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• Chapter two
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.
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 = 101.325 kPa
• T = 60°F = 520°R = 288.72°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.
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.
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
• 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 1026 molecules/lbmole 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
379.4 cu ft.
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:
• 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
• 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
• 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
• 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,
• 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 Rankin, and moles in pound moles. Avogadro's Law states
that 1 lb-mole of any ideal gas occupies 379.4 cu ft at
60°F and 14.7 psia. Therefore,
= 10.73 psia cu ft/lb-mole °R
Table 2-1 gives numerical values of R for various systems of units.
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 multicomponent 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.
• 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
• 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.
• 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.
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.
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:
• 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
• 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.
•
•
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,
• 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.
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
Fig. 2-2. Compressibility factors for methane.
Courtesy Gas Processors Suppliers Association.
Fig. 2-3. Compressibility factors for ethane.
Courtesy Gas Processors Suppliers Association.
Fig. 2-4. Compressibility factors for propane.
Courtesy Gas Processors Suppliers Association
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.
Real Gas Mixtures
Assuming ideal behavior, the value calculated would be p
= 13.03 (.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.
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.
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.
Fig. 2-6. Compressibility factors for natural
gases. Courtesy Gas Processors Suppliers Association.
Fig. 2-7. Generalized plot of compressibility
factors at low reduced pressures. Courtesy Gas Processors
Suppliers Association.
Fig. 2-8. Compressibility factors for gases near
atmospheric pressure. Courtesy Gas Processors Suppliers
Association.
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.
• 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:
Fig. 2-9. Pseudo critical properties of natural
gases. Courtesy Gas Processors Suppliers Association.
Compressibility of Natural Gas
• Gas compressibility is defined as:
• Because the gas law of real gas gives:
viscosity
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,
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 1970. 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.
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.
• 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 = 0.2327 A = 0.0287 + 0.2327 = 0.2614
= 120 [(0.2614) 0.9 - (0.2614)1.6] + 15 [(0.2327)0.5
- (0.2327)4]
= 29 oF
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.
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.
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
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 gastransmission lines.
• 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
• 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.