6.1a. Flash vaporization of a heptane-octane mixture.
A liquid mixture containing 50 mole % n-heptane (A), 50 mole % n-octane (B), at 303 K, is to be continuously flash-vaporized at a pressure of 1 atm to vaporize 30 mole % of the feed. What will be the composition of the vapor and liquid and the temperature in the separator if it behaves as an ideal stage?
Solution
From the program in Figure 6.3,
6.2a. Flash vaporization of a heptane-octane mixture.
A liquid mixture containing 50 mole % n-heptane (A), 50 mole % n-octane (B), at 303 K, is to be continuously flash-vaporized at a temperature of 350 K to vaporize 30 mole % of the feed. What will be the composition of the vapor and liquid and the pressure in the separator if it behaves as an ideal stage?
Solution
From the program in Figure 6.3,
6.3d. Flash vaporization of a ternary mixture.
Modify the Mathcad¨ program of Figure 6.3 for ternary mixtures. Test your program with the data presented in Example 6.2 for a mixture of benzene (A), toluene (B), and o-xylene (C). Critical temperatures and pressures,and the parameters of the Wagner equation for estimating vapor pressure (equation 6-5) are included in the following table (Reid, et al., 1987).
Component Tc, K Pc, bar A B C D
benzene 562.2 48.9 Ð 6.983 1.332 Ð 2.629 Ð 3.334
toluene 591.8 41.0 Ð 7.286 1.381 Ð 2.834 Ð 2.792
o-xylene 630.3 37.3 Ð 7.534 1.410 Ð 3.110 Ð 2.860
Solution
Parameters of the Wagner equation, A = benzene, B, toluene, C = o-xylene:
Initial estimates
6.4d. Flash vaporization of a ternary mixture.
Consider the ternary mixture of Example 6.2 and Problem 6.3. Estimate the temperature, and composition of the liquid and vapor phases when 60% of the mixture has been vaporized at a constant pressure of 1 atm.
Solution
6.5d. Flash vaporization of a ternary mixture.
Consider the ternary mixture of Example 6.2 and Problem 6.3. It is desired to recover in the vapor 75% of the benzene in the feed, and to recover in the liquid 70% of the o-xylene in the feed. Calculate the temperature, pressure, fraction of the feed vaporized, and the concentration of the
liquid and gas phases
Solution
6.6b.Batch distillation of a heptane-octane mixture.
Repeat the calculations of Example 6.3, but for 80 mole % of the liquid distilled.
Solution
Batch distillation of a mixture of heptane and octane
Initial estimate
6.8a. Binary batch distillation with constant relative volatility.
Consider the binary batch distillation of Example 6.3. For this system, n-heptane with n-octane at 1 atm, the average relative volatility is a = 2.16 (Treybal, 1980). Using equation (6-102) derived in Problem 6.7, compute the composition of the residue after 60 mole% of the feed is batch-distilled.
Solution
Initial estimate:
6.9b. Binary batch distillation with constant relative volatility.
Consider the binary batch distillation of Example 6.3. For this system, n-heptane with n-octane at 1 atm, the average relative volatility is a = 2.16 (Treybal, 1980). The mixture will be batch-distilled until the average concentration of the distillate is 65 mole % heptane. Using equation (6-102) derived in Problem 6.7, compute the composition of the residue, and the fraction of the feed that is distilled.
Solution
Initial estimates:
6.10b. Mixtures of light hydrocarbons: m-value correlations.
What is the bubble point of a mixture that is 15 mole % isopentane, 30 mole % n-pentane, and 55 mole % n-hexane? The pressure is 1.0 atm.
Solution
Initial estimate
6.11c. Mixtures of light hydrocarbons: m-value correlations.
A solution has the following composition, expressed as mole percent: ethane, 0.25 %; propane, 25 %; isobutane, 18.5 %; n-butane, 56 %; isopentane, 0.25 %. In the following, the pressure is 10 bars. Use equation (6-103) and Table 6.4 to calculate equilibrium distribution coefficients.
a) Calculate the bubble point
Solution
Initial estimate
b) Calculate the dew point
Solution
Initial estimate
c) The solution is flash-vaporized to vaporize 40 mol % of the feed. Calculate the composition of the products.
Solution
Initial estimates
Check!
6.12b. Binary batch distillation with constant relative volatility.
A 30 mole % feed of benzene in toluene is to be distilled in a batch operation. A product having an average composition of 45 mole % benzeneis to be produced. Calculate the amount of residue left, assuming that a = 2.5 and F = 100 moles.
Solution
Initial estimates:
6.13b. Batch distillation of a mixture of isopropanol in water.
A mixture of 40 mole % isopropanol in water is to be batch-distilled at 1 atm until 70 mole % of the charge has been vaporized. Calculate the composition of the liquid residue remaining in the still pot, and the average composition of the collected distillate. VLE data for this system, in mole fraction of isopropanol, at 1 atm are (Seader and Henley, 1998):
T, K 366 357 355.1 354.3 353.6 353.2 353.3 354.5
y 0.220 0.462 0.524 0.569 0.593 0.682 0.742 0.916
x 0.012 0.084 0.198 0.350 0.453 0.679 0.769 0.944
Composition of the azeotrope is x = y = 0.685; boiling point of the azeotrope = 353.2 K.
Solution
Initial estimate
6.15a. Continuous distillation of a binary mixture of constant relative volatility.
For continuous distillation of a binary mixture of constant relative volatility, Fenske equation (6-58) can be used to estimate the minimum number of equilibrium stages required for the given separation, Nmin.
Use Fenske equation to estimate Nmin for distillation of the benzene-toluene mixture of Example 6.4. Assume that, for this system at 1 atm, the relative volatility is constant at a = 2.5.
Solution
6.16a. Continuous distillation of a binary mixture of constant relative volatility.
For continuous distillation of a binary mixture of constant relative volatility, the minimum reflux ratio can be determined analytically from the following equation (Treybal, 1980):
(6-105)
Use equation (6-105) to estimate Rmin for distillation of the benzene-toluene mixture of Example 6.4. Assume that, for this system at 1 atm, the relative volatility is constant at a = 2.5.
Solution
Initial estimate
6.17b. Continuous rectification of a water-isopropanol mixture.
A water-isopropanol mixture at its bubble point containing 10 mole % isopropanol is to be continuously rectified at atmospheric pressure to produce a distillate containing 67.5 mole % isopropanol. Ninety-eight percent of the isopropanol in the feed must be recovered. VLE data are given in Problem 6.13. If a reflux ratio of 1.5 times the minimum is used, how many theoretical stages will be required:
(a) If a partial reboiler is used?
Solution
6.24c. A distillation-membrane hybrid for ethanol dehydration.
Many industrially important liquid systems are difficult or impossible to separate by simple continuous distillation because the phase behavior contains an azeotrope, a tangent pinch, or an overall low relative volatility. One solution is to combine distillation with one or more complementary separation technologies to form a hybrid. An example of such a combination is the dehydration of ethanol using a distillation-membrane hybrid.
In a given application, 100 moles/s of a saturated liquid containing 37 mole % ethanol and 63 mole % water must be separated to yield a product which is 99 mole % ethanol, and a residue containing 99 mole % water. The solution will be fed to a distillation column operating at atmospheric pressure, with a partial reboiler and a total condenser. The reflux ratio will be 1.5 the minimum. The distillate will enter a membrane with parameters am = 70 and q = 0.6. The membrane boosts the concentration so that the permeate stream is the ethanol-rich product (xP = 0.99). The retentate stream is returned as a saturated liquid to the column to the tray at the nearest liquid concentration.
a) Calculate the molar flow rate of the product and of the residue.
Solution
Initial estimates:
b) Calculate the molar flow rate and composition of the distillate coming out of the column.
Solution
Initial estimates
6.26b. Fenske-Underwood-Gilliland method.
A distillation column has a feed of 100 kmoles/h. The feed is 10 mole % LNK, 55 mole % LK, and 35 mole % HK and is a saturated liquid. The reflux ratio is 1.2 the minimum. We desire 99.5 % recovery of the light key in the distillate. The mole fraction of the light key in the distillate should be 0.75. Use the FUG approach to estimate the number of ideal stages required and the optimal location of the feed-stage. Equilibrium data:
aLNK = 4.0 aLK = 1.0 aHK = 0.75
Solution
Kilomoles in distillate:
Kilomoles in bottoms:
Determine minimum reflux: Saturated liquid, q = 1
Initial estimate
Determine number of ideal stages at R = 1.2 Rmin: Gilliland correlation
Initial estimate
Kirkbride equation:
Initial estimate:
Feed at stage 11
6.27b. Fenske-Underwood-Gilliland method.
One hundred kmoles/h of a ternary bubble-point mixture to be separated by distillation has the following composition:
Component Mole fraction Relative volatility
A 0.4 5
B 0.2 3
C 0.4 1
a) For a distillate rate of 60 kmoles/h, five theoretical stages, and total reflux, calculate the distillate and bottoms composition by the Fenske equation.
Solution
Initial estimates:
b) Using the separation in part a) for components A and C, determine the minimum reflux ratio by the Underwood equation.
Solution
Initial estimate:
Initial estimate:
Initial estimate:
c) For a reflux ratio of 1.2 times the minimum, determine the number of theoretical stages required, and the optimum feed location.
Solution
Initial estimate
Kirkbride equation:
Initial estimate:
Feed at stage 5
6.35c Flash Calculations: the Rachford-Rice Method for Ideal Mixtures.
a) Show that the problem of flash vaporization of a multicomponent ideal mixture can be reformulated as suggested by Rachford and Rice (Doherty and Malone, Conceptual Design of Distillation Systems, McGraw-Hill, New York, NY, 2001):
b) Solve Example 6.2 using the Rachford-Rice method.
Solution
Initial estimate: