Solution Mechanism of Elemental Sulfur in Hydrogen Sulfide under

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Thermodynamics, Transport, and Fluid Mechanics

Solution mechanism of elemental sulfur in hydrogen sulfide under conditions of natural gas transmission Changjun Li, Gang Liu, and Yang Peng Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b04339 • Publication Date (Web): 10 Dec 2018 Downloaded from http://pubs.acs.org on December 15, 2018

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Industrial & Engineering Chemistry Research

Solution mechanism of elemental sulfur in hydrogen sulfide under conditions of natural gas transmission Changjun Li a, b, Gang Liu a, * Yang Peng c aSchool

of Petroleum Engineering, Southwest Petroleum University, Chengdu 610500, China

bCNPC

Key Laboratory of Oil & Gas Storage and Transportation, Southwest Petroleum University,

Chengdu 610500, China cGas

Management Office, PetroChina Southwest Oil & Gas Field Company, Chengdu 610215, China

*Corresponding author: Email address: [email protected] (Gang Liu)

Abstract: Predicting the solubility of elemental sulfur in natural gas is an important task in the prevention of sulfur deposition. The knowledge of the sulfur solution mechanism in hydrogen sulfide is of great help for establishing an accurate model of sulfur solubility. In this paper, a comprehensive model is established based on phase equilibrium theory considering both the physical sulfur solution in hydrogen sulfide and the chemical reaction between sulfur and hydrogen sulfide. In this model, a new vapor pressure expression of elemental sulfur and a new formula for the binary interaction coefficient between sulfur and hydrogen sulfide, considering both temperature and solvent density, are proposed. Our new model can adapt to lower temperature, and the threshold value can be as low as 273.15 K. Furthermore, we find that our model can better fit the experimental data of elemental sulfur in hydrogen sulfide. By analyzing the sulfur solution mechanism in hydrogen sulfide under conditions of transmission, we found that the solution mechanism is mainly driven by the chemical solution when pressure is above 5.0 MPa, and it is determined by both the physical solution and the chemical solution when the pressure is below 5.0 MPa. In addition, increasing

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temperature can facilitate the physical solution and inhibit the chemical reaction below pressures of 5.0 MPa, but temperature has little effect on the sulfur solution mechanism at pressures above 5.0 MPa.

Key words: Solution mechanism, Gas-solid equilibrium, Vapor pressure, Sulfur, High hydrogen sulfidecontent natural gas

1. Introduction Sulfur deposition is a powerful resistance factor for ensuring safety and efficiency during development of high-hydrogen sulfide-content natural gas fields.1,2 In general, solid sulfur is dissolved in the highhydrogen sulfide-content natural gas in forms of gaseous sulfur. However, with a change in pressure, temperature and the content of gas components, supersaturated precipitation of gaseous sulfur may occur because of the decrease in the sulfur solubility of gas mixtures. Thus, the knowledge of sulfur solubility is a great help for judging the probability of sulfur deposition and enacting prevention measures. For sulfur solubility in sour gas, many experimental results have already indicated that the hydrogen sulfide in sour gas has a larger impact on sulfur solubility than methane and carbon dioxide in sour gas.3-12 Additionally, owing to the existence of hydrogen sulfide in sour gas, the sulfur solubility in sour gas also depends on the chemical reaction between sulfur and hydrogen sulfide, but not the physical solution.13-14 Therefore, the study of the sulfur solution mechanism in hydrogen sulfide is an important contribution. Due to the work of numerous researchers,15-19 association models of Chrastil’s type have already been used to fit the experimental data of solubility quite well. However, these models do not do a very good job of explaining the mechanism of sulfur solution in sour gas mixtures, especially in hydrogen sulfide. The thermodynamic model of sulfur solubility, based on an equation of state is helpful in revealing the mechanism of sulfur solutions.13,20 This model was developed early and was successfully applied in a


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correlation of experimental data of sulfur solubility by Gu et al..8 For predicting sulfur solubility under natural gas reservoir conditions, Heidemann et al. improved the thermodynamic model and analyzed the changing rules of sulfur phases with temperature and pressure.20-21 There are a number of species ranging up to S8, and elemental sulfur can produce a chemical reaction with hydrogen sulfide to form sulfanes such as H2S9.22 In their subsequent work, Heidemann et al. established a chemical equilibrium equation of state model considering chemical reactions between eight elemental sulfur species from S1 to S8 and hydrogen sulfide.13 The changing rules of eight species of elemental sulfur in the vapor and liquid phase with temperature is presented, and the results show that the content of S8 is dominant in mixtures of elemental sulfur.13 However, the Heidemann model is mainly suitable for the conditions of gas reservoirs and wellbore, not the conditions of gas transmission. In recent years, sulfur deposition has occurred frequently in gas transmission pipelines and gas process equipment,23-25 because gas transmission temperature is often below 323 K.26 Based on Heidemann’s model, Cézac et al. proposed two new fugacity expressions of solid sulfur by correlating solid sulfur fugacity with liquid sulfur fugacity, and calculated the amount of sulfur deposition caused by a drop in temperature and pressure in natural gas transmission and distribution networks.13-14,26-27 IAdditionally, unlike the values of binary interaction coefficients between sulfur and hydrogen sulfide, carbon dioxide or methane in many other thermodynamic models,9,13,20,28 they are dependent on temperature in the model of Cézac et al.14 As is shown in Gu’s article8, these values of binary interaction coefficients cannot always maintain constants upon a change in temperature. Given the above, it is difficult to establish an accurate prediction model of sulfur solubility because the sulfur solution mechanism of sulfur in hydrogen sulfide has been unclear under conditions of gas transmission. In this paper, a comprehensive model of sulfur solubility in hydrogen sulfide is established,



considering both the physical solution and chemical reaction. Based on this model, the solution mechanism of sulfur in hydrogen sulfide under gas transmission conditions will be revealed clearly.

2. Phase equilibrium model of elemental sulfur Based on Heidemann’s work,13 the content of S8 in eight sulfur species decreased with increasing temperature, and other sulfur species including from S1 to S7 increased with increasing temperature.13 This could be because a higher temperature helped to break down S8 to smaller sulfur molecules. In contrast, S8 is generated more easily at lower temperatures by the combination reactions of smaller sulfur molecules including S1, S2, … , S7. Furthermore, the mole fraction of S8 in vapor mixtures of sulfur is above 82%, and this value tends to increase with a further decrease in temperature,13 because the temperature of natural gas transmission is often below 323 K, and even near 273.15 K in winter. The S8 content of sulfur vapor mixtures in gas transmission pipelines has an absolute advantage. Additionally, the newest experimental results of sulfur deposition in separators after a wellhead show that the content of S8 is 84.4% in solid powder and 93.5% in colloid substances, respectively.29 Moreover, the other species of elemental sulfur (S1…S7) were not detected in the deposition of solids.29 Therefore, elemental sulfur contains almost none of the other species in gas transmission pipelines and gas process equipment, except for S8. In conclusion, because the object of this study is mainly natural gas transmission after the gas wellhead, elemental sulfur is treated as a single molecule S8 under all conditions. Predicting elemental sulfur solubility in hydrogen sulfide is, in essence, the calculating of the phase equilibrium of S8 in hydrogen sulfide. S8 of fluids will exist in the forms of a physical solution and chemical solution. Significantly, the chemical solution of S8 is obtained from the process of forming sulfane H2S9 by the combination reaction between S8 and hydrogen sulfide shown in Eq. (1). Therefore, the solubility of S8


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in hydrogen sulfide should be the sum of the physical solubility and chemical solubility, that is, the sum of the content of S8 and sulfane H2S9 in the gas phase, as expressed by Eq. (2).

  H 2S9 H 2S+S8  

(1)

ySV8  ySphy  ySchem 8 8

(2)

2.1 Physical equilibrium model of elemental sulfur Physical solubility of elemental sulfur refers to the content of free molecules of S8 in the fluid phase. It can be described using thermodynamic phase equilibrium theory. The phase equilibrium condition of the gas-solid system requires that the fugacity of gaseous S8 is identical with that of the solid phase, as expressed by Eq. (3)30



fSS8 T , P   fSV8 T , P, ySphy 8 where



(3)

fSS8 is the fugacity of elemental sulfur S8 in the solid phase, Pa;

fSV8 is the fugacity of

elemental sulfur S8 in the vapor phase, Pa. P is the absolute pressure, Pa; and T is the temperature, K. ySphy 8

is the mole fraction of gaseous S8 and is also the physical solubility of S8. These parameters are all measured at the same temperature T and pressure P. 2.1.1 Fugacity of solid S8 The solid sulfur fugacity can be expressed by Eq. (4); it relates the solid sulfur fugacity to the saturation vapor pressure of sulfur.30 fSS8 T , P  =Ssat PSsat exp 8 8



VSS8 P  PSsat 8



RT

(4)

where Ssat is the fugacity factor of vapor sulfur. R is the gas constant, 8.314 J/(mol·K). PSsat is the 8

8

vapor pressure of sulfur at temperature T, Pa. VSS is the molar volume of solid sulfur, m3/mol. 8

2.1.2 Fugacity of vapor S8



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Elemental sulfur fugacity in the vapor phase can be expressed by Eq. (5):30





 ySphy  SV8  P fSV8 T , P, ySphy 8 8

(5)

where SV is the fugacity coefficient of gaseous sulfur. 8

2.1.3 Physical solubility of S8 By combining Eq. (4) and Eq. (5), the physical solubility of sulfur can be expressed by Eq. (6):

phy S8

y

Ssat PSsat exp VSS  P  PSsat  RT   SV P 8

8

8

8

(6)

8

In Eq. (6), there are two important parameters including the vapor pressure of sulfur PSsat and the 8

fugacity coefficient of gaseous sulfur SV . 8

2.2 Chemical equilibrium model of elemental sulfur As is shown in Eq. (1), when gaseous S8 combines with hydrogen sulfide forming sulfane H2S9, S8 will be transformed from the solid phase to the vapor phase, supplemented equally. In fact, the sulfur solubility will increase because of the chemical solution. Therefore, the chemical solution of S8 cannot be ignored. According to the relationship of chemical reaction equilibrium, when the system of the chemical reaction is balanced, the following equation can be established:30

n

 fi V     

 P i

ik

n

ik

   yiViV  i

 n    ik i    exp   i 1 RT    

(7)

V V V where n is the number of components in the chemical reactions; f i , yi and i are fugacity,

mole fraction and fugacity coefficient of component i in the vapor phase, respectively; ik

is the

 stoichiometric coefficient of component i in the chemical reaction k; i is the standard chemical potential

of component i.


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In this model, the chemical reaction is shown in Eq. (1). When the reaction is in equilibrium, Eq. (7) can become:

y where yHV S

yHV2S9 HV2S9



V V H 2S H 2S

 y



phy V S8 S8





 H S  SΘ  HΘ S 2 9 8 2  exp   RT  

 

(8)

 

is the mole fraction of gaseous H2S9, and its value is equal to the chemical solubility

2 9

; HV2S9 is the fugacity coefficient of gaseous H2S9; yHV2S is the mole fraction of gaseous hydrogen ySchem 8 sulfide; HV S is the fugacity coefficient of gaseous hydrogen sulfide; and HΘ S , S and HΘ S are the 2

2 9

8

2

standard chemical potential of H2S9, S8 and H2S, respectively. Based on Eq. (8), the chemical solubility ySchem can be expressed by Eq. (9): 8

chem S8

y

y

V H 2S9

y 

 y



V V H 2S H 2S



phy V S8 S8



V H 2S9

 exp     

 H 2S9



 SΘ8  HΘ2S   RT  

(9)

3. Important parameters of the phase equilibrium model 3.1 Vapor pressure of solid sulfur The vapor pressure of elemental sulfur is an important parameter of solid phase fugacity expression. Shuai and Meisen regressed a vapor pressure expression of solid sulfur based on Neumann’s experimental data.31-32 Their expression is widely used in aspects of physical parameter calculation of elemental sulfur. However, when the expression is used in calculating the solid sulfur fugacity, the temperature range of application needs be above 330 K,14 because the temperature of natural gas transmission is often below 323 K. Furthermore, the value of sulfur vapor pressure is quite low at temperatures of natural gas transmission, so an exact expression is necessary. In this section, we try to build a new formula for sulfur vapor pressure for adapting to the temperature range, especially lower temperatures.



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Because a transition temperature (368.65 K) exists between two different forms including

-

 - and

sulfur.33 As is shown in Table S1 (SUPPORTING INFORMATION), we chose experimental data from

Neumann and Bradley for regressing the formula of sulfur vapor pressure below 368.65 K. 31,34 As is shown in Eq. (10), a new expression of sulfur vapor pressure based on the Antoine equation is regressed by the least squares method.35 The experimental data from Briske is used to verify the prediction accuracy of the formula at lower temperatures. 36

ln Psat  33.33 

12834.49 T  8.87

T  368.65 K

(10)

As is shown in Table S2, we add the calculated results of sulfur vapor pressure at temperatures from 273.15 K to 362.05 K, using the formulas presented in Bradley and Sun’s studies

9, 34.

The relative errors

between the experimental data and the data predicted by these four formulas are shown in Table S3. The average relative errors of the sulfur vapor pressure evaluated by this new expression, Shuai’s formula, Bradley’s formula and Sun’s formula for 18 investigated experimental values are -0.20%, 111.47%, -3.55%, and 18.55%, respectively. The results still show that the new expression of the present study better fits the experimental data. Furthermore, the new expression has high prediction accuracy as low as 273.15 K.

3.2 Fugacity coefficient of gaseous components 3.2.1 PR EoS In this model, the Peng-Robinson equation of state (PR EoS) is used to calculate the fugacity coefficient of gaseous components. The basic form of PR EoS is expressed by Eq. (11) 21:

P=

RT a  V  b V   b V   b 

where a and b are parameters of PR EoS;



and



(11)

are constants depending on the type of EoS; and

V is molar volume, m3/mol.


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3.2.2 Binary interaction coefficient between S8 and hydrogen sulfide The binary interaction coefficient between S8 and hydrogen sulfide exerts direct and crucial influence upon the fugacity of gaseous components and requires a more reasonable description. Due to the lack of direct experimental data, the value of binary interaction coefficients between S8 and solvent components including hydrogen sulfide, carbon dioxide and methane are often regressed by sulfur solubility experimental data.8-9,13-14,20,28,37 Gu et al. first thought that the binary interaction coefficients between S8 and hydrogen were related to temperature.8 Then, Cézac and Li et al. proposed a formula dependent on temperature for predicting the binary interaction coefficient.14,37 In this paper, we consider that the changing density of gas mixtures could cause a change in the distance between sulfur molecules and hydrogen sulfide molecules. This change may result in a binary interaction coefficient between S8 and hydrogen sulfide in a certain degree. In fact, the density of natural gas mixtures often changes with gas transmission temperature and pressure. Therefore, the new expression of the binary interaction coefficient between S8 and hydrogen sulfide will add the influence caused by the density of the solvent and can be expressed by Eq. (12): kij  a1   a2  a3   T   a4  a5   T 2

(12)

where  is the density of solvent, kg/m3; a1 , a2 , a3 , a4 and a5 are constant coefficients that can be regressed by experimental data of sulfur solubility in hydrogen sulfide. Owing to the lack of experimental data for sulfur solubility under the conditions of natural gas transmission, we chose a temperature of experimental data below 373.15 K. Based on Roof, Brunner and Gu’s experimental data of elemental sulfur in hydrogen,4,6,8 the new expression of the binary interaction



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coefficient between sulfur and hydrogen sulfide, regressed by the least squares method, can be expressed by Eq. (13):

kS8 -H2S  7.5683   3.3365  102  9.6006  106   T   3.5320  105  2.6436  108   T 2 (13) 3.3 Parameters of sulfane H2S9 in PR EoS Owing to the lack of critical parameters and acentric factors of sulfane H2S9, the parameters a and b in the PR EoS of sulfane H2S9 cannot be calculated directly. According to the method presented by Heidemann and Prausnitz

38-39

as follows, we can calculate the PR EoS parameters of sulfane H2S9 based on the

corresponding parameters of source species. NS

Ai   ji Aj

(14)

j 1

NS

bi   ji b j

(15)

j 1

NS NS

aij   ki lj akl

(16)

k 1 l 1

where  ji are stoichiometric coefficients; Aj are PR EoS parameters of source species, for instance, S8 and hydrogen sulfide in Eq. (1).

3.4 Standard chemical potential Heidemann et al. regressed a formula depending on temperature for calculating the standard chemical potential of S8, hydrogen sulfide and sulfane H2S9 shown in Eq. (17).13

i RT

=

c1  c2 ln T  c3  c4T  c5T 2  c6T 3 T

(17)

where c1 , ..., c6 are six constants. Their values are shown in Table S4. The calculation flow chart of sulfur solubility is given in Figure S1 (SUPPORTING INFORMATION). This calculation has four loops, including the calculation of the binary interaction coefficient kS8 -H2S , the


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compression factor Z, physical sulfur solubility ySphy and the density of gas mixtures. Only once these four 8

parameters are calculated is the calculation finished.

4. Results and discussions 4.1 Comparisons between this model and the same type of models Because the temperature of gas transmission is often below 323 K and there is a lack of experimental data for corresponding temperatures at present, we can only select the experimental data at temperatures of 316.26 K and 338.71 K to test the model precision of this article. Predictions of sulfur solubility in hydrogen sulfide at temperatures of 316.26 K and 338.71 K and at pressures ranging from 7.03 to 31.16 MPa using different models is shown in Table S5. We find the prediction results of Heidemann’s model and this model agree well with the experimental data. In contrast, the calculated solubility of Sun’s model is much higher than experimental data, as shown in Table S5. The RE stands for relative error calculated by Eq. (18). Additionally, ARE and AARE are average relative error and absolute average relative error, calculated by Eq. (19) and Eq. (20) respectively. RE 

ARE% 

Z ipred  Z iexp Z iexp

(18)

100 N  Z ipred  Z iexp    Z exp  N i 1  i 

pred exp 100 N  Z i  Z i AARE%    Z exp N i 1  i 

(19)

   

(20)

pred exp where Z i is predicted sulfur solubility of the models, and Z i is the sulfur solubility of

experiments.



As is shown in Table S5 in the SUPPORTING INFORMATION file, we provide the relative error between the experimental data and simulated data using Heidemann’s model, Sun’s model and this model. According to Table S5, we find that average relative errors (ARE%) generated by the aforementioned models are -12.66%, 245.57% and 4.20%, respectively. The average absolute relative errors (AARE%) are 12.66%, 245.57% and 7.62%, respectively. The results show that this model can better fit sulfur solubility.

4.2 Solution mechanism of sulfur in hydrogen sulfide under gas transmission conditions 4.2.1 Sulfur solubility in hydrogen changes with pressure The temperature and pressure of gas transmission are often far lower than those of the gas reservoir and wellbore. In this case, in order to analyze the solution mechanism of sulfur in hydrogen sulfide under conditions of gas transmission, we set temperatures ranging from 273.15 K to 323.15 K and pressures ranging from 1.0 MPa to 12.0 MPa. Total sulfur solubility, physical sulfur solubility and chemical sulfur solubility change with pressures ranging from 1.0 MPa to 12.0 MPa, as shown in Figure 1, Figure 2 and Figure 3, respectively. The different colored symbols represent different temperatures from 273.15 K to 323.15 K. We find the sulfur solubility increases first and then does not change substantially. The value of sulfur solubility has a sudden increase at pressures from 3.0 MPa to 5.0 MPa, depending on temperature, except for at temperatures of 273.15 K and 283.15 K (shown in Figure 2). Because the sulfur content of the mixtures shown in Roof’s work is below 0.01, 4 the formation of liquid phase hydrogen sulfide owing to increasing pressure or decreasing temperature is the most important reason. Figure 4 shows the phase equilibria diagram of pure hydrogen sulfide at the temperatures and pressures of interest using PR EoS.

21

The gas-liquid equilibria line divides the diagram

into two different areas. The region above the line region represents the liquid phase of hydrogen sulfide,


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and the subline region represents gaseous hydrogen sulfide. As is shown in Figure 4, an important phenomenon is that gaseous hydrogen sulfide will become liquid when the pressure increases from 1.0 MPa to 12.0 MPa, provided that the temperature remains constant. Once the combination conditions of pressure or temperature move from the gaseous phase to liquid phase on the gas-liquid phase equilibria line, with increasing pressure or decreasing temperature, the density of hydrogen sulfide in the majority of mixtures will be exhibit a sudden increase. Because of the sudden increase in the mixtures, density causes the sharp decrease in the distance between hydrogen sulfide molecules and S8 molecules and substantially increases the chance of a chemical reaction between hydrogen sulfide and S8. Therefore, more sulfane H2S9 is produced and eventually causes an increase in the total sulfur solubility and chemical sulfur solubility. 10-2

10-2

10-3

10-3

10-4 Increase 10

-5

10-6 10-7

273.15 K 283.15 K 293.15 K 303.15 K 313.15 K 323.15 K

10-8 10

-9

10-10

2

4

6 P/ (MPa)

8

10

12

Physical sulfur solubility/ (mol/mol)

Total sulfur solubility/ (mol/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


273.15 K 293.15 K 313.15 K

10-4 10-5 10-6

283.15 K 303.15 K 323.15 K

Increase

10-7 10-8 10-9 10-10 10

Decrease

-11

10-12

2

4

6 P/ (MPa)

8

10

Figure 1. Total sulfur solubility in hydrogen

Figure 2. Physical sulfur solubility in hydrogen

sulfide changing with pressure



12


10-3 10-4 Increase 10-5 10-6 10-7 10

273.15 K 283.15 K 293.15 K 303.15 K 313.15 K 323.15 K

-8

10-9 10-10

2

4

6 P/ (MPa)

8

10

12

12 11 10 9 8 Liquid 7 6 5 Gas-Liquid phase equilibria line 4 3 2 Gas 1 0 270 275 280 285 290 295 300 305 310 315 320 325 Temperature/ (K)

Pressure/ (MPa)

10-2 Chemical sulfur solubility/ (mol/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 3. Chemical sulfur solubility in hydrogen

Figure 4. Gas-Liquid phase equilibria line of


hydrogen sulfide

Figure 5 and Figure 6 show that the ratio of physical sulfur solubility to total sulfur solubility and the ratio of chemical sulfur solubility to total sulfur solubility in hydrogen sulfide change with pressure, respectively. As is shown in Figure 5, the ratio of physical sulfur solubility decreases from 61.16% to approximately 0.001% with pressures increasing from 1.0 MPa to 12.0 MPa. In contrast, the ratio of chemical sulfur solubility increases from 38.84% to approximately 99.999%, with pressure increasing from 1.0 MPa to 12.0 MPa, as shown in Figure 6. We find that the ratio of both solution mechanisms ranges from 33.52%~66.48%, and the ratio shows a contrary tendency with increase in pressure from 1.0 MPa to 3.0 MPa. However, the ratio of physical sulfur solubility is near 0%, and the ratio of chemical sulfur solubility is near 100%, with pressures increasing from 5.0 MPa to 12.0 MPa; these two types of solubility change very little in the pressure scope. Red dashed frames in Figure 5 and Figure 6 represent the abruptly changing region of the two types of solubility because of changes in density mixtures. The results show that the sulfur solubility in hydrogen sulfide is determined by both the physical and chemical solution when the pressure is below some constants (3.0 MPa < P < 5.0 MPa), and the sulfur solubility in hydrogen sulfide is mainly determined by the chemical solution when the pressure is above these values.


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100 Ratio of physical sulfur solubility/ (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


273.15 K 283.15 K 293.15 K 303.15 K 313.15 K 323.15 K

80 Maximum 1： 61.16% 60 40

Abrupt change of mixtures density

20 Maximum 2： 2.47% 0

2

4

6 P/ (MPa)

8

10

12

100

Ratio of chemical sulfur solubility/ (%)

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80

Maximum 2： 99.999%

Maximum 1： 66.48%


60

40

273.15 K 283.15 K 293.15 K 303.15 K 313.15 K 323.15 K

20

0

2

4

6 P/ (MPa)

8

10

Figure 5. Ratio of physical sulfur solubility in

Figure 6. Ratio of chemical sulfur solubility in

hydrogen sulfide changing with pressure

hydrogen sulfide changing with pressure

4.2.2 Sulfur solubility in hydrogen changes with temperature Total sulfur solubility, physical sulfur solubility and chemical sulfur solubility change with temperatures ranging from 273.15 K to 323.15 K, as shown in Figure 7, Figure 8 and Figure 9, respectively. The different colored symbols represent pressures from 2.0 MPa to 12.0 MPa. The sulfur solubility increases with an increase in temperature and at six different pressures except for 4 MPa, as shown in these three figures. We find that when pressure is 4.0 MPa, sulfur solubility increases first and then has a sudden decrease at a temperature of approximately 300 K with increasing temperature, and the sulfur solubility only increases slightly when the temperature is above 300 K. Additionally, the total sulfur solubility is always below 1.03×10-8 (mol/mol) at temperatures from 273.15 K to 323.15 K and at a pressure of 2.0 MPa. The total sulfur solubility, physical sulfur solubility and chemical sulfur solubility increase from 4.96×10-8 to 2.72×10-3, from 6.40×10-12 to 6.72×10-5 and from 5.38×10-12 to 2.65×10-3, respectively, with temperatures increasing from 273.15 K to 323.15 K and a pressure above 6.0 MPa. These results show that temperature has a significant influence on sulfur solubility.


12

10-2

10-3

10-3

10-4

2 MPa 4 MPa 6 MPa 8 MPa 10 MPa 12 MPa

Increase

10-5 10-6

Decrease

10-7 10-8 10-9 280

290

300 T/ (K)

310

320

Physical sulfur solubility/ (mol/mol)

10-2

10-10

10-4 10-5 10-6

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10-7

Increase

Decrease

10-8 10-9 10-10

280

290

300 T/ (K)

310

320

Figure 7. Total sulfur solubility in hydrogen

Figure 8. Physical sulfur solubility in hydrogen

sulfide changing with temperature

sulfide changing with temperature

10-2 Chemical sulfur solubility/ (mol/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Total sulfur solubility/ (mol/mol)


10-3 10-4 10

Increase

-5

10-6

Decrease

10-7


10-8 10-9 10-10

280

290

300 T/ (K)

310

320

Figure 9. Chemical sulfur solubility in hydrogen sulfide changing with temperature Figure 10 shows that ratio of physical sulfur solubility changes with temperatures increases from 273.15 K to 323.15 K and at six different kinds of pressure from 2.0 MPa to 12.0 MPa. The ratio of physical sulfur solubility increases from 0.001% to 50.23% with an increase in temperature. The curve appears to change abruptly at approximately 300 K when the pressure is 4 MPa. The curves are near the horizontal axis of ratio 0% when pressure is above 6.0 MPa. To show the two parts clearly, two drawings of partial enlargements are plotted in Figure 10-(a) and Figure 10-(b). As is shown in Figure 10-(a), we posit that the reason for the


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abrupt change is mainly due to the abrupt changes in mixture density, owing to the changes in system temperature. Figure 10-(b) shows that the ratio of physical sulfur solubility increases with temperatures increasing from 300 K to 323.15 K and above 6.0 MPa. The maximum is 2.47% at 323.15 K and 12.0 MPa, as shown in Figure 10-(b). 100 90 Ratio of physical sulfur solubility/ (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


80 70


40

4 MPa

30 Abrupt change of

10

mixtures density

0

Maximum:50.23%

60

20

3.0

50

2.5

Maximum:33.13% 40

2.0

30

(a) 280

290

6 MPa 8 MPa 10 MPa 12 MPa

300

310

320

Maximum:2.47%

1.5

(a)

20

1.0

(b) 10

0.5

0

0.0 280

290

300 T/ (K)

310

320

(b) 305

310 315 T/ (K)

320

Figure 10. Ratio of physical sulfur solubility in hydrogen sulfide changing with temperature Figure 11 shows that the ratio of chemical sulfur solubility changes with temperatures increasing from 273.15 K to 323.15 K and at six different kinds of pressure from 2.0 MPa to 12.0 MPa. The ratio of chemical sulfur solubility decreases from 99.999% to 49.78% with increasing temperature. The curve also appears to change abruptly at approximately 300 K when the pressure is 4 MPa. Additionally, the curves are near the horizontal axis of ratio 100% when the pressure is above 6.0 MPa. To show the two parts clearly, two drawings of partial enlargements are plotted in Figure 11-(a) and Figure 11-(b). As is shown in Figure 11(a), we posit that the reason for the abrupt changes is also mainly due to the abrupt changes in mixture density. Figure 11-(b) shows that the ratio of chemical sulfur solubility decreases with temperatures increasing from 300 K to 323.15 K and above 6.0 MPa. The minimum is 97.53% at 323.15 K and 12.0 MPa, as shown in



Figure 11-(b). These results show that the influence of temperature on the ratio of sulfur solubility is not very significant when pressure is above 5.0 MPa. 100

100

90 Ratio of chemical sulfur solubility/ (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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90

(b)

80

Abrupt change of

80

(a)

mixtures density

70 60

4 MPa

70

Minimum:66.87%

60

50

(a) 280

Minimum:49.78%

40

99.5

30 20 10 0

2 MPa 4 MPa 6 MPa 8 MPa 10 MPa 12 MPa 280

290

300

98.5 98.0 97.5

300 T/ (K)

310

320

6 MPa 8 MPa 10 MPa 12 MPa

99.0

290

310

100.0

320

Minimum: 97.53%

(b) 305

310

315

320

T/ (K)

Figure 11. Ratio of chemical sulfur solubility in hydrogen sulfide changing with temperature

5. Conclusion In this paper, we established a comprehensive model considering both the physical solution and chemical reaction for revealing the solution mechanism of sulfur in hydrogen sulfide at temperatures and pressures (T≤323 K, P≤12.0 MPa) of natural gas transmission. A new expression of sulfur vapor pressure and a more reasonable formula for the binary interaction coefficient between sulfur and hydrogen sulfide are obtained through this model. The results show that our model can fit the experimental data of sulfur solubility in hydrogen sulfide at lower temperatures better than other models of similar type such as Heidemann’s model and Sun’s model. By analyzing the sulfur solubility in hydrogen sulfide at temperatures from 273.15 K to 323.15 K and at pressures from 1.0 MPa to 12.0 MPa, a series of abrupt changing points of solubility appear under certain conditions. The physical sulfur solubility and chemical sulfur solubility changes very little with increase of


Page 19 of 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


pressure, except for abrupt changing points and significant increases with increasing temperature when the pressure is above 5.0 MPa. Additionally, we find that the sulfur solubility in hydrogen sulfide at the temperatures of gas transmission is mainly controlled by the chemical reaction between sulfur and hydrogen sulfide when the pressure is above 5.0 MPa. Moreover, the sulfur solubility in hydrogen sulfide is determined by both the physical solution and chemical reaction when the pressure is below 3.0 MPa.

Acknowledgments This study was financially supported by the National Natural Science Foundation of China (No. 51674213, 51504206 and 51604233).

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100 Ratio of physical sulfur solubility/ (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

273.15 K 283.15 K 293.15 K 303.15 K 313.15 K 323.15 K

80 Maximum 1： 61.16% 60 40

Page 24 of 24


20 Maximum 2： 2.47% 0

2

4

6 P/ (MPa)

8

TOC Graph


10

12

Solution Mechanism of Elemental Sulfur in Hydrogen Sulfide under

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