2 Jan, 2018

# Ideal Water Content Correlation for Sweet Natural Gas

The analysis of Figures 1 through 3 indicates that the for pressures up to 100 psia (690 kPa) the Raoult’s law water content deviations from real state water content are within about +4% and -4%. The water vapor content of natural gases in equilibrium with water is commonly estimated from Figure 6.1 of Campbell book [1] or Figure 20.4 of Gas Processors and Suppliers Association [2]. In the October, November, December 2007, February 2014 and September 2014 Tips of the Month (TOTM), we studied in detail the water phase behaviors of sweet and sour natural gases and acid gas systems. We presented several correlations and evaluated the accuracy of different methods for estimating the water content of sweet natural gas, sour natural gas, and acid gas systems.

In this TOTM, we will evaluate pressure and temperature applicability ranges and accuracy of the ideal water content correlation for sweet natural gases. In addition, the performance of the ideal water content correlations will be compared with the equation of state based rigorous calculation methods.

**Equilibrium Water Content at Low Pressures **

Assuming vapor phase is an ideal gas and liquid phase is an ideal solution, the equality of water fugacities at equilibrium simplifies to the Raoult’s law.

** ** (1)

Where: *y _{w}* = mole fraction water in the vapor phase

*P ^{V}* = vapor pressure of water at system temperature

*P* = system pressure

*x _{w}* = mol fraction water in the liquid water phase

The liquid mole fraction can be taken as *x _{w}* = 1.0 because of the low solubility of the hydrocarbon phase in the aqueous phase and to cover cases where no liquid hydrocarbon is present – just vapor + liquid water. Thus, for a known pressure and water vapor pressure the mole fraction water in the vapor phase is found from Equation 1.

Under ideal conditions, the mole fraction of water in the gas phase can be estimated by dividing water vapor pressure, *P ^{V}*, at the specified temperature, T, by the system pressure, P. The vapor pressure of pure water, from 0 to 360 °C, (32 to 680 °F) can be calculated by the following correlation [3].

(2)

Where:

τ = 1 – (T/T_{C})

The critical temperature,* T _{C}* = 647.096 K (1164.77 °R) and critical pressure,

*P*= 22064 kPa, (3199.3 psia)

_{C}*T*in K (°R), and

*P*in kPa (psia), and

^{V}a_{1} = −7.85951783, a_{2} = 1.84408259, a_{3} = −11.7866497, a_{4} = 22.6807411,

a_{5} = −15.9618719, a_{6} = 1.80122502

Knowing one kmole of water = 18 kg (lbmole=18 lb_{m}) and one kmole of gases occupy 23.64 Sm^{3} at standard condition of 15 °C and 101.3 kPa (one lbmole of gases occupy 379.5 SCF at standard condition of 60 °F and 14.7 psia), the ideal water content is calculated by:

(3)

**Bukacek Correlation**

Bukacek [4] suggested a relatively simple correlation for the water content of lean sweet gases as follows:

(4)

(5)

where *T* is in °F and *P ^{V}* and

*P*are absolute pressures in psia (kPa).

This correlation is reported to be accurate for temperatures between 60 and 460°F (15.5 and 238°C) and for pressure from 15 to 10,000 psia (0.105 to 69.97 MPa). The pair of equations in this correlation is simple in appearance. The added complexity that is missing is that it requires an accurate estimate of the vapor pressure of pure water. In this study, we have used equation 2 for water vapor pressure.

**Evaluation of the Raoult’s Law (Ideal) Water Content**

The performance of the Raoult’s law for estimating water content of sweet natural gases was evaluated against Bukacek correlation [4], GCAP software [5] and two simulation programs. The water content of GCAP is based on Figure 6.1 of Campbell book [1]. The SRK EOS (Soave-Redlich-Kwong equation of state) with its default binary interaction parameters was used in both simulation programs. The composition of gases needed for simulation study are shown in Table 1. The Raoult’s law, GCAP program and Bukacek correlation are independent of gas composition.

In simulators, there are several options to predict the equilibrium water content of a gas stream which may give different answers. In this study, the mole fraction of water in the desired stream is multiplied 47430 to get lb_{m}/MMscf (or 761420 to get kg/10^{6} Sm^{3}).

Figure 1 through 5 present the percent deviations of water content estimated by Raoult’s law from GCAP program, and two simulation programs (Sim B and Sim C). In each figure, the percent deviations of Raoult’s law water content from those predicted by GCAP, Sim B and Sim C are presented on the vertical axis. The Raoult’s law and GCAP methods are independent of composition while Sim B and Sim C are composition dependent.

The pressure values are 25, 50, 100, 200, and 300 psia (172, 344, 690 1379, and 2069 kPa); respectively. For each pressure, the results for four isotherms of 40, 80, 120, and 160 °F (4.4, 26.7, 48.9, 71.1 °C) are presented.

Figure 1 indicates that at low pressure of 25 psia (172 kPa), the deviations of Raoult’s law water content from the other three methods are small and within -4 to +1%, span of 5%.

Figure 2 indicates that at low pressure of 50 psia (345 kPa), the deviations of Raoult’s law water content from the other three methods are small and within -3 to +2%, span of 5%.

Figure 3 indicates that at low pressure of 100 psia (690 kPa), the deviations of Raoult’s law water content from the other three methods are small and within -1 to +4%, span of 5%.

**Fig 1.** Water content by Raoult’s law vs GCAP and two simulators at 25 psia (172 kPa)

**Fig 2. **Water content by Raoult’s law vs GCAP and two simulators at 50 psia (345 kPa)

**Fig 3.** Water content by Raoult’s law vs GCAP and two simulators at 100 psia (690 kPa)

The analysis of Figures 1 through 3 indicates that the for pressures up to 100 psia (690 kPa) the Raoult’s law water content deviations from real state water content are within about +4% and -4%.

Figure 4 indicates that at the higher pressure of 200 psia (1379 kPa), the deviations of Raoult’s law water content from the other three methods are higher and within 0 to +9%, span of 9%. This figure also indicates that the Raoult’s law percent deviation from GCAP is the largest while simulator B gives lower values of deviations.

Figure 5 indicates that at the higher pressure of 300 psia (2069 kPa), the deviations of Raoult’s law water content from the other three methods are within +5 to +14%, span of 9%. This figure also indicates that the Raoult’s law percent deviations from GCAP is the largest while simulator B gives lower values of deviations.

In general, for a combination of pressure and temperature which results in less dense gas (low pressure and high temperature), there are fewer deviations of Raoult’s law from simulator results that are based on an EOS (equation of state).

Table 2 presents the absolute percent deviations and the overall average absolute percent deviations of Raoult’s law from GCAP, Sim B, Sim C, and Bukacek methods for 140 evaluated points. Note for each temperature, four gases with compositions shown in Table 1 were evaluated. Table 2 indicates that Raoult’s law results have the least deviation from Bukacek and the most deviation is from GCAP and the overall average absolute percent deviations is less than 4 % for pressures up to 300 psia (2069 kPa) and temperatures up to 160°F (71°C).

**Fig 4.** Water content by Raoult’s law vs GCAP and two simulators at 200 psia (1379 kPa)

**Fig 5. **Water content by Raoult’s law vs GCAP and two simulators at 300 psia (2069 kPa)

**Table 2.** Raoult’s law water content average absolute percent deviations from 4 methods

In addition to the sweet natural gas system, we have determined the equilibrium water mole fraction of propane vapor by simulators B and C, Bukacek method, and Raoul’s law (ideal). Table 3 presents the percent deviation of these 4 methods from the smoothed experimental water mole fraction reported in the GPA RR 132 [6]. The accuracy of these four methods are within experimental data. It should be noted that for temperatures of 53.8°F and 47.9°F, the corresponding experimental pressures were 98 psia and 90 psia, respectively. Since at these pressures and temperatures the state of propane was liquid, these two pressures were reduced slightly to 97.35 psia and 88.6 psia to produce 100% propane vapor.

**Table 3.** Propane vapor water content predictions vs RR 132 experimental data [6]

**Conclusions:**

The performance of Raoult’s law for predicting the water content of sweet natural gases against 4 methods is presented. The four methods are GCAP, Simulators A and B and Bukacek correlation. The following conclusions can be made:

1. The Raoult’s law (Eq. 1) combined with an expression to estimate water vapor pressure (Eq. 2) is a simple tool for predicting the water content of sweet natural gases.

2. In general, for a combination of pressure and temperature which results in less dense gas (low pressure and high temperature), there are fewer deviations of Raoult’s law from simulator results that are based on an EOS (equation of state).

3. Table 2 indicates that Raoult’s water content predictions have the least deviation from Bukacek correlation and the most deviations from GCAP.

4. The overall average absolute percent deviations for the systems considered in this tip are less than 4% and the maximum deviation is less than 13.6% (Table 2) for pressures up to 300 psia (2069 kPa) and temperatures up to 160°F (71°C).

To learn more about similar cases and how to minimize operational problems, we suggest attending our **G4 (**Gas Conditioning and Processing**),** **G5** (Practical Computer Simulation Applications in Gas Processing)**, **and **G6** (Gas Treating and Sulfur Recovery) courses.

*PetroSkills *offers consulting expertise on this subject and many others. For more information about these services, visit our website at http://petroskills.com/consulting, or email us at consulting@PetroSkills.com.

*By: Dr. Mahmood Moshfeghian*

*Interested in receiving Tip of the Month email updates? Sign up today!*

References

- R. Kobayashi, “Water content of ethane, propane, and their mixtures in equilibrium with water and hydrates,” Gas Processor Association Research Report (GPA RR 132), Tulsa, Oklahoma, 1991.andSong, K
- GCAP 9.2.1, Gas Conditioning and Processing, PetroSkills/Campbell, Norman, Oklahoma, 2015.
- Bukacek, R.F., "Equilibrium Moisture Content of Natural Gases" Research Bulletin IGT, Chicago, vol 8, 198-200, 1959.
- Wagner, W. and Pruss, A., J. Phys. Chem. Reference Data, 22, 783–787, 1993.
- GPSA Engineering Data Book, Section 20, Volume 2, 13
^{th}Edition, Gas Processors and Suppliers Association, Tulsa, Oklahoma, 2012. - Campbell, J.M., Gas Conditioning and Processing, Volume 1: The Basic Principles, 9
^{th}Edition, 2^{nd}Printing, Editors Hubbard, R. and Snow–McGregor, K., Campbell Petroleum Series, Norman, Oklahoma, 2014.