Real Gas Mixtures

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 T_c and P_c 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

Physical and chemical gas parameters

The results of analysis

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