Problem 1. Hydrogen gas at a pressure of 1.25 bar is contained in a thick-walled neoprene rubber sphere which has inner and outer radii of 70 mm and 80 mm, respectively. The concentration of hydrogen at the outer surface of the sphere is negligible and leakage is so small that steady-state conditions can be assumed to occur for a long time. The solubility of hydrogen in rubber is 2.37 x 10-3 kmol m-3 (bar)-1 and the diffusivity is 1.8 x 10-10 m2 s-1.
Calculate the rate at which hydrogen escapes from the sphere. (Assume the inner surface of rubber is saturated with hydrogen.)
Problem 2. (a) Ammonia gas is being absorbed by water in a wetted-wall column. At one level of the column, the following data applies:
gas-phase mass transfer coefficient 5.22 x 10-9 kmol m-2 s-1 Pa-1
liquid-phase mass transfer coefficient 3.88 x 10-5 m
Henry's constant 0.955 kPa (kmol m-3)-1.
Estimate the overall mass transfer coefficient KL.
(b) What is the ratio of the individual mass transfer resistances in Question 2 (a)?
(c) Use the following additional information to find the mass transfer flux in the column:
mole fraction of ammonia in liquid* 1.351 x 10-3
mole fraction of ammonia in gas* 0.065
total pressure of system 1.013 bar
mole mass of ammonia 17
*Note: these values will need to be converted to concentrations in kmol m-3.
(d) What is the partial pressure of the ammonia gas at the gas/liquid interface?
(e) What is the molar concentration of the ammonia in the liquid at the interface?
Problem 3. Based on your experience or from reference books, choose a real industrial example of mass transfer which uses a column as its contacting device. Suggest reasons why the particular column was used in preference to other designs.
You will need two sheets of graph paper to complete this TMA.
Problem 4. (a) Assuming that Raoult's law applies to all possible mixtures of two components, 'A' and 'B', plot a "pressure/composition" diagram at constant temperature T for the full range of mixtures from the data below. The diagram should show how the partial pressures of each component and the total pressure varies with composition.
Data:
Pure vapour pressure of 'A' at temperature T = 67 kPa
Pure vapour pressure of 'B' at temperature T = 20 kPa
(b) Using your diagram in (a), state the partial pressures and the total pressure at the reference temperature, of a mixture of 'A' and 'B' having 0.4 mole fraction 'A'.
(c) Confirm these values using Raoult's law equation.
(d) State what is meant by an 'Ideal liquid mixture'.
(e) From an internet search, state what is meant by
(i) 'negative deviation from ideality'.
(ii) 'positive deviation from ideality'.
Problem 5. A mixture of octane and nonane containing 0.70 mole fraction (m.f.) octane, at its boiling point, is to be continuously separated in a distillation column. The top product is to have a composition of 0.98 m.f. octane and the bottom product must be no richer than 0.05 m.f. octane.
The reflux ratio is set at 3 and the equilibrium data is given below.
| xoct |
0 |
0.1 |
0.2 |
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.9 |
1 |
| yoct |
0 |
0.18 |
0.33 |
0.46 |
0.57 |
0.67 |
0.75 |
0.82 |
0.89 |
0.95 |
1 |
(a) Determine the number of theoretical plates required to perform the operation.
(b) State which plate the feed should be introduced onto.
(c) (i) What effect would altering the reflux ratio have on the number of plates required?
(ii) In an actual industrial column, the number of plates is fixed at the design stage. In this case, what effect would a change in the reflux ratio have on the column's operation and how can this effect be used as a means of control?
(d) If a packed column were to be used, determine the height of packing required, assuming an H.E.T.P. of 1.2 m.
Problem 6. (a) Write brief notes to explain what is meant by the following distillation techniques:
(i) batch distillation
(ii) continuous distillation
(iii) simple (or single stage) distillation
(iv) fractional (or multi-stage) distillation.
(b) Select distillation techniques for the separation of the following mixtures, giving reasons for the techniques chosen.
(i) 50 kg of a mixture of A (boiling point 160°C) and B (boiling point 405°C) where B is sensitive to heat.
(ii) 500 kgh-1 of a mixture of C (boiling point 75°C) and D (boiling point 85°C).
Problem 7. 100 kmol of the mixture, whose equilibrium diagram is shown in FIGURE 1, is to be batch fractionally distilled until the contents of the still have been reduced to 0.20 mole fraction T. The still initially contains 0.70 mole fraction T. The column to be used has 3 theoretical stages and will be operated with a fixed reflux ratio of 3. Determine:
(a) the amount of bottom product produced
(b) the amount and composition of the overall top product removed.
Hint: you will need to choose final distillate values between 0.6 and 0.99 mole fraction T.
FIG. 1
Problem 8. (a) State how the solubility of a gas changes with temperature and pressure.
(b) Sketch, on the same axes, equilibrium curves for each of the following gases dissolved in water, indicating clearly the curve for each material:
(i) hydrogen
(ii) ammonia.
(c) State how partial pressure is related to solution concentration at equilibrium for:
(i) an ideal solution
(ii) a non-ideal solution at low concentrations.
(d) (i) State two uses of equilibrium data in gas absorption.
(ii) Briefly explain how the data is used.
Problem 9. (a) What is meant by diffusion? What will cause diffusion to occur?
(b) (i) Explain what is meant by 'stagnant films' and how they arise.
(ii) How do they affect the absorption process?
Problem 10. (a) State the two mathematical formulas for the rates of diffusion across gas and liquid films in gas absorption.
(b) How are these modified in the overall rate of absorption equations?
(c) (i) Explain why the liquid film controls the rate of gas absorption when the gas being absorbed is relatively insoluble.
(ii) How is the overall rate of absorption maximised in this case?
(d) Suggest two pieces of equipment that could be used to maximise the rate of absorption of an insoluble gas.
Problem 11. (a) A coal gas is to be 'freed' of 95% of its benzene content (a contaminant) by countercurrent washing with an oil in a plate column. The original amount of benzene vapour is 1%. The equilibrium data at the conditions of the absorption process is:
| X |
0.005 |
0.02 |
0.04 |
0.06 |
0.08 |
0.1 |
0.12 |
| Y |
0.0006 |
0.0023 |
0.0047 |
0.0071 |
0.0094 |
0.0118 |
0.0141 |
NOTE: X and Y are mole ratios.
If the liquid to gas ratio used is to be 1.5 times the minimum, find the number of theoretical stages required for the system to perform the required duty.
(b) Within the lessons of this module, a method of calculating the height of packing for a given separation was given. This cannot be used with the information available in (a).
(i) What other information would be required for the height of packing in ye calculated?
(ii) Describe a simpler way of estimating the height of packing required for a given duty, stating the additional information required in this case.
(iii) What is the main problem that occurs in packed columns which will affect the performance of a column of this estimated height?
NOTE: You may need to refer to your own experience or standard reference books to answer parts of the following questions.
Problem 12. (a) By means of well labelled sketches and brief notes describe the construction and operating principles of packed columns.
(b) State five desirable properties of column packing materials.
(c) Sketch and describe two types of packing in common industrial use.
(d) State two materials used in the manufacture of column packings giving one advantage and one disadvantage for each.
Problem 13. (a) Compare the performance of bubble cap, sieve and valve plates (of about the same size). Your answers should make reference to the following:
• efficiency
• cost
• operation
• maintenance
• capacity
and any other factors you think might be relevant and important.
(h) Name two types of packing arrangement used in pact:ed columns, stating one advantage and one disadvantage for each type compared to the other.
Problem 14. (a) Define the following terms used in extraction, quoting an appropriate industrial example in each case:
(i) solute
(ii) solvent
(iii) extract
(iv) raffinate.
(b) Draw block diagrams to illustrate the following methods of extraction:
(i) simple multiple contact
(ii) countercurrent multiple contact.
Problem 15. (a) State three factors which influence the effectiveness of:
(i) solid-liquid extraction
(ii) liquid-liquid extraction.
(b) In each case, explain how your chosen factors influence the effectiveness of extraction.
Problem 16. (a) 670 kg h-1 of a slurry containing 120 kg solute and 50 kg solvent is to be extracted. The maximum permitted amount of solute in the final raffinate is 5 kg h-1. When a simple mixer-settling unit is used to separate extract and raffinate, the amount of solvent retained by the solid is 50 kg. Assuming perfect mixing and a constant ratio of solvent in extract and raffinate, determine the number of stages and the strength of the total extract for each of the following conditions:
(i) Simple multiple contact is used for the extraction with a solvent addition of 100 kg h-1 per stage
(ii) The same total amount of solvent as in (i) is provided in countercurrent operation
(iii) Half the total amount of solvent in (i) is used in countercurrent operation.
(b) Which of these methods would you recommend for the extraction? Give three reasons for your choice.
(c) Suggest two alternative ways of carrying out the extraction and the circumstances under which they might be used.
Problem 17. 40 kg s-1 of heptane is to be used to extract sunflower oil from sunflower seeds in a counter-current process which uses a centrifuge to separate extract and raffinate. 100 kg s-1 of sunflower seeds which contain 40% oil are to be extracted until the final raffinate contains less than 2% by mass of oil. The ratio of solution to insoluble solids in the raffinate is 1:4 by mass and no insoluble solids are present in the extract. There is sufficient solvent to ensure all the oil is dissolved.
Determine:
(a) the composition and amount of the final extract and raffinate
(b) the number of stages required.
A blank triangular diagram is provided in
Fig 1:
Problem 18. 1000 kg h-1 of a 25% dioxane in water solution are to be extracted using benzene as the solvent (at concentrations quoted in this example, benzene is totally immiscible with water). The extraction can either be carried out:
(i) using 500 kg h-1 benzene at each stage of simple multiple contact or
(ii) using 1500 kg h-1 benzene in countercurrent multiple contact.
Determine and specify the number of stages, in each case, required to extract 95% of the original dioxane. The equilibrium data is given as follows:
| x(g/kg water) |
48 |
100 |
168 |
191 |
257 |
312 |
350 |
| y(g/kg benzene) |
45 |
91 |
178 |
214 |
315 |
394 |
451 |
Problem 19. The table overleaf shows experimentally determined extract and raffinate concentrations of ethanoic acid (Solute A) in water (original solvent S) and an extracting solvent, L, called methyl isobutylketone at 20°C. (Results are rounded off to whole percentages.)
Note: methyl isobutylketone is abbreviated to MIBK and ethanoic acid to HAc¯
|
EXTRACT WEIGHT %
|
Mixture
|
RAFFINATE WEIGHT %
|
|
|
MIBK (L)
|
Water (S)
|
|
|
MIBK (L)
|
Water (S)
|
|
HAc (A)
|
HAc (A)
|
|
0
|
98
|
2
|
1
|
0
|
2
|
98
|
|
2
|
95
|
3
|
2
|
3
|
2
|
95
|
|
9
|
86
|
5
|
3
|
12
|
2
|
86
|
|
17
|
74
|
9
|
4
|
20
|
4
|
76
|
|
25
|
61
|
14
|
5
|
26
|
6
|
68
|
|
31
|
47
|
22
|
6
|
33
|
12
|
55
|
|
34
|
35
|
31
|
7
|
35
|
22
|
43
|
(a) Plot the ternary equilibrium diagram for this system on FIGURE 2 at the end of this TMA - you should take several photocopies of this for use in this question.
(b) 50 kg of feed solution of 50% A in S (HAc in water) is to be extracted such that the raffinate is less than 5% A MAO . The extraction can be performed in one of two ways:
(i) 50 kg of L (MIBK solvent) added at each stage of simple multiple contact
OR (ii) 65 kg of L (MIBK solvent) in counter current multiple contact.
Use your equilibrium diagram to obtain and specify the number of stages in each case.
Fig .2