New model estimates water content in saturated natural gas

It uses the Soave Redlich Kwong equation of state for calculating fugacity coefficient of water in a natural gas mixture. Equations 1-8 are the steps for deriving the new model:

Equations 1 and 2 apply for every component ‘i‘ in the mixture at equilibrium.⁴ Equation 3 defines the fugacity coefficient.¹⁸

One obtains Equations 4 from Equations 1-3. Equation 5 applies to water vapor in a natural gas mixture at equilibrium with liquid water.

X_w equals 1 for water because liquid water in hydrocarbon liquid is immiscibility in the hydrocarbon phase.^{4 18} This results in Equation 6.

One obtains Equation 7 from the definition of fugacity of pure liquid,19 and the combination of Equations 6 and 7 yields Equation 8.

From Equation 8, one can estimate the water vapor mole fraction in natural gas at a given P, T, P_w, V_w, and Φ_w.

From Equation 8, it is clear that the accuracy of estimated water content depends on the accuracy of estimating water liquid molar volume (V_w), water vapor pressure (P^w), and the fugacity coefficient of water in natural gas (Φ_w.).

Liquid molar volume

The model uses Equation 9, which is new, for estimating liquid water molar volume. The equation has a maximum error of 1.5% when compared to steam tables published by Perry.¹⁸

In Equation 9:

• V^w = Liquid molar volume, cc/g mol
• T = Temperature, K.
• C₁ = 0.9797709.
• C₂ = 20.0577378.
• C₃ = 201451143.
• C₄ = 0.653131.
• C₅ = 20.302549.
• C₆ = 0.2773145.

F depends on temperature as follows:

• F = 1.09 for 150 < T < 273 K.
• F = 1 for 273 < T < 510 K.
• F = (1.01 + .00001 ¥T) for 510 < T < 610 K.
• F = (1.1 + T/50) for T > 610 K.

Water vapor pressure

To determine the most accurate method for calculating water vapor pressure, the authors evaluated the following three methods:

1. Clapeyron method (M1).^{18 19}
2. Lee-Kesler relationship of Pitzer correlation (M2).^{18 19}
3. Riedel’s vapor pressure equation (M3).^{18 19}

Riedel’s M3 was found to be the most accurate when compared to Perry’s steam table data.¹⁸

A correction factor, based on temperature from steam tables data, further improved M3. This correction for M3 is called M4.

The maximum error found for these methods was M1 - 40%, M2 - 45%, M3 - 20%, and M4 - 2%.

One can use Equations 10-19 to estimate the vapor pressure. In these equations the constants and variables are as follows:

• T_c = 647 K.
• T_b = 373 K.
• T_br = T_b/T_c T_r = T/ T_c.
• Ψb is a function of T_br.
• P_v is water vapor pressure calculated by Riedel’s method (Equation 18).
• P_w is the corrected vapor pressure calculated by the modified Riedel method.
• K is the correction factor that depends on system temperature (T) as shown in Table 1.

Water fugacity coefficient

From literature, it is clear that the use of the equation of state is more accurate for calculating the fugacity coefficient.

The Soave Redlich-Kwong equation of state (SRK ) is the most suitable one for a water and natural gas system.

The new model uses the SRK for calculating the fugacity coefficient of water in natural gas, and adds accuracy by including the interaction parameters of water with hydrocarbons and water with CO₂ and H₂S.

The procedure first calculates the fugacity coefficient of water in a gas mixture from Equation 20, in which the factors C₁, A, B, and Z are calculated with the Soave Redlich Kwong equation of state by Equations 21 and 22.

The units of P and P_c are in psia, and T is in Rankine. R is the gas constant, C_a = 0.4274802327, and C_b = 0.086640350.

The next step, Equation 23, calculates Si that is a function temperature parameter of SRK for each component i.

Equations 24 and 25 calculate SRK parameters for total gas and water mixtures a and b.

In the final step, Equations 26-28 calculate the compressibility factor Z, and Equations 29-30 calculate C₁ and C₂.

Water content

In the new model, the following steps calculate the water content in saturated natural gas at P and T:

1. Calculate liquid water molar volume (V_w) with Equation 9.
2. Calculate water vapor pressure (P_w) with Equations 10-19.
3. Calculate fugacity coefficient of water in gas mixture (Φ^w) with Equations 20-30.
4. Calculate water mole fraction in saturated gas mixture with Equation 8.

Evaluation of new model

The authors evaluated the new mathematical model by using published experimental data to determine the validity and accuracy of estimating natural gas-water content when applied for different conditions and different mixtures of natural gas containing CO₂ and H₂S.

The new model was compared to the results of the following 10 methods.

1. MacCarthy, et al., chart (1950).⁶
2. Katz chart (1956).¹¹
3. Sharma and Campbell (1969).^{4 22}
4. Campbell chart (1970).⁴
5. GPSA (1972).⁷
6. Robinson, et al. (1976).²⁰
7. Sloan (1986).²³
8. Gordon chart (1993).²⁷
9. Kasim (1996).¹⁰
10. Dalton’s Law.^{4 11}

The data selected for the evaluation have the following features:

• Reliability. The data have been used by many previous investigators of water content in natural gas.
• Variety. The data cover a wide range of pressure and temperature conditions and include different mixtures of natural gas with acid gases.

They include pressures up to 10,000 psia and temperatures up to 460° F. The different mixtures include sweet natural gas and natural gas containing CO₂ and H₂S.

References

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5. Heikel, H., Properties of Water and Steam in SI Units, University of Helwan, Egypt
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17. Olds R.H., Sage, B.H., and Lacey, W.N., "Composition of the Dew point of Methane - Water System," Ind. Eng. Chem., Vol. 34, 1942, p. 1223.
18. Perry, R.H., Green, D., and , Maloney, J., Perry’s Chemical Engineers Hand Book, International Edition, McGraw-Hill, 1984.

19. Reid, R.C., Prausnitz, J.M., and Sherwood, T.K., The Properties of Gases and Liquids, McGraw-Hill, New York, 1977.
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21. Sharma, S., and Campbell, J.M., "Predict natural gas water content with total gas usage," OGJ, Aug. 4, 1969, p. 136.
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26. Song. K.Y., and Kobayshi, R., "Water Content of CO2 in Equilibrium with Liquid and/or Hydrates," SPE Formation Evaluation, December 1987.
27. Wichert, G.C., and Wichert, E., "Chart estimates water content of sour natural gas," OGJ, Mar. 29, 1993, p. 61.

The authors

Ahmed Haridy is the Dahshour gas plant section head for Gulf of Suez Petroleum Co., (GUPCO). He has been with GUPCO since 1992, working in process engineering. Haridy holds a BS in petroleum refining engineering, and an MS in chemical engineering and petroleum refining from Suez Canal University. He is an SPE member.

M.E. Awad is assistant professor, chemical engineering department, Suez Canal University and vice-dean of the Technical & Commercial Institute, Suez. Awad received his diploma in petroleum refining from Suez Canal University and has a DEA and PhD. in chemical engineering from Ecole Central de Lyon, Clande Bernard University, Lyon, France.

Khald Abd-el-Fatah is assistant professor, petroleum engineering department, Cairo University, Giza, Egypt. Abd-el-Fatah holds a BS in petroleum engineering and a PhD from Cairo University.

Farouk Kenawy is a consultant in Cairo and formerly was an executive advisor to the Minster of Petroleum of Egypt. He also previously was chairman of GUPCO and Belayim Petroleum Co. Kenawy has a BS in petroleum engineering from Cairo University and a PhD from Moscow Petroleum Institute. He is a member of SPE.