a prediction of water content in sour ng

7/30/2019 A Prediction of Water Content in Sour Ng

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KING SAUD UNIVERSITY

COLLEGE OF ENGINEERING

RESEARCH CENTER

Final Research Report No. 28/426

A PREDICTION OF WATER CONTENT IN SOUR

NATURAL GAS

By

Dr. Khaled Ahmed Abdel Fattah

RabiI 1428 H

April 2007 G


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TABLE OF CONTENTS

Page

ACKNOWLEDGMENT i

ENGLISH ABSTRACT ii

ARABIC ABSTRACT iii

LIST OF TABLES iv

LIST OF FIGURES xii

NOMENCLATURE xvii

LIST OF ABBREVIATIONS xix

CHAPTER 1: INTRODUCTION 1

CHAPTER 2: LITERATURE REVIEW3

2.1 INTRODUCTION 3

2.2 GRAPHICAL CORRELATIONS 6

2.2.1 McKetta and Wehe Correlation 6

2.2.2 Katz Chart Correlation 6

2.2.3 Maddox Correlation 7

2.2.4 Campbell Correlation 11

2.2.5 Robinson et al. Correlation 11

2.2.6 Gordon and Wichert Correlation 162.3 EMPIRICAL CORRELATIONS 19

2.3.1 Ideal Model 19

2.3.2 Biukachek Correlation 19

2.3.3 Bukacek Correlation 21

2.3.4 Sloan Correlation 21

2.3.5 Kazim Correlation 22

2.3.6 Ning Correlation 23

CHAPTER 3: NEW EMPIRICAL MODEL FOR ESTIMATING WATER3.1 NEW EMPIRICAL MODEL 24

3.2 ACID GAS CORRECTION FACTOR 27

CHAPTER 4: STATISTICAL ERROR ANALYSIS


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4.1 AVERAGE PERCENT RELATIVE ERROR 29

4.2 AVERAGE ABSOLUTE PERCENT RELATIVE ERROR 29

4.3 MINIMUM/MAXIMUM ABSOLUTE PERCENT RELATIVE 30

4.4 STANDARD DEVIATION 30

CHAPTER 5: COMPUTER PROGRAMS 31

CHAPTER 6: RESULTS AND DISCUSSION 34

6.1 SWEET NATURAL GAS 38

6.2 NATURAL GAS CONTAINING CARBON DIOXIDE 43

6.3 NATURAL GAS CONTAINING HYDROGEN SULFIDE 40

6.4 NATURAL GAS CONTAINING BOTH CARBON DIOXIDE

AND HYDROGEN SULFIDE

48

CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS 53

7.1 CONCLUSIONS 53

7.2 RECOMMENDATIONS 54

REFERENCES 55

APPENDIX [A] 58


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ACKNOWLEDGMENT

I would like to express my appreciation and thanks to the Saudi Basic Industry

Company (SABIC) and the research center of College of Engineering in King Saud

University for their financial support and cooperation.


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ABSTRACT

The accuracy of estimating water content of natural gas is extremely important

for designing processing units and pipelines networks for natural gas in order to avoid

any hazards that may be caused by the presence of the water in the natural gas such as

hydrate formation, plugging of flow system and damage to the production equipment.

Condensed water may form water slugs, which will tend to decrease the flow efficiency

and increase the pressure drop in the pipeline. The presence of the free water in the

pipeline system may also cause corrosion problems.

In this research, common correlations used for estimating water content of

natural gas were studied and computer programs were designed for the empirical

methods, and the water content values were estimated from charts accompanying to the

graphical methods. A new empirical model for estimating water content in acid gases

was developed.

The calculated results of the new empirical model and the common correlations

such as Kazim, Katz, Campbell, Maddox, Sloan, Ideal model, Ning, Gordon, McKetta,

Bukacek and Biukachek were compared to the published experimental data in order to

be a guide for designers and operators to select the best correlations for their particular

environment. The obtained results of the new correlation for calculating water content

in natural gas provides high accuracy with average absolute relative errors equal to

0.86% for sweet natural gas, 2.16% for gas containing H2S above 10%, and 2.18% for

gas containing CO2 above 10%.


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.

.

.

% 0.862.16%

10%% 2.18

10.%


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LIST OF TABLES

Table No. Page

1 Components of Typical Natural Gases 1

2 Values of the Correlation Coefficients in Equation 1 7

3 Values of the Coefficients in Equation 6 20

4 Values of Constants in Equation 9 21

5 Values of the Constants Used in Equations 11 and 12 22

6 Values of the Constants in Equation 13 23

7 Values of the Constants in Equations 15 and 16 27



10 Comparison of Water Content for Case No. 1 at Temperature = 100 F

and Pressures from 200 psia to 9000 psia 35


and Pressures from 200 psia to10000 psia 35







15 Comparison of Water Content for Case No. 1 at Temperatures from

100 to 340 F and Pressures from 200 psia to 10000 psia 37


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and Pressures from 1000 psia to 2000 psia

39












100 to 160F and Pressures from 1000 psia to 2000 psia 42


100 to 160F and Pressures from 1000 psia to 2082 psia 42

24 Comparison of Water Content for Case No. 4 at Temperature T=130 F


25 Comparison of Water Content for Case No. 4 at Temperature =160 F








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31 Comparison of Water Content for Case No. 7 at Temperature 100 F and

Pressures from 1885 psia to 2387 psia 48

32 Comparison of Water Content for Case No. 7 at Temperature 225 F and


33 Comparison of Water for Case No. 7 at Temperature 350 F and


34 Comparison of Water Content for Case No. 8 at Temperature100 F


35 Comparison of Water Content for Case No. 8 at Temperature 225F and


36 Comparison of Water Content for Case No. 8 at Temperature 350 F


37 Comparison of Water Content for Case No. 7 of Temperatures from


38 Comparison of Water Content for Case No. 8 of Temperatures from


39 Gas Composition of the Studied Cases 58


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x

LIST OF FIGURES

Figure No. Page

. 1 Typical Diagram for Water Content Vs. Pressure 4

2. Typical Diagram for Water Content Vs. Temperature 4

3. Water Content of Carbon Dioxide 5

4. Water Content of Hydrogen Sulfide 5

5. Water Content of Natural Gas Using McKetta and Wehe Chart 8

6. Water Content of Natural Gas Using Katz Chart 9

7. Maddox Correction for the Water Content of CO2 10

8. Maddox Correction for the Water Content of H2S 10

9. Effective Water Content of H2S in Natural Gas Vs. Temperature 12

10. Effective Water Content of CO2 in Natural Gas Vs. Temperature 12

11. Water Content of Natural Gas Using Campbell Chart 13

12. Calculated Water Content of Acid Gas Mixtures to 2000 psia 14



15. Water Content of Natural gas Using Gordon Chart 17

16. Water Content Ratios 18

17 Relationship Between the variable (W1) and Temperature 26

18 Relationship Between the variable (W2) and Temperature 26

19 Water Content Correlations Program 32

20 Flow Chart of Main Program 33


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xi

NOMENCLATURE

A = Variable.

a = Constant.

B = Variable.

c = Constant.

CAcid = Acid Correction Factor.

Eq = Equivalent.

Fcorr = Correction Factor.

P = Pressure, psia

Pc = Critical Pressure, psia

Pv = Vapor Pressure, psia

R = Ratio.

Req = Ratio Equivalent of New Model.

STD = Standard Deviation

T = Temperature ,oF

W = Total Water Content of Natural Gas, lbm/MMscf

W1 = New Model Variable.

W2 = New Model Variable.

y = Mole Fraction in Vapor Phase.

Subscripts

a = Absolute

i = Component in Mixture.

max = Maximum

min = Minimum


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xii

H2S = Hydrogen Sulfide.

CO2 = Carbon Dioxide.

HC = Hydrocarbon.


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1

CHAPTER 1

INTRODUCTION

Natural gas is a subcategory of petroleum that is naturally occurring, complex

mixture of hydrocarbons, with minor amount of inorganic compounds. Table 1 shows

composition of a typical natural gas. It indicates that methane is major component of the

gas mixture. The inorganic compounds nitrogen, carbon dioxide, and hydrogen sulfide

are not desirable because they are not combustible and cause corrosion and other

problems in gas production and processing system.

Table 1: Components of Typical Natural Gases [1]

Hydrocarbons Non Hydrocarbons

Component Mole % Component Mole %

Methane 84.07 Nitrogen 3.45

Ethane 5.86 Carbon dioxide 1.3

Propane 2.2 Hydrogen sulfide 0.63

Butane 0.93

Pentane 0.52

Hexane 0.28

Heptane and + 0.76

Natural gas is used as a source of energy in all sectors of the economy. The

consumption of natural gas in all end-use classifications (residential commercial,

industrial and power generation) has increased rapidly since World War II. This growth


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has resulted from several factors, including development of new markets, replacement

of coal as fuel for providing space and industrial process heat, use natural gas in making

petrochemical and fertilizers, and strong demand for low sulfur- fuels [2]-[9].

The main reason for removing water vapor from natural gas is that water vapor

becomes liquid water under low temperature and/or high-pressure conditions.

Specifically, water content can affect long-distance transmission of natural gas due to

the following facts:

- Liquid water and natural gas can form hydrates that may plug the pipeline and

other equipment.

- Natural gas containing CO2 and/or H2S is corrosive when liquid water is present.

The main objective of this work is evaluating the most commonly used

correlations for estimating water content of natural gas to be a guide for designers and

operators to select the best correlations for their particular environment and introducing

a new empirical model for estimating water content in sour gas.


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3

CHAPTER 2

LITERATURE REVIEW

2.1 INTRODUCTION

Water content of natural gas can be defined as mole fraction of water vapor in

gas mixture at equilibrium with liquid water. The amount of water vapor in the gas will

be governed by pressure, temperature, and gas composition [2], [3] and [10].

The water content of natural gas is a decreasing function of the pressure. That is,

the amount of water in the gas continually decreases as the pressure increases, as shown

in Fig.1. On the other hand, the water content of gas is an increasing function of

temperature, the higher the temperature, the more water in the gas, as shown in Fig. 2.

Also, the effect of gas composition on water content is very clear especially when the

gas contains CO2 and / or H2S where both CO2 and H2S contain more water at

saturation than sweet natural gas. Figs. 3 and 4 display saturated water content of pure

CO2 and H2S respectively [11]-[14].


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1

10

100

1000

10000

0 200 400 600 800 1000 1200

Pressure, psi

WaterContent,Ib

/MMscf Temperature

Fig. 1: Typical Diagram for Water Content Vs. Pressure [3]

1

10

100

1000

10000

0 50 100 150 200 250

Temperature, F

WaterContent,Ib/MMscf

Pressure

Fig. 2: Typical Diagram for Water Content Vs. Temperature [3]


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Fig. 3: Water Content of Carbon Dioxide [12]

Fig. 4: Water Content of Hydrogen Sulfide [12]


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Many correlations had been developed for estimating the water content of

natural gas. These correlations can be divided into graphical correlations [12], [14]-[18],

empirical correlations [3], [18]-[20] and thermodynamics models [16], [21] and [22].

The thermodynamic models give good results for estimating the amount of water

vapor in natural gas but these models take long time and difficult for calculations

because they depend on Equation of State. However, the main advantage of empirical

correlations and graphical correlations is the availability of input data and the simplicity

of calculations. More over, they give us good results. The empirical and graphical

correlations have still kept their popularity among engineers in the natural gas industry.

2.2 GRAPHICAL CORRELATIONS

In these correlations, charts are used to calculate water content as function of

pressure and temperature.

2.2.1 McKetta and Wehe Correlation [23]

McKetta and Wehe chart for determining the natural gas water content, as

shown in Fig. 5, has been widely used for many years in the design of sweet natural gas

dehydrators [23] and [24].

2.2.2 Katz Chart Correlation [16]

Katz et al. published their chart for predicting the water content of natural gas as

it is shown in Fig 6. This chart is based on experimental data published by several

investigators [25]-[27].


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Fig. 5: Water Content of Natural Gas Using McKetta and Wehe Chart [12]


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Fig. 6: Water Content of Natural Gas Using Katz Chart [16]

Temperature, F

WaterContent,

lbb/MMscf


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2.2.3 Maddox Correlation [28]

Maddox proposed a method for calculating the water content of sour gas. This

correlation assumes that the water content of sour gas is the sum of three terms: (1) a

sweet gas contribution, (2) a contribution from CO2 and (3) a contribution from H2S.

Charts are provided to estimate the contributions for CO2 and H2S. The chart for

CO2 is for temperatures between 80 and 160 F, and the chart for H2S is for

temperatures between 80 and 280 F as it is shown in Figs. 7 and 8. The water content

of both CO2 and H2S were correlated as a function of the pressure using only the

following relation:

20 1 2log( ) log (log )W a a P a P= + + (1)

Where W is the water content in lb/MMscf and a set of coefficients, a0, a1, and a2 was

obtained for each isotherm. The coefficients are listed in Table 2.

Table 2 Values of the Correlation Coefficients in Equation 1

Temperature (F ) a0 a1 a2

Carbon Dioxide

80 6.0901 -2.5396 0.3427

100 6.1870 -2.3779 0.3103

130 6.1925 -2.0280 0.2400

160 6.1850 -1.8492 0.2139

Hydrogen Sulfide

80 5.1847 -1.9772 0.3004

100 5.4896 -2.0210 0.3046

130 6.1694 -2.2342 0.3319

160 6.8834 -2.4731 0.3646

220 7.9773 -2.8597 0.4232280 9.2783 -3.3723 0.4897


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Fig. 7: Maddox Correction for the Water Content of CO2 [28]

Fig. 8: Maddox Correction for the Water Content of H2S [28]


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11

2.2.4 Campbell Correlation [15]

Campbell proposed the following relation to calculate weighted average water

content of sour natural gas [15].

2 2 2 2HC HC CO CO H S H SW=y W +y W +y W (2)

Where :

W H2S = Water content of H2S from Fig. 9

W CO2 = Water content of CO2 from Fig. 10

W HC = Water content of sweet gas from Fig. 11

2.2.5 Robinson et al. Correlation [29]

Robinson et a1. developed an approach to calculate the water content of sour

natural gases. Their correlation was based on a modification by Soave for the Redlich

and Kwong (SRK) equation of state to calculate partial fugacity coefficients of a

component in a mixture. The correlation was computer oriented but to make it usable

without a computer, they generated a series of charts at pressures of 300, 1000, 2000,

3000, 6000 and 10,000 psia and temperatures from 50 to 350 oF as it is shown in Figs.

12, 13 and 14 [29].

Because of the limited experimental data at that time, this correlation is

cumbersome to use due to the multiple interpolations involved.


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Fig. 9: Effective Water Content of H2S in Natural Gas Vs. Temperature [15]

Fig. 10: Effective Water Content of CO2 in Natural Gas Vs. Temperature [15]


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Fig. 11: Water Content of Natural Gas Using Campbell Chart [15]


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Fig. 13: Calculated Water Content of Acid

Gas Mixtures to 6000 psia [29]Fig. 12: Calculated Water Content of Acid

Gas Mixtures to 2000 psia [29]


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Fig. 14: Calculated Water Content of Acid Gas Mixtures to 10000

psia [29]


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2.2.6 Gordon and Wichert Correlation [ 30]-[31]

Gordon and Wichert proposed a relatively simple correction based on the

equivalent H2S content of the gas. The equivalent H2S content used in this correlation is

that defined by Equation (3).

2 2 20.7

H S H S COEq y y= + (3)

They presented a chart where temperature, pressure, and equivalent H2S are

given, and then one can obtain a correction factor, Fcorr. Correction factor is ranged from

0.9 to 5.0. Then the water content of the sour gas is calculated as follows:

corr HC W F W= (4)

Where:

WHC = Water content of sweet gas, from Fig. 15

Fcorr = Correction factor, from Fig. 16

This method is limited to an H2S equivalent of 50 mol% and is applicable for

temperatures from 50F to 350F and pressure from 200 to 10,000 psia [30]-[31].


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Fig. 15: Water Content of Natural Gas Using Gordon Chart [31]


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2.3 EMPIRICAL CORRELATIONS

2.3.1 Ideal Model [2]

In this model, the water content of a gas is assumed equal to the ratio of the

vapor pressure of pure water divided by the total pressure of the system. This yields the

mole fraction of water in the gas in pounds per MMscf.

47484Pv

WP

= (5)

This model is reasonably good at very low pressures. This equation can be used

with reasonable accuracy for sweet natural gas and pressures up to about 200 psia [2].

2.3.2 Biukachek Correlation [32]

Biukachek correlation permitting determination of water content of natural gases

for pressures up to 10,000 psia and for temperature ranged from 40 to 230oF. The

following expression is used for calculating gas water content:

= +A

W BP

(6)

Where:

A = Coefficient equal to the water content of ideal gas.

B = Coefficient dependent on the gas composition.

The values of A and B are given in Table 3 and can be calculated by regression analysis

as it is shown in the computer program.


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Table 3: Values of the Coefficients in Equation 6

Temperature,

FA B

Temperature

, FA B

-40 0.1451 0.00347 89.6 36.1 0.1895

-36.4 0.178 0.00402 93.2 40.5 0.207

-32.8 0.2189 0.00465 96.8 45.2 0.224

-29.2 0.267 0.00538 100.4 50.8 0.242

-25.6 0.3235 0.00623 104 56.25 0.263

-22 0.393 0.0071 107.6 62.7 0.285

-18.4 0.4715 0.00806 111.2 69.25 0.31

-14.8 0.566 0.00921 114.8 76.7 0.335

-11.2 0.6775 0.01043 118.4 85.29 0.363

-7.6 0.8909 0.01168 122 94 0.391

-4 0.966 0.0134 125.6 103 0.422

-0.4 1.144 0.0151 129.2 114 0.4543.2 1.35 0.01705 132.8 126 0.487

6.8 1.59 0.01927 136.4 138 0.521

10.4 1.868 0.021155 140 152 0.562

14 2.188 0.0229 143.6 166.5 0.599

17.6 2.55 0.0271 147.2 183.3 0.645

21.2 2.99 0.03035 150.8 200.5 0.691

24.8 3.48 0.0338 154.4 219 0.741

28.4 4.03 0.0377 158 238 0.793

32 4.67 0.0418 161.6 260 0.84135.6 5.4 0.0464 165.2 283 0.902

39.2 6.225 0.0515 168.8 306 0.965

42.8 7.15 0.0571 172.4 335 1.023

46.4 8.2 0.063 176 363 1.083

50 9.39 0.0696 179.6 394 1.148

53.6 10.72 0.0767 183.2 427 1.205

57.2 12.39 0.0855 186.8 462 1.25

60.8 13.94 0.093 190.4 501 1.29

64.4 15.75 0.102 194 537.5 1.327

68 17.87 0.112 197.6 582.5 1.327

71.6 20.15 0.1227 201.2 624 1.405

75.2 22.8 0.1343 204.8 672 1.445

78.8 25.5 0.1453 208.4 725 1.487

82.4 28.7 0.1595 212 776 1.53

86 32.3 0.174 230 1093 2.62


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2.3.3 Bukacek Correlation [33]

Bukacek suggested a relatively simple correlation for the water content of sweet

gas. The water content is calculated using the following equations:

47,484 PvW BP

= + (7)

3083.87log 6.69449

459.6B

T

= +

+(8)

This correlation is reported to be accurate for temperatures between 60 to 460 F

and for pressures from 15 to 10,000 psia.

2.3.4 Sloan Correlation [34]-[35]

Sloan fitted the water content of natural gas versus both temperature and

pressure. His equation is valid for temperatures between -40 and 120 oF and for

pressures from 200 to 2000 psia.

252 41 3 62

( ){ ln( ) (ln( )) }

c L n Pc cW EX P c c P c P

T TT= + + + + + (9)

Where:

T = Temperature in R

c1 to c6 = Constants are given in Table 4

Table 4: Values of Constants in Equation 9

Constants Value

c1 2.8910758E+01

c2 -9.668146E+03c3 -1.663358E+00

c4 -1.308235E+05

c5 2.0353234E+02

c6 3.8508508E-02


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2.3.5 Kazim Correlation [13]

Kazim proposed analytical correlation for calculating the water content of

natural gases based on of McKetta and Wehe graphs. His equation was valid for

temperatures up to 180o

F and pressures from 300 to 1200 psia. He proposed the

following equation:

TW A B= (10)

A and B are variables defined as:

14

1

350

600

i

ii

PaA

=

= (11)

14

i=1

350

600B

i

i

Pb

= (12)

The values of the constants ai and bi are given in Table 5.

Table 5: Values of the Constants Used in Equations 11 and 12

Constants T


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The correlations validity is limited to lean sweet gas mixture. The proposed

correlation predicts water content with an average deviation 4% from the graphical

correlation of McKetta and Wehe.

2.3.6 Ning Correlation [36]

This correlation is based on the McKetta and Wehe chart. This basic equation is

simple in appearance:

2

0 1 2ln W a a T a T = + + (13)

The values for a0, a1, and a2 are tabulated in Table 6as function of pressure up to

14,500 psia.

Table 6: Values of the Constants in Equation 13 [47]

P,

psiaa0 a1 a2

P,

psiaa0 a1 a2

15 -30.0672 0.1634 -1.7452 X 10-4

725 -26.8976 0.1232 -1.1618 X 10-4

29 -27.5786 0.1435 -1.4347 X 10-4

870 -25.1163 0.1128 -1.0264 X 10-4

44 -27.8357 0.1425 -1.4216 X 10-4

1160 -26.0341 0.1172 -1.0912 X 10-4

58 -27.3193 0.1383 -1.3668 X 10-4

1450 -25.4407 0.1133 -1.0425 X 10-4

73 -26.2146 0.1309 -1.2643 X 10-4 2176 -22.6263 0.0973 -8.4136 X 10-5

87 -25.7488 0.1261 -1.1875 X 10-4

2901 -22.1364 0.0946 -8.1751 X 10-5

116 -27.2133 0.1334 -1.2884 X 10-4

4351 -20.4434 0.0851 -7.0353 X 10-5

145 -26.2406 0.1268 -1.1991 X 10-4

5802 -21.1259 0.0881 -7.4510 X 10-5

218 -26.1290 0.1237 -1.1534 X 10-4

7252 -20.2527 0.0834 -6.9094 X 10-5

290 -24.5786 0.1133 -1.0108 X 10-4 8702 -19.1174 0.0773 -6.1641 X 10-5

435 -24.7653 0.1128 -1.0113 X 10-4

10153 -20.5002 0.0845 -7.1151 X 10-5

580 -24.7175 0.1120 -1.0085 X 10-4

14500 -20.4974 0.0838 -7.0494 X 10-5


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CHAPTER 3

NEW EMPIRICAL MODEL FOR ESTIMATING WATER

CONTENT OF NATURAL GAS

The petroleum industry spends millions of dollars to combat the formation of

hydrates. Therefore, the accuracy of estimating the natural gas water content at the

prevailing temperatures and pressures is extremely important for optimizing the cost of

piping systems and processing units. Thus, water should be removed from the natural

gas before it is sold to the pipeline company. For these reasons, the water content of

natural gas is an important engineering consideration. Therefore, an accurate and

simplified correlation for predicting the calculations of water content in natural gas is

desirable [37].

3.1 NEW EMPIRICAL MODEL

Actual gases approach perfect gas behavior at high temperatures and low

pressure. At high pressures and low temperatures this is not so since, real gases deviate

considerably from the ideal gas concept, because gas molecules (1) have finite volumes

and (2) tend to attract and repel each other depending upon their separation distance,

which in turn is dependent upon system pressure and temperature. Thus, this simple

approach is valid only at low pressure where the ideal law is valid. The behavior of

most real gases does not deviate drastically from the behavior predicted by this

equation. Therefore, the best way of writing an equation for real gas is to add a

correction factor into the ideal gas equation.


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So, the water content is calculated using an ideal contribution and a deviation factor. We

suggested a relatively simple correlation for the water content of sweet gas:

12H C

WW W

P

= +(14)

Where WHC is water content of natural gas, lb/MMscf, P is absolute pressure psia, and

W1 and W2 are functions that depend on temperature.

The widely used graphs of Campbell [15], Katz [16], and McKetta and Wehe [23] were

used as the basis for calculating the variables W1, W2 as shown in the following Figs.17

and 18 respectively.


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1.E+00

1.E+01

1.E+02

1.E+03

0 50 100 150 200 250 300 350 400

Temperature,oF

VariableW2

Fig. 18: Relationship between the Variable (W2) and Temperature

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

0 50 100 150 200 250 300 350 400

Temperature,oF

VariableW1

Fig. 17: Relationship between the Variable (W1) and Temperature


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Best curve fitting program [9, 24, 51] was designed for the curves in Fig. 17 and18.

The equations resulted are:

5-1

1

1

i

i

i

W b T

=

= (15)

5-1

2

1

i

i

i

W c T=

= (16)

The values of constant bi and ci given in Table 7

Table 7: Values of the Constants in Equations 15and 16

Constant Value Constant Valueb1 2.508E+05 c1 1.376E+00

b2 -6.946E+03 c2 -5.785E-04

b3 7.658E+01 c3 1.257E-03

b4 -3.788E-01 c4 -3.528E-06

b5 1.032E-03 c5 5.114E-08

3.2 Acid Gas Correction Factor

Acid gases can contain more water than sweet natural gases. The presence of

acid gases should be taken into account, using an appropriate correlation. A new

approach has been developed, based on experimental data [1], [2], [10], [22], and [38],

to provide a quick calculation of the correction factor for the presence the acid gases in

natural gas. The following expressions for the acid gas corrections were proposed:

22 20.75 COH S H S yEq y= + (17)

2

20 1

2

1eq

H S

aa T aR

Eq

= + +

(18)


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( )0 1 2

2

0 1

0 1 2

2

1 ) 1500( (

( ) 1500 3000

( ) 3000

eq

eqAcid

eq

ln P psiab b b PR

C Exp b b b P P psiaR

bb b P psiaRP

+ +

= + + <

+ + >

LLLLL

LL

LLLL(19)

The values of the constants in Equations 18 and 19 were found by regression analysis

and tabulated in Tables 8 and 9.

Table 8: Values of the Constants in Equation 18

Constants Value

a0 -4.095E-02

a1 -1.363E-03

a2 1.444E-01

Table 9: Values of the Constants in Equation 19

Value

Constants

P1500 psia 1500< P 3000 psia P >3000 psia

b0 3.59E-01 5.16E-02 1.04E+00

b1 7.46E-04 -2.84E-02 5.48E-02

b2 -3.26E-06 1.04E-03 -1.91E+00


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CHAPTER 4

STATISTICAL ERROR ANALYSIS

The statistical error analyses were used to check the performance, as well as the

accuracy of the water content in natural gas correlations [39]-[42]. The accuracy of the

correlations was compared with the experimental values using various statistical

methods. The criteria used in this work are average percent relative error, average

absolute percent relative error, minimum and maximum absolute percent relative error,

and standard deviation

4.1 AVERAGE PERCENT RELATIVE ERROR

This is an indication of the relative deviation in percent from the experimental

values and is given by:

( )1

1n

r i

i

E En

=

= (20)

Where Ei is the relative deviation in percent of an estimated value from an

experimental value and is defined by:

( )exp 100 1,2,...exp

i

i

X XestE i n

X

= =

(21)

4.2 AVERAGE ABSOLUTE PERCENT RELATIVE ERROR

1n

a i

ii

E En

=

(22)

It indicates the relative absolute deviation in percent from the experimental values.

A lower value implies a better correlation.


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4.3 MINIMUM/MAXIMUM ABSOLUTE PERCENT RELATIVE ERROR

After the absolute percent relative error for each data point is calculated both the

minimum and maximum values are scanned to know the range of error for each

correlation:

m in1

m inn

ii

E E=

= (23)

m ax1

m axn

ii

E E=

= (24)

The accuracy of a correlation can be examined by maximum absolute percent

relative error. The lower the value of maximum absolute percent relative error, the

higher the accuracy of the correlation is.

4.4 STANDARD DEVIATION

Standard deviation is a measure of dispersion and is expressed as:

( )2

1

1- 1

n

i

i

S T D E n

=

=

(25)

Where (n-1) are the degrees of freedom in multiple regressions. A lower value of

standard deviation means a smaller degree of scatter.


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CHAPTER 5

COMPUTER PROGRAMS

Computer programs were designed for estimating the water content of natural

gas using FORTRAN and VISUAL BASIC softwares. The water content of natural gas

using all empirical correlations mentioned in this work was developed by using Visual

Basic program. Fig. 19 shows the front page of this program. Also, the main program

has subroutines to calculate all the empirical correlations used in this work and also

estimates gas properties such as vapor pressure, specific gravity and the statistical errors

in comparison with the other correlations. Fig. 20 shows the flow chart of the main

program.


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Fig. 19: Water Content Correlations Program


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33

Fig. 20: Flow Chart of Main Program

START

T, P, Wexp, WKatz , WMcKetta, WMaddox, WCampbell,WGordon , WBukacek, WNing, WSloan, WKazim, WIdeal

Model, WBiukachek, WNew Model

END

Gas properties [yi . MWi , Tci Pci ]Condition of gas [T, P, Wexp]

WKatz-WMcKetta-WMaddox-WCampbell-WGordon

Call Subroutines

NING

IDEA

LMODEL

BIUKACHEK

BU

KACK

K

AZIM

S

LOAN

NEW

MODEL

( )ex p10 0

ex pi

W Wes tE

W

=

1

1 nr i

i

E En =

=

1 na i

ii

E En

=

n

im ini= 1

E = m in E

n

im axi= 1

E = m ax E n

2 2

x i

i= 1

1S = E

n - 1

T, P, EiKatz , EiMcKetta, EiMaddox, EiCampbell, EiGordon ,EiBukacek, EiNing, EiSloan, EiKazim, EiIdeal Model,

EiBiukachek, EiNew Model

T, P, SxKatz , SxMcKetta, SxMaddox, SxCampbell,SxGordon , SxBukacek, SxNing, SxSloan, SxKazim,

SxIdeal Model, SxBiukachek, SxNew Model


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CHAPTER 6

RESULTS AND DISCUSSION

The literature data [17],[22],[38], and [43]-[46] are used to demonstrate the

reliability, the validity and the accuracy of estimating water content of natural gas using

different techniques, over wide ranges of temperatures up to 340oF and pressures up to

10000 psia and for different mixtures of natural gas containing different amounts of acid

gases. Four cases of gas mixtures were studied in this work. These mixtures are:

1- Sweet natural gas, methane (C1, 100%).

2- Natural gas containing Carbon dioxide (C1, &CO2)

3- Natural gas containing Hydrogen sulfide(C1& H2S)

4- Natural gas containing both Carbon dioxide and Hydrogen

sulfide (C1&CO2 & H2S)

6.1 SWEET NATURAL GAS

This group of data includes 89 data points that cover a wide range of pressures

from 200 to 10000 psia and temperatures from 100 to 340oF and the gas composition is

100% methane. Tables 10 to 14 show comparison between the average absolute percent

relative error, minimum absolute percent relative error, maximum absolute percent

relative error, and standard deviation of all correlations at temperatures 100, 160, 220,

280, and, 340o

F. Table 15 shows comparison between the average absolute percent


relative error, and standard deviation of all correlations for the range of temperatures

from 100oF to 340

oF and pressures from 200 psia to 10000 psia.


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Table 10: Comparison of Water Content for Case No. 1 at Temperature = 100 F


Range Condition of Correlation All Range Condition

CORRELATION Ea Emax Emin STD Ea Emax Emin STD

KATZ 3.731 7.843 0 2.765 3.731 7.843 0 2.765

MCKETTA 8.265 13.15 2.222 4.571 8.265 13.15 2.222 4.571CAMPBELL 5.21 18.033 0 4.359 5.21 18.033 0 4.359

GORDEN 4.716 9.259 0.649 3.764 4.716 9.259 0.649 3.764

MADDOX 8.265 13.15 2.222 4.571 8.265 13.15 2.222 4.571

NEW 1.351 7.831 0.015 0.59 1.351 7.831 0.015 0.59

SLOAN 3.194 6.216 1.405 8.42 12.575 32.137 1.405 5.569

NING 6.861 13.959 0.523 6.141 6.861 13.959 0.523 6.141

KAZIM 0.976 1.637 0.089 63.29 70.961 100 0.089 27.406

IDEAL MODEL 43.241 73.435 5.955 15.533 43.241 73.435 5.955 15.533

BUKACEK 1.308 7.617 0.035 0.563 1.308 7.617 0.035 0.563

BIUKACHEK 4.043 6.876 0.436 2.511 4.043 6.876 0.436 2.511

Table 11: Comparison of Water Content for Case No. 1 at Temperature = 160

Fand Pressures from 200 psia to10000 psia



KATZ 2.636 12.412 0 15.244 2.636 12.412 0 15.244

MCKETTA 5.592 10.38 1.256 14.988 5.592 10.38 1.256 14.988

CAMPBELL 3.66 10.256 0.427 23.757 3.66 10.256 0.427 23.757

GORDEN 4.297 8.837 0.477 18.977 4.297 8.837 0.477 18.977

MADDOX 5.592 10.38 1.256 14.988 5.592 10.38 1.256 14.988

NEW 1.34 3.853 0.026 1.994 1.34 3.853 0.026 1.994

SLOAN O/RT* O/RT O/RT O/RT O/RT O/RT O/RT O/RT

NING 3.218 11.551 0.123 23.894 3.218 11.551 0.123 23.894

KAZIM 2.868 5.951 0.857 338.526 74.426 100 0.857 142.209

IDEAL MODEL 38.202 70.848 3.537 53.664 38.202 70.848 3.537 53.664

BUKACEK 1.193 3.661 0.068 1.67 1.193 3.661 0.068 1.67

BIUKACHEK 3.548 7.041 1.303 6.715 3.548 7.041 1.303 6.715

*O/R-T: out the range of temperature


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KATZ 2.152 5.254 0 31.145 2.152 5.254 0 31.145

MCKETTA 4.706 13.628 0.923 61.519 4.706 13.628 0.923 61.519CAMPBELL O/RT O/RT O/RT O/RT O/RT O/RT O/RT O/RT

GORDEN 4.698 31.142 0.16 152.748 4.698 31.142 0.16 152.748

MADDOX O/RT O/RT O/RT O/RT O/RT O/RT O/RT O/RT

NEW 0.327 1.018 0.002 1.513 0.327 1.018 0.002 1.513

SLOAN O/RT O/RT O/RT O/RT O/RT O/RT O/RT O/RT

NING 2.825 6.24 0.364 39.805 2.825 6.24 0.364 39.805

KAZIM O/RT O/RT O/RT O/RT O/RT O/RT O/RT O/RT

IDEAL MODEL 32.045 63.809 2.048 138.267 32.045 63.809 2.048 138.267

BUKACEK 0.542 1.068 0.265 4.414 0.542 1.068 0.265 4.414

BIUKACHEK 6.479 12.885 1.44 33.718 6.479 12.885 1.44 33.718

Table 13: Comparison of Water Content for Case No. 1 at Temperature = 280

Fand Pressures from 200 psia to 10000 psia



KATZ 3.832 6.798 0.125 122.518 3.832 6.798 0.125 122.518

MCKETTA 2.455 6.192 0 108.626 2.455 6.192 0 108.626

CAMPBELL O/RT O/RT O/RT O/RT O/RT O/RT O/RT O/RT

GORDEN 4.759 18.445 0.107 340.997 4.759 18.445 0.107 340.997


NEW 0.624 1.033 0.258 35.313 0.624 1.033 0.258 35.313

SLOAN O/RT O/RT O/RT O/RT O/RT O/RT O/RT O/RTNING 4.299 8.539 0.32 239.896 4.299 8.539 0.32 239.896


IDEAL MODEL 28.133 58.455 0.751 311.392 28.133 58.455 0.751 311.392

BUKACEK 0.932 1.365 0.54 47.332 0.932 1.365 0.54 47.332

BIUKACHEK O/RT O/RT O/RT O/RT O/RT O/RT O/RT O/RT


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KATZ 2.077 4.772 0.183 117.445 2.077 4.772 0.183 117.445

MCKETTA O/RT O/RT O/RT O/RT O/RT O/RT O/RT O/RTCAMPBELL O/RT O/RT O/RT O/RT O/RT O/RT O/RT O/RT

GORDEN 2.000 2.000 2.000 175.461 2.000 2.000 2.000 175.461


NEW 0.690 2.207 0.024 168.505 0.690 2.207 0.024 168.505


NING 2.330 4.844 0.151 305.513 2.330 4.844 0.151 305.513


IDEAL MODEL 25.956 54.713 0.209 650.402 25.956 54.713 0.209 650.402

BUKACEK 0.798 2.540 0.078 196.263 0.798 2.540 0.078 196.263

BIUKACHEK O/RT O/RT O/RT O/RT O/RT O/RT O/RT O/RT

Table 15: Comparison of Water Content for Case No. 1 at Temperatures from 100

to 340 F and Pressures from 200 psia to 10000 psia



KATZ 2.876 12.412 0.000 76.145 2.876 12.412 0.000 76.145

MCKETTA 5.212 13.628 0.000 4323.842 24.383 100.000 0.000 3856.35

CAMPBELL 4.413 18.033 0.000 6732.408 42.710 100.000 0.000 4184.74

GORDEN 4.087 31.142 0.107 181.631 4.087 31.142 0.107 181.631

MADDOX 7.121 13.150 2.185 7925.724 63.384 100.000 1.256 4224.42

NEW 0.861 7.831 0.002 75.679 0.861 7.831 0.002 75.679

SLOAN 3.194 6.216 1.405 465.846 10.368 33.630 1.353 131.386

NING 3.873 13.959 0.123 171.965 3.873 13.959 0.123 171.965

KAZIM 1.922 5.951 0.089 143016.9 112.790 1307.03 0.089 40336.2

IDEAL MODEL 33.406 73.435 0.209 323.644 33.406 73.435 0.209 323.644

BUKACEK 0.951 7.617 0.035 88.760 0.951 7.617 0.035 88.760

BIUKACHEK 4.703 12.885 0.436 1464.842 28.462 221.943 0.410 1126.03


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From Tables 10 to 15, it is clear that:

1. New, Bukacek, Kazim, Katz, Sloan, Ning, Gordon, Campbell, McKetta,

Biukachek, and Maddox correlations give good results of water content of

natural gas when using these correlations at their limited conditions.

2. Ideal Model gives large values of average absolute relative error (33.406%)

when using with pressure greater than 200 psia because it is limited to low

pressure.

3. New, Bukacek, Katz, Ning, and Gordon correlations, are better correlations for

the range of temperatures from 100oF to 340

oF, and range of pressures from 200

psia to 10000 psia.

4. The Katz correlation is the best one of the graphical correlations for the range of

temperatures from 100oF to 340

oF, and range of pressures from 200 psia to

10000 psia.

5. McKetta, Biukachek, Ideal Model, Campbell, Maddox, Sloan, and Kazim

correlations cannot be used outside their limited range of conditions.

6. The new model predictions are in good agreement with experimental data of

sweet natural gas for the pressures up to 10000 psia and temperatures up to

340oF with average absolute relative error 0.861 %

6.2 NATURAL GAS CONTAINING CARBON DIOXIDE

This group of data includes 16 data points. This covers concentration of carbon

dioxide in natural gas up to 20% and for pressures up to 2082 psia and temperatures up

to 160oF. The gas compositions are 89% methane, with 11% carbon dioxide for 8 data

points, and 80% methane, with 20% carbon dioxide for the other 8 data points. Tables

16 to 21 show comparison between the average absolute percent relative error,


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minimum absolute percent relative error, maximum absolute percent relative error, and

standard deviation of all correlations at temperatures 100oF, 130

oF, and 160

oF.

Table 16: Comparison of Water Content for Case No. 2 at Temperature = 100 Fand Pressures from 1000 psia to 2000 psia



KATZ 10.488 12.530 6.980 6.546 10.488 12.530 6.980 6.546

MCKETTA 7.227 12.530 2.172 4.980 7.227 12.530 2.172 4.980

CAMPBELL 5.208 9.149 2.563 3.395 5.208 9.149 2.563 3.395

GORDEN 3.75 5.810 2.367 2.932 3.750 5.810 2.367 2.932

MADDOX 4.555 6.115 3.412 3.325 4.555 6.115 3.412 3.325

NEW 1.6 3.682 0.423 1.146 1.600 3.682 0.423 1.146

SLOAN 11 15.755 7.650 6.812 11.000 15.755 7.650 6.812

NING 7.162 7.952 6.765 4.820 7.162 7.952 6.765 4.820

KAZIM 4.727 4.727 4.727 1-PO.* 68.242 100.000 4.727 46.962

IDEAL MODEL 37.465 46.305 29.575 23.408 37.465 46.305 29.575 23.408

BUKACEK 7.549 10.075 5.963 4.710 7.549 10.075 5.963 4.710

BIUKACHEK 11.376 14.217 9.454 7.138 11.376 14.217 9.454 7.138

*1-PO.: one point

Table 17: Comparison of Water Content for Case No. 2 at Temperature = 130F




KATZ 3.595 4.752 2.439 6.825 3.595 4.752 2.439 6.825

MCKETTA 2.585 2.730 2.439 4.423 2.585 2.730 2.439 4.423

CAMPBELL 3.747 4.390 3.105 6.121 3.747 4.390 3.105 6.121

GORDEN 1.458 1.756 1.160 2.376 1.458 1.756 1.160 2.376

MADDOX 2.427 2.495 2.359 4.119 2.427 2.495 2.359 4.119

NEW 4.29 5.300 3.280 7.841 4.290 5.300 3.280 7.841

SLOAN O/RT O/RT O/RT O/RT O/RT O/RT O/RT O/RTNING 2.461 2.923 1.998 4.014 2.461 2.923 1.998 4.014

KAZIM 1.206 1.206 1.206 1-PO. 50.603 100.000 1.206 102.513

IDEAL MODEL 25.514 30.724 20.305 41.571 25.514 30.724 20.305 41.571

BUKACEK 1.826 2.592 1.061 3.011 1.826 2.592 1.061 3.011

BIUKACHEK 1.604 2.824 0.385 2.940 1.604 2.824 0.385 2.940


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KATZ 5.992 8.665 2.136 17.587 5.992 8.665 2.136 17.587

MCKETTA 7.74 8.665 7.175 22.660 7.740 8.665 7.175 22.660CAMPBELL 2.133 2.581 1.594 6.094 2.133 2.581 1.594 6.094

GORDEN 2.04 2.765 0.820 6.909 2.040 2.765 0.820 6.909

MADDOX 1.364 2.325 0.554 4.366 1.364 2.325 0.554 4.366

NEW 0.761 1.286 0.469 2.813 0.761 1.286 0.469 2.813


NING 5.639 6.964 4.780 16.314 5.639 6.964 4.780 16.314

KAZIM 0.844 0.844 0.844 1-PO. 66.948 100.000 0.844 214.489

IDEAL MODEL 27.387 31.990 20.526 78.080 27.387 31.990 20.526 78.080

BUKACEK 5.642 8.037 2.949 16.270 5.642 8.037 2.949 16.270

BIUKACHEK 7.441 9.886 4.636 21.260 7.441 9.886 4.636 21.260


and Pressures from 1000 psia to 2000 psiaRange Condition of Correlation All Range Condition


KATZ 14.149 21.610 6.687 11.069 14.149 21.610 6.687 11.069

MCKETTA 14.149 21.610 6.687 11.069 14.149 21.610 6.687 11.069

CAMPBELL 5.947 10.805 1.089 5.148 5.947 10.805 1.089 5.148

GORDEN 2.395 3.390 1.400 1.836 2.395 3.390 1.400 1.836

MADDOX 5.122 5.932 4.311 3.940 5.122 5.932 4.311 3.940

NEW 2.431 3.302 1.560 2.248 2.431 3.302 1.560 2.248

SLOAN 9.319 17.903 0.735 8.464 9.319 17.903 0.735 8.464

NING 12.053 16.444 7.662 9.193 12.053 16.444 7.662 9.193

KAZIM 4.428 4.428 4.428 1-PO. 52.214 100.000 4.428 47.286

IDEAL MODEL 35.428 47.675 23.181 26.991 35.428 47.675 23.181 26.991

BUKACEK 12.539 19.410 5.667 9.860 12.539 19.410 5.667 9.860

BIUKACHEK 8.819 16.405 1.232 7.784 8.819 16.405 1.232 7.784


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KATZ 8.384 13.924 1.074 12.631 8.384 13.924 1.074 12.631

MCKETTA 9.726 10.886 8.140 13.711 9.726 10.886 8.140 13.711

CAMPBELL 3.898 4.403 3.392 5.732 3.898 4.403 3.392 5.732

GORDEN 1.094 1.427 0.629 1.737 1.094 1.427 0.629 1.737

MADDOX 2.013 4.020 0.266 3.139 2.013 4.020 0.266 3.139

NEW 1.709 2.276 0.913 2.609 1.709 2.276 0.913 2.609


NING 12.269 18.760 7.448 17.226 12.269 18.760 7.448 17.226

KAZIM 6.7 6.700 6.700 1-PO. 68.900 100.000 6.700 105.426

IDEAL MODEL 31.049 43.855 18.434 43.218 31.049 43.855 18.434 43.218

BUKACEK 11.229 18.835 4.560 16.106 11.229 18.835 4.560 16.106

BIUKACHEK 5.881 11.890 2.741 9.059 5.881 11.890 2.741 9.059





KATZ 8.018 11.711 0.653 24.632 8.018 11.711 0.653 24.632

MCKETTA 11.523 16.883 5.975 31.966 11.523 16.883 5.975 31.966

CAMPBELL 4.063 5.174 3.250 11.310 4.063 5.174 3.250 11.310

GORDEN 1.079 2.214 0.450 4.539 1.079 2.214 0.450 4.539

MADDOX 3.229 4.623 1.820 9.482 3.229 4.623 1.820 9.482

NEW 2.484 4.852 0.316 10.347 2.484 4.852 0.316 10.347


NING 9.142 14.281 3.337 25.863 9.142 14.281 3.337 25.863

KAZIM 0.658 0.658 0.658 1-PO. 66.886 100.000 0.658 210.209

IDEAL MODEL 25.543 36.163 12.797 70.979 25.543 36.163 12.797 70.979

BUKACEK 8.739 14.204 1.479 25.832 8.739 14.204 1.479 25.832

BIUKACHEK 6.382 9.292 4.638 17.755 6.382 9.292 4.638 17.755

Tables 22 and 23 show comparison between the average absolute percent


relative error, and standard deviation of all correlations for the range of temperatures

from 100oF to 60

oF and pressures from 1000 to 2082 psia.


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to 160F and Pressures from 1000 psia to 2000 psia



KATZ 7.079 12.530 2.136 10.357 7.079 12.530 2.136 10.357


GORDEN 2.536 5.810 0.820 4.111 2.536 5.810 0.820 4.111

MADDOX 2.827 6.115 0.554 3.321 2.827 6.115 0.554 3.321

NEW 1.958 5.300 0.423 3.379 1.958 5.300 0.423 3.379

SLOAN 11.000 15.755 7.650 27.426 8.539 15.755 1.643 14.660

NING 5.415 7.952 1.998 9.218 5.415 7.952 1.998 9.218

KAZIM 2.259 4.727 0.844 231.226 63.347 100.000 0.844 123.595

IDEAL MODEL 30.698 46.305 20.305 46.317 30.698 46.305 20.305 46.317

BUKACEK 5.403 10.075 1.061 9.125 5.403 10.075 1.061 9.125

BIUKACHEK 7.458 14.217 0.385 12.039 7.458 14.217 0.385 12.039


to 160F and Pressures from 1000 psia to 2082 psia


CORRELATION Ea Emin Emax STD Ea Emax Emin STD

KATZ 9.688 21.61 0.653 15.377 9.688 21.61 0.653 15.377

MCKETTA 11.506 21.610 5.975 19.057 11.506 21.610 5.975 19.057

CAMPBELL 4.472 10.805 1.089 7.051 4.472 10.805 1.089 7.051

GORDEN 1.413 3.390 0.450 2.689 1.413 3.390 0.450 2.689

MADDOX 3.246 5.932 0.266 5.542 3.246 5.932 0.266 5.542

NEW 2.180 4.852 0.316 5.767 2.180 4.852 0.316 5.767

SLOAN 9.319 17.903 0.735 35.644 8.108 17.903 0.666 13.472

NING 11.042 18.760 3.337 16.969 11.042 18.760 3.337 16.969

KAZIM 3.929 6.700 0.658 237.530 63.973 100.000 0.658 126.965

IDEAL MODEL 30.079 47.675 12.797 45.576 30.079 47.675 12.797 45.576

BUKACEK 10.623 19.410 1.479 16.693 10.623 19.410 1.479 16.693

BIUKACHEK 6.803 16.405 1.232 11.053 6.803 16.405 1.232 11.053


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1. Gordon, New model, Campbell, Bukacek, Ning and Maddox correlations are the

best correlations that can deal with gas containing carbon dioxide.

2. Ideal Model can not deal with gas containing carbon dioxide, because its average

absolute relative error is equal to 30.079%

3. The new model can be applied for estimating the water content of natural gas

containing carbon dioxide (up to 20%) with average absolute relative error (2.18%)

at pressures up to 2082 psia and temperatures up to 160oF.

6.3 NATURAL GAS CONTAINING HYDROGEN SULFIDE

This group of data includes 17 data points that cover hydrogen sulfide

concentrations up to 30% and for pressures up to 2000 psia and temperatures up 160oF.

The gas compositions are 89% methane, 11% hydrogen sulfide for 5 data points, 80%

methane, 20% hydrogen sulfide for 8 data points, and 70% methane, with 30%

hydrogen sulfide for 4 data points. Tables 24 to 28 show comparison between the

average absolute percent relative error, minimum absolute percent relative error,

maximum absolute percent relative error, and standard deviation of all correlations.

Tables 29 and 30 show comparison between the average absolute percent relative error,

minimum absolute percent relative error, maximum absolute percent relative error, and

standard deviation of all correlations


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Table 24: Comparison of Water Content for Case No. 4 at Temperature T=130 F




KATZ 5.123 6.542 3.704 8.602 5.123 6.542 3.704 8.602


GORDEN 1.957 2.804 1.111 3.354 1.957 2.804 1.111 3.354

MADDOX 5.784 6.729 4.839 9.721 5.784 6.729 4.839 9.721

NEW 2.904 5.267 0.54 7.134 2.904 5.267 0.54 7.134

SLOAN O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T

NING 4.992 7.006 2.979 8.507 4.992 7.006 2.979 8.507

KAZIM 2.194 2.194 2.194 1-PO. 51.097 100 2.194 107.041

IDEAL MODEL 27.37 33.637 21.102 45.902 27.37 33.637 21.102 45.902

BUKACEK 3.369 6.688 0.05 7.157 3.369 6.688 0.05 7.157

BIUKACHEK 3.765 6.911 0.62 7.441 3.765 6.911 0.62 7.441

Table 25: Comparison of Water Content for Case No. 4 at Temperature =160 F




KATZ 5.924 7.997 2.136 17.295 5.924 7.997 2.136 17.295

MCKETTA 7.671 7.997 7.379 22.434 7.671 7.997 7.379 22.434

CAMPBELL 4.481 5.303 3.279 13.607 4.481 5.303 3.279 13.607

GORDEN 2.499 5.426 0.249 8.936 2.499 5.426 0.249 8.936

MADDOX 4.906 8.117 2.771 15.035 4.906 8.117 2.771 15.035

NEW 1.663 2.674 0.244 5.809 1.663 2.674 0.244 5.809


NING 5.57 6.283 4.78 16.029 5.57 6.283 4.78 16.029

KAZIM 0.844 0.844 0.844 1-PO. 66.948 100 0.844 214.264IDEAL MODEL 27.338 31.493 20.526 77.855 27.338 31.493 20.526 77.855

BUKACEK 5.574 7.365 2.949 15.928 5.574 7.365 2.949 15.928

BIUKACHEK 7.375 9.227 4.636 20.958 7.375 9.227 4.636 20.958


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KATZ 9.603 13.345 4.372 14.217 9.603 13.345 4.372 14.217


GORDEN 1.558 3.744 0.41 2.746 1.558 3.744 0.41 2.746

MADDOX 11.903 15.69 4.959 17.422 11.903 15.69 4.959 17.422

NEW 1.392 2.439 0.548 2.077 1.392 2.439 0.548 2.077


NING 14.206 18.309 10.534 20.421 14.206 18.309 10.534 20.421

KAZIM 9.81 9.81 9.81 999 69.937 100 9.81 109.021

IDEAL MODEL 37.701 47.391 27.246 54.144 37.701 47.391 27.246 54.144

BUKACEK 13.33 18.768 7.741 19.123 13.33 18.768 7.741 19.123

BIUKACHEK 13.573 18.673 8.358 19.449 13.573 18.673 8.358 19.449





KATZ 11.646 18.816 4.201 55.196 11.646 18.816 4.201 55.196

MCKETTA 11.094 21.203 5.862 40.907 11.094 21.203 5.862 40.907

CAMPBELL 9.644 17.945 0.799 70.999 9.644 17.945 0.799 70.999

GORDEN 3.715 5.624 2.08 19.864 3.715 5.624 2.08 19.864

MADDOX 7.587 14.371 0.051 26.418 7.587 14.371 0.051 26.418

NEW 2.163 3.842 0.387 8.249 2.163 3.842 0.387 8.249


NING 12.804 21.199 6.789 63.805 12.804 21.199 6.789 63.805

KAZIM 5.602 10.079 2.937 230.364 43.361 100 2.937 162.892

IDEAL MODEL 25.534 45.706 11.007 87.711 25.534 45.706 11.007 87.711

BUKACEK 9.491 21.128 4.503 33.557 9.491 21.128 4.503 33.557

BIUKACHEK 11.052 22.852 5.819 39.481 11.052 22.852 5.819 39.481


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KATZ 15.354 20.334 11.204 50.425 15.354 20.334 11.204 50.425


GORDEN 1.458 2.428 0.613 5.246 1.458 2.428 0.613 5.246

MADDOX 16.295 18.547 14.202 53.583 16.295 18.547 14.202 53.583

NEW 1.493 3.856 0.286 6.249 1.493 3.856 0.286 6.249


NING 15.51 19.214 12.755 50.765 15.51 19.214 12.755 50.765

KAZIM 8.741 9.366 8.117 366.38 54.371 100 8.117 211.53

IDEAL MODEL 27.014 35.432 18.848 88.329 27.014 35.432 18.848 88.329

BUKACEK 14.672 19.938 9.613 48.088 14.672 19.938 9.613 48.088

BIUKACHEK 9.467 15.188 3.967 32.168 9.467 15.188 3.967 32.168

Table 29: Comparison of Water Content for Case No. 4 at Temperatures from

130 to 160F and Pressures from 1000 psia to 1566 psia



KATZ 5.603 7.997 2.136 12.964 5.603 7.997 2.136 12.964

MCKETTA 6.652 7.997 3.704 16.436 6.652 7.997 3.704 16.436

CAMPBELL 3.72 5.303 1.259 9.881 3.72 5.303 1.259 9.881

GORDEN 2.282 5.426 0.249 6.537 2.282 5.426 0.249 6.537

MADDOX 5.257 8.117 2.771 11.69 5.257 8.117 2.771 11.69

NEW 2.159 5.267 0.244 5.44 2.159 5.267 0.244 5.44


NING 5.339 7.006 2.979 12.106 5.339 7.006 2.979 12.106

KAZIM 1.519 2.194 0.844 321.366 60.608 100 0.844 160.683

IDEAL MODEL 27.351 33.637 20.526 59.644 27.351 33.637 20.526 59.644

BUKACEK 4.692 7.365 0.05 11.818 4.692 7.365 0.05 11.818

BIUKACHEK 5.931 9.227 0.62 15.279 5.931 9.227 0.62 15.279


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KATZ 10.88 18.816 4.201 42.411 10.88 18.816 4.201 42.411

MCKETTA 12.377 21.203 5.862 32.884 12.377 21.203 5.862 32.884

CAMPBELL 9.275 17.945 0.799 54.091 9.275 17.945 0.799 54.091

GORDEN 2.906 5.624 0.41 15.088 2.906 5.624 0.41 15.088

MADDOX 9.206 15.69 0.051 22.034 9.206 15.69 0.051 22.034

NEW 1.874 3.842 0.387 6.333 1.874 3.842 0.387 6.333


NING 13.33 21.199 6.789 49.452 13.33 21.199 6.789 49.452

KAZIM 6.654 10.079 2.937 208.091 53.327 100 2.937 136.228

IDEAL MODEL 30.097 47.391 11.007 72.344 30.097 47.391 11.007 72.344

BUKACEK 10.93 21.128 4.503 27.349 10.93 21.128 4.503 27.349BIUKACHEK 11.997 22.852 5.819 31.604 11.997 22.852 5.819 31.604


1. Ideal Model cannot deal with gas containing hydrogen sulfide, with average

absolute relative error equals to 27.351% with H2S concentration equal to 11%.

2. Maddox and Campbell correlations can deal with gas containing hydrogen sulfide

concentration up to 20%, with average absolute percent relative error equals to

9.206% and 9.275% respectively. Also, as the concentration of hydrogen sulfide is

decreased the average absolute relative error is decreased.

3. New model, Gordon, and Campbell correlation are best correlations for predicting

the water content in natural gas containing low or high concentrations of hydrogen

sulfide up to 30% H2S, with average absolute relative error equals to 1.493%,

1.458%, and 10.52%.

4. The new model results are in good agreement with experimental data for hydrogen

sulfide concentrations up to 30% with average absolute relative error equals to

1.493% and at pressures up to 2000 psia and temperatures up to160 oF.


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6.4 NATURAL GAS CONTAINING BOTH CARBON DIOXIDE AND

HYDROGEN SULFIDE

This group of data includes 18 data points cover hydrogen sulfideconcentrations

up to 80% and carbon dioxide up to 60%, and pressures ranged from 699 to 2597 psia

and temperatures ranged from 100 to 350oF. The gas composition is 10% methane,

80% hydrogen sulfide, and 10% carbon dioxide for 7 data points and 30% methane,

10% hydrogen sulfide, and 60% carbon dioxide for 11 data points. Tables 31 to 36 show

comparison between the average absolute percent relative error, minimum absolute

percent relative error, maximum absolute percent relative error, and standard deviation

of all correlations used at temperatures 100, 160, and 350 oF.

Table 31: Comparison of Water Content for Case No. 7 at Temperature 100 F




KATZ 91.289 91.653 90.925 562.897 91.289 91.653 90.925 562.897

MCKETTA 90.572 91.064 90.079 558.464 90.572 91.064 90.079 558.464

CAMPBELL 50.495 68.396 32.593 328.102 50.495 68.396 32.593 328.102

GORDEN O/R-H2SO/R-H2S O/R-H2S O/R-H2S O/R-H2S O/R-H2SO/R-H2SO/R-H2S

MADDOX 72.656 72.866 72.445 448.068 72.656 72.866 72.445 448.068

NEW 34.427 49.058 19.796 232.472 34.427 49.058 19.796 232.472

SLOAN 90.756 90.756 90.756 999.000 91.383 92.011 90.756 563.453

NING 91.179 91.616 90.741 562.210 91.179 91.616 90.741 562.210

KAZIM O/R-P O/R-P O/R-P O/R-P O/R-P O/R-P O/R-P O/R-P

IDEAL MODEL 94.586 95.165 94.008 583.211 94.586 95.165 94.008 583.211

BUKACEK 91.544 92.030 91.057 564.455 91.544 92.030 91.057 564.455

BIUKACHEK 91.167 91.691 90.643 562.129 91.167 91.691 90.643 562.129

O/R-H2S: equivalent of H2S > 50%


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KATZ 43.042 62.807 18.269 768.269 43.042 62.807 18.269 768.269

MCKETTA 40.072 60.113 15.261 726.158 40.072 60.113 15.261 726.158

CAMPBELL O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T


MADDOX O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T

NEW 8.899 12.665 5.189 152.997 8.899 12.665 5.189 152.997


NING 40.408 62.148 14.531 740.253 40.408 62.148 14.531 740.253

KAZIM O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T

IDEAL MODEL 50.959 71.440 25.436 889.264 50.959 71.440 25.436 889.264


Table 33: Comparison of Water for Case No. 7 at Temperature 350 F and

Pressures from 1595 psia to 2635 psia



KATZ 22.795 42.115 3.475 2260.736 22.795 42.115 3.475 2260.73

MCKETTA O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T




NEW 26.987 48.916 5.058 2191.374 26.987 48.916 5.058 2191.37


NING 24.729 38.470 10.987 2117.367 24.729 38.470 10.987 2117.36

KAZIM O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T O/R-TIDEAL MODEL 26.635 50.929 2.340 2729.487 26.635 50.929 2.340 2729.48

BUKACEK 24.182 39.699 8.665 2160.694 24.182 39.699 8.665 2160.69

BIUKACHEK O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T


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KATZ 45.052 64.130 25.962 52.587 45.052 64.130 25.962 52.587

MCKETTA 39.220 59.182 15.563 47.355 39.220 59.182 15.563 47.355

CAMPBELL 10.412 17.868 3.411 13.583 10.412 17.868 3.411 13.583

GORDEN 7.332 18.160 1.283 10.694 7.332 18.160 1.283 10.694

MADDOX 25.415 42.089 7.973 32.538 25.415 42.089 7.973 32.538

NEW 7.100 22.580 0.333 12.556 7.100 22.580 0.333 12.556

SLOAN 33.004 56.714 14.649 61.151 40.832 64.316 14.649 49.930

NING 44.259 62.277 24.403 51.339 44.259 62.277 24.403 51.339

KAZIM 23.537 27.932 19.142 138.816 61.769 100.000 19.142 80.146

IDEAL MODEL 56.519 78.584 29.620 65.156 56.519 78.584 29.620 65.156






KATZ 28.880 37.525 12.787 319.570 28.880 37.525 12.787 319.570

MCKETTA 29.242 37.116 14.348 323.382 29.242 37.116 14.348 323.382


GORDEN 5.041 6.792 1.233 57.817 5.041 6.792 1.233 57.817


NEW 1.862 4.036 0.390 25.176 1.862 4.036 0.390 25.176


NING 27.389 38.210 10.747 305.136 27.389 38.210 10.747 305.136


IDEAL MODEL 41.941 53.594 24.214 457.380 41.941 53.594 24.214 457.380

BUKACEK 30.189 39.073 15.916 330.742 30.189 39.073 15.916 330.742

BIUKACHEK 28.196 37.938 12.684 311.576 28.196 37.938 12.684 311.576


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KATZ 28.386 31.422 22.516 1685.608 28.386 31.422 22.516 1685.60

MCKETTA O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T


GORDEN 6.225 8.157 2.943 380.842 6.225 8.157 2.943 380.842


NEW 2.235 4.081 1.164 167.874 2.235 4.081 1.164 167.874


NING 22.314 27.345 13.417 1339.816 22.314 27.345 13.417 1339.81


IDEAL MODEL 36.005 41.951 25.338 2143.570 36.005 41.951 25.338 2143.57

BUKACEK 24.283 28.912 15.955 1450.237 24.283 28.912 15.955 1450.23BIUKACHEK O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T O/R-T

Tables 37 and 38 show comparison between the average absolute percent


relative error, and standard deviation of all correlations for temperatures from 100 to

350 oF. From Tables 31 to 38, it is clear that:

1. Campbell correlation predicts the water content for gas having 60%CO2 with

average absolute relative error equals to 10.41%. As the concentration of hydrogen

sulfide decreases the average absolute relative error decreases.

2. New model, and Gordon correlation are the best correlations to estimate the water

content of natural gas having concentrations of hydrogen sulfide and carbon dioxide

up to 55% EqH2S, with the average absolute relative error equals to 3.868% and

6.197% for 60% CO2 concentrations.

3. The effect of hydrogen sulfide on water content in natural gas is greeter than the

effect of the same amount of carbon dioxide.


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Table 37: Comparison of Water Content for Case No. 7 of Temperatures from

100 to 350 F and Pressures from 1096 psia to 2635 psia



KATZ 51.042 91.653 3.475 1049.464 51.042 91.653 3.475 1049.46

MCKETTA 60.272 91.064 15.261 3528.803 71.623 100.000 15.261 2881.25

CAMPBELL 50.495 68.396 32.593 7069.875 64.985 100.000 29.267 2886.26


MADDOX 72.656 72.866 72.445 7321.335 92.187 100.000 72.445 2988.92

NEW 21.361 49.058 5.058 903.971 21.361 49.058 5.058 903.971

SLOAN 90.756 90.756 90.756 1-PO. 51.007 92.011 13.204 990.729

NING 50.434 91.616 10.987 991.234 50.434 91.616 10.987 991.234

KAZIM O/R-T-P O/R-T-P O/R-T-P O/R-T-P O/R-T-P O/R-T-P O/R-T-P O/R-T-P

IDEAL MODEL 56.474 95.165 2.340 1249.788 56.474 95.165 2.340 1249.78BUKACEK 51.418 92.030 8.665 1012.669 51.418 92.030 8.665 1012.66

BIUKACHEK 61.067 91.691 15.357 2385.902 62.112 95.576 15.357 1948.08

Table 38: Comparison of Water Content for Case No. 8 of Temperatures from 100




KATZ 34.626 64.130 12.787 774.417 34.626 64.130 12.787 774.417

MCKETTA 34.231 59.182 14.348 3217.067 52.168 100.000 14.348 2691.59

CAMPBELL 10.412 17.868 3.411 4928.434 42.501 100.000 3.411 2699.41

GORDEN 6.197 18.160 1.233 173.336 6.197 18.160 1.233 173.336

MADDOX 25.415 42.089 7.973 5024.416 72.878 100.000 7.973 2751.98

NEW 3.868 22.580 0.333 76.641 3.868 22.580 0.333 76.641

SLOAN 33.004 56.714 14.649 1357.968 30.967 64.316 12.485 607.302

NING 32.140 62.277 10.747 622.691 32.140 62.277 10.747 622.691

KAZIM 23.537 27.932 19.142 8703.469 86.098 100.000 19.142 2752.27

IDEAL MODEL 45.624 78.584 24.214 991.469 45.624 78.584 24.214 991.469

BUKACEK 33.615 64.292 15.916 673.991 33.615 64.292 15.916 673.991

BIUKACHEK 34.615 62.747 12.684 1817.053 40.535 62.747 12.684 1520.25


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CHAPTER 7

CONCLUSIONS AND RECOMMENDATIONS

7.1 CONCLUSIONS

[1] At or near atmospheric pressure, ideal model is valid and may be used to

estimate the water content of the natural gas for pressure less than 200 psi.

[2] The new model results are in good agreement with the experimental data and

demonstrating reliability of the model.

[3] The best correlations for predicting the water content in sweet natural gas

according to their average absolute relative errors are:

New model (0. 86%)

Bukacek correlation (0.95%)

Katz correlation (2.87%)

Ning correlation (3.87%)

Gorden correlation (4.09%)

[4] The new model can be applied to different mixtures of gases for pressures up to

10000 psia, and temperatures up to 340oF where:

Sweet natural gas with average absolute relative error of 0.86%.

Natural gas containing carbon dioxide and/or hydrogen sulfide (up to EqH2S

55%) with average absolute relative error of 3.868%.

[5] All the correlations are recommended for predicting the water content of sweet

gases at the conditions discussed in this work. These correlations are used at low

concentrations of carbon dioxide and hydrogen sulfide up to 10%.


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[6] The effect of hydrogen sulfide concentration on amount of water

content is greater than effect of carbon dioxide concentration.

7.2 RECOMMENDATIONS

[1] More experimental data are required to study the effect of hydrogen sulfide and

carbon dioxide on water content at high pressures and temperatures.

[2] Extension of this work should be done to study the effect of salt content on the

calculations of water content in natural gas.

[3] The developed model should be tested for different compositions of natural gas

to study the effect of gas composition on water content calculations.


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43, No. 20, 2005, pp. 1802.

[2] J. J Carroll, Natural Gas Hydrates, Gulf Professional Publishing, ElsevierScience, New York, USA, 2003, pp. 232-253.

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[4] A. Chapoy, A. H. Mohammadi, A. Chareton, B. Tohidi, and D. Richon,Experimental Measurement and Phase Behavior Modeling of Hydrogen

SulfideWater Binary System, Ind. Eng. Chem. Res., Vol. 44, No. 19, 2005,

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[5] A. Chapoy, A. H. Mohammadi, A. Chareton, B. Tohidi, and D. Richon,Measurement and Modeling of Gas Solubility and Literature Review of the

Properties for the Carbon DioxideWater System, Ind. Eng. Chem. Res., Vol.43, No. 7, 2004, pp. 1794-1802.

[6] V. Ganapathy, Compute Dew Point of Acid Gases, Hydrocarbon Processing,Feb. 1993, pp.93-98.

[7] J. Otakar, and M. Lee, Particulate Probe Answers Water Content Questions forAlabama Gas Pipeline, Oil & Gas Journal, Sep. 2000, pp. 68-73.

[8] E. D. Sloan, Natural Gas Hydrates, JPT, Dec. 1991, pp. 1414-141.[9] R. A. Wattenbarger and L. John, Gas Reservoir Engineering, Society of

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[14] J. N. Robinson, R.G. Moore, R. A. Heidemann, Estimation of Water Content ofSour Natural Gases, SPE J., Aug. 1977, pp. 281.

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70.

[18] S. Sharma, and J. M. Campbell, Predict Natural Gas Water Content with TotalGas Usage, Oil & Gas Journal, Aug. 1969, pp. 136-137.

[19] W. R. Behr, Correlation Eases Absorber Equilibrium Line Calculations forTEG Natural Gas Dehydration, Oil & Gas Journal, Nov. 1983, pp. 96-98.

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APPENDIX [A]

Table 39: Gas Composition of the Studied Cases

Case No. CO2 H2S C1 Ref.

1 0.00% 0.00% 100.00% 0.554 27,32,44,61

2 11.00% 0.00% 89.00% 0.660 12,17,27,30

3 20.00% 0.00% 80.00% 0.747 12,17,27,30

4 0.00% 11.00% 89.00% 0.622 12,17,27,30

5 0.00% 20.00% 80.00% 0.679 12,17,27,30

6 0.00% 30.00% 70.00% 0.741 12,17,27,30

7 10.00% 80.00% 10.00% 1.149 12,17,27,30

8 60.00% 10.00% 30.00% 1.196 12,17,27,30

a prediction of water content in sour ng

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