Tutorial Sheet No. 4 (2014):

Process Equipment Design for Phase-Equilibria Systems.

Please complete and hand-in Questions 2 & 5 by 3pm Monday 7th

April 2014.

1) a) Calculate the bubble point pressure and composition of the vapour in equilibrium with a

liquid at 40 C containing:

5 mole % methane (CH4)

20 mole % ethane (C2H6)

25 mole % propane (C3H8)

20 mole % isobutane (C4H10)

30 mole % n-butane (C4H10)

Use an initial guess of 1000 kPa.

[12.5 marks]

b) Calculate the dew point pressure and composition of the liquid in equilibrium with a

vapour at 40 C containing:

5 mole % methane (CH4)

20 mole % ethane (C2H6)

25 mole % propane (C3H8)

20 mole % isobutane (C4H10)

30 mole % n-butane (C4H10)

Use an initial guess of 1000 kPa.

[12.5 marks]

Supplied Data: Data Sheet No. (1): De Priester Nomogram for Phase-Equilibrium

Constants for Hydrocarbons (High Temperature Range).

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2) Many thermodynamic process engineering design problems consider a system in which

either a vapour phase is just being formed from a boiling liquid phase, or a liquid phase is just

being formed from a saturated vapour phase. In order to take into account molecular

interactions in real systems, the liquid-vapour equilibrium constant, Ki, can be used in some

hydrocarbon systems.

a) For a non-ideal system, show that the Design Performance Equation to predict the

component mole fraction xi in the liquid stream from a flash vessel processing a liquid

feed stream of component mole fraction xFi is:

L) - (1 KL

xx

i

Fii

where L is the product liquor molar flow from the flash vessel operating at a system

pressure P and a system temperature T. Identify the assumptions used in the

derivation.

[5 marks]

b) A liquid stream containing 15 mol% ethane (C2H6), 35 mol% propane (C3H8) and 50

mol% n-butane (C4H10) enters a flash vessel at 40 C. If 40% of the stream remains as

a liquid (based on the molar flow), calculate the pressure of the vessel and the

composition of the exit streams.

[10 marks]

c) The vapour stream from a gas well is a mixture containing 50 mol% methane, 10

mol% ethane, 20 mol% propane and 20 mol% n-butane. The stream is fed to a partial

condenser at a pressure of 17.25 bar and a temperature of 27 C. Determine the mole

fraction of the gas which condenses and the composition of the liquid and gas phases

leaving the condenser.

[10 marks]

Data supplied:

Data Sheet No. (1): De Priester Nomogram for Phase Equilibrium Constants for

Hydrocarbons (High Temperature Range).

3

3) For a non-ideal system, show that the Design Performance Equation to predict the

component mole fraction xi in the liquid stream from a flash vessel processing a liquid feed

stream of component mole fraction xFi is:

L) - (1 KL

xx

i

Fii

where L is the product liquor molar flow from the flash vessel operating at a system pressure

P and a system temperature T. Identify the assumptions used in the derivation.

[5 marks]

A liquid of composition 25 mole % ethane, 15 mole % n-butane and a third unknown

component enters a separation vessel which operates at a pressure of 750 kPa and

temperature of 6 C. If 87% of the solution leaves the vessel as the liquid stream, calculate:

a) The equilibrium constant, Ki, for the unknown component. [10 marks]

b) The composition of the vapour and liquid leaving the separation unit. [7 marks]

c) Determine the chemical name of the third remaining component in the liquid mixture. [3 marks]

Supplied Data : Data Sheet No. (2): De Priester Nomogram for Phase-Equilibrium

Constants for Hydrocarbons (Low Temperature Range).

4

4) Acetone (1) and methanol (2) form an azeotrope boiling at 55.7 C and 760 mmHg pressure, with a mole fraction of 80% acetone. Given the following Antoine equations, where

o

ip is in mmHg and T is in C:

Acetone: 229.664

1210.595 - 7.11714 log 110

Tp

o

Methanol: 239.726

1582.271 - 8.08097 log 210

Tp

o

a) Determine the Van Laar coefficients from the azeotrope data and the following

equations;

1

2

11

2212 ln

ln

ln1

x

xA

2

2

22

1121 ln

ln

ln1

x

xA

[5 marks]

b) Calculate the azeotropic boiling point and composition at P = 1520 mmHg. Use A12

and A21 as calculated above and:

2

2

1

21

12

121

1

ln

x

x

A

A

A

2

1

2

12

21

212

1

ln

x

x

A

A

A

[15 marks]

c) Calculate the lowest pressure at which an azeotrope exists.

[5 marks]

Supplied Data: 1 atm = 760 mmHg

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5) Acetone (1) and Hexane (2) form an azeotrope containing 41 wt% of Hexane, boiling at

49.8 C at a pressure of 760 mmHg. Pure component vapour pressures may be calculated

using the following equation and Antoine coefficients:

)(log

*

10CT

BApi

Antoine Coefficients RMM

kg / kmol A B C

Acetone (1) 7.1327 1219.97 230.653 58.08

Hexane (2) 7.01051 1246.33 232.988 86.18

with *ip in mmHg and T in C.

a) Calculate the normal boiling points for Acetone and Hexane at 1 atm.

[4 marks]

b) Use the azeotropic data and the following equations to estimate the van Laar constants

A12 and A21.

2

11

22112

ln

ln 1 ln

x

xA

2

22

11221

ln

ln 1 ln

x

xA

[7 marks]

c) Using the Antoine equations and Van Laar coefficients calculated in part (b), estimate

the boiling point and vapour composition at 760 mmHg of a liquid containing 20 %

by mole of Acetone.

2

112221

2

2

2

21121

][ln

xAxA

xAA

2

221112

2

1

2

12212

][ln

xAxA

xAA

[8 marks]

d) Find the dew point of a vapour containing 50 % by mole of Acetone.

[6 marks]

Supplied Data: 1 atm = 760 mmHg

6

Data Sheet No. (1): De Priester Nomogram for Phase Equilibrium Constants for

Hydrocarbons (High Temperature Range)

7

Data Sheet No. (2): De Priester Nomogram for Phase Equilibrium Constants for

Hydrocarbons (Low Temperature Range)