A separation stream off the main reactor effluent contains almost exclusively ethyl benzene, benzene, and toluene at 1 bar and 100°C. You determine that the stream flow rate is made up of 34 kg/s of benzene, 10 kg/s of toluene, and 57.75 kg/s of the other component. You send this mixture into a flash distillation unit operating at 0.6 bar and 100°C.
- A. Estimate if this mixture flashes.
- B. If the mixture flashes, determine the composition and amount of the equilibrium liquid and vapor.
- C. You send the liquid exiting the flash distillation unit into another flash distillation unit operating at 1.5 bar and 140°C. Determine if this mixture flashes. If so, determine the composition and amounts of the equilibrium phases.
- D. What percentage of the original benzene that left the reactor is now a vapor (you have to consider both flash units).
(A)
Interpretation:
Estimate if this mixture flashes.
Concept Introduction:
The expression to obtain the mole fraction for component 1 is,
Here, molar flow rate of components 1, 2, and 3 is
The expression to obtain the mole fraction for component 2 is,
The expression to obtain the mole fraction for component 3 is,
The Antoine equation for the components 1 and 2 is,
Here, Antoine constants or coefficients are A, B, and C, vapor pressure is
The expression of bubble point pressure using Raoult’s Law is,
Here, liquid phase mole fraction for components 1, 2, and 3 is
The expression to obtain the dew point pressure is,
Here, vapor phase composition for the components 1, 2, and 3 is
Explanation of Solution
Convert the mass flow rates into molar flow rates to obtain the composition of the incoming stream by using the molecular weights of the three substances as in Table (1).
Substances | Mass flow rate | Molecular weight | Molar flow rate |
Ethyl benzene (1) | 57.75 | 0.10617 | 6.13 |
Benzene (2) | 34 | 0.07811 | 2.66 |
Toluene (3) | 10 | 0.09214 | 0.92 |
Write the expression to obtain the mole fraction for component 1.
Substitute
Write the expression to obtain the mole fraction for component 2.
Substitute
Write the expression to obtain the mole fraction for component 3.
Substitute
Write the Antoine equation for the components 1 and 2.
Refer Appendix E, “Antoine Coefficients”; obtain the constants A, B, and C for components as in Table (1).
Constants | Ethyl benzene (1) | benzene (2) | toluene (3) |
A | 6.95719 | 6.90565 | 6.95464 |
B | 1,424.255 | 1,211.033 | 1,344.800 |
C | 213.21 | 220.790 | 219.48 |
Substitute
Substitute
Substitute
Write the expression of bubble point pressure using Raoult’s Law.
Substitute 0.632 for
Write the expression to obtain the dew point pressure.
Substitute 0.632 for
Since the working pressure (0.6 bar = 450.04 mmHg) is between the bubble (584.52 mmHg) and dew points (353.27 mmHg) pressure, it will flash at this temperature.
(B)
Interpretation:
If the mixture flashes, determine the composition and amount of the equilibrium liquid and vapor.
Concept Introduction:
The expression of overall material balance is,
Here, molar flow rate of the mixture is
The expression of material balance on ethyl benzene is,
Here, the composition of the inlet stream 1 is
The expression of material balance on benzene is,
Here, the composition of the inlet stream 2 is
The Raoult’s law for ethyl benzene is,
Here, vapor pressure for component 1 is
The Raoult’s law for benzene is,
Here, vapor pressure for component 2 is
The Raoult’s law for toluene is,
Explanation of Solution
Write the expression of overall material balance.
Substitute
Write the expression of material balance on ethyl benzene.
Substitute 0.632 for
Write the expression of material balance on benzene.
Substitute 0.274 for
Write the Raoult’s law for ethyl benzene.
Substitute 256.98 mmHg for
Write the Raoult’s law for benzene.
Substitute 1350.49 mmHg for
Write the Raoult’s law for toluene.
Substitute 256.98 mmHg for
Solve equations (14), (16), and (18) and obtain the values of
Substitute 0.760 for
(C)
Interpretation:
Determine if this mixture flashes. If so, determine the composition and amounts of the equilibrium phases.
Concept Introduction:
The expression of overall material balance is,
The expression of material balance on ethyl benzene is,
Here, the composition of the inlet stream 1 is
The expression of material balance on benzene is,
Here, the composition of the inlet stream 2 is
The Raoult’s law for ethyl benzene is,
The Raoult’s law for benzene is,
The Raoult’s law for toluene is,
Explanation of Solution
The bubble point pressure is 450.33 mmHg, while the dew point pressure is 309.88 mmHg. The system pressure is 0.5 bar (375.03 mmHg) and hence the system will flush one more time.
Write the expression of overall material balance.
Substitute
Write the expression of material balance on ethyl benzene.
Substitute 0.760 for
Write the expression of material balance on benzene.
Substitute 0.153 for
Write the Raoult’s law for ethyl benzene.
Substitute 256.98 mmHg for
Write the Raoult’s law for benzene.
Substitute 1,350.49 mmHg for
Write the Raoult’s law for toluene.
Substitute 256.98 mmHg for
Solve equations (26), (28), and (30) and obtain the values of
Substitute 0.837 for
(D)
Interpretation:
What percentage of the original benzene that left the reactor is now a vapor?
Concept Introduction:
The expression to obtain the amount of benzene in the vapor exiting the 1st flash distillation unit is,
The expression to obtain the amount of benzene in the vapor exiting the 2nd flash distillation unit is,
The expression to obtain the percentage of benzene in vapor is,
Explanation of Solution
The original benzene that left the reactor is
Write the expression to obtain the amount of benzene in the vapor exiting the 1st flash distillation unit.
Substitute
Write the expression to obtain the amount of benzene in the vapor exiting the 2nd flash distillation unit.
Substitute
Write the expression to obtain the percentage of benzene in vapor.
Substitute
Thus, the percentage of benzene in vapor is
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