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1. Please prove that the expression of “a” and “b” for van der Waals EOS in Table C1 of the composition model lectures are correct.

2. Starting with Equation C3, show the derivation of Equation C4.

3. A hydrocarbon mixture entering a separator has the following feed composition.

Components |
Moles, (mol) |
B.P. (˚F) |
M (lbm/lbmole) |
Pc (psia) |
Tc (˚F) |
ω |

Nitrogen |
0.13 |
- |
28.02 |
493 |
-232.4 |
0.04 |

CO |
0.18 |
- |
44.01 |
1070.6 |
87.9 |
0.23 |

Methane |
50 |
- |
16.04 |
667.8 |
-116.6 |
0.01 |

Ethane |
15 |
- |
30.07 |
707.8 |
90.1 |
0.1 |

Propane |
12 |
- |
44.1 |
616.3 |
206 |
0.15 |

i-Butane |
5 |
- |
58.12 |
529.1 |
275 |
0.18 |

n-Butane |
3 |
- |
58.12 |
550.7 |
305.7 |
0.19 |

i-Pentane |
1 |
- |
72.15 |
490.4 |
369.1 |
0.23 |

n-Pentane |
3 |
- |
72.15 |
488.6 |
385.7 |
0.25 |

Hexane |
4.25 |
- |
86.18 |
436.9 |
453.7 |
0.3 |

Heptane + |
6.44 |
355 |
143 |
350 |
650 |
0.38 |

- Write a computer program that performs VLE calculations based on SRK and PR equation of state to obtain the K values of the components, and the compositions of the gas and the liquid phases, simultaneously. The separator pressure and temperature are 1000 psia and 90 ˚F, respectively. Run your program at separator conditions and compare the results between SRK and PR.
- Calculate the fluid properties (density, viscosity and surface tension) of both liquid and gas phases at 1000 psia, and 90 ˚F. Compare the fluid properties calculated based on the results between SRK and PR. (Note: The critical volume for each component can be calculated based on the given information, and they are different for SRK and PR).
- Use Pipesim
^{TM}or PVTSim or any other commercial simulator to check the results from your program, for SRK and PR equations of state. Make comparisons for compositions of liquid and gas phases, bubble and dew point values, and fluid properties.

4. Using your program (or Pipesim / PVTsim), calculate oil and gas densities at standard conditions. Convert oil density to API index and gas density to a specific gas gravity (sgg). Using API index and sgg, find at separator conditions 1000 psia and 90 ˚F (provide result for 3 correlations of your choice):

Physical Property |
Correlation(s) |

Solution Gas Oil Ratio, R_{s} (scf/STBO) |
Standing Vazquez and Beggs Glaso Lasater Al-Marhoun Kartoatmodjo |

Oil Formation Volume Factor, B_{o} (bbl/STBO) |
Vazquez and Beggs Standing Glaso Al-Marhoun Kartoatmodjo |

Specific Gravity of Dissolved Gas, γ_{g} |
Mass balance equation |

Specific Gravity of Free Gas, γ_{g} |
Mass balance equation |

Live Oil Density, ρ_{o} (lbm/cu ft) |
Mass balance equation |

You may find it useful to have:

Reservoir temperature, [F] |
123 |

Reservoir pressure, [psia] |
2500 |

Oil produced, [STB/D] |
175 |

Gas produced, [MMSCF/D] |
0.5 |

5. Compare and discuss the oil density results from your compositional and black oil models.

__Remarks__

- To complete the homework, you may use the programming language of your choice
- Be organized with your program and Excel Worksheet
- Create a report of your Homework in a Word File
- If your homework is not submitted on time, you will lose 25% of your total score

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