Chapter two.

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1 Chapter two

2 Gas Properties The ability to calculate the performance of a gas producing system, including the reservoir and the piping system, requires knowledge of many gas properties at various, pressures and temperatures. If the natural gas is in contact with liquids, such as condensate or water, the effect of the liquids on gas properties must be evaluated. This presentation presents the best and most widely used methods to perform the necessary calculations. Some of the information presented will be used only in reservoir calculations and some will be used only in the piping system design.

3 IDEAL GASES The understanding of the behavior of gases with respect to pressure and temperature changes is made clearer by first considering the behavior of gases at conditions near standard conditions of pressure and temperature; that is: p = 14.7 psia = kPa T = 60°F = 520°R = °K At these conditions the gas is said to behave ideally, and most of the early work with gases was conducted at conditions approaching these conditions.

4 Characteristics of ideal gas
(1) the volume occupied by the molecules is small compared to the total gas volume; (2) all molecular collisions are elastic; and (3) there are no attractive or repulsive forces among the molecules. The basis for describing ideal gas behavior comes from the combination of some of the so called gas laws proposed by early experimenters.

5 Early Gas Laws Boyle's Law. Boyle observed experimentally that the volume of an ideal gas is inversely proportional to the pressure for a given weight or mass of gas when temperature is constant. This may be expressed as: Charles' Law. While working with gases at low pressures, Charles observed that the volume occupied by a fixed mass of gas is directly proportional to its absolute temperature, or

6 Avogadro's Law. Avogadro's Law states that under the same conditions of temperature and pressure, equal volumes of all ideal gases contain the same number of molecules. This is equivalent to the statement that at a given temperature and pressure one molecular weight of any ideal gas occupies the same volume as one molec­ular weight of another ideal gas. It has been shown that there are 2.73 x molecules/lb-mole of ideal gas and that one molecular weight in pounds of any ideal gas at 60°F and 14.7 psia occupies a volume of cu ft.

7 The Ideal Gas Law The three gas laws described previously can be com­bined to express a relationship among pressure, volume, and temperature, called the ideal gas law. In order to combine Charles' Law and Boyle's Law to describe the behavior of an ideal gas when both temperature and pressure are changed, assume a given mass of gas whose volume is V1 at pressure pl and temperature Ti, and imagine the following process through which the gas reaches volume V2 at pressure p2 and temperature T2:

8 In the first step the pressure is changed from a value of p1 to a value of p2 while temperature is held constant. This causes the volume to change from V1 to V. In Step 2, the pressure is maintained constant at a value of p2, and the temperature is changed from a value of T1 to a value of T2. The change in volume of the gas during the first step may be described through the use of Boyle's Law since the quantity of gas and the temperature are held constant. Thus

9 where V represents the volume at pressure p2 and temperature T1
where V represents the volume at pressure p2 and temperature T1. Charles' Law applies to the change in the volume of gas during the second step since the pressure and the quantity of gas are maintained constant; therefore Elimination of volume, V, between the two equations : Or

10 Thus for a given quantity of gas, pV/T = a constant
Thus for a given quantity of gas, pV/T = a constant. The constant is designated with the symbol R when the quantity of gas is equal to one molecular weight. That is, where VM is the volume of one molecular weight of the gas at p and T. Therefore, the equation of state for one molecular weight of any ideal gas is

11 For n moles of ideal gas this equation becomes
where V is the total volume of n moles of gas at temperature, T, and pressure, p. Since n is the mass of gas divided by the molecular weight, the equation can be written as or, since m/V is the gas density,

12 This expression is known by various names such as the ideal gas law, the general gas law, or the perfect gas law. This equation has limited practical value since no known gas behaves as an ideal gas; however, the equation does describe the behavior of most real gases at low pressure and gives a basis for developing equations of state which more adequately describe the behavior of real gases at elevated pressures. The numerical value of the constant R depends on the units used to express temperature, pressure, and volume. As an example, suppose that pressure is expressed in psia, volume in cubic feet, temperature in degrees Ran-kin, and moles in pound moles. Avogadro's Law states that 1 lb-mole of any ideal gas occupies cu ft at 60°F and 14.7 psia. Therefore,

13 Table 2-1 gives numerical values of R for various systems of units.
= psia cu ft/lb-mole °R Table 2-1 gives numerical values of R for various systems of units.

14 Ideal Gas Mixtures The previous treatment of the behavior of gases ap­plies only to single component gases. As the gas engi­neer rarely works with pure gases, the behavior of a multi-component mixture of gases must be treated. This requires the introduction of two additional ideal gas laws. Dalton's Law: Dalton's Law states that each gas in a mixture of gases exerts a pressure equal to that which it would exert if it occupied the same volume as the total mixture. This pressure is called the partial pressure. The total pressure is the sum of the partial pressures. This law is valid only when the mixture and each component of the mixture obey the ideal gas law. It is sometimes called the Law of Additive Pressures.

15 partial pressure exerted by each component of the gas mixture can be calculated using the ideal gas law. Consider a mixture containing nA moles of component A, nB moles of component B and nc moles of component C. The partial pressure exerted by each component of the gas mixture may be determined with the ideal gas equation: According to Dalton's Law, the total pressure is the sum of the partial pressures

16 It follows that the ratio of the partial pressure of component j, pj, to the total pressure of the mixture p is: where yj is defined as the mole fraction of the jth component in the gas mixture. Therefore, the partial pressure of a component of a gas mixture is the product of its mole fraction times the total pressure.

17 Amagat's Law: Amagat's Law states that the total volume of a gaseous mixture is the sum of the volumes that each component would occupy at the given pressure and temperature. The volumes occupied by the individual components are known as partial volumes. This law is correct only if the mixture and each of the components obey the ideal gas law. The partial volume occupied by each component of a gas mixture consisting of nA moles of component A, nB moles of component B, and so on, can be calculated using the ideal gas law.

18 Thus, according to Amagat, the total volume is:
It follows that the ratio of the partial volume of component j to the total volume of the mixture is: This implies that for an ideal gas the volume fraction is equal to the mole fraction.

19 Apparent Molecular Weight
Since a gas mixture is composed of molecules of various sizes, it is not strictly correct to say that a gas mixture has a molecular weight. However, a gas mixture behaves as if it were a pure gas with a definite molecular weight. This molecular weight is known as an apparent molecular weight and is defined as:

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21 The specific gravity of a gas is defined as the ratio of the density of the gas to the density of dry air taken at standard conditions of temperature and pressure. Symbolically, Assuming that the behavior of both the gas and air may be represented by the ideal gas law, specific gravity may be given as

22 where Mair is the apparent molecular weight of air
where Mair is the apparent molecular weight of air. If the gas is a mixture, this equation becomes: where Ma is the apparent molecular weight of the gas mixture. Example 2-4: Calculate the gravity of a natural gas of the following composition.

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24 REAL GASES Several assumptions were made in formulating the equation of state for ideal gases. Since these assumptions are not correct for gases at pressures and temperatures that deviate from ideal or standard conditions, corrections must be made to account for the deviation from ideal behavior. The most widely used correction method in the petroleum industry is the gas compressibility factor, more commonly called the Z-factor. It is defined as the ratio of the actual volume occupied by a mass of gas at some pressure and temperature to the volume the gas would occupy if it behaved ideally. That is,

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26 Therefore, the equation of state for any gas becomes
where, for an ideal gas, Z = 1. The compressibility factor varies with changes in gas composition, temperature, and pressure. It must be determined experimentally. The results of experimental determinations of compressibility factors are normally given graphically and usually take the form shown in Figure 2-1. The shape of the curve is consistent with present knowledge of the behavior of gases; at very low pressure the molecules are relatively far apart and the conditions of ideal gas behavior are more likely to be met. At low pressure the compressibility factor approaches a value of 1.0, which would indicate that ideal gas behavior does in fact occur.

27 Real Gas Mixtures Compressibility factor charts are available for most of the single component 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 to the critical 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

28 Fig. 2-2. Compressibility factors for methane
Fig Compressibility factors for methane. Courtesy Gas Processors Suppliers Association.

29 Fig. 2-3. Compressibility factors for ethane
Fig Compressibility factors for ethane. Courtesy Gas Processors Suppliers Association.

30 Fig. 2-4. Compressibility factors for propane
Fig Compressibility factors for propane. Courtesy Gas Processors Suppliers Association

31 Real Gas Mixtures where Tc and pc are the critical temperature and pressure for the gas, respectively. The values must be in absolute units. Example 2-6: Calculate the density of ethane at 900 psia and 110°F. The critical properties, from Table 2-2, are Tc = 550°R, pc = 708 psia, M = 30.1 Ibm/lb-mole.

32 Real Gas Mixtures Assuming ideal behavior, the value calculated would be p = (.34) = 4.43 lbm/ft3. 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.

33 Real Gas Mixtures 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 multi-component mixtures, the quantities of pseudo critical temperature and pseudo critical pressure have been conceived. These quantities are defined as These pseudo critical 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.

34 Real Gas Mixtures Example 2-7:
Calculate the pseudo critical temperature and pseudo critical pressure of the following natural gas mixture. Use the critical constants given in Table 2-2. The compressibility factors for natural gases have been correlated using pseudo critical properties and are pre­sented in Figures 2-6, 2-7, and 2-8.

35 Fig. 2-6. Compressibility factors for natural gases
Fig Compressibility factors for natural gases. Courtesy Gas Processors Suppliers Association.

36 Fig Generalized plot of compressibility factors at low reduced pressures. Courtesy Gas Processors Suppliers As­sociation.

37 Fig. 2-8. Compressibility factors for gases near atmospheric pressure
Fig Compressibility factors for gases near atmospheric pressure. Courtesy Gas Processors Suppliers Association.

38 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. The following example illustrates this conversion. Example 2-9: A gas mixture consists of 50% d, 30% C2, and 20% C3 by weight. Calculate the apparent molecular weight and specific gravity of this mixture.

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40 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 2-9 can be used to estimate the pseudo critical properties. The properties can also be calculated using the following equations:

41 Fig. 2-9. Pseudo critical properties of natural gases
Fig Pseudo critical properties of natural gases. Courtesy Gas Processors Suppliers Association.

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44 Compressibility of Natural Gas
Gas compressibility is defined as: Because the gas law of real gas gives:

45 viscosity

46 GAS FORMATION VOLUME FACTOR
Reservoir engineering and pipeline flow calculations require the volumes at in situ conditions of pressure and temperature, and there fore a convenient conversion factor from standard conditions to in situ conditions is needed. This conversion factor is called the gas formation volume factor and is defined as the actual volume occupied by the gas at some pressure and temperature divided by the volume that the gas would occupy at standard conditions. That is,

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48 CORRECTION FOR NONHYDROCARBON IMPURITIES
Natural gases frequently contain materials other than hydrocarbons, such as nitrogen (N2), carbon dioxide (C02), and hydrogen sulfide (H2S). The presence of these impurities affects the value obtained from the Z-factor chart. A procedure for adjusting the critical properties of the gas was proposed by Wichert and Aziz2 in The adjusted critical properties are then used in calculating the reduced properties, and the Z-factor is then obtained from Figure 2-6. The procedure for obtaining the Z-factor for sour gases is: 1-Determine ppc and Tpc for the gas using the gas composition or Figure 2-9 and 2-Calculate the adjusted critical properties.

49 3. Calculate, the reduced properties using the corrected critical properties.
4. Find Z from Figure 2-6 or using the correlation given in the Appendix.

50 Example: A gas containing 2.87% C02 and 23.27% H2S has a critical pressure of 822 psia and a critical temperature of 465°R. Find the gas compressibility factor, Z, for p = 1000 psia, T= 100°F. Solution: B = A = = = 120 [(0.2614) (0.2614)1.6] + 15 [(0.2327)0.5 - (0.2327)4] = 29 oF

51 OTHER EQUATIONS OF STATE
One of the limitations in the use of the compressibility equation to describe the behavior of gases is that the compressibility factor is not constant, and therefore mathematical manipulations cannot be made directly but must be accomplished through graphical or numerical techniques. Many equations of state have been proposed for describing gas behavior and many modifications and improvements have been made. Only two of the most commonly used equations will be described. These will be used later in the calculation of phase behavior.

52 Benedict-Webb-Rubin Equation (BWR)
An earlier equation presented by Beattie and Bridgeman3 was modified and resulted in an equation with eight empirical constants. The parameters Bo, Ao, Co, a, b, c, a, and  are constants for pure compounds and are functions of composition for mixtures. The constants for pure compounds are given in Table 2-3. These constants may be combined for use with mixtures of gases according to the following mixture rules.

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54 Redlich-Kwong Equation (RK):
The Redlich-Kwong Equation4 involves only two em­pirical constants as opposed to the eight required in the BWR equation. The original RK equation is To simplify the calculations with the RK equation, especially for application to mixtures, other constants have been defined as

55 The Dehydration and Sweetening of Natural Gas
Natural gas destined for the pipeline market must meet certain requirements of water-vapor content and hydrogen sulfide content. The water content is normally reduced to about 6 to 8 lb of water per MMcf of gas. The hydrogen sulfide content of sour gases is reduced to 0.1 to 0.25 grain per 100 cu ft to make them "sweet." Processes are available for treating gases to prepare them for the pipeline market and for eventual domestic or commercial consumption. DEHYDRATION OF NATURAL GAS The dehydration of natural gas is the removal of the water that is associated with natural gases in vapor form. The natural gas industry has recognized that dehydration is necessary to ensure smooth operation of gas-transmission lines.

56 Dehydration prevents the formation of gas hydrates and reduces corrosion. Unless gases are dehydrated, liquid water may condense in the pipelines and accumulate at low points along the line, reducing the flow capacity of the line. Several methods have been developed to dehydrate gases on an industrial scale. Familiarity with all the methods is necessary in selecting the best and most economical method to solve a given drying problem. The methods of dehydration in current usage are Adsorption Absorption Direct cooling Compression followed by cooling Chemical reaction

57 Absorption Adsorbents such as alumina, silica gel, and bauxite comprise the desiceants used in adsorption processes. The absorption processes most frequently used em­ploy di- and triethylene glycol as desiceants. The last three methods have minor usage and will be discussed briefly. Dehydration by Cooling The saturated-water content of natural gas decreases with increased pressure or decreased temperature (Fig. 5-8). Thus, hot gases saturated with water vapor may be partially dehydrated by direct cooling. Gases subjected to compression are normally "after-cooled," and this cooling may well remove water from the gas. Unless the cooling process reduces the temperature to the lowest value that the gas will encounter at the prevailing pressure, cooling does not prevent further condensation of water. The use of Joule-Thomson or expansion cooling in wellhead separators to dehydrate natural gas is dis­cussed in Chap. 13.

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