- 3.1 Mole fraction and apparent molecular weight of gas mixtures
- 3.2 Specific gravity of gas mixtures
Molecular weight
Molecules of a particular chemical species are composed of groups of atoms that always combine according to a specific formula. The chemical formula and the international atomic weight table provide us with a scale for determining the weight ratios of all atoms combined in any molecule. The molecular weight, M, of a molecule is simply the sum of all the atomic weights of its constituent atoms. It follows, then, that the number of molecules in a given mass of material is inversely proportional to its molecular weight. Therefore, when masses of different materials have the same ratio as their molecular weights, the number of molecules present is equal. For instance, 2 lbm hydrogen contains the same number of molecules as 16 lbm methane. For this reason, it is convenient to define the unit "lbm mol" as a mass of the material in pounds equal to its molecular weight. Similarly, a "g mol" is its mass in grams. One lbm mol or one g mol of any compound, therefore, represents a fixed number of molecules. This number for the g mol was determined in 1998 by the US National Institute of Standards and Technology to be 6.02214199×10 23 . The number of significant digits shown is the accuracy to which it has been determined experimentally.
Critical temperature and pressure
Typical pressure/volume/temperature (PVT) relationships for a pure fluid are illustrated in Fig. 1. The curve segment B-C-D defines the limits of vapor/liquid coexistence, with B-C being the bubblepoint curve of the liquid and C-D being the dewpoint curve of the vapor. Any combination of temperature, pressure, and volume above that line segment indicates that the fluid exists in a single phase. At low temperatures and pressures, the properties of equilibrium vapors and liquids are extremely different (e.g., the density of a gas is low, while that of a liquid is relatively high). As the pressure and temperature are increased along the coexistence curves, liquid density, viscosity, and other properties generally decrease while vapor density and viscosity generally increase. Thus, the difference in the physical properties of the coexisting phases decreases. These changes continue as the temperature and pressure are raised until a point is reached at which the properties of the equilibrium vapor and liquid become equal. The temperature, pressure, and volume at this point are called the "critical" values for that species. Location C on Fig. 1 is the critical point. The critical temperature and pressure are unique values for each species and are useful in correlating physical properties. Critical constants for some of the commonly occurring hydrocarbons and other components of natural gas can be found in Table 1.
Specific gravity (relative density)
The specific gravity of a gas, γ, is the ratio of the density of the gas at standard pressure and temperature to the density of air at the same standard pressure and temperature. The standard temperature is usually 60°F, and the standard pressure is usually 14.696 psia. However, slightly different standards are sometimes used in different locations and in different units. The ideal gas laws can be used to show that the specific gravity (ratio of densities) is also equal to the ratio of the molecular weights. By convention, specific gravities of all gases at all pressures are usually set equal to the ratio of the molecular weight of the gas to that of air (28.967). Although specific gravity is still frequently used, this traditional term is not used under the SI system; it has been replaced by "relative density."
Mole fraction and apparent molecular weight of gas mixtures
The analysis of a gas mixture can be expressed in terms of a mole fraction, yi, of each component, which is the ratio of the number of moles of a given component to the total number of moles present. Analyses also can be expressed in terms of the volume, weight, or pressure fraction of each component present. Under limited conditions, where gaseous mixtures conform reasonably well to the ideal gas laws, the mole fraction can be shown to be equal to the volume fraction but not to the weight fraction. The apparent molecular weight of a gas mixture is equal to the sum of the mole fraction times the molecular weight of each component.
Specific gravity of gas mixtures
The specific gravity (γg) of a gas mixture is the ratio of the density of the gas mixture to that of air. It is measured easily at the wellhead in the field and therefore is used as an indication of the composition of the gas. The specific gravity of gas is proportional to its molecular weight (Mg) if it is measured at low pressures where gas behavior approaches ideality. Specific gravity also has been used to correlate other physical properties of natural gases. To do this, it is necessary to assume that the analyses of gases vary regularly with their gravities. Because this assumption is only an approximation and is known to do poorly for gases with appreciable non hydrocarbon content, it should be used only in the absence of a complete analysis or of correlations based on a complete analysis of the gas.
Dalton’s law
The partial pressure of a gas in a mixture of gases is defined as the pressure that the gas would exert if it alone were present at the same temperature and volume as the mixture. Dalton’s law states that the sum of the partial pressures of the gases in a mixture is equal to the total pressure of the mixture. This law can be shown to be true if the ideal gas laws apply.
Amagat’s law
The partial volume of a gas in a mixture of gases is defined as the volume that the gas would occupy if it alone were present at the same temperature and pressure as the mixture of the gases. If the ideal gas laws hold, then Amagat’s law (that the sum of the partial volumes is equal to the total volume) also must be true.
Nomenclature
| M | = | molecular weight |
| Mg | = | average molecular weight of gas mixture |
| yi | = | mole fraction of component i in a gas mixture |
| γg | = | specific gravity for gas |
Noteworthy papers in OnePetro
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External links
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