4.4.1 Composition of Gas Mixtures Known
If the composition of the mixture is known, the pseudo-critical properties of gas mixtures can be calculated by using various mixing rules. The simplest mixing rule was proposed by Kay.3Kay’s mixing rule is the molar weighted average of the critical properties of the pure components of the gas mixture. It is written as:
(4.19) (4.20)
In Eqs. (4.19) and (4.20), is the mole fraction of component ; are the critical pressure and critical temperature, respectively, of component . Eqs. (4.19) and (4.20) are suit-able for low-molecular-weight, homologous gas mixtures with specific gravity less than 0.75.
These equations can be used for quick estimation of pseudo-critical properties and ultimately for calculation of gas compressibility factors. However, it should be noted that this method under estimates gas compressibility factors, with errors as high as 15%.2
The mixing rules proposed by Stewart, Burkhart, and Voo (termed SBV)4and modified by Sutton (termed SSBV)2improved the accuracy of calculating the pseudo-critical properties of high molecular weight gas mixtures. The mixing rules proposed by Stewart et al.4 for high molecular weight gas mixtures are:
(4.21)
(4.22)
(4.23)
(4.24)
In Eqs. (4.21) and (4.22), mole fraction of component, , in mixture; critical temperature of component, , in R; and i ° pc = critical pressure of component, , in psia.i
4.4 Pseudo-critical Properties of Gas Mixtures 67
ptg Sutton2modified the SBV equations (Eqs. (4.21) to (4.24)) for gas mixtures that contain
high concentrations of heptane plus fraction (up to 14.27 mole %). The SSBV modifications are:
(4.25)
The critical properties of pure components in a mixture are provided in Table 4.1. The crit-ical properties of the heptanes-plus fraction must be determined from correlations. Sutton2 reported that the Kessler-Lee5equations provide the lowest error in comparison with other methods.
The Kessler-Lee5equations are:
(4.32)
(4.33)
The boiling point, , is estimated from the Whitson6equation:
(4.34)
The application of the SSBV equations for calculation of pseudo-critical properties of a mixture is shown in Example 4.3. The units of the terms in all the equations are as shown in the example.
4.4.2 Correction for Non-Hydrocarbon Gas Impurities
Gas mixtures may contain varying amounts of hydrogen sulfide, carbon dioxide, nitrogen, and water vapor as impurities. The critical properties of hydrocarbon mixtures should be corrected
Tb,C7+ =
A
4.5579 * M0.15178C7+ * g0.15427C7+B
3ptg for the presence of these substances. Sutton7reported that the correlations proposed by Wichert
and Aziz8for correcting for the presence of hydrogen sulfide and carbon dioxide are superior to other published methods. The Wichert and Aziz correlations are:
(4.35) (4.36)
(4.37)
At present, there are no satisfactory published correlations for correcting for the presence of nitrogen and water vapor. In Section 4.4.3, a method proposed by Standing9that could be used to correct for the presence of water and nitrogen in hydrocarbon gas mixtures is presented. The units of the terms in all the equations are as shown in Example 4.3.
4.4.3 Composition of Gas Mixture Unknown
The critical properties of gas mixtures can be calculated from Sutton7correlations when the com-position of the mixture is not known. Sutton7based the correlation on hydrocarbon gas gravity, which is calculated using the method proposed by Standing:9
(4.38)
The original Standing equation (Eq. (4.38)) can be modified slightly to account for the presence of water vapor as with the other impurities:
(4.39)
The hydrocarbon gas gravity, , is calculated as:
(4.40)
According to Standing,9the mixture’s pseudo-critical properties are calculated as follows:
(4.41) (4.42)
Note that if hydrogen sulfide and carbon dioxide are present in the gas mixture, then calculated from Eqs. (4.41) and (4.42) should be corrected by using the Wichert and Aziz correlations (Eqs. (4.35), (4.36), and (4.37)).
Sutton7 proposed two sets of correlations for calculating hydrocarbon pseudo-critical properties based on hydrocarbon gas gravity. The first set of correlations is for associated gas from oil reservoirs. The second set of correlations is to be used for gas condensates.
ppc and Tpc
Tpc = yHCTpc,HC + yH2sTc,H2S + yCO2Tc,CO2 + yN2Tc,N2 + yH2OTc,H2O ppc = yHCppc,HC + yH2Spc,H2S + yCO2pc,CO2 + yN2pc,N2 + yH2Opc,H2O gg,HC = gg - (yH2SMH
2S + yCO2MCO
2 + yN2MN
2 + yH2OMH
2O)>MAIR
yHC gg,HC
yHC = 1 - yH2S - yCO2 - yN2 - yH2O
yHC = 1 - yH2S - yCO2 - yN2
p*pc = ppc(Tpc - j) Tpc + yH2S(1 - yH2S)j
T*pc = Tpc - j
j = 120
C
(yCO2 + yH2S)0.9 - (yCO2 + yH2S)1.6D
+ 15A
y0.5H2S - y4H2SB
4.4 Pseudo-critical Properties of Gas Mixtures 69
ptg The correlations to be used for associated hydrocarbon gas gravity as proposed by Sutton
are:
(4.43) (4.44)
Equations (4.43) and (4.44) are applicable over a hydrocarbon gas gravity range of . The equations apply if the gas mixture contains less than 10 mol % hydrogen sulfide, less than 55.8 mol % carbon dioxide, and less than 21.7 mol % nitrogen. The correlations were derived from a database that contained 3256 compositions with 4817 gas com-pressibility factor measurements. The average absolute error reported by Sutton7for compress-ibility factors calculated with the correlations is 0.80%.
The correlations for condensate hydrocarbon gas gravity proposed by Sutton7are:
(4.45) (4.46)
Equations (4.45) and (4.46) are applicable over a hydrocarbon gas gravity range of . The composition of the gas mixture should contain less than 90 mole % hydrogen sulfide, less than 89.9 mole % carbon dioxide and less than 33.3 mole % nitrogen. The database for these correlations contained 2264 compositions with 10177 compressibility factor measurements. The average absolute error reported by Sutton7for compressibility factors calcu-lated with the correlations is 1.11%.
4.5 Wet Gas and Gas Condensate
In this section, methods for calculating the specific gravities of wet and condensate gases are pre-sented. As defined previously in Section 4.3, a wet gas forms no liquids inside the reservoir but condenses liquids in the separators and flowlines. A condensate gas will condense liquids inside the reservoir if reservoir pressure falls below the dew point. The methods presented here are not applicable to a condensate reservoir if reservoir pressure falls below the dew point. Before these methods are applied, it is important to ensure that excessive liquid condensation has not occurred in the flowlines before the sampling point at the separators. The first method is a recombination method that is used when the compositions of the gas and liquid phases sampled at the separa-tors are determined from laboratory measurements. The second method is based on correlations when the compositions of the produced phases are not known.
4.5.1 Recombination Method
The recombination method is illustrated with a two-stage separation system consisting of a sep-arator and a stock tank. The compositions of the sepsep-arator gas, stock-tank gas, and stock-tank oil are known.
0.554 … gg,HC … 2.819
Tpc,HC = 164.3 + 357.7gg,HC - 67.7g2g,HC
ppc,HC = 744 - 125.4gg,HC + 5.9g2g,HC
0.554 … gg,HC … 1.862
Tpc,HC = 120.1 + 429gg,HC - 62.9g2g,HC
ppc,HC = 671.1 + 14gg,HC - 34.3g2g,HC
ptg Example 4.1 Calculation of Gravity of a Wet Gas by the Recombination Method
Problem
Suppose a gas reservoir produces wet gas through a two-stage separation system consisting of a sep-arator and a stock tank. The gas-oil ratio (GOR) of the sepsep-arator is given as 62,000 scf/STB. The stock-tank GOR is 350 scf/STB. Stock-tank oil gravity is 50.6 API. Calculate the composition of the reservoir gas given the compositions of the separator and stock-tank fluids as shown in Table 4.2.
Solution
The specific gravity of oil is defined as the density of oil relative to the density of water at the same temperature and pressure:
(4.47)
In Eq. (4.47), are densities of oil and water, respectively, in pounds per cubic foot.
The specific gravity of oil can be related to API gravity ( API) as:
(4.48)
From Eq. (4.48), stock-tank oil specific gravity,
.
Molecular weight of stock-tank oil from Table 4.2 is .