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Real Gas Mixtures

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Compressibility factor charts are available for most of the single the single components light hydrocarbon gases, but in practice a single component gas is rarely encountered. In order to get Z-factors for natural gas mixtures, the law of corresponding states is used. This law states that the ratio of the value of any intensive property to the value of that property at the critical state is related to the ratios of the prevailing absolute temperature and pressure by the same function for all similar substances. This means that all pure gases have the same Z-factor at the same values of reduced pressure and temperature, where the reduced values are defined as

 

and

where Tc and Pc are the critical temperature and pressure for the gas, respectively. The value must be in absolute units. Figure 3 shows the changes of Z-factor for pure hydrocarbon gases as a function of reduced pressure and temperature.

 

 

Fig.3. Compressibility factors for pure hydrocarbon gases as a function of reduced pressure and temperature

It has been shown that the Law of Corresponding States works better for gases of similar molecular characteristics. This is fortunate since most of the gases that the petroleum engineer deals with are composed of molecules of the same class of organic compounds known as paraffin hydrocarbons. The Law of Corresponding States has been extended to cover mixtures of gases that are closely related chemically. Since it is somewhat difficult to obtain the critical point for multicomponent mixtures, the quantities of pseudocritical temperature and pressure have been conceived. These quantities are defined as

and (2)

This pseudocritical quantities are used for mixtures of gases in exactly the same manner as the actual critical temperatures and critical pressures are used for pure gases. It must be understood, however, that these pseudocritical properties were devised simply for use in correlating compressibility factors and in no way relate to the actual critical properties of gas mixture.

Compressibility factors are a function of composition as well as temperature and pressure. It has been pointed out that the components of most natural gases are hydrocarbons of the same family, and therefore a correlation of this type is possible.

In some cases the composition of a gas will be given in weight or mass percent rather than mole percent. In this event, the composition must be first converted to mole fraction or percent before the mixture properties can be calculated (example 1).

If the volume fraction is given at conditions other than standard, the volume fraction must be converted to a mole fraction basis, taking into account the deviation from ideal behavior (example 2)

 

Examle 1 Examle 2
A gas mixture consists of by weight, Calculate the apparent molecular weight and specific gravity of the mixture A gas has the following composition measured at 2,500 psia and 3000F. Calculate the composition in mole fraction, The volume percents at these conditions are: 67 - % C1, 30% - C2, and 1 % - C3, 2% - CO2
Assume 100 lbm of gas as a basis To convert from volume to moles, assume 100 ft3 as a basis, Then use
Component Mass, mj. lbm Mj, lbm/lb-mole nj, lb-mole yj yjMj Component Vj, ft3 Tr pr Z V/Z nj
C1     3.13 0.68 10.9 C1   2.20 3.72 0.963 69.6 21.30 0.595
C2     1.00 0.22 6.6 C2   1.40 3.53 0.708 42.5 13.00 0.363
C3     0.45 0.10 4.4 C3   1.14 4.06 0.585 1.8 0.55 0.015
total     n=4.58 1.00 21.9 CO2   1.30 2.32 0.658 3.2 0.48 0.027
, for C1, = = total           n=38.83 1.000

 

In most cases the composition of a natural gas will be known and the apparent molecular weight and critical properties can be calculated as previously described. Occasionally, however, only the gas gravity will be known. Also, it is very easy to measure the gas gravity in the field. If the composition is unknown, or if accuracy requirements do not justify the longer calculations, Figure 4 can be used to estimate the pseudocritical properties.

 

Fig.4. Pseudocritical properties of natural gases.

 

The properties can also be calculated using the following equations

For gas:

For condensate fluids:

 

The example of gas composition passport (using in Ukraine only) follows bellow.

 

Passport of natural gas quality

Date of gas sampling

Place of gas sampling

Conditions of gas sampling

Temperature Pressure
7 0C 13.1 atm

Physical and chemical gas parameters

Temperature Pressure
20 0C 0.1 MPa

The results of analysis

Components: Fact quantity, vol. %
Methane CH4 97.841
Ethane C2H6 0.554
Propane C3H8 0.420
n-Butane C4H10 0.107
Isobutane C4H10 0.145
n-Pentane C5H12 0.047
Isopentane C5H12 0.062
Neopentane C5H12 0.001
n-Hexane C6H14 0.056
n-Heptane C7H16 0.009
n-Octane C8H18 0.004
n-Nonane+above C9H20 0.002
Carbon Dioxide CO2 0.104
Oxygen O2 0.007
Nitrogen N2 0.641
Parameters:    
Mechanical impurities g/m3  
Mercaptane sulfide g/m3  
Hydrogen Sulfide H2S 0.000
Specific gravity absolute units 0.573
Gas gravity kg/m3 0.691
Net calorific value Kcal/m3 8,107
Higher Wobbe index Kcal/m3 11,811

 


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