## Vapor-Liquid Equilibrium

Assignment Rules:

For calculations, clearly show all your work step by step in an organized and logical order. Also, show the meaning and the unit of your results.

Please explain all calculation steps in word clearly and use “insert equation in word document” to write all equations (formula). You should write formula with symbols and then replace each symbol with its value in the same location.

Total Mark: 10

**Oil and gas hydrocarbons:**

Hydrocarbons are covalent compounds composed of carbon and hydrogen atoms. Atoms combine in a number of ways to satisfy the valence requirements. Hydrocarbons are separated into “families” of homologous series. Carbon atoms link together to form chains and/or ring structures. Natural gas and crude oil consist primarily of “straight chain” hydrocarbon molecules. Most of the hydrocarbons of concern fall in the paraffin series.

Natural gas consists of methane (CH4), which is the main component, and other components, including ethane, propane, n-butane, i-butane, n-pentane, i-pentane, hexanes, heptanes, octanes, and heavier hydrocarbons. Hexanes and heavier are referred to as hexane plus. Natural gas also includes diluents of carbon dioxides, nitrogen, and smaller quantities of hydrogen sulfide, water vapor, and oxygen.

**Flash Calculations:**

The amount of hydrocarbon fluid that exists in the gaseous phase or theliquid phaseat any points at the process is determined by a flash calculation.For a given pressure and temperature,the amount of each component in the gas phase will depend not only on pressure andtemperature, but also on the partial pressure of thecomponent. Therefore,the amount of gas depends upon the total composition of thefluids.

This is best understood by assigning an equilibrium “*K*” value to eachcomponent. The *K *value is a strong function of temperature and pressureand of the composition of the vapor and liquid phase. It is defined as:

Where: K_{i}=constant for component i at a given temperature and pressure,

V_{i}=moles of component i in the vapor phase,

V =total moles in the vapor phase,

L_{i}=moles of component *i*in the liquid phase,

L =total mole in the liquid phase.

**Determine equilibrium K-values of a pure component from coefficients of Antoine’s equation (neglecting the influence of stream composition):**

** **

Where:

P is the absolute pressure in bar.

T is the absolute temperature in Kelvin.

A_{i}, B_{i} and C_{i} are constant for a given component (i) as shown in the following Table:

No. | Component | Ai |
Bi |
Ci |

1. | Ethane | 9.0435 | 1511.4 | -17.16 |

2. | Propane | 9.1058 | 1872.5 | -25.16 |

3. | Iso-Butane | 8.9179 | 2032.76 | -33.15 |

4. | n-Butane |
9.058 | 2154.9 | -34.42 |

5. | n-Pentane |
9.2131 | 2477.1 | -39.94 |

6. | n-Hexane |
9.2164 | 2697.6 | -48.78 |

** **

Also, equilibrium k-value for a given component can be determined from different charts available in literature.

** **

Flash calculations combine the total material balance, the component (N) balance and the equilibrium constant.

Total stream balance: F = L + V (1)

Component (N) balance: F z_{i} = x_{i} L+ y_{i} V (2)

Equilibrium relation: y_{i} = K_{i} x_{i} (3)_{ }

Using all three equations can derive the following:

The value of (V/F) is assumed and each x_{i} is calculated from equation (4). If the sum of all x_{i} is equal 1, then the assumption is correct. If the sum of x_{i} is not equal 1, then, another assumption should be used.

** **

**Calculation of the Dew Point of a vapor stream:**

For a flashed vapor stream with known composition and total flow rate, it is possible to determine the “Dew Point” using the equilibrium K-value (VLE) method.

If P is given and fixed, then, T should be change until the following equation is met:

Temperature, which satisfies the above equation, is the dew point of the vapor stream.

**Calculation of the Bubble Point of a liquid stream:**

For a flashed liquid stream with known composition and total flow rate, it is possible to determine the “Bubble Point” using the equilibrium K-value (VLE) method.

If P is given and fixed, then, T should be change until the following equation is met:

Temperature, which satisfies the above equation, is the bubble point of the liquid stream.

Problem 2:

As in assignment 1, a liquid stream at 0.4 bar and T = 230 K enter a flash drum. The mixture contains 20 mole propane,20 mole Iso-Butane, 20 mole n-Butane and 20 mole n-Pentane. Isothermal flashing was adjusted atdifferent pressures (0.20, 0.24, 0.28, 0.32 and 0.36 bar) and temperatures (230, 232, 234, 236, 238 and 240 K).

- Calculate the composition and total flow rate of vapor and liquid flashed streams at different temperatures and pressures.

See attached excel file.