17CGA002 Stagewise Processes assignment
{` Loughborough University STAGEWISE PROCESSES 17CGA002 `}
Q1 60 kg of an organic solvent (S) is to be used to extract solute (A) from 200 kg of an aqueous solution containing 170 kg of water and 30 kg of A. The organic solvent and water may be taken to be immiscible. The equilibrium distribution of solute (A) between the organic solvent (S) and water is given by:
Y = 1.7 X
where: Y ≡ kg A/kg pure S; and X ≡ kg A/kg pure water.
You are required to use an analytical approach to solve the problems set out below for this question Q1.
When answering each question, sketch the process, define all variables and label all inlet and outlet streams.
- Three stages are connected in a cross-current arrangement. If 10 kg of solvent is used in the first stage, 20 kg in the second stage and 30 kg in the final stage, calculate how much solute (A) is left in the raffinate streams leaving each stage. Can this system achieve 80% overall removal (extraction) of the solute? What total percent removal is achieved? How may the separation be improved?
- How would the extraction change (in Q1 (i) above) if 120 kg of total solvent was used and an equal amount was introduced in each of the three stages connected in a cross-current arrangement i.e. 40 kg in each stage? How much solute (A) is left in the raffinate solution leaving the third stage and how much is extracted in each stage? With an infinite number of stages connected in a cross-current setup, calculate how much solute (A) will be left in the raffinate stream leaving the process.
- If 3 stages are connected in a counter-current arrangement, how much of the solute (A) will be extracted in each stage using 60 kg of solvent and how much would be left in the raffinate stream leaving the process?
Q2 Solute (A) is to be extracted from an aqueous solution using an organic solvent (S). The organic solvent (S) and water are insoluble in each other. The feed solution is a binary mixture consisting of 20 kg of solute (A) and 100 kg of water. 100 kg of the organic solvent (S) is available for the extraction process. Equilibrium data for the distribution of solute (A), organic solvent (S) and water are given in Table Q2.
Table Q2. To be used for question Q2 (i) and Q2 (ii)
X |
0 |
0.025 |
0.05 |
0.1 |
0.15 |
0.20 |
0.25 |
0.30 |
Y |
0 |
0.154 |
0.204 |
0.269 |
0.316 |
0.355 |
0.388 |
0.417 |
Y = kg A / kg pure S and X = kg A / kg pure water
You are required to use a graphical approach to solve problems in question Q2.
When answering each question sketch the process and label all inlet and outlet streams.
- If a single equilibrium stage is used how much solute (A) will be extracted? Consider a cross-current system with three equilibrium stages. If 20 kg of solvent is used in the first stage, 30 kg of solvent in the second stage and 50 kg in the third stage, calculate how much solute (A) will be extracted in each stage. How can complete extraction be achieved (i.e. no solute left in the raffinate stream leaving the process)?
- It is desired to remove 90% of acetone from a binary gas mixture (acetone/air) using a counter-current absorption tower. The total inlet gas flow to the tower is 60 kg h^{-1} (containing 0.6 kg h^{-1} of acetone) and the total inlet pure water flow rate to be used to absorb acetone is 180 kg h^{-1}. The equilibrium distribution for the acetone (A) in the gas-liquid is given by: y = 2.53x where x = kg A/(kg water + kg A); y = kg A/(kg air + kg A). Determine the number of theoretical equilibrium stages required for this separation and write down the compositions of the gas and liquid streams leaving each stage.
Q3 A counter-current gas absorption tower is being considered to remove SO_{2} from air using water as the solvent. The tower operates at 30C and a pressure of 4 atm. The inlet gas flow rate is 2 mol/h and the inlet gas mole fraction of SO_{2} is 0.3. The Henry’s Law constant for SO_{2} / H_{2}O system is 2 atm/mole fraction. The required outlet gas molar composition is 0.05 or less.
For this problem, you may assume that water and air are mutually insoluble.
(Hint: You will need to work on a solute-free basis).
- Use Henry’s law to find an equation linking the mole ratio of SO_{2} in the gas phase to the mole ratio of SO_{2} in the water phase.
- How many equilibrium stages are needed for the separation when the inlet water flow rate is 1 mol/h? The inlet water is pure (i.e. solute-free). Use an analytical approach to solve this problem.
- What would be the minimum water flow rate to achieve the required separation (i.e. operating under pinch conditions)?
Q4 Acetone (A)-water (W)-trichloroethane (TCE) ternary equilibrium data are given below.
- Plot tie-lines 2, 3, 4, 5 and 7 using the equilibrium tie-line data given in Table Q4 on the triangular diagram (provided at the end of the examination paper) and sketch-in the two-phase envelope.
- Plot the equilibrium data as a two dimensional x-y plot with the acetone composition in the water-rich layer plotted on the x-axis and the acetone composition in the TCE-rich layer plotted on the y-axis.
- 40 kg of a binary solution of acetone-water containing 50% mass fraction of acetone is extracted using two equilibrium stages connected in a crosscurrent mode with each stage using 20 kg of pure TCE. Find the fraction of original acetone that is extracted in each stage and in total.
Table Q4. Equilibrium tie line data
Tie line no. |
Wt % in water layer |
Wt % in TCE layer | ||||
TCE |
Water |
Acetone |
TCE |
Water |
Acetone | |
1 |
0.5 |
93.5 |
6.0 |
91.0 |
0.3 |
8.7 |
2 |
0.9 |
88.1 |
11.0 |
84.6 |
0.4 |
15.0 |
3 |
1.0 |
72.0 |
27.0 |
59.2 |
2.3 |
38.5 |
4 |
1.6 |
62.7 |
35.7 |
47.5 |
4.3 |
48.2 |
5 |
2.1 |
57.0 |
40.9 |
40.0 |
6.0 |
54.0 |
6 |
3.8 |
50.2 |
46.0 |
33.7 |
8.9 |
57.4 |
7 |
6.5 |
41.7 |
51.8 |
26.3 |
13.4 |
60.3 |
FIGURE FOR QUESTION 4