrations? What could go wrong? Look in your thermodynamics textbook for ideas.
C. Derivations
C1. Determine the effect of pressure on the temperature, separation and diameter of a flash drum.
C2. Solve the Rachford-Rice equation for V/F for a binary system.
C3. Assume that vapor pressure can be calculated from the Antoine equation and that Raoult’s law can be used to calculate K values. For a binary flash system, solve for the drum pressure if drum temperature and V/F are given.
C4. Derive Eq. (2-24) and show that it is correct.
C5. Choosing to use V/F to develop the Rachford-Rice equation is conventional but arbitrary. We could also use L/F, the fraction remaining liquid, as the trial variable. Develop the Rachford-Rice equation as f(L/F).
C6. In flash distillation a liquid mixture is partially vaporized. We could also take a vapor mixture and partially condense it. Draw a schematic diagram of partial condensation equipment. Derive the equations for this process. Are they different from flash distillation? If so, how?
C7. Plot Eq. (2-40) vs. V/F for Example 2-2 to illustrate that convergence is not as linear as the Rachford-Rice equation.
C8. Show how to use a temperature composition diagram to solve a binary flash distillation problem when the drum temperature, feed mole fraction, drum pressure, and feed rate are specified. Show how to determine x, y, L, and V.
C9. For a vapor-liquid-liquid flash distillation, derive Eqs. (2-62) and (2-63) and the equations that allow calculation of all the mole fractions once V/F and Lliquid_1/F are known.
D. Problems
*Answers to problems with an asterisk are at the back of the book.
D1.* We are separating a mixture of methanol and water in a flash drum at 1 atm pressure. Equilibrium data are listed in Table 2-7.
a. Feed is 60 mol% methanol, and 40% of the feed is vaporized. What are the vapor and liquid mole fractions and flow rates? Feed rate is 100 kmol/h.
b. Repeat part a for a feed rate of 1500 kmol/h.
c. If the feed is 30 mol% methanol and we desire a liquid product that is 20 mol% methanol, what V/F must be used? For a feed rate of 1000 lbmol/h, find product flow rates and compositions.
d. We are operating the flash drum so that the liquid mole fraction is 45 mol% methanol. L = 1500 kmol/h, and V/F = 0.2. What must the flow rate and composition of the feed be?
e. Find the dimensions of a vertical flash drum for Problem 2.D1c.
Data: ρw = 1.00 g/cm3, ρm,L = 0.7914 g/cm3, MWw = 18.01, MWm = 32.04. Assume vapors are ideal gas.
f. If z = 0.4, p = 1 atm, and Tdrum = 77°C, find V/F, xm, and ym.
g. If F = 50 mol/h, z = 0.8, p = 1 atm, and ym = 0.892 mole fraction methanol, find V, L, and xm. Table 2-7. Vapor-liquid equilibrium data for methanol water (p = 1 atm) (mol%)
D2.* Two flash distillation chambers are hooked together as shown in the diagram. Both are at 1 atm pressure. The feed to the first drum is a binary mixture of methanol and water that is 55 mol%
methanol. Feed flow rate is 10,000 kmol/h. The second flash drum operates with (V/F)2 = 0.7 and the liquid product composition is 25 mol% methanol. Equilibrium data are given in Table 2-7.
a. What is the fraction vaporized in the first flash drum?
b. What are y1, y2, x1, T1, and T2?
D3. We are separating a mixture of methanol and water in a flash drum at 1.0 atm pressure. Use the equilibrium data listed in Table 2-7. Feed rate is 10.0 kmol/h.
a. The feed is 40 mol% methanol and 60% of the feed is vaporized. Find mole fractions and flow rates of vapor and liquid products. Estimate the temperatures by linear interpolation for both vapor and liquid products.
b. The feed is 40 mol% methanol, the product temperatures are both 78.0°C. Find the mole fractions of liquid and vapor products and V/F.
c. We desire a vapor product that is 80 mol% methanol and want to operate at V/F = 0.3. What must the feed composition be?
D4. We have a mixture that is 20 mol% propane, 35 mol% n-butane, and 45 mol% n-hexane. If a flash
drum operates at 400 kPa, what is the highest temperature at which the flash drum can operate and still have vapor and liquid present? Use the DePriester chart for equilibrium.
D5. We have a feed that is a binary mixture of methanol and water (55.0 mol% methanol) that is sent to a system of two flash drums hooked together. The vapor from the first drum is cooled, which partially condenses the vapor, and then is fed to the second flash drum. Both drums operate at a pressure of 1.0 atm and are adiabatic. The feed rate to the first drum is 1000 kmol/h. We desire a liquid product from the first drum that is 30.0 mol% methanol (x1 = 0.30). The second drum operates at a fraction vaporized of (V/F)2 = 0.25. The equilibrium data are in Table 2-7.
a. Sketch the process labeling the different streams.
b. Find the following for the first drum: vapor mole fraction y1, fraction vaporized (V/F)1, and vapor flow rate V1.
c. Find the following for the second drum: vapor mole fraction y2, liquid mole fraction x2, and vapor flow rate V2.
D6. A feed that is 45.0 mol% n-butane, 35.0 mol% n-pentane, and 20.0 mol% n-hexane is fed at a rate of 1.0 kmol/min to a flash drum operating at 50°C and 200 kPa. Find V/F, liquid mole fractions and vapor mole fractions. Use the DePriester charts.
D7. A flash drum is separating methane from propane at 0°C and 2500 kPa. The feed is 30.0 mol%
methane and 70.0 mol% propane. Find V/F, y and x. Use the results of Problem 2.C2. Use the DePriester chart for K values.
D8.* You want to flash a mixture with a drum pressure of 2 atm and a drum temperature of 25°C. The feed is 2000 kmol/h. The feed is 5 mol% methane, 10 mol% propane, and the rest n-hexane. Find the fraction vaporized, vapor mole fractions, liquid mole fractions, and vapor and liquid flow rates. Use DePriester charts.
D9.* We wish to flash distill an ethanol-water mixture that is 30 wt % ethanol and has a feed flow of 1000 kg/h. Feed is at 200°C. The flash drum operates at a pressure of 1 kg/cm2. Find: Tdrum, wt frac of liquid and vapor products, and liquid and vapor flow rates.
D10. We have a mixture that is 35 mol% n-butane with unknown amounts of propane and n-hexane. We are able to operate a flash drum at 400 kPa and 70°C with xC6 = 0.7. Find the mole fraction of n-hexane in the feed, zC6, and the value of V/F.
D11. A vapor stream which is 40.0 mol% ethanol and 60.0 mol% water is partially condensed and sent to a flash drum operating at 1.0 atm.
a. What is the highest vapor mole fraction which can be produced?
b. If 60.0 % of the feed is liquefied, what are the outlet mole fractions of liquid and vapor?
D12. Find the dimensions (htotal and D) for a horizontal flash drum for Problem 2.D1c. Use htotal/D = 4.
D13. The phenol-cresol system has an approximately constant relative volatility at αp–c = 1.76. Phenol
is more volatile. At equilibrium, if cresol mole fraction in the liquid is 0.3, what is the mole fraction of cresol in the vapor?
D14. We are feeding 100 kmol/h of a mixture that is 30 mol% n-butane and 70 mol% n-hexane to a flash drum. We operate with V/F = 0.4 and Tdrum = 100°C. Use Raoult’s law to estimate K values from vapor pressures. Use Antoine’s equation to calculate vapor pressure,
where VP is in mm Hg and T is in °C.
n-butane: A = 6.809, B = 935.86, C = 238.73 n-hexane: A = 6.876, B = 1171.17, C = 224.41 Find pdrum, xi and yi
D15.* We have a flash drum separating 50 kmol/h of a mixture of ethane, isobutane, and n-butane. The ratio of isobutane to n-butane is held constant at 0.8 (that is, ziC4/znC4 = 0.8). The mole fractions of all three components in the feed can change. The flash drum operates at a pressure of 100 kPa and a temperature of 20°C. If the drum is operating at V/F = 0.4, what must the mole fractions of all three components in the feed be? Use Figure 2-11 or 2-12 or Eq. (2-30).
D16. A feed that is 50 mol% methane, 10 mol% n-butane, 15 mol% n-pentane, and 25 mol% n-hexane is flash distilled. F = 150 kmol/h. Drum pressure = 250 kPa, drum temperature = 10°C. Use the DePriester charts. Find V/F, xi, yi, V, L.
D17. We are separating a mixture of acetone (MVC) from ethanol by flash distillation at p = 1 atm.
Equilibrium data are listed in Problem 4.D7. Solve graphically.
a. 1000 kmol/day of a feed that is 70 mol% acetone is flash distilled. If 40% of the feed is vaporized, find the flow rates and mole fractions of the vapor and liquid products.
b. Repeat part a for a feed rate of 5000 kmol/day.
c. If feed is 30 mol% acetone, what is the lowest possible liquid mole fraction and the highest possible vapor mole fraction?
d. If we want to obtain a liquid product that is 40 mol% acetone while flashing 60% of the feed, what must the mole fraction of the feed be?
D18.* We wish to flash distill a feed that is 10 mol% propane, 30 mol% butane, and 60 mol% n-hexane. Feed rate is 10 kmol/h, and drum pressure is 200 kPa. We desire a liquid that is 85 mol%
n-hexane. Use DePriester charts. Find Tdrum and V/F. Continue until your answer is within 0.5°C of the correct answer. Note: This is a single trial and error, not a simultaneous mass and energy balance convergence problem.
D19.* A flash drum operating at 300 kPa is separating a mixture that is fed in as 40 mol% isobutane, 25% n-pentane, and 35% n-hexane. We wish a 90% recovery of n-hexane in the liquid (that is, 90% of the n-hexane in the feed exits in the liquid product). F = 1000 kmol/h. Find Tdrum, xj, yj, V/F.
D20. A flash drum operating at a pressure of 2.0 bar and a temperature of 0°C is separating a mixture of ethane (E), n-butane (B), and n-pentane (P). The fraction vaporized is V/F = 0.25. The feed mole fraction of ethane is zE = 0.20. Find the mole fraction of n-butane, zB, in the feed. Use the DePriester chart.
D21. We wish to flash distill a feed that is 55 mol% ethane and 45 mol% n-pentane. The drum
operates pdrum = 700 kPa and Tdrum = 30°C. Feed flow rate is 100,000 kg/h.
a. Find V/F, V, L, liquid mole fraction, vapor mole fraction.
b. Find the dimensions in metric units required for a vertical flash drum. Assume the vapor is an ideal gas to calculate vapor densities. Use DePriester chart for VLE. Be careful of units.
Arbitrarily pick htotal/D = 4.
MWethane = 30.07, MWpentane = 72.15
Liquid densitites: ρE = 0.54 g/ml (estimated), ρP = 0.63 g/ml
D22. A flash drum is separating a feed that is 50 wt % n-propanol and 50 wt % isopropanol with F=100 kmol/h. Tdrum = 90°C and pdrum = 101.3 kPa. Use the Rachford-Rice equation to find V/F.
Note: This does not have to be trial and error. Then find y and x. Determine K values from Raoult’s law using Antoine equation for vapor pressure. Watch your units.
The Antoine constants are (Dean, 1985):
n-propanol: A = 7.84767, B = 1499.2, C = 204.64 isopropanol: A = 8.11778, B = 1580.9, C = 219.61 where the form of the Antoine equation is
D23. We wish to flash distill 1000 kmol/h of a feed that is 40 mol% methane, 5 mol% ethylene, 35%
mole ethane, and 20 mol% n-hexane. Drum pressure is 2500 kPa and drum temperature is 0°C.
Use the DePriester charts. Find V/F, xi, yi, V, F.
D24. We plan to separate a mixture of propane and n-hexane at 300 kPa.
a. Using the data in the DePriester charts, plot y propane versus x propane for this mixture at this pressure.
b. If the feed is 30 mol% propane, and 40 mol% of the feed is vaporized, what are the liquid and vapor mole fractions, and what is the drum temperature? Solve graphically.
b. If the feed is 30 mol% propane, and 40 mol% of the feed is vaporized, what are the liquid and vapor mole fractions, and what is the drum temperature? Solve graphically.