articulo - contenido de agua - metodos analiticos

ARTICLE IN PRESSCHERD-1599; No. of Pages 15

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chemical engineering research and design x x x ( 2 0 1 4 ) xxx–xxx

Contents lists available at ScienceDirect

Chemical Engineering Research and Design

j ourna l h omepage: www.elsev ier .com/ locate /cherd

nalytical methods to calculate water content inatural gas

in Zhua,∗, Luling Lia, Jia Zhua,b, Li Qinc, Junming Fana

Key Laboratory of Gas Process Engineering, School of Chemistry and Chemical Engineering, Southwest Petroleumniversity, Chengdu 610500, PR ChinaSuining Field of Sichuan Oil and Gas Mine, Petro-China Southwest Oil & Gas Field Company, Suining 629000, PRhinaCarbon Black Plant of Luzhou, Petro-China Southwest Oil & Gas Field Company, Luzhou 646000, PR China

a b s t r a c t

This work presents a review on the main analytical methods for estimating water content in natural gas samples of

different types and with different contents. The analytical methods for sweet natural gas are mainly developed for gas

under conditions of temperatures of 223.15–510.93 K and pressures of 0.1–100 MPa. The calculation of water content

in sour natural gas should be calculated in a temperature range from 288.15 to 444.26 K and a pressure range from 0.5

to 69 MPa. By combining correction methods with analytical methods for sweet natural gas randomly and comparing

the results with the experimental value published in the literature, it was found that the simplified thermodynamic

mode & Bahadori correction method, the simplified thermodynamic mode & Mohammadi correction method, the

Sloan & Bukacek–Maddox correction method and the Bahadori & Khaled correction method could reproduce with

the least AAD%. Additionally, by comparing the results of these analytical methods with the experimental data

in literatures, this work presented the optimum analytical methods for sweet natural gas and sour natural gas,

respectively, at different temperatures and at different pressures.

© 2014 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Keywords: Water content; Sweet natural gas; Sour natural gas; Analytical method; Evaluate; Combination mode

fore, some corrections including charts and correlations should be

applied, when it comes to analyzing water content in sour natural gas.

. Introduction

n the initial design of the facilities of production, transmission, and

rocessing of natural gas (NG), the dissolved water in the gas phase

f NG is an essential factor to be considered. The main forms that the

issolved water exists in are liquid water, gas hydrates and ice. The for-

ation of a liquid phase may cause corrosion or/and two-phase flow

roblems. Additionally, a decrease in the temperature (or an increase

n the pressure) will make the problems caused by the gas hydrates

r ice more worse. The acid gases contained in NG may generate acid

iquor, which would integrate with free water, resulting in the corrosion

f pipeline, instruments, valves etc. Consequently, to prevent corro-

ion and to avoid the formation of ice or gas hydrate, it is necessary

o remove saturated water from the acid gas concentration by dehy-

ration facilities before transmitting and processing. For engineers,

ccurate prediction of water content is the foundation of calculating

Please cite this article in press as: Zhu, L., et al., Analytical methods to

http://dx.doi.org/10.1016/j.cherd.2014.05.021

∗ Corresponding author at: No.8 Xindu Avenue, Xindu District, ChengduE-mail address: [email protected] (L. Zhu).

ttp://dx.doi.org/10.1016/j.cherd.2014.05.021263-8762/© 2014 The Institution of Chemical Engineers. Published by

the consumption of dehydrate agents and for predicting the aqueous

dew points.

NG can be divided into two categories: sweet natural gas (gas whose

acid concentration is less than 5% of the gas mixture) and sour natural

gas (gas whose acid concentration is more than 5% of the gas mix-

ture) (Zhu, 2008). Many related approaches have been conducted for

the estimation of water content in NG. To sum up, the methods for

sweet natural gas are composed of three main types: charts plotted with

limited experimental data, thermodynamic models based on phase

equilibrium, and empirical or semi-empirical correlations developed

with limited application. Because an increase in the amount of lique-

fied H2S or CO2 significantly enhances the solubility of water, presence

of acid gases (i.e. hydrogen sulfide and carbon dioxide) makes the water

content increase obviously (Carroll, 2002; William et al., 2012). There-

calculate water content in natural gas. Chem. Eng. Res. Des. (2014),

City, 610500, PR China. Tel.: +86 15884505696.

Elsevier B.V. All rights reserved.

dx.doi.org/10.1016/j.cherd.2014.05.021

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dx.doi.org/10.1016/j.cherd.2014.05.021


2 chemical engineering research and design x x x ( 2 0 1 4 ) xxx–xxx

Nomenclature

W water content in mg/Sm3 (288.15 K, 0.101 MPa)T absolute temperature (K)P total pressure (MPa)C parameter in Eq. (1)a parameter in Eqs. (2), (4), (5), (6), (9), (23), (24),

(32) and (35)b parameter in Eqs. (4), (6), (29), (30), (31) and (35)A parameter in Eqs. (7) and (8)B parameter in Eqs. (18) and (19)� parameter in Eqs. (20) and (21)S the mole fraction of brine in waterd the average relative molecular massF the correction factor between sweet natural gas

and sour natural gasV the average molar volume over the pressure

interval P to Psw or P to P0

V the molar volumeM molecular massy the mole fraction in the gas phaseK the standard equilibrium constantx the mole fraction in liquid phaseR the universal gas constantAAD the average absolute deviationAD the absolute deviationa equation of state parameterb equation of state parameterZ the compressibility factorNG natural gasMIM modified ideal modelSTM simplified thermodynamic modelMTM modified thermodynamic model

Greek symbols� the chemical potentialϕ fugacity coefficient

Superscriptso the standard situationequi the equivalent situationl the liquid phase

SubscriptsH2O waterH2S hydrogen sulfideCO2 carbon dioxideCH4 methaneNHC the non-hydrocarbon gases such as H2S, CO2

HC the hydrocarbon gasessweet sweet natural gassour sour natural gassw the water in saturation statec the critical situation0 the reference situationi the component imix the mixture gasr the reduce situation

In order to describe the water content of gas in equilibrium with

hydrocarbon, several charts have been presented, some of these being:



the McKetta–Wehe chart (GPSA, 1998), the Campbell chart (Campbell,

1991), the Katz chart (Khaled, 2007) etc. Of the available candidates,

the McKetta–Wehe chart is the most popular, with surprising accuracy

for sweet natural gas containing over 0.7 (mole fraction) of methane

(GPSA, 1998). Furthermore, some correction charts, i.e. the Wichert

chart (Wichert and Wichert, 1993), the Campbell chart (Campbell, 1991),

and the Robinson chart (Robinson et al., 1978), have been developed for

estimating water content of sour natural gas. However, because of the

difficulty in obtaining accurate data and the need for interpolations,

charts cannot be widely used.

Based on the phase equilibrium, several thermodynamic models

are available for the estimation of water content in sweet natural gas.

Some models utilize the equality in the activity coefficient of water in

different phases, and others refer to the equation of state. Addition-

ally, with the different models applied in liquid–vapor, hydrate–vapor,

ice–vapor and liquid–hydrate–vapor regions, thermodynamic models

always have high accuracy. However, these models are too complicated

to be performed by simple tools (Mohammadi et al., 2004a; Mohammadi

and Richon, 2007).

By matching the existing data to the equations, researchers

have obtained some empirical or semi-empirical correlations that

are simple, convenient and operated with high degree of accuracy.

Consequently, these correlations remain popular among engineers.

Increasing numbers of correlations such as the Bahadori method

(Bahadori et al., 2009) and the Behr method (Behr, 1983) have been

reported. Nonetheless, the presence of large amounts of heavy hydro-

carbon may make the correlations, based on methane, (i.e., not a

heavy hydrocarbon), such as the Behr method (Behr, 1983) and the

Sharma–Campbell method (Sharma and Campbell, 1969), have lower

accuracy. In general, most of the correlations are used for the sweet

natural gas containing few heavy hydrocarbons at the applicable con-

ditions. Unfortunately, due to the shortage of consistent experimental

values, these correlations also need further verification for low tem-

perature conditions.

Summarily, with the difficulty of reading accurately, the need

for interpolation of charts as well as the complexity of thermo-

dynamic models, the brief and non-robust analytical methods are

always popular because of their high accuracy, speediness, conve-

nience, and their programmable nature. Analytical methods generally

include empirical correlations and semi-empirical correlations, as well

as some simplified thermodynamic models. With the limitation of

application, analytical methods are not available for every case, and

a comprehensive report about the optimal methods at given con-

ditions is still absent. As the analytical methods for sour natural

gas are modified versions of the analytical method for sweet nat-

ural gas, the choice of which sweet natural gas analytical method

should be used, together with the correction method to estimate water

content in sour natural gas remains a controversial problem at all

time.

The main aim of this work is summarizing the main analytical

methods of estimating water content in natural gas by category and

choosing the optimal analytical method of sweet natural gas for every

correction method to accurately predict the water content in sour nat-

ural gas. Then, taking the results and the applicable range of each

analytical method into consideration, the optimum analytical method

for sweet or sour natural gas at specific temperature and pressure is

focused on.

2. Analytical methods for sweet natural gas

The analytical methods for estimating water content in sweetnatural gas mainly consist of three catalogs, namely cor-relations originally regressed from chart data, correlationsoriginally regressed from experimental data, and equationsreferring to the calculation of the phase equilibrium inwater–hydrocarbon systems. In this work, a review of theanalytical methods for estimating water content in sweet


natural gas is presented and is detailed in the followingsections.

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chemical engineering research and design x x x ( 2 0 1 4 ) xxx–xxx 3

Table 1 – Constants C in Eq. (1).

C1 C2 C3 C4 C5 C6

21.58610805 −1.280044975 −4808.426205 113.0735222 −40377.6358 3.8508508 × 10−2

Table 2 – Constants a in Eq. (2).

P/MPa a0 a1 a2 P/MPa a0 a1 a2

0.1 −30.0672 0.1634 −1.7452 × 10−4 5 −26.8976 0.1232 −1.1618 × 10−4

0.2 −27.5786 0.1435 −1.4347 × 10−4 6 −25.1163 0.1128 −1.0264 × 10−4

0.3 −27.8357 0.1425 −1.4216 × 10−4 8 −26.0341 0.1172 −1.0912 × 10−4

0.4 −27.3193 0.1383 −1.3668 × 10−4 10 −25.4407 0.1133 −1.0425 × 10−4

0.5 −26.2146 0.1309 −1.2643 × 10−4 15 −22.6263 0.0973 −8.4136 × 10−5

0.6 −25.7488 0.1261 −1.1875 × 10−4 20 −22.1364 0.0946 −8.1751 × 10−5

0.8 −27.2133 0.1334 −1.2884 × 10−4 30 −20.4434 0.0851 −7.0353 × 10−5

1.0 −26.2406 0.1268 −1.1991 × 10−4 40 −21.1259 0.0881 −7.4510 × 10−5

1.5 −26.1290 0.1237 −1.1534 × 10−4 50 −20.2527 0.0834 −6.9094 × 10−5

2 −24.5786 0.1133 −1.0108 × 10−4 60 −19.1174 0.0773 −6.1641 × 10−5

3 −24.7653 0.1128 −1.0113 × 10−4 70 −20.5002 0.0845 −7.1151 × 10−5

−4 −5

2

TMepfp

2FStb

W

wtsapr

2Ecc

W

d

waa

ranging from 1 to 15 MPa.

Table 3 – Constants a and b in Eq. (4).

a1 706,652.14 b1 2893.11193a2 −8915.814 b2 −41.86941a3 42.607133 b3 0.229899

−4

4 −24.7175 0.1120 −1.0085 × 10

.1. Correlations regressed from chart data

hese correlations are generally from regressing the data ofcKetta–Wehe chart (GPSA, 1998), a chart considering the

ffects of gas gravity and brine. With the nonlinear and com-lexity characters of the chart, most of these correlations areailed to be included in the whole chart, except the methodroposed by Ning et al. (2000).

.1.1. Sloan methodor the low temperature region, Sloan (Kobayashi et al., 1987;loan, 1998; Sloan et al., 1976) reported a method by providinghe variable water content as a function of T and P, as showny Eq (1):

H2O,sweet

= 16.02 × exp[

C1 + C2 ln P + C3 + C4 ln P

T+ C5

T2+ C6(ln P)2

](1)

here the water content (WH2O) is in mg/Sm3, the tempera-ure (T) is in K, and the pressure (P) is in MPa. The subscriptweet refers to sweet natural gas, and the constants C1 to C6

re listed in Table 1. This correlation is accurate for the tem-erature ranging from 233.15 to 323.15 K and for the pressureanging from 1.4 to 13.8 MPa.

.1.2. Ning et al. methodqs. (2) and (3) conducted by Ning et al. (2000) illustrated theorrelations depending on the main chart and the correctionhart of McKetta–Wehe chart, respectively.

H2O,sweet = (714.855 + 1.1T + 369.673d − 1.42Td)

× (1 − 0.02247S) × exp(a0 + a1T + a2T2) (2)

=∑ Miyi

28.966(3)

here S and d are the mole fraction of brine in water, and the



verage relative molecular mass, respectively. The average rel-tive molecular mass d could be calculated by Eq. (3), where M

100 −20.4974 0.0838 −7.0494 × 10

and y are the molecular mass, and the mole fraction of compo-nent i in gas, respectively. In order to calculate the coefficientsa0, a1, a2 depending on the pressure, an integrated table hasbeen presented in Table 2. It should be noted that this corre-lation has taken the effect of gas gravity into account, and itis more suitable for 0.1 MPa< P <100 MPa.

2.1.3. Khaled methodConcerning that water content in NG tends to rise withincreasing temperature or decreasing pressure, Khaled(2007) proposed the following equations regressed data ofMcKetta–Wehe chart, Campbell chart and Katz chart.

WH2O = 16.02

(∑5i=1ai × Ti−1

P+∑5

i=1bi × Ti−1

)(4)

where a and b are parameters listed in Table 3. The applicabletemperature and pressure range of this correlation are from310.93 to 444.26 K and from 1.38 to 68.95 MPa, respectively.

2.1.4. Bahadori methodBahadori (Bahadori et al., 2009) stated the water content wasa function of pressure and temperature and proposed a newalternative to predict the water content in sweet natural gas,as shown by Eq. (5):

WH2O,sweet = 10

∑3

i=0

∑3

j=0aij×Tj×(log P+3)i

(5)

where a is the constant presented in Table 4. This method canbe used to estimate water content of sweet natural gas fortemperature ranging from 288.15 to 393.15 K and for pressure


a4 −0.0915312 b4 −5.68959 × 10a5 7.46945 × 10−5 b5 5.36847 × 10−7

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a10 −19.46736072 a30 −15.1343742a11 0.062742134 a31 0.102010483a12 0.000238447 a32 −0.000216579a13 −5.6739 × 10−7 a33 1.348433 × 10−7

a20 30.07101715 a40 1.955498725a21 −0.171087078 a41 −0.013966992a22 0.000226883 a42 3.26487 × 10−5

a23 3.12335 × 10−8 a43 −2.42011 × 10−8

calculation of phase equilibrium is a good choice. Combined

2.2. Correlations regressed from experimental data

Except the method of Zhu et al. (Zhu, 2008; Zhu et al., 2003),most of correlations (such as Behr method (Behr, 1983) andKazim method (Kazim, 1996)) regressed experimental data ofwater content in equilibrium with methane.

2.2.1. Zhu et al. MethodSimilar to the method of Khaled, Zhu et al. (Zhu, 2008; Zhuet al., 2003) had reported an equation as below by regressingwater content data in hydrocarbon gas mixture at experimen-tal condition. Due to the restriction of experimental data, theapplicable range of this method is a little complicated, asexhibited in Fig. 1.

WH2O = 101.325

7∑i=0

ai(T − 273.15)i

P+

7∑i=0

bi(T − 273.15)i (6)

where a0–a7, b0–b7 are constants listed in Table 5.

2.2.2. Behr methodBased on the experimental data of water content in methane



for pressure ranging from 1.379 to 20.679 MPa, Behr (1983)

Fig. 1 – Comparison of the applicable

investigated the following equation:

WH2O = A0 exp

[A1 + A2 + A3 ln P + A4(ln P)2

T2

+A5 ln P + A6(ln P)2 + A7(ln P)3

+ A8 + A9 ln P + A10(ln P)2 + A11(ln P)3

T3

](7)

Coefficients A0–A11 were obtained on the basis of fittingdew point of natural gas versus the water content value andshowed in Table 6.

2.2.3. Kazim methodAccording to the experimental data of water content at dif-ferent temperature conditions, Kazim (1996) put forward ananalytical expression for calculating the water content insweet natural gas, as shown in Eq. (8)

WH2O,sweet = 16.02A1A1.8T−459.672 (8)

Ai =4∑

j=1

ai,j

(145.0377 P − 350

600

)j−1

(9)

where A is a parameter linked with pressure and calculatedby Eq. (9). The constants ai,j of Eq. (9) are listed in Table 7. Thisapproach is suitable for temperature up to 355.37 K and forpressure ranging from 2 to 8.3 MPa.

2.3. Equations referring to the calculation of phaseequilibrium in water-hydrocarbon systems

To avoid the limitation of application, a method based on the


with the saturated vapor pressure of liquid water and ice,

range of each analytic method.

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Table 5 – Constants a and b in Eq. (6).

a0 a1 a2 a3 a4 a5 a6 a7

4.65925 3.37802 × 10−1 1.11426 × 10−2 2.04372 × 10−4 1.91021 × 10−6 1.56275 × 10−8 1.99046 × 10−10 -1.23039 × 10−12

b0

4.67351 × 101 4.60019 8.68387 × 10−3 -4.65719 × 10−3 9.32789 × 10−5 2.06031 × 10−6 -4.78943 × 10−8 2.37537 × 10−10

Table 6 – Constants A in Eq. (7).

A0 A1 A2 A3 A4 A5

16.02 15.01438824 −1,397,805.38 1.20055 0.12061 0.55096A6

−0.70827 0.09904 129,261,863 −1.29214 −0.25962 −0.01738


j Temperature ranges

T < 310.93 K 310.93 K ≤ T ≤ 355.37 K

a1,j a2,j a1,j a2,j

1 4.34322 1.03776 10.38175 1.026742 1.35912 −0.02865 −3.41588 −0.012353 −6.82391 0.04198 −7.93877 0.02313

5

tarc

P

P ×10−5

wvt

2ImtpRc

W

2Taimb

W

4 3.95407 −0.0194

hese correlations agree well with the experimental data, event low-temperature conditions. In these methods, the satu-ated vapor pressure is regarded as an essential factor, whichan be calculated as below (Mohammadi et al., 2004b)

sw = 10−6 exp(

73.649 − 7258.2T

− 7.3073

× ln T + 4.1653 × 10−6T2)

(10)

sw,ice = 1.31579 × 10−1032.5576407/T+51.0557191×log T−0.0977×T+7.0358

here Psw, subscript liq and ice correspond to the saturatedapor pressure of water, and the liquid water, and ice, respec-ively.

.3.1. Model of saturated vapor pressuren a water–hydrocarbon system of NG, hydrocarbon is nor-

ally saturated with water at reservoir conditions. Therefore,his approach (Wang, 1994) assumes the partial water vaporressure equivalents to the saturated vapor pressure of water.elated to the partial pressure law of Dalton, the water contentan be expressed by the following equation:

H2O,sweet = 761900.42 Psw

P − Psw(12)

.3.2. Modified ideal model (MIM)he ideal model is always used to estimate water contentt low-temperature conditions while the calculation accuracys not satisfied at high temperature. A new modified ideal

odel (MIM), as the extension of ideal model, was presentedy Mohammadi et al. (2005) and expressed by Eq. (13).

( )



H2O,sweet = 761900.42 Psw

P× exp

11.81479 × P0.92951

T(13)

5.8495 −0.01155

×T2−102.5115496 (11)

As the report pointed out, this modified ideal model can geta great agreement with experimental values for temperatureranging from 273.15 to 477.59 K and for pressure up to 14.4 MPa.

2.3.3. Simplified thermodynamic model (STM)Depending on the phase equilibrium system, thermodynamicmodel always has high accuracy. However, it is too difficult tobe performed by handheld calculations. To simplify the ther-modynamic model, Mohammadi et al. (Mohammadi et al.,2004a, 2004b) developed a simplified thermodynamic modelto estimate water content, considering the physical effectsdirectly, which was shown in Eq. (14):

WH2O,sweet =761900.42 Psw exp

[(P−Psw)VH2O

RT

]ϕH2OP

(14)

where ϕH2O and VH2O are respectively the fugacity coeffi-cient of water in the gas phase calculated by Eq. (15), andthe average molar volume of condensed water over the pres-sure interval P–Psw. The calculation of VH2O varies from thedifferent formations of water in NG and calculated by Eqs.(16) and (17). R is the universal gas constant which equalsto 8314 m3 MPa mol−1 K−1. Additionally, as reported in otherreferences, this correlation is accurate only for temperatureranging from 273.15 to 377.59 K and for pressure up to 13.8 MPa.

ϕH2O = exp

(((0.069−30.905)

T

)P+(

0.3179T

−0.0007654)

P2

)(15)

VH2O,Liq = 4.501 × 10−2 − 6.710 × 10−4T + 1.784 × 10−6T2 (16)


VH2O,ice = 19.655 + 0.0022364 × (T − 273.15) (17)

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T/K CO2 T/K H2S

a0 a1 a2 a0 a1 a2

299.8167 2.202797 −1.058120906 0.3427 299.8167 2.314489 −0.678582201 0.3004310.9278 2.496936 −1.036484877 0.3103 310.9278 2.544338 −0.70422576 0.3046327.5944 2.930297 −0.990489109 0.2400 327.5944 2.890856 −0.799408896 0.3319344.2611 3.18733 −0.924518418 0.2139 344.2611 3.241253 −0.896948037 0.3646

– – – – 377.5944 3.773303 −1.030222461 0.4232410.9

.670

where a is constant listed in Table 9.


Effective watercontent of H2S

Effective watercontent of CO2

a10 −2.28473455055 × 106 −1.51705929796 × 106

a11 4.10134356738 × 105 2.53953558137 × 105

a12 −0.0233870949722 × 106 −0.0218779871207 × 106

a13 1.55604987964 × 102 7.00199672753 × 102

a20 2.28569862175 × 104 1.54692319504 × 104

a21 −4.28913302821 × 103 −2.75431390822 × 103

a22 2.84221095695 × 102 2.51540890528 × 102

a23 −4.35332471889 −8.37305127559a30 −76.4984711141 −52.8444857343a31 0.0149326955228 × 103 9.97118369879a32 −1.11025652987 −9.5940533224 × 10−1

a33 2.34671115643 × 10−2 3.30375581283 × 102

a40 0.0857373579771 0.0605410197916a41 −1.73248422725 × 10−2 −1.20630929063 × 10−2

– – – –

2.3.4. Bukacek methodUnlike the above methods, by amending the ideal model(Carroll, 2002, 2003), Bukacek also provided a calculatedmethod integrated with the method of estimating saturatedvapor pressure of Saul–Wagner (Bukacek, 1955; Carroll, 2003),which is expressed as below

WH2O,sweet = 761900.42 Psw

P+ 16.016 B (18)

B = 10−1713.26/T+6.69449 (19)

Psw = Pc × exp

(Tc × (−7.85823� + 1.83991�1.5 − 11.7811�3 + 22

T

� = Tc − T

Tc(21)

where Tc and Pc are the critical temperature of water and thecritical pressure of water, respectively. It is reported that theerror of this method is within ±5% for temperature rangingfrom 288.15 to 511.15 K and for pressure ranging from 0.1 to69 MPa.

3. Analytical methods for sour natural gas

When acid gases are contained in the NG, the analytical meth-ods for sweet natural gas may have lower accuracy due to thehigher solubility of water in acid gases, compared with hydro-carbon, and some corrections should be made to the abovemethods to correct for the additional water content. Generalcorrection methods are composed of three aspects: correctedby Maddox’s component contribution model, corrected by anequivalent mole fraction of Robinson’s H2S model, or correctedby directly taking the effect of acid gas on the physical prop-erties into account.

3.1. Correlations corrected by Maddox’s componentcontribution model

Maddox’s component contribution model (Carroll, 2003;Maddox et al., 1988) assumes water content in sour naturalgas is the sum of contribution made by sweet natural gas, H2Sand CO2. Thus, it can be expressed as follows:

WH2O,sour = yHC × WH2O,sweet + yCO2 × WCO2 + yH2S × WH2S (22)

where y is the mole fraction, and the subscript “HC”, “sour”refers to hydrocarbon and sour natural gas. This model isapplicable only for the mixture gas whose acid gas is less than0.4. The contribution of sweet natural gas can be calculated byan appropriate correlation or chart discussed as before. Then



the estimation of water content in acid gas is the most criticalstep as below

278 4.277016 −1.255345485 0.4897

5�3.5 − 15.9393�4 + 1.77516�7.5))

(20)

3.1.1. Bukacek–Maddox correction methodMaddox and Bukacek (Maddox et al., 1988) proposed a correc-tion approach to complete the component contribution model.This correlation is expressed as Eq. (23) and it is accurate underthe condition of a pressure range from 0.7 to 20.7 MPa, and atemperature range from 300.15 to 411.15 K for H2S and from300.15 to 344.15 K for CO2.

log WNHC = a0 + a1 log P + a2(log P)2 (23)

where subscript NHC stands for H2S or CO2. The temperaturedependent coefficient a is given in Table 8. The contributionof sweet natural gas, as the reference (Maddox et al., 1988)reported, can be predicted by McKetta–Wehe chart.

3.1.2. Bahadori correction methodBahadori (Bahadori et al., 2009) designed a new correctionmethod as below to provide good information about the equi-librium water content in sour natural gas for a larger rangeof conditions, including temperature ranging from 298.15 to393.15 K and pressure ranging from 1 to 15 MPa. Meanwhile,Bahadori also developed a method introduced in Section 2.1.4for the estimation water content in sweet natural gas, whichis always used together with this correction method.

WNHC =∑3

i=0

∑3

j=0aij × Pj × Ti (24)


a42 1.41055829053 × 10−3 1.21662951101 × 10−3

a43 −3.56668823871 × 10−5 −4.31605047324 × 10−5

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Table 10 – Constants a and b in Eqs. (29)–(32).

a0 a1 a2

−4.095 × 10−2 −1.82865639 × 10−3 1.93733 × 10−1

b0 b1 b2

P < 10.34 MPa 3.59 × 10−1 7.46 × 10−4 −4.7282 × 10−4

10.34MPa∼20.68 MPa 5.16 × 10−2 −2.84 × 10−2 1.25249 × 10−2

−2

3f

AHwcot

y

wmf

Wfw

F

W

wsac

3CTme

F

(Tp0bcM

3WKttwug

P > 20.68 MPa 1.04

.2. Correlations corrected by an equivalent moleraction of Robinson’s H2S model

nalyzing the experimental data of water content in CO2 and

2S, Robinson discovered the saturated water content of CO2

as 0.75 times equivalence to saturated water content of aomparable amount of H2S under same conditions and devel-ped an equivalent mole fraction of H2S model calculated byhe below expression (Robinson et al., 1980).

equiH2S = yH2S + 0.75 yCO2 (25)

here the superscript “equi” refers to equivalent H2S. Thisodel is suitable for mixture gas with y

equiH2S less than 0.4 (mole

raction) (Carroll, 2003; Robinson et al., 1980).On the basis of the equivalent mole fraction of H2S model,

ichert (Wichert and Wichert, 1993) proposed a correctionactor F combined water content of sweet natural gas andater content in sour natural gas directly.

= f (yequiH2S , T, P) (26)

H2O,sour = F × WH2O,sweet (27)

here the subscripts “sour” and “sweet” respectively refer toour natural gas and sweet natural gas, and f corresponds to

function. There are mainly two methods to estimate theorrection factor F as following.

.2.1. Mohammadi correction methodonsidering correction factor F as a variable of the function of, P and also the equivalent mole fraction of acid gas, Moham-adi (Mohammadi et al., 2004b, 2005) developed the following

quation to calculate F.

= 1 + yequiH2S

[−0.03185 T

T0− 0.01538 TP

T0P0+ 0.02772 P

P0

](28)

In the above equation, T0 and P0 are reference pressure0.101 MPa) and reference temperature (273.15 K), respectively.he Mohammadi correction method should be used in a tem-erature range from 310 to 420 K and a pressure range from.5 to 35 MPa. To estimate water content of sour natural gasy this way, according to Mohammadi et al., 2004b, the waterontent in sweet natural gas should be firstly calculated bycKetta–Wehe chart or the modified ideal model.

.2.2. Khaled correction methodith different expressions in different pressure conditions,

haled (Khaled, 2007) provided a new approach for calculatinghe correction factor F on general condition as well as on highemperature or pressure conditions. This correction methodith the same applicable range as Khaled method is always



sed together with to estimate water content in sour naturalas, and is expressed as below

5.48 × 10 −23.6857

P < 10.34 MPa:

F = ln

(1

b0 + Requi(b1 + b2P)

)(29)

10.34 MPa ≤ P ≤ 20.68 MPa:

F = exp(b0 + Requi(b1 + b2√

P) (30)

P > 20.68 MPa:

F =(

b0 + Requi

(b1 + b2√

P

))2

(31)

In the above equations, the coefficient Requi relates to T andthe equivalent mole fraction of acid gases is calculated by Eq.(32).

√Requi = 1/(a0 +

√T(a1 + a2/

√y

equiH2S )) (32)

where a and b are constants listed in Table 10.

3.3. Correlations corrected by taking the effect of acidgas on the physical properties into account

The difference in water content between sweet natural gas andsour natural gas results in a difference in the physical proper-ties of the NG. Researchers quantified these effects using somesimple correlations and developed analytical methods for sournatural gas. All of the analytical methods are based on the cal-culation of phase equilibrium in water–hydrocarbon–acid gassystem and do not require the estimation of the water contentin sweet natural gas in advance.

3.3.1. Wang et al. methodIn water–hydrocarbon system, the partial water vapor pres-sure referred to the saturated vapor pressure of water. Basedon this theory, researchers designed Eq. (12) to estimate watercontent in sweet gas. Similarly as in water–hydrocarbon–acidgas system, Wang et al. (Wang, 1994) proposed the followingcorrected equations.

WH2O,sour = 761900.42 Psw,sour(1 − ysalt − yH2S − yCO2 )P − Psw,sour(1 − ysalt − yH2S − yCO2 )

(33)

Psw = Pc exp[

f

(T

Tc

)×(

1 − Tc

T

)](34)

f

(T

Tc

)= 7.21275 + a

[0.745 − T

Tc

]2+ b

[0.745 − T

Tc

]c

(35)

where Tc, Pc and the subscript “salt” are the critical tem-perature of water (647.3 K), the critical pressure of water


(22.12 MPa), and the salts, respectively. The constants a, b andc applied to T and Tc are equal to 3.981, 1.05 and 3, respectively,

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Table 11 – The Comparison of the estimating value of predictive approach and experimental data for sweet natural gas (Mohammadi et al., 2004b, 2005).

T/K P/MPa Exp. data/(mg/Sm3) Predictive value/(mg/Sm3)

Sloan Ning et al. Khaled Bahadori Zhu et al. Behr Kazim Model of Psw MIM STM Bukacek

CH4 + H2O240.00 3.450 9.88746 14.6021 14.5432 – – – 14.2327 18.234 5.98233 – – –254.00 6.900 16.63987 18.0607 25.6841 – – 14.8818 23.2376 27.090 12.26818 – – –268.15 1.500 225.0804 250.847 268.901 – – 242.393 175.224 – 202.063 – – –282.98 1.000 1125.402 – 1048.63 – – 1028.684 – – 925.677 963.972 962.146 –288.15 4.000 497.7619 415.673 445.585 – 410.1247 437.9177 412.662 415.983 324.962 376.916 376.489 –288.15 6.000 334.8355 304.788 324.565 – 303.3382 327.8632 281.239 301.591 216.610 268.981 269.124 –288.15 8.000 253.3722 246.447 268.945 – 249.4215 272.8369 206.388 279.275 162.446 215.601 215.840 –288.15 1.000 1430.868 – 1419.91 – 1358.927 1428.40 – 1301.51 1353.67 1349.50 –293.11 10.00 271.7042 278.702 308.413 – 289.2065 304.246 215.719 – 177.830 250.457 247.909 290.952293.11 1.000 1929.26 – 1887.71 – 1828.822 1930.20 – 1782.05 1851.01 1843.28 1890.51298.11 10.00 378.6174 367.243 399.944 – 382.9775 385.204 287.491 – 241.052 337.526 330.728 382.742303.11 1.000 3536.977 – 3292.19 – 3246.476 3436.41 – 3242.80 3357.41 3336.32 3403.44303.13 17.56 230.3565 – 406.531 – 361.1246 349.264 202.383 – 184.143 – – 360.640308.12 17.50 282.9065 – 509.728 – 466.2574 441.705 265.260 – 244.801 – – 462.659313.11 10.00 840.0322 795.834 845.300 839.3556 841.8197 806.736 641.584 – 561.981 773.971 737.138 828.651313.11 1.000 5900.322 – 5605.50 – 5580.316 5919.36 – – 5657.37 5831.62 5783.53 5879.18313.12 25.00 503.2154 – 553.534 498.6448 493.7654 466.121 – – 224.813 – – 492.176

Mohammadi’s gases mixture (94 mol% methane + 4mol%ethane + 2mol% n-butane)288.15 6.020 239.237 304.0291 269.345 – 302.61 327.1308 280.2468 300.8260 215.8906 215.8531 267.8381 –297.93 6.000 540.949 531.5104 544.365 – 536.191 543.2643 498.4195 523.2586 397.5418 397.4085 483.0809 537.8864297.95 10.05 318.474 362.7582 335.939 – 378.3929 381.0635 283.2702 – 237.5722 237.5425 325.4228 378.2609303.10 1.068 3276.17 – 2335.575 – 3052.526 3226.095 – – 3033.762 3022.463 3127.808 3196.166303.00 3.661 967.614 1031.461 1092.023 – 1037.932 1050.534 1041.408 1045.680 877.4689 876.6712 983.9658 1051.559303.13 17.56 338.284 – 406.1704 – 361.0989 349.1989 202.3638 – 184.1431 – – 360.6383313.14 17.50 592.000 – 637.4745 594.6245 596.8615 563.7447 343.6993 – 321.5448 – – 588.9837322.00 1.924 4906.64 4657.062 5585.577 4933.883 4819.883 5029.846 3879.429 – 4647.219 4621.751 4857.855 4995.013321.80 4.174 2323.80 2390.901 2152.614 2456.676 2466.908 2487.332 2438.266 2375.413 2113.789 2109.166 2347.206 2482.544333.00 2.915 5500.92 – 6945.25 5701.111 5629.553 5826.277 5341.693 5373.133 5211.205 5180.601 5533.208 5741.59347.30 0.567 52,494.9 – 51478.98 49774.16 51855.76 – – 53518.93 50086.19 50563.79 50931.13347.20 4.115 7542.81 – 6791.777 7760.225 7734.233 7912.374 7506.226 7350.37 6923.733 6872.304 7420.8 7782.981361.00 4.599 11580.9 – 12809.3 12081.38 12065.65 12165.24 11537.76 12581.51 10848.38 10723.53 11498.79 12122.81361.20 0.954 53180.7 – 62839.75 – 52386.34 54351.49 – – 55764.28 52095.43 52765.8 53411.67

AAD%a

“–” the corresponding method cannot be used in this situation.

a AAD% = 100

N∑i=1

∣∣(WExp−WPre)/WExp

∣∣N .

dx.doi.org/10.1016/j.cherd.2014.05.021



Table 12 – The optimum method for sweet natural gas at different conditions.

The range of T The range of P Suitable method

223.15–273.15 K P≤0.00054053T3 − 0.419T2 + 108.1492T − 9274.1 Zhu et al.273.15–288.71 K P≤13.8 MPa STM

13.8–100 MPa Zhu et al.288.71–295.15 K P≤13.8 MPa STM

13.8–15 MPa Bukacek/Bahadori15 MPa–69 MPa Bukacek

295.15–310.93 K P≤13.8 MPa STM13.8–15 MPa Bukacek/Bahadori15–69 MPa Bukacek69–100 MPa Zhu et al.

310.93–413.15 K 0.1–1.38 MPa Zhu et al.1.38–69 MPa Khaled69–100 MPa Zhu et al.

413.15–444.26 K 0.1–1.38 MPa Bukacek1.38–69 MPa Khaled69–100 MPa Ning et al.

444.26–510.93 K 0.1–69 MPa Bukacek69–100 MPa Ning et al.

we

3Ismeict

W P0)V

wrEo(u1cti

hile Tc is up to T. On the contrary, a is equivalent to 4.33, b isquivalent to 185 and c is equivalent to 5.

.3.2. Modified thermodynamic model (MTM)n comparison to sweet natural gas, higher water holding ofour natural gas mainly results in the high solubility of polarolecules (such as H2S, CO2) (Mohammadi et al., 2006; Zirrahi

t al., 2010). In terms of the main factors of acid gas solubil-ty, researchers corrected Eq. (14) by taking these factors intoonsideration (Zirrahi et al., 2010) and proposed a modifiedhermodynamic model (MTM), shown as below

H2O,sour =761900.42 Ko

H2O,sour(1 − xH2S − xCO2 − xCH4 ) exp[(P −

ϕH2O,sourP

here KoH2O,sour, x and VH2O,sour are the standard equilib-

ium constant of water in sour natural gas calculated byq. (37) (Zirrahi et al., 2010), the mole fraction of acid gasesr hydrocarbons in the aqueous phase estimated by Eq.

38) (Salari et al., 2008), and the average partial molar vol-me over the pressure interval P0–P which is equivalent to8.18 × 10−6 m3/mol. The fugacity of water in the gas phasean be calculated by the modified RK-EOS which is widely used



o express the deviation of a CO2 + H2S + H2O mixture fromdeal behavior. The details of the implemented equations of

Table 13 – The AAD% of the combination formulas.

Sour

Bukacek–Maddox Bah

Sloan 5.394 8Ning et al. 8.037 13Khaled 9.409 7Bahadori 10.15 8Zhu et al. 9.731 8Behr 10.22 17Kazim 8.547 8Model of Psw 10.73 13MIM 10.84 19STM 7.428 7Bukacek 9.339 7

H2O,sour/RT]

(36)

state are given in Appendix A (Salari et al., 2008; Zirrahi et al.,2010).

log KoH2O,sour = −2.209 + 0.03097(T − 273.15)

− 1.098 × 10−4(T − 273.15)2

+ 2.048 × 10−7(T − 273.15)3 (37)

ln(yi10 P/55.508 xi) = �l(0)i

RT− ln �i (38)

where �l(0)i

and �i are the standard chemical potential ofcomponent i in aqueous phase and the fugacity of compo-nent i. Duan and his co-workers (Duan and Sun, 1992, 2003;


Duan et al., 2007; Ziabakhsh-Ganji and Kooi, 2012) provided amethod listed in Appendix B to calculate these parameters.

Sweet

adori Mohammadi Khaled

.456 5.784 7.389

.38 8.360 9.906

.513 6.736 6.404

.433 8.071 5.502

.023 7.107 5.825

.75 13.46 20.41

.455 12.14 11.86

.59 16.46 21.92

.98 21.96 21.81

.311 4.895 7.050

.555 6.631 6.6133

dx.doi.org/10.1016/j.cherd.2014.05.021



4. Discussions and results

Due to the non-independency of estimating water contentin sour natural gas, this work first discussed the analyticalmethods for sweet natural gas. Fig. 1 shows the applicablerange of the analytical methods, except for the model basedon saturated vapor pressure without reporting in reference.As shown in Fig. 1, the analytical methods of sweet naturalgas are used for estimating water content in a temperaturerange from 223.15 to 510.93 K and a pressure range from 0.1to 100 MPa, with the majority of the method being availablefor temperature ranging from 288.15 to 413.15 K and pressureranging from 1.38 to 13.8 MPa. There is still little research in theliterature commenting on analytical methods at lower tem-peratures and pressures. The Zhu et al. method, Ning et al.method, Bukacek method and Khaled method have a largerrange of temperatures and/or pressures, compared to othermethods.

As the effect of hydrocarbons can be ignored, atleast to some extent, the water content of sweet nat-ural gas is affected only by temperature and pressure.Therefore, this work assumes the water content in sweetnatural gas is independent of gas composition and stud-ies the systems of pure methane and gas mixtures(94 mol%methane + 4 mol%ethane + 2 mol% n-butane), respec-tively. Table 11 shows the results of the analytical methods ofsweet natural gas and the comparison with the experimentalvalues of the references (Chapoy et al., 2005; Zirrahi et al., 2010;Kondori et al., 2013; Eslamimanesh et al., 2011). As shown inTable 11, due to the formation of ice or hydrate, not all of theanalytical methods are available at low temperatures and/orpressures.

Table 11 shows the predicted values for a model basedon saturated vapor pressure and the modified ideal modelare closed. Nevertheless, as the shortage of the applicablerange, the modified ideal model has an AAD% (the percent-age of average absolute deviation) (Mohammadi et al., 2004b)of 10.351 which is less than the AAD% of 20.392 regeneratedby the model based on saturated vapor pressure. Accordingto the relationship between AD% (the percentage of absolutedeviation) of the model based on saturated vapor pressure,the results show the AD% increases with increasing pressure.Especially at high-pressure conditions, the AD% is extremelyunacceptable. It may be caused by the non-ideality situa-tion under condition of high-pressure. The Behr method alsoshows large deviations with an AAD% of nearly 20. BothNing et al. method and Kazim method need interpolation,as the nonlinear function of temperature or pressure, thesemethods may lead to the higher AAD% with wider applica-ble range. As shown in Table 11, Ning et al. method witha larger applicable range is reproduced with a larger AAD%of 16.930, compared to Kazim method. The other analyticalmethods show good agreement with the experimental data(Chapoy et al., 2005; Mohammadi et al., 2004b), especiallythe Khaled method, produced with AAD% of 2.3186. However,Khaled method is only available at the temperature rangefrom 310.93 to 444.26 K. When out of the applicable range,the other method should be requested. Taking the appli-cable range of each approach into consideration, this workmakes a suggestion about the optimum method at specificconditions and listed them in Table 12. In order to avoid theinfluences of selected samples, this work considers methods



within a ±0.5 deviation from the optimum as being accept-able.

The analytical correction methods corrected by the com-ponent contribution model or the equivalent mole fractionof the H2S model should be used together with the methodsof estimating water content in sweet natural gas. Except theBukacek–Maddox correction method is reported partially, theother methods have been reported the corresponding methodto estimate water content in sweet natural gas. The reportstudying the optimum method of sweet gas for the correctionmethod to generate the less AAD% is absent.

To find out the best combination modes, combining themethods for sweet natural gas and the correction methodsrandomly, then calculating water content in allusion to thegas samples (GPSA, 1998; Lukacs and Robinson, 1963; Ng et al.,2001) given in Table 14 is necessary. From Fig. 1, we could getthe applicable range of each combination method by findingthe common applicable range of the method for sweet nat-ural gas and the correction method. As can be seen, due tothe restriction on the application of correction method, mostof the combination modes, expect some methods correctedby the Khaled correction method, are only available in gen-eral situations. The comparison between the results of thesecombination formulas and the experimental data is listed inTable 13.

As shown in Table 13, there is an obvious difference amongthe AAD%s of each combination mode, so choosing an opti-mum one is extremely important. When the Bukacek–Maddoxcorrection method is used, all the AAD%s among the experi-mental and predicted value lie in an acceptable ranging from5.394 to 10.84. The other correction methods are sensitiveto the method for sweet natural gas, especially the Khaledcorrection method which would regenerate AAD%s rangingfrom 21.92 to 5.502. For these sensitive correction methods,choosing an optimum method to estimate the water contentin sweet natural gas is extremely important. Studying theresults of each method for sweet natural gas using togetherwith each correction method, we can know the Behr method,the model based on saturated vapor pressure and the modi-fied ideal model reproduce with AAD%s of more than 10, nomatter with which correction method. On the contrary, theresults of the combination modes related to the Sloan method,the Khaled method, the Zhu et al. method, the simplifiedthermodynamic model and the Bukacek method are alwaysacceptable. As Table 13 shows, for Bukacek–Maddox correc-tion method and Khaled correction method the optimummethod to estimate water content in sweet natural gas are theSloan method and the Bahadori method. Both the Bahadoricorrection method and the Mohammadi correction methodreproduce the least AAD% combining with the simplified ther-modynamic method. Table 14 lists the results of the fourcombination modes, Wang et al. method and modified ther-modynamic model with a comparison of experimental dataof methane + carbon dioxide gas mixture, methane + hydrogensulfide gas mixture and methane + carbon dioxide + hydrogensulfide gas mixture, respectively.

As it can be seen, the result of Wang et al. method isunacceptable, with an AAD% of more than 40. The modifiedthermodynamic model has a great agreement with the exper-imental value. Nevertheless, the calculation of this model isso difficult that could not be accepted in industry, except forthe samples with more than 0.4 (mole fraction) of acid gases.Similarly to the methods for sweet natural gas, these analyti-cal methods also have limited application. As shown in Fig. 1,


the calculation of water content in sour natural gas could beworked for temperature between 288.15 and 444.26 K and the

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atural

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hem

. En

g. R

es. D

es. (2014),

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.2014.05.021 AR

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11

Table 14 – The comparison of the estimating value and experimental data (GPSA, 1998; Lukacs and Robinson, 1963; Ng et al., 2001).

T/K P/MPa Mole fraction Exp. value/(mg/Sm3) Prediction value/(mg/Sm3)

CH4 CO2 H2S Sloan &Bukacek–Maddox

STM &Bahadori

STM &Mohammadi

Bahadori &Khaled

Wang et al. MTMa

Methane + carbon dioxide gas mixture273.15 0.5000 0.9983b 0.0017 0.0000 906.66 – – – – 2268.82 –273.15 0.5000 0.9827c 0.0173 0.0000 929.52 – – – – 2233.26 –273.15 0.5000 0.7488d 0.2512 0.0000 1340.9 – – – – 1700.52 –288.15 1.5000 0.9983b 0.0017 0.0000 891.42 – 915.73 – – 1508.00 –288.15 1.5000 0.9827c 0.0173 0.0000 883.80 – 911.78 – – 1484.39 –311.15 13.800 0.8900 0.11 0.0000 615.62 602.81 579.31 586.60 655.02 441.787 625.41311.15 13.800 0.8000 0.20 0.0000 615.62 628.33 577.78 634.94 655.09 397.090 649.52344.15 6.9000 0.8900 0.11 0.0000 4320.0 – 4387.6 4287.9 4600.5 3619.65 4539.2344.15 6.9000 0.8000 0.20 0.0000 4259.0 – 4464.0 4434.8 4600.6 3252.14 4398.3

Methane + hydrogen sulfide gas mixture327.15 10.300 0.9200 0.0000 0.0800 1683.8 – 1613.1 1510.5 1647.6 1236.48 1690.4344.15 6.9000 0.8300 0.0000 0.1700 4411.4 – 4605.0 4478.3 4600.7 3374.61 4441.2344.15 9.4300 0.7300 0.0000 0.2700 3733.3 – 4100.5 3784.0 3636.0 2153.59 3678.2344.26 2.4680 0.7900 0.0000 0.2100 11429 – 10503 10973 10938 9083.39 11,742344.26 4.2120 0.8100 0.0000 0.1900 7085.7 – 6727.2 6805.5 6882.1 5432.58 7318.0344.26 6.3760 0.7100 0.0000 0.2900 5257.1 – 5074.4 5047.0 4915.6 3136.78 5546.1344.26 6.9620 0.8300 0.0000 0.1700 4693.3 – 4598.3 4466.9 4589.5 3359.22 4856.1344.26 9.5950 0.7300 0.0000 0.2700 3961.9 – 4084.3 3757.5 3606.2 2125.80 4156.9344.26 9.6160 0.8400 0.0000 0.1600 3619.0 – 3756.4 3482.9 3600.1 2458.63 3806.1

Methane + carbon dioxide + hydrogen sulfide gas mixture322.04 1.3790 0.7500e 0.0625 0.1875 7136.7 6717.6 6204.9 6842.5 6692.1 6075.3 7287.3322.04 1.3790 0.7500e 0.1875 0.0625 6659.0 6719.4 6131.3 6823.0 6692.2 6075.3 6760.5322.04 10.339 0.7500e 0.1875 0.0625 1425.5 1475.5 1525.1 1319.9 1298.8 805.03 1329.1322.04 10.339 0.7500e 0.0625 0.1875 1382.1 1679.1 1467.2 1352.5 1298.8 805.03 1229.1366.48 1.3790 0.7500f 0.1875 0.0625 451,817 – 39,917 45,284 45,705 37,117 46,304366.48 1.3790 0.7500f 0.0625 0.1875 45,466 – 40,432 45,359 45,705 37,117 46,902366.48 4.1360 0.7500e 0.1875 0.0625 22,798 – 15,240 16,321 16,558 12,006 18,305366.48 10.339 0.7500f 0.1875 0.0625 8517.33 – 8588.8 7697.2 7874.9 4760.0 8532.8366.48 10.339 0.7500f 0.0625 0.1875 7960.3 – 8720.6 7841.4 7875.1 4760.0 7312.2

AAD%

a The modified thermodynamic model.b Composition of this mixture is 86.5% methane, 6.2% ethane, 1.6% propane, 0.7% C4

+, 4.9% nitrogen, 0.1% helium.c Consists of this mixture is 84.9% methane, 3.6% ethane, 0.7% propane, 0.3% C4

+, 10.5% nitrogen.d Composition of this mixture is 93.6% methane, 3.4% ethane, 0.5% propane, 0.4% C4

+, 2.0% nitrogen, 0.5% helium.e This mixture composes of 95% methane and 5% propane.f This mixture consists of methane, ethane, propane, i-butane, n-butane with a molar ratio equal to 90:6:2.5:0.6:0.9.

dx.doi.org/10.1016/j.cherd.2014.05.021



Table 15 – The optimum method for sour natural gas at different conditions.

The range of T The range of P Optimum method (method for sweet & correction)

288.15–299.82 K 1–13.8 MPa STM & Bahadori/Bukacek & Bahadori13.8–15 MPa Bukacek & Bahadori/Khaled & Bahadori

299.82–310 K 0.4–1.38 MPa STM & Bukacek-Maddox1.38–13.8 MPa Solan & Bukacek-Maddox13.8–20.7 MPa Ning et al. & Bukacek-Maddox

310–310.93 K 0.5–13.8 MPa STM & Mohammadi13.8–15 MPa Bahadori & Mohammadi/Zhu et al. & Mohammadi15–35 MPa Zhu et al. & Mohammadi

310.93–420 K 0.5–13.8 MPa STM & Mohammadi13.8–15 MPa Bahadori & Khaled/Zhu et al. & Khaled15–35 MPa Zhu et al. & Khaled

420–444.26 K 1.38–13.8 MPa Bahadori & Khaled/Zhu et al. & Khaled
1.38–69 MPa
pressure between 0.5 and 69 MPa. Table 15, by comparing theAAD%s among these analytical methods, suggests the opti-mum method for sour natural gas with a mole fraction of acidgases of less than 0.4 at different conditions.

5. Conclusions

This paper presented a review of the mainly widely usedanalytical methods of the estimating water content in NG.Additionally, this paper classified and evaluated these meth-ods, as well as suggesting optimum approaches at differentconditions.

The analytical methods of calculating the water contentin sweet natural gas are mainly divided into three kinds: cor-relations regressed from charts, correlations regressed fromexperimental data, and equations referred to the calculationof the phase equilibrium in the water–hydrocarbon system.The analytical methods for sour natural gas always need cor-rection, as methods are usually initially devised to calculatethe water content in sweet natural gas. The correction methodhas three aspects: corrected by Maddox’s component contri-bution model, corrected by an equivalent mole fraction ofRobinson’s H2S model, and corrected by directly taking theeffect of acid gases on the physical properties into account.

The simplified thermodynamic model is the best choicefor the Bahadori and the Mohammadi correction methods toestimate water content in sweet natural gas. Among thesemethods used the method of the Bukacek–Maddox to correctthe correlations of estimating water content in sweet natu-ral gas, the AAD% of Sloan and Bukacek–Maddox correctionmethod is the least with a value of less than 5.394. At the sametime, using the method of Khaled to correct, the best partneris Bahadori method with an AAD% of less than 5.502%.

Comparing the experimental data of references with the



calculation results of these correlations, and taking the appli-cable range of each method into consideration, this article had

Table A1 – Intermolecular attraction and repulsion of acid gase

aCO2 7.54 × 108–4.13 × 105T (Zirrahi et al., 2010) aH2O–CO2bCO2 27.8 (Ziabakhsh-Ganji and Kooi, 2012) aH2O-H2S

aCH4 4.9838 × 105 (Zirrahi et al., 2010) aH2O-CH4

bCH4 29.58 (Zirrahi et al., 2010) aH2O-CO2-CH4aH2S 5.1319 × 105 (Zirrahi et al., 2010) aH2O-H2S-CH4bH2S 30.01 (Zirrahi et al., 2010) aH2O-H2S-CO2bH2O 18.18 (Ziabakhsh-Ganji and Kooi, 2012) aH2O-H2S-CH4-CO

The units of ai and bi are MPa cm6 K0.5 mol−2 and cm3/mol, respectively.

Zhu et al. & Khaled

made a suggestion about the optimum method to estimatewater content in NG at different conditions and reproducewith the less AAD%.

Limited to the experimental data in the low temperatureregion, the analytical method of estimating water content ofnatural gas at low temperature conditions is still absent. Theresults presented are suitable for sweet natural gas at the tem-perature over 233.15 K and for sour natural gas at temperatureover 288.15 K. Therefore, when new methods for the calculat-ing water content in low temperature are proposed, the resultsdeveloped here will be inaccurate.

Acknowledgements

The authors would like to thank the financer, the supporters,and co-workers in key laboratory of gas process engineering.

Appendix A. Equations of state for H2O andmix rules

The Redlich–Kwong equation of state (RK-EOS) is expressedby:

P = RT

V − b+ a

T0.5V(V + b)(A1)

where a and b are the intermolecular attraction and repulsionlisted in Table A1. For mixtures, amix and bmix are calculatedby standard mixing rules as follows, some of the calculatedresults are also listed in Table A1.

amix =∑

i

∑j

yiyj(aiaj)0.5 (A2)

∑


bmix =i

yibi (A3)

s and water..

7.89 × 108 (Zirrahi et al., 2010)2,978,194,521.9−5218264T (Zirrahi et al., 2010)−42,151.44P + 3.257690003 × 108−9205.39T + 29,371,125.57(Zirrahi et al., 2010)−2.664509778 × 108 (Zirrahi et al., 2010)−3.823642554 × 108 (Zirrahi et al., 2010)5.0856254151 × 109 (Zirrahi et al., 2010)

2 −1.28744589983 × 1010 (Zirrahi et al., 2010)

dx.doi.org/10.1016/j.cherd.2014.05.021



Table B1 – Parameters c in Eqs. (B1)–(B3).

H2S CO2 CH4

c1 42.564957 28.9447706 8.3143711c2 −8.6260377 × 10−2 −0.0354581768 −7.2772168 × 10−3

c3 −6084.3775 −4770.67077 2.1489858 × 103

c4 −102.76849 −3.07405726 −30.092013c5 6.871443 × 10−5 1.02782768 × 10−5 −1.4019672 × 10−5

c6 3.5665902 × 10−2 33.8126098 6.6743449 × 105

c7 −10.590768 −0.907301486 4.8468502 × 103

c8 8.4482895 × 10−3 9.0403714 × 10−2 7.6985890 × 10−2

c9 0 −1.14934031 × 10−2 −5.0253331 × 10−5

c10 0 932.713393 0

Table B2 – Parameters a for CO2, H2S and CH4 respectively in Eqs. (B4)–(B7).

H2S CO2 CH4

a1 5.2386075 × 10−2 8.99288497 × 10−2 8.72553928 × 10−2

a2 −2.7463906 × 10−1 −4.94783127 × 10−1 −7.52599476 × 10−1

a3 −9.6760173 × 10−2 4.77922245 × 10−2 3.75419887 × 10−1

a4 1.3618104 × 10−2 1.03808883 × 10−2 1.07291342 × 10−2

a5 −8.8681753 × 10−2 −2.82516861 × 10−2 5.49626360 × 10−3

a6 4.1176908 × 10−2 9.49887563 × 10−2 −1.84772802 × 10−2

a7 3.6354018 × 10−4 5.20600880 × 10−4 3.18993183 × 10−4

a8 2.2719194 × 10−3 −2.93540971 × 10−4 2.11079375 × 10−4

a9 −7.6962514 × 10−4 −1.77265112 × 10−3 2.01682801 × 10−5

a10 −2.1948579 × 10−5 −2.51101973 × 10−5 −1.65606189 × 10−5

a11 −1.1707631 × 10−4 8.93353441 × 10−5 −1.19614546 × 10−4

a12 4.0756926 × 10−5 7.88998563 × 10−5 −1.08087289 × 10−4

a13 5.7582260 × 10−2 −1.66727022 × 10−2 4.48262295 × 10−2

a14 1.000 1.398 0.754−2 −2 −2

c

l

wtmtcm

a

V

a15 6.0000 × 10

The fugacity coefficient of water in sour natural gas is cal-ulated by Eq. (A4)

n ϕH2O,sour = ln(

V

V − bmix

)+ bH2O

V − bmix

−[2aH2O-acid ln (V + bH2O/V)

]RT1.5bmix

+ amixbH2O

[ln (V + bH2O/V) − bmix/bmix + V

]RT1.5b2

mix

− lnPV

RT(A4)

here aH2O-acid is a parameter expanded as Eq. (A5) whichakes the interaction force between water and the acid gas

olecules for mixtures of acid gas into account and assumeshat yH2O equal to 0. As �H2O,sour refers to the fugacity coeffi-ient of water in the vapor phase, researchers always take theaximum root of Eq. (A6) as the molar volume of mixture gas.

H2O–acid = yCO2 aH2O–CO2 + yCH4 aH2O–CH4 + yH2SaH2O–H2S

+ yCH4 yCO2 aH2O–CO2–CH4

+ yH2SyCO2 aH2O–CO2–H2SyH2SyCH4 aH2O–CH4–H2S

+ yCO2 yCH4 yH2SaH2O–CH4–CO2–H2S (A5)

3 − V2RT

P− V

(RTbmix/P − amix

10 PT0.5+ b2

mix

)− amixbmix

10 PT0.5= 0



(A6)

2.9600 × 10 7.7167 × 10

Appendix B. Equation of state for supercriticalfluids CO2, H2S and CH4

The �l(0)i

is dependent upon component i, temperature andtotal pressure. Pitizer et al. developed several equations forH2S, CO2, CH4 to calculate �

l(0)i

/RT which were given by:

�l(0)H2S

RT= c1 + c2T + c3 + c4P

T+ c5T2 + c6 + c7P

680 − T+ c8P (B1)

�l(0)CO2

RT= c1 + c2T + c3 + c4P

T+ c5T2 + c6 + c7P

630 − T+ c8P

+ c9P ln T + c10P2

(630 − T)2(B2)

�l(0)CH4

RT= c1 + c2T + c3 + c4P

T+ c5T2 + c6 + c7P

T2+ c8P + c9P ln T

(B3)

where c is constant related to the component and listed inTable B1.

The equations of state for CO2, H2S and CH4 proposed byDuan et al. and expressed as following:

Z = PrVr/Tr = 1 + a1 + a2/T2r + a3/T3

r

Vr+ a4 + a5/T2

r + a6/T3r

V2r

+a7 + a8/T2r + a9/T3

r

V4r

+ a10 + a11/T2r + a12/T3

r

V5r

+a13(a14 + a15/V2r ) exp

−a15/V2r

T3r V2

r

(B4)


dx.doi.org/10.1016/j.cherd.2014.05.021



where Z, Pr, Vr and Tr are the compressibility factor, reducedpressure, reduced volume, and reduced temperature, respec-tively. a is evaluated from PVT and the saturation pressure dataof the component i. Their value is given in Table B2, respec-tively. Pr and Tr are defined as:

Pr = Pi

Pc(B5)

Tr = T

Tc(B6)

where Pc and Tc are the critical pressure and crit-ical temperature of the component. For the compo-nent CO2, Pc = 7.382 MPa, Tc = 304.41 K; for the componentCH4, Pc = 4.641 MPa, Tc = 190.6 K; for the component H2S,Pc = 9.08 MPa, Tc = 373.6 K. Pi refers to the partial pressure ofcomponent i.

Vr should be obtained through solving Eq. (B4) by substitut-ing Eq. (B5) and Eq. (B6) into it, then the compressibility factorZ could be calculated.

Substitute Z into Eq. (B7) to calculate the fugacity coeffi-cient of component i

ϕi = exp

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

Z − 1 − ln Z + a1 + a2/T2r + a3/T3

r

Vr

+a4 + a5/T2r + a6/T3

r

2V2r

+ a7 + a8/T2r + a9/T3

r

4V2r

+a10 + a11/T2r + a12/T3

r

5V5r

+a13a14 + 1 − (a14 + 1 + a15/V2

r ) exp(−a15/V2r )

2T3r a15

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(B7)

where i refers to component i such as CO2, H2S and CH4. Theconstant a is same as the parameter of Eq. (B4).

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