Correlation and Prediction of Acid Gases Solubility in Various Aqueous Alkanolamine Solutions Using Electrolyte Cubic Square-Well Equation of State

Authors

1 Department of Chemical Engineering, Shahrood Branch, Islamic Azad University, Shahrood, Iran

2 Chemical Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

Abstract

The object of this work is solubility correlation and prediction of CO2 and H2S in various aqueous alkanolamines using the electrolyte cubic square-well equation of state (eCSW EoS) (Haghtalab, A.,Mazloumi, S. H., (2010), Electrolyte Cubic Square-Well Equation of State for Computation of the Solubility CO2 and H2S in Aqueous MDEA Solutions,  Ind. Eng. Chem. Res.,49,6221-623). The eEoS systematically is applied to describe the solubility of acid gases in various alkanolamine solutions, including MDEA, MEA, DEA, AMP, DIPA, TEA, DGA and PZ.In calculations of chemical equilibrium all of the molecular and ionic species have been taken in to account. Also, in order to improve the modeling, the N2O analogy method was used to calculate the molecular interaction parameters in binary acid gas and alkanolamine solutions. The results of the method are in good agreements with experiments. To investigate the accuracy of the modeling, the simultaneous solubility of mixed CO2 and H2S in aqueous MEA, DEA, MDEA, TEA and AMP solutions are also predicted. Acceptable results were achieved for the quaternary systems. In this work, over 3000 experimental data points were used in order to correlate and predict the solubility ofCO2 and H2Sin the various alkanolamine solutions.

Highlights

An electrolyte equation of state is applied to model acid gases solubility in various alkanolamine solutions.

The results are in good agreement with the experiments.

The extension of the model for quaternary systems has been successfully carried out.     

Keywords

Main Subjects


1. Introduction

Acid gas impurities such as and must be reduced or even removed from natural gas, because existence of these gases causes some industrial and environmental problems such as equipment corrosion, environment pollution and etc. The chemical absorption methods using alkanolamines are widely used for removal of these impurities from gas flow. Along with the experimental works, thermodynamic modeling is a useful and necessary tool in design of the processes. In literature many models have been presented to correlate and predict the acid gas solubility in alkanolamine solutions. These models may be divided in three categories. The first is empirical models. In these models, the activity coefficients of all species are assumed to be equal to unity. The fitting parameters are the equilibrium constants. The model of (Kent & Eisenberg, 1976) is one of the well-known models, which is commonly used by process engineers because of having low complexity and low computational effort. Another method is excess Gibbs energy model in which an activity coefficient model is used to describe the nonideality of the liquid phase. These models usually consist of two or three terms. One of these terms is normally based on the Debye-Huckle expression or its extensions, which used for the contribution of long range interactions. The Born term may be added to represent the contribution of mixed solvents effects. Also for the nonidealites of the vapor phase, an equation of state (EoS) may be used. The method has been well established and implemented by several authors. The most important weakness of these types of models is that the pressure effect on the activity coefficient has not usually been taken into account. Also Henry's constants for solubility of the fugacious components, such as acid gases, should be available. (Deshmukh & Mather, 1981), (Clegg & Pitzer, 1992), (David M. Austgen, Rochelle, Peng, & Chen, 1989), (Ali Haghtalab & Tafti, 2007), (Ali  Haghtalab & Shojaeian, 2010) and (Alhseinat, Mota-Martinez, Peters, & Banat, 2014) are some example works in this category.

The third method is based on  approach in which an EoS models is used to represent the nonideality of the liquid and vapor phases. This approach that is almost new technique for computations of solubility of acid gases in alkanolamine solutions, is not subjected to the mentioned weakness. In recent years, the application of a suitable EoS for computation of a VLE of alkalonamine systems is an interesting topic. However, the published papers on this approach are more limited than the previous approach (Fürst & Planche, 1997) have used two different EoSs, one for liquid phase and one for vapor phase, in order to calculate solubility of the acid gases in alkanolamine mixtures. (Kuranov, Rumpf, Maurer, & Smirnova, 1997) and (Smirnova, Victorov, & Kuranov, 1998) have applied the hole model and SRK EoS for representation of the vapor-liquid equilibrium in the alkanolamine solutions. (Vallée, Mougin, Jullian, & Fürst, 1999) have studied the solubility of acid gases in aqueous solution. They used the electrolyte EoS which was developed by (Fürst & Renon, 1993). The same eEoS has been also used by (Chunxi & Fürst, 2000) in order to study the solubility of acid gases in aqueous  solutions. (Fürst & Renon, 1993) eEoS have been adopted to represent the solubility of  in aqueous piperazine solutions by (P. W. Derks, Dijkstra, Hogendoorn, & Versteeg, 2005). For computation of the VLE of the quaternary  and systems, the Born term was added to (Fürst & Renon, 1993) eEoS in order to improve the modeling by (P J G Huttenhuis, Agrawal, Solbraa, & Versteeg, 2008; P J G Huttenhuis, Agrawal, & Versteeg, 2008). They also extended the eEoS to represent the mixed ,  and in the aqueous solution (P. J. G. Huttenhuis, Agrawal, & Versteeg, 2009). (Ali Haghtalab & Seyed Hossein Mazloumi, 2009) have used eCSW EOS for correlation of the solubility of and  in aqueous  solutions in a wide range of acid gas loading, temperature, and pressure(Ali Haghtalab & Mazloumi, 2010). They have been also predicted the solubility of mixed acid gases in aqueous alkanolamine solution. (Zoghi, Feyzi, & Dehghani, 2012) have applied mPR-CPA EoS for representation of the VLE in the  system.

The aim of the present work is to correlate and predict the solubility of acid gases in various alkanolamine solutions using the eCSW EoS (A. Haghtalab & S. H. Mazloumi, 2009). (Ali Haghtalab & Mazloumi, 2010)have assumed that the effects of second dissociation of acid gases are negligible. Also they did not compute the binary interaction parameters in binaries  and . In this work, all of the molecular and ionic species are considered in calculations of chemical equilibrium. In addition, using  analogy approach, the effect of acid gases in alkanolamine in binary systems is calculated in order to improve the modeling of the ternary  systems. In this work, over 3000 experimental data points is used for modeling of solubility of acid gases in various alkanolamine solutions in a wide range of acid gas loadings, temperatures, and pressures.

This work is, in fact, an extension and modification of the previous work of (Ali Haghtalab & Mazloumi, 2010). In this work, some of the simplified assumptions of Haghtalab and Mazloumi such as ignoring second dissociation of acid gases and zero interaction between amine and acid gases have been corrected. Then the modified method has been extended for the various aqueous alkanolamine solutions such as MDEA, PZ, AMP and TEA. So the present model is a reliable thermodynamic method that may be implemented for design and optimization of acid gas sweetening units using alkanolamine solutions.

2. Thermodynamic Framework

2.1. Chemical Equilibrium

When acid gases dissolve in aqueous alkanolamine solutions some equilibrium reactions occur. Thus, chemical equilibrium must be incorporated in the modeling of alkanolamine-acid gas systems due to reactive absorption in liquid phase. (Ali Haghtalab & Mazloumi, 2010) assumed that the effects of second dissociation of acid gases are insignificant, so they did not calculate the effect of  and  in modeling. Also  and  have not been taken into account. In this work, not only, the second dissociations of acid gas reactions are considered, but also, the concentration of  and  are involved in computing of chemical equilibrium.

For the  and  systems, the following chemical reactions will take place:

Water dissociation:

                                 (1)

Bicarbonate formation:

                        (2)

Bisulfide formation:

                         (3)

Carbonate formation:

                      (4)

Sulfide formation:

                            (5)

AMINE protonation:

                (6)

Carbamate formation:

        (7)

It should be note that the carbamate formation just occurs when the primary and secondary amines have been presented in liquid phase. The dielectric constant for a pure solvent is expressed as:

                        (8)

where the coefficients of the Eq. (8) are given
 in table 1.The mole fraction based chemical equilibrium constants of the reactions are expressed as:

                        (9)

where  is mole fraction, the activity coefficient, and  the reaction stoichiometry of the species . The coefficients A, B, C and D are constants that are given in table 2. In this work as in that of (Ali Haghtalab & Mazloumi, 2010), the symmetrical activity coefficient for water is used:

                  (10)

 

Table 1. Dielectric Constants of Pure Solvents

Solvent

 

         

Ref

 

 

-19.291

29815

0.019678

13.189

-3.1144

(Maryot & Smith, 1951)

 

 

-18.5843

14836

0

0

0

(Fang-Yuan Jou, Otto, & Mather, 1994)

 

 

61.7172

0

-0.136743

4.943303

0

(Hsieh, Chen, & Li, 2007)

 

 

103.221

0

-0.37311

38.0795

0

(Hsieh et al., 2007)

 

 

61.7172

0

-0.136743

4.943303

0

(Hsieh et al., 2007)

 

 

28.8244

0

-0.07191

-7.4526

0

(Hsieh et al., 2007)

 

 

51.2299

0

-0.113191

3.98317

0

(Hsieh et al., 2007)

 

 

-8.16976

8989.3

0

0

0

(Chunxi & Fürst, 2000)

 

 

148.9

0

-0.62491

77.1

0

(Mazloumi et al., 2012)

 

 

 

 

 

Table 2. Chemical Reactions and Coefficients of Equilibrium Constants of the Reactions

Ref

T(K)

D

C

B

A

Reactions

(Posey & Rochelle, 1997)

273-498

0

-22.4773

-13445.9

132.899

 

(Posey & Rochelle, 1997)

273-498

0

-36.7816

-12092.1

213.465

 

(Posey & Rochelle, 1997)

273-498

0

-35.4819

-12431.7

216.049

 

(David M Austgen, Rochelle, & Chen, 1991)

287-423

0

-33.5471

12995.4

214.582

 

(David M Austgen et al., 1991)

287-343

0

0

-3338.0

-32.0

 

(P.J.G. Huttenhuis, Agrawal, Hogendoorn, & Versteeg, 2007)

278-423

0

10.06

-1116.5

-77.262

 

(Y.-g. Li & Mather, 1996)

273-323

0.010517

0

-3088.69

-10.6518

 

(L. B. Lee, 1996)

273-323

-0.0009848

0

-6166.1156

-4.90736

 

(L. B. Lee, 1996)

298-393

0

0

-2275.1900

0.030669

 

(L. B. Lee, 1996)

273-323

0.0099612

0

-4214.0671

-13.2964

 

(L. B. Lee, 1996)

298-393

0

0

-2057.4377

1.655469

 

(Silkenbaumer, Rumpf, & Lichtenthaler, 1998)

Not reported

0

-22.4773

-7261.78

142.58612

 

(Silkenbaumer et al., 1998)

Not reported

0

0

2546.6

-11.555

 

(L. B. Lee, 1996)

273-323

0.0099612

0

-4214.0671

-13.2964

 

(L. B. Lee, 1996)

298-393

0

0

-2057.4377

1.655469

 

(D.M. Austgen, 1989)

Not reported

-0.005037

0

-8431.65

1.6957

 

(D.M. Austgen, 1989)

298-373

0

0

5274.4

-8.8334

 

(P. W. Derks et al., 2005)

273-323

-0.015096

0

3814.4

18.135

 

(P. W. Derks et al., 2005)

273-333

0

0

3616.1

-4.6185

 

 

 

and for the other species with the reference state of infinite dilution in water, the unsymmetrical activity coefficient is used:

                  (11)

The eCSW EoS (introduced by details in appendix A.) was used in order to calculate the fugacity coefficient of all component, molecular and ionic species.

2.2. Phase Equilibrium

The eCSW EoS are applied in order to perform the phase equilibrium calculations for molecular components. (Kuranov, Rumpf, Smirnova, & Maurer, 1996) assumed that in the vapor phase only the acid gases and water molecules are present, because alkanolamines have low vapor pressure in temperature range of 298-413 K. The VLE relation is:  

                                            (12)

where and  are the mole fraction of component in the liquid and the vapor phase, respectively. Also, is the fugacity coefficient of water and acid gas molecules, calculated using the eCSW EoS. In addition to VLE and chemical equations, mass balance equations are needed in order to solve the governing system of equations.

2.3. Mole and Charge Balance

The following mole and charge balance equations are required for the  and systems.

Water mole balance:

                                                     (13)

Amine mole balance:

                                                                (14)

Acid gases balance:

                                                       (15)

                                                                            (16)

 

 

Charge balance:

                                             (17)

                                                        (18)

where , and  are loading of acid gas  in alkanolamine, the number of moles, and the charge number of ions, respectively. It should be noted that, if the alkanolamine is tertiary amine, the number of moles of  set equal to zero. to obtain initial moles, the density of pure solvents are needed that are given in table 3. For modeling the  and systems, the mole and charge balance equations and chemical equilibrium equations should be solved simultaneously to obtain the equilibrium concentrations of all components in liquid phase. These equations represent the nonlinear system and in this work, the method of (Smith & Missen, 1988) is used to solve the equations.

 

Table 3. Density of Pure Solvents

Ref

Density

Sol.

(Fang-Yuan Jou et al., 1994)

   

(Fang-Yuan Jou et al., 1994)

   

(L. B. Lee, 1996)

   

(Y.-g. Li & Mather, 1996)

   

(L. B. Lee, 1996)

   

(Henni, Hromek, Tontiwachwuthikul, & Chakma, 2003)

   

(Kundu, Mandal, & Bandyopadhyay, 2003)

   

(Abukashabeh, Alhseinat, Al-Asheh, & Bana, 2014)

   

(Peter W. Derks, Hogendoorn, & Versteeg, 2005)

   

 It is assumed that the density of DGA is as same as DEA, because of having same molecular weight.

  concentration of PZ in aqueous solution. (mol/lit)

 

 

Table 4. Specifications of the Experimental Data Sources Used for the Solubility of Acid Gases in Aqueous  Solution

Np

Loading

(mole gas/mole MDEA)

Temp(K)

Wt%

Author

 

 

 

 

 

13

0.02-0.26

298

23

(Lemoine, Li, Cadours, Bouallou, & Richon, 2000)

42

0.01-0.88

303, 313, 323

23, 45

(Haji-Sulaiman, Aroua, & Bnamor, 1998)

30

0.0087-0.4923

298, 323, 348, 373

50

(M. K. Park & Sandall, 2001)

77

0.008-1.303

298, 313, 348

25, 46

(Sidi-Boumedine et al., 2004a)

34

0.1658-0.8133

328, 343, 358

50

(Mamun, Nilsen, & Svendsen, 2005)

14

0.006-0.65

313

23

(David M Austgen et al., 1991)

78

0.105-1.157

313, 333, 373, 393, 413

18, 19, 32

(Kuranov et al., 1996)

58

0.0087-0.8478

323, 348, 373

20, 50

(Rho et al., 1997)

28

0.126-1.243

313, 353, 393

32, 48

(Á. P.-S. Kamps et al., 2001)

34

0.000591-0.1177

313, 323

23, 50

(Rogers, Bullin, & Davison, 1998)

5

0.124-1.203

313

23

(Macgregor & Mather, 1991)

 

 

 

 

 

27

0.0151-0.2299

298

11,23

(Lemoine et al., 2000)

25

0.039-1.116

313, 373

46

(Sidi-Boumedine et al., 2004b)

71

0.480-1.933

313, 333, 373, 393, 413

18,32

(Kuranov et al., 1996)

26

0.153-1.428

313, 353, 393

48

(Á. P.-S. Kamps et al., 2001)

22

0.00627-0.313

313

23,50

(Rogers et al., 1998)

18

0.382-1.725

313

23

(Macgregor & Mather, 1991)

602

Total

 

 

 

 


3. Results and Discussion

3.1. The Database

In the present work, in order to validate the model, the experimental database of (Ali Haghtalab & Mazloumi, 2010) for aqueous MDEA was used. For solubility of and  in aqueous , the database of many references were studied and agreeing of experiment was reviewed. Since, the discrepancy of various experimental data was slight, so no experimental data was removed. For aqueous , the found of database is same as that of (Vallée et al., 1999) and the other references were added to the database. For modeling of the solubility of  and  in these three common solutions ( ,  and ), more than 1600 experimental data points have been used. In table 5, the databases of the experimental data for the solubility of acid gases in MDEA,  and  solutions have been shown. Also, this table shows the experimental data of the solubility of acid gases in  solution. The references of experimental data used in modeling of the solubility of  and  in aqueous , ,   and  solutions were given in table 6.

 

 

Table 5. Specifications of the Experimental Data Sources Used for the Solubility of Acid Gases in Aqueous
, and Solutions

Np

Loading

(mole gas/mole MEA)

Temp(K)

Conc. Amine

Author

 

 

 

 

 

80

0.0117-1.247

298-373

30 Wt%

(Fang-Yuan Jou et al., 1995)

60

0.413-1.325

298-353

2.5 M

(Bhairi, 1984)

13

0.177-0.998

313-373

15.2 Wt%

(Lawson & Garst, 1976)

8

0.267-0.676

313-353

2.5 M

(David M Austgen et al., 1991)

19

0.155-0.3882

393

30 Wt%

(Mamun et al., 2005)

9

0.408-0.913

298

10 Wt%

(J.-Y. Park, Yoon, & Lee, 2003)

6

0.172-0.833

353

2.5 M

(Jane & Li, 1997)

 

 

 

 

 

96

0.108-1.61

298-393

2.5, 5 N

(Jong Il Lee et al., 1976)

45

0.0052-1.63

313-373

15.2 Wt%

(Lawson & Garst, 1976)

18

0.717-1.454

298

2.5 M

(Bhairi, 1984)

337

Total

 

 

 

 

 

 

 

 

104

0.072-2.695

298-373

0.5, 2, 3.5 N

(Jong Il Lee et al., 1972)

30

0.376-1.167

311-380

25 Wt%

(Lawson & Garst, 1976)

25

0.598-2.012

298

0.5, 2 M

(Bhairi, 1984)

44

0.042-0.3669

313, 373

2 M

(Lal et al., 1985)

14

0.463-0.736

298

1-2.5 M

(Oyevaar, Fonteln, & Westerterp, 1989)

6

0.299-0.725

373

4.2 M

(Dawodu & Meisen, 1994)

45

0.091-0.786

303-313

2.4 M

(Haji-Sulaiman et al., 1998)

24

0.021-1.088

298, 348

41.78 Wt%

(Sidi-Boumedine et al., 2004a)

14

0.00663-0.2331

323

20.2 Wt%

(Rogers, Bullin, Davison, Frazier, & Marsh, 1997)

 

 

 

 

 

112

0.0051-1.76

298-373

2,3.5 N

(Jong Il Lee et al., 1973a)

166

0.0050-3.04

298-373

0.5-3.5 N

(Jong Il Lee et al., 1973b)

89

0.0038-1.582

313-380

25 Wt%

(Lawson & Garst, 1976)

673

Total

 

 

 

 

 

 

 

 

40

0.126-0.96

293-353

2, 3 M

(Tontiwachwuthikul, Meisen, & Lim, 1991)

51

0.412-0.938

303-323

2-3.4 M

(Kundu et al., 2003)

66

0.1535-1.19465

313-353

2.43-6.24 m

(Silkenbaumer et al., 1998)

30

0.217-0.756

332-378

20 Wt%

(Jamal, 2002)

20

0.33-0.60

303-353

2 M

(Haji-Sulaiman & Aroua, 1996)

8

0.385-0.939

313

3 M

(Yang, Soriano, Caparanga, & Li, 2010)

8

0.432-0.991

313

2 M

(Jane & Li, 1997)

36

0.136-1.325

313, 373

2, 3 M

(Roberts & Mather, 1988)

24

0.033-1.265

313, 343

2 M

(Teng & Mather, 1990)

 

 

 

 

 

41

0.173-0.936

313-373

30 Wt%

(M.-H. Li & Chang, 1994)

9

0.618-1.021

313

2 M

(Jane & Li, 1997)

27

0.140-1.715

313, 373

2 M

(Roberts & Mather, 1988)

360

Total

 

 

 

Table 6. Specifications of the Experimental Data Sources Used for the Solubility of Acid Gases in Aqueous
, ,   and  Solutions

Np

Loading

(mole gas/mole DIPA)

Temp(K)

Conc. Amine

Author

 

 

 

 

 

45

0.067-1.111

313, 373

2.5 M

(Isaacs et al., 1977)

 

 

 

 

 

26

0.098-1.414

313, 373

2.5 M

(Isaacs et al., 1977)

23

0.58-1.37

313-353

2.95 m

(Mazloumi et al., 2012)

77

0.087-0.932

295-353

10-37 Wt%

(Uusi-Kyyny, Dell’Era, Penttilä, Pakkanen, & Alopaeus, 2013)

171

Total

 

 

 

 

 

 

 

 

30

0.0405-0.5022

313-373

30 Wt%

(Cheng, Caparanga, Soriano, & Li, 2010)

 

 

 

 

 

17

0.000271-0.531

298-333

15-50 Wt%

(Atwood, Arnold, & Kindrick, 1957)

47

Total

 

 

 

 

 

 

 

 

46

0.129-0.798

323, 373

60 Wt%

(Martin, Otto, & Mather, 1978)

43

0.52-1.302

298-333

20-60 Wt%

(Chen, 1991)

 

 

 

 

 

36

0.057-1.091

323, 373

60 Wt%

(Martin et al., 1978)

125

Total

 

 

 

 

 

 

 

 

92

0.501-1.68

313-393

1.995-3.950 m

(A. P.-S. Kamps, Xia, & Maurer, 2003)

52

0.36-1.23

298-343

0.2, 0.6 M

(P. W. Derks et al., 2005)

33

0.0519-0.807

313-393

0.989-4.443 m

(Ermatchkov et al., 2006)

 

 

 

 

 

82

0.597-2.429

313-393

2, 4 m

(Xia, Kamps, & Maurer, 2003)

25

0.520-1.037

313

2 m

(Speyer & Maurer, 2011)

284

Total

 

 

 

 


3.2. The Pure Parameters

, , and are the adjustable parameters of the eCSW EoS for pure components. These parameters that are given in Table 7 are calculated by simultaneous optimization of the saturated vapor pressure and the liquid density of the pure components. The parameters of acid gases, water, and  were taken from (Ali Haghtalab & Mazloumi, 2010). Also, for and , (Mazloumi, Haghtalab, Jalili, & Shokouhi, 2012) have calculated the pure parameters of the CSW EoS. The parameters of the CSW EoS for , , , , , and  have been fitted, using the vapor pressure data alone. One should note that for  the new parameters are fitted in wider range of temperature than (Mazloumi et al., 2012) work, so that the new parameters of the eCSW presented here, for , are different from those of their paper. However, the parameters of , were taken from (Mazloumi et al., 2012). In this work, it is assumed that for the ionic species such as , , and  the parameters of CSW EoS are the same as those of the corresponding molecular species, i.e., ,  and , except for the diameters of the  and the . Diameter of is taken from the literature (P J G Huttenhuis, Agrawal, Solbraa, et al., 2008). For , it is assumed that the diameters of these kinds of ions, such as , is equal summation of the diameters of the  and the .

 

Table 7. Parameters of the eCSW Equation of State

Species

 (k)

   

 range

AAD%

AAD%

Ref

 

772.657

1.4641

2.317

0.44-0.94

5.8

3.5

(Ali Haghtalab & Mazloumi, 2010)

 

462.655

1.3090

2.819

0.77-0.95

0.6

2.2

(Ali Haghtalab & Seyed Hossein Mazloumi, 2009)

 

524.895

1.3330

2.885

0.73-0.96

2.6

1.9

(Ali Haghtalab & Mazloumi, 2010)

 

811.075

1.5596

2.202

0.44-0.96

2.2

--

(Avlund, Kontogeorgis, & Michelsen, 2008)

 

1066.566

1.5336

2.023

0.43-0.95

0.9

--

(Avlund et al., 2008)

 

631.444

2.0702

1.389

0.45-0.92

1.9

--

(Wright, Dollimore, Dunn, & Alexander, 2004)

 

558.160

2.0813

0.890

0.44-0.95

7.7

--

(Chen, 1991)

 

1048.417

1.5026

2.235

0.58-0.95

1.6

--

(Uusi-Kyyny et al., 2013)

 

536.269

1.8866

1.658

0.45-0.93

0.8

--

(Pappa et al., 2006)

 

1261.451

1.4270

1.692

0.44-0.95

2.3

--

(Ali Haghtalab & Mazloumi, 2010)

 

847.891

1.4341

3.384

0.59-0.97

1.4

--

(Mazloumi et al., 2012)

 

772.657

1.4641

2.317

 

 

 

 

 

772.657

1.4641

2.317

 

 

 

 

 

462.655

1.3090

3.120

 

 

 

 

 

462.655

1.3090

3.120

 

 

 

 

 

524.895

1.3330

2.885

 

 

 

 

 

524.895

1.3330

2.885

 

 

 

 

 

811.075

1.5596

2.202

 

 

 

 

 

811.075

1.5596

5.021

 

 

 

 

 

1066.566

1.5336

2.023

 

 

 

 

 

1066.566

1.5336

4.842

 

 

 

 

 

631.444

2.0702

1.389

 

 

 

 

 

558.160

2.0813

0.890

 

 

 

 

 

558.160

2.0813

4.010

 

 

 

 

 

1890.666

1.2232

1.633

 

 

 

 

 

1890.666

1.2232

4.452

 

 

 

 

 

536.269

1.8866

1.658

 

 

 

 

 

536.269

1.8866

4.778

 

 

 

 

 

1261.451

1.4270

1.692

 

 

 

 

 

847.891

1.4341

3.384

 

 

 

 

 

847.891

1.4341

6.203

 

 

 

 

 


3.3. The Binary Interaction Parameters

Before the ternary systems can be simulated, first the following binary molecular systems  have to be studied and optimized. It is assumed that the interaction paramert of binaries in function of temprature is used:

                                                (19)

where  is absolute temprature in kelvin.

Three type of adjastable binery mulecular interaction parameters exist in the moleding of the solubility of acid gases in alkanolamines. These molecular intraction parameters are as follow.

3.3.1. Acid Gas-Water interaction

For determination of  in binaries  and  the data of the solubility of acid gases in water are available in literature. (Ali Haghtalab & Mazloumi, 2010) calculated the solubility of these binary systems in wide range of temperature and pressure. In this work, the interaction parameters of binary systems  and  are taken from their work and shown in table 8.

3.3.2. Alkanolamine-Water Interaction

For determination of  in binary , (Ali Haghtalab & Mazloumi, 2010), used the interaction energy parameters of the NRTL in order to obtaine the activity cofficient data of water, then, they calculated the intercation parameters in binary  by eCSW EoS. In this work, for binaries  and , following (Ali Haghtalab & Mazloumi, 2010), the binary interaction parameters are determined and the results are given in table 8. As one can see, only the parameter of  is fitted and for bineries  and  no experimental data are correlated. The VLE data of the  system are availabe in work of (Pappa, Anastasi, & Voutsas, 2006). So the interaction between  and water are calculated using eCSW EoS. Also the interaction parameters of binaries , ,  and  set to be zero.

3.3.3. Alkanolamine-Acid Gas Interaction

In litrature, three approach are used to obtain the binary interaction parameters of acid gas in alkanolamine, becuase there is no available experimental data for the solubility of  and  in pure alkanolamines. In the first method, as (Solbra, 2002) work, the interaction parameters of alkanolamine-acid gas are calculated by optimaziation of the solubility of experimental data of acid gases in electrolyte ternary systems. In the second approach, following (Ali Haghtalab & Mazloumi, 2010), the binary interaction parameters of the solubility of  and  in alkanolamines, are assumed to be zero for the molecular binary systems. In the last approach,  anology, the experimental data of physical solubility of  in alkanolamines are converted to the physical solubility data of acid gas in alkanolamines. In this work, as work of (P J G Huttenhuis, Agrawal, Solbraa, et al., 2008; P J G Huttenhuis, Agrawal, & Versteeg, 2008),  anology are applyed to determinte the binery interaction parameters of  and  in alkanolamines. In this way, the interaction between alkanolamine and acid gas in the nonreactive ternary system are computed using the interaction parameters of water-alkanolamine and water-acid gas that have been already obtained.

 

Table 8. Percent of Absolute Average Deviation in Correlation of the Bubble Pressure and in Predicting of Activity Coefficient of Binary Subsystems

Ref

Np

AAD%

 

Trange (K)

system

 

 

 

   

 

 

(Kiepe, Horstmann, Fischer, & Gmehling, 2002)

39

2.6

-76.56

0.3414

313-393

 

(Chapoy et al., 2005; Selleck, Carmichael, & Sage, 1952)

53

2.3

-43.87

0.2607

298-411

 

(Chang, Posey, & Rochelle, 1993)

50

2.1

0

0

298-393

 

(Chang et al., 1993)

50

1.1

0

-0.0356

298-393

 

(Chang et al., 1993)

50

1.8

0

0

298-393

 

(Pappa et al., 2006)

27

12.45

0

0

361-436

 


3.3.4. The  Anology

There are always few amounts of water in pure alkanolamines, so the physical solubility of  and  cannot be measured directly. The  anology helped in order to predict the physical solubility in alkanolamines. Acid gases (  and ) and  are rather similar molecules, but the only diffrent of them is,  only dissolve physically (not chemically) in alkanolamines. Base on this fact, the physically solubility of acid gase in alkanolamines as term of Henry constant can be computed as:

                                                              (20)

It shoud be pointed out that in the above relation, for determination of physical solubility of acid gas in aqueous alkanolamine solutions, the solubility of acid gas in water,  in water, and  in aqueous alkanolamine solutions are needed. For the solubility of  and  in water, (P J G Huttenhuis, Agrawal, Solbraa, et al., 2008) compared the emprical correlation of (Jamal, 2002), and (Versteeg & Van-Swaaij, 1988) with experimental data of (F.-Y. Jou, Carroll, Mather, & Otto, 1992) and their work . They observed that the experimental data are more in line with relation of (Jamal, 2002), so they have used this correlation. In this work, the relation of (Jamal, 2002) was used for prediction the solubility of  and  in water. Also, for the solubility of  in water, the correlation of (Chapoy, Mohammadi, Tohidi, Valtz, & Richon, 2005) was used. So having the solubility of  in aqueous alkanolamines, the physical solubility of  and  in alkanolamines is measured. Shown in table 9 is the database of experimental data of several arthurs that was used for the solubility of  in aqueous , , , , , and .One should note that in reference (Abu-Arabi, Tamimi, & Al-Jarrah, 2001) the physical solubility of  in aqueous  solution, has been directly measured by protonation method.

 

Table 9. Experimental Database for the Solubility of  in Various Alkanolamines

Author

T (K)

Amine Conc. Wt%

np

 

 

 

 

(Jamal, 2002)

293-393

10-30

24

(M. H. Li & Lai, 1995)

303-313

30.0

3

(Little, Versteeg, & Van-Swaaij, 1992)

303-348

1.1-24.3

30

(Laddha, Diaz, & Danckwerts, 1981)

298

6.7-12.5

2

(Yaghi & Houache, 2008)

293-333

5.0-30.0

30

 

 

 

 

(Jamal, 2002)

293-393

10.0-30.0

24

(M. H. Li & Lee, 1996)

303-313

30.0

3

(Haimour, 1990)

288-303

10.8-31.7

12

(Little et al., 1992)

303-333

2.6-36.8

23

(Versteeg & Oyevaar, 1989)

298

2.0-80.8

17

(Versteeg & Van-Swaaij, 1988)

298

4.7-31.3

10

(Sada, Kumazawa, & Butt, 1977)

298

4.7-31.3

5

(Laddha et al., 1981)

298

5.2-20.6

3

(Yaghi & Houache, 2008)

293-333

5.0-30.0

30

 

 

 

 

(Jamal, 2002)

293-293

10.0-30.0

24

(M. H. Li & Lai, 1995)

303-313

30.0

3

(Al-Ghawas, Hagewiesche, Ruiz-Ibanez, & Sandall, 1989)

298-323

10.0-50.0

35

(Al-Ghawas, Ruiz-Ibanez, & Sandall, 1989)

293-313

15.3-30.2

15

(Versteeg & Van-Swaaij, 1988)

293-333

4.1-31.9

50

(Haimour & Sandall, 1984)

288

10.0-40.0

20

(Pawlak & Zarzycki, 2002)

293

10.0-90.0

8

(M. K. Park & Sandall, 2001)

298-353

50.0

5

 

 

 

 

(Jamal, 2002)

293-393

10.0-30.0

27

(M. H. Li & Lai, 1995)

303-313

30.0

3

(Saha, Bandyopadhyay, & Biswas, 1993)

288-303

3.5-29.1

24

(Xu, Otto, & Mather, 1991)

283-310

17.8-27.0

8

 

 

 

 

(Yaghi & Houache, 2008)

293-333

5.0-30.0

30

 

 

 

 

(Abu-Arabi et al., 2001)

293-333

10-30

18

 

 

Total

486

 

Figure 1, shows the result of this indirect method for determination of binery interaction parameters of the  system. Good agreement observed between experiment (Haimour & Sandall, 1984) and the eCSW model in low and intermadiate temperature. Also, in table 10, the cofficients of Eq. (44) for the binery systems and the percents of average absolute deviation (AAD%) are given. It should be note that for other alkanolamines, such as  and , the interaction parameters of these systems were assumed to be zero.

 

 

Figure 1. Physical Solubility of   in Aqueous   at Various Temperatures, the Experimental Data were Taken from (Haimour & Sandall, 1984).

Table 10. Binary Interaction Parameters of Binary Acid Gas-Alkanolamine Systems by Using  Analogy

System

np

 

AAD%

 

 

   

 

 

89

0.2226

-78.58

4.63

 

"

0.1603

0.02

12.62

 

127

0.0857

0.01

11.35

 

"

-1.1480

35.39

9.47

 

158

0.2149

-7.89

5.18

 

"

-1.234

40.43

8.03

 

61

0.1359

-114.60

7.01

 

"

-.4155

0.06

6.69

 

30

0.2115

-27.24

3.33

 

"

0.0367

0.00

8.57

 

22

-0.0467

3.07

4.98

Total

486

 

 

 

 

 


3.4. The Ternary Systems

The results of the modeling of the solubility of  and  in the various alkaolamines are presented in this section. The calculation is basis on the reactive bubble pressure algorithm that is consists of two main loops. The nonlinear mass balance, charge balance and chemical equilibrium equations are solved in internal loop by (Smith & Missen, 1988) approach. The outputs of inner loop are mole fractions of all components in liquid phase that are used for the inputs of external loop. The VLE calculations are carried out in external loop. This procedure continues until the calculations converge. The mole fraction of acid gases and water in liquid phase, and total bubble pressure are the outputs of the algorithm. As discussed in section 2.3. , because of low vapor pressure of alkanolamine in the temperature range of 298-413 K, the presence of alkanolamine in the vapor phase is negligible (Kuranov et al., 1996).

In section 3.2., the molecular interaction parameters for binary systems have been already computed and explained, so that the ionic interaction parameters must be optimized using the solubility data of acid gases in the ternary systems of the alkanolamine solutions. It should be pointed out that the binary ionic interaction parameters are temperature dependent through Eq. (44). As it was explained by (Chunxi & Fürst, 2000), the solvation effect of the anion is less than that of the cation, and the interaction between anions and other component present in the liquid phase is negligible. Therefore, it has been assumed that the interactions of the cations with other components have more influence than the interactions of the anion species with other components. Moreover, because the concentration of  is low, the interaction parameters of this cationic specie with other component are ignored (Zoghi et al., 2012). So for the  system, the ionic binary interactions are: , , , , , , and . It should be noted that  is involved in computation when the alkanolamine is the primary or secondary amine. For the system, , , ,  , and  are the interactions. As one can observe three interaction parameters are the same in the both ternary systems. In order to have fewer adjustable parameters, the same values for the binary parameters , , and  are considered in both ternary systems. Thus, for modeling of the solubility of  and  in various alkanolamines, all of the experimental data points of the both ternary systems were used simultaneously, and the binary interaction parameters were fitted. For the solubility of  and  in aqueous , the results of the work of (Ali Haghtalab & Mazloumi, 2010) were compared with our work. As mentioned, the difference is that in this work , ,  and  were involved in the computing of chemical equilibrium. Also, the effect of  analogy on the model for solubility of acid gases in aqueous  was reviewed. In table 11, the comparison of the result of this work and those obtained by (Ali Haghtalab & Mazloumi, 2010), have been shown. They correlated six ionic interaction parameters and used five scenario to calculate the ionic interactions for the  and the systems. In this work, three other ionic interaction parameters are added and correlated; , , and . The other ionic interaction parameters for solubility of acid gases in aqueous  are same as those of (Ali Haghtalab & Mazloumi, 2010). The total error was improved by 2 present in AAD%. Figures 2 and 3, respectively, show the comparison of calculated and experimental (Kuranov et al., 1996) total pressure of the  and the  systems in 32.2 wt% concentration of  at various temperature. As one can see the results are more in line with the experimental data. Also, in order to investigate the precision of the result of the concentration of the some species in the liquid phase, Figure 4 shows a comparison of eCSW EoS with the results obtained by NMR study (Jakobsen, Krana, & Svendsen, 2005) at 23 wt% of  and 313 K, for the  system. Good agreement between the results of the model and the result of NMR method (Jakobsen et al., 2005) are obtained. In modeling the  and the systems, to investigate the accuracy of the model, just the experimental data of (Fang-Yuan Jou, Mather, & Otto, 1995), (Jong Il Lee, Otto, & Mather, 1976) and (Lawson & Garst, 1976) are used to obtain the interaction parameters then the data of the other references were used in order to predict the solubility of acid gases, so that, over 337 experimental data points were involved in calculations to correlate and predict the solubility of acid gases in aqueous .

 

Table 11. Comparison of the Results of This Work and Those Obtained by Haghtalab and Mazloumi (2010) for the  and the  Systems

Haghtalab and Mazloumi (2010)

This Work

np

Author

BIAS%

AAD%

**BIAS%

*AAD%

 

 

 

 

 

 

 

 

13.6

14.2

11.7

11.7

13

(Lemoine et al., 2000)

12.4

15.0

9.5

13.9

42

(Haji-Sulaiman et al., 1998)

10.8

20.7

5.3

12.6

30

(M. K. Park & Sandall, 2001)

2.0

7.2

-1.7

11.7

77

(Sidi-Boumedine et al., 2004a)

-0.9

6.5

-5.4

7.7

34

(Mamun et al., 2005)

-5.7

15.4

-4.3

14.4

14

(David M Austgen et al., 1991)

6.1

6.3

1.5

5.6

78

(Kuranov et al., 1996)

10.1

16.9

0.7

8.0

58

(Rho et al., 1997)

1.5

3.7

-7.6

10.4

28

(Á. P.-S. Kamps et al., 2001)

0.0

21.7

14.6

14.6

34

(Rogers et al., 1998)

12.2

17..2

5.1

16.8

5

(Macgregor & Mather, 1991)

 

 

 

 

 

 

28.1

26.8

13.2

13.2

27

(Lemoine et al., 2000)

1.6

8.0

3.6

9.5

25

(Sidi-Boumedine et al., 2004b)

0.8

1.4

2.2

2.4

71

(Kuranov et al., 1996)

-1.2

5.8

3.7

7.3

26

(Á. P.-S. Kamps et al., 2001)

-18.0

20.9

0.0

11.9

22

(Rogers et al., 1998)

-24.8

21. 6

0.0

10.5

18

(Macgregor & Mather, 1991)

3.6

11.6

2.32

9.5

602

total

 
               
 

 

Figure 2. Comparison of Calculated and Experimental (Kuranov et al., 1996) Total Pressure of the  System in 32.2 wt% Alkanolamine at Various Temperatures.

 

Figure 3. Comparison of Calculated and Experimental (Kuranov et al., 1996) Total Pressure of the  System in 32.2 wt % Alkanolamine at Various Temperatures.

 

Figure 4. Comparison of Calculated Mole Fraction of Various Species with those Obtained by NMR Study
 (Jakobsen et al., 2005) for Solubility   in 23 wt %  at 313 K.

 

Also, for modeling the  and the  systems, this procedure is repeated and the data of (Jong Il Lee, Otto, & Mather, 1972) and (Lal, Otto, & Mather, 1985) for the solubility of , and the data of (Jong Il Lee, Otto, & Mather, 1973a, 1973b) for solubility of , are selected to correlate, because the data of these references are in wide range of temperature, amine concentration, and acid gas loading. Then, other references are used to predict the solubility of acid gases in aqueous . Also in these systems more than 670 experimental data points were used. The results of correlation and prediction for system of these primary and secondary amines have been shown in table 12. As it is observed from this table, the errors are a little high. Generally, when the experimental data are in wide range of temperature, pressure and acid gas loading, the values of errors in modeling are not low. For example, (Y.-G. Li & Mather, 1997), have obtained the errors in range of 12 to 52 percents of absolute average deviationin correlating and predicting the solubility of acid gases in aqueous  (Vallée et al., 1999) using the model of (Clegg & Pitzer, 1992). And also, in this work, no experimental data were removed from the database. In Figure 5, the comparison of the calculated and experimental (Fang-Yuan Jou et al., 1995) partial pressure against acid gas loading for the  system by 30 wt % of  at various temperatures have been presented. Similarly, the results of eCSW EoS for the solubility of in the aqueous  have been shown in Figure 6. Also, Figure7 shows the prediction of the eCSW model for the  system at various concentrations, temperature, and data sources (Bhairi, 1984; Lawson & Garst, 1976). As one can see the results of the present eEoS are in good agreement with experimental data. For the  and the  systems, the results of modeling of the solubility of acid gases in aqueous  have been presented in Figures 8 and 9. These figures show the comparison of calculated and experimental (Jong Il Lee et al., 1972, 1973b) partial pressure of  and  in alkanolamine, respectively. Also, in Figure 10 the comparison of calculated mole fraction of various species with mole fraction obtained by NMR study (Bottinger, Maiwald, & Hasse, 2008) for  solubility in 30 wt %  at 313 K have been shown. As one can see from the figures, very good accuracy of the eEoS model is observed.

 

Table 12. Percent of Absolute Average Deviation in Predicting and Correlating the Bubble Pressure of the Solubility of Acid Gases in Aqueous and  Solutions for Ternary Systems

Pred.

Corr.

np

Author

BIAS%

AAD%

BIAS%

AAD%

 

 

 

 

 

 

 

 

 

 

16.53

25.00

80

(Fang-Yuan Jou et al., 1995)

-4.18

17.94

 

 

60

(Bhairi, 1984)

-3.06

13.34

 

 

13

(Lawson & Garst, 1976)

7.52

16.51

 

 

8

(David M Austgen et al., 1991)

-6.30

13.82

 

 

19

(Mamun et al., 2005)

-2.75

7.30

 

 

9

(J.-Y. Park et al., 2003)

0.00

8.70

 

 

6

(Jane & Li, 1997)

 

 

 

 

 

 

 

 

1.95

16.93

96

(Jong Il Lee et al., 1976)

 

 

15.30

15.56

45

(Lawson & Garst, 1976)

-0.23

14.72

 

 

18

(Bhairi, 1984)

 

 

 

 

337

Total

 

 

 

 

 

 

 

 

-7.73

17.85

104

(Jong Il Lee et al., 1972)

-9.34

15.67

 

 

30

(Lawson & Garst, 1976)

-19.85

19.85

 

 

25

(Bhairi, 1984)

 

 

-2.28

4.11

44

(Lal et al., 1985)

1.57

14.48

 

 

14

(Oyevaar et al., 1989)

1.94

7.00

 

 

6

(Dawodu & Meisen, 1994)

2.30

23.11

 

 

45

(Haji-Sulaiman et al., 1998)

-11.08

17.32

 

 

24

(Sidi-Boumedine et al., 2004a)

8.47

14.02

 

 

14

(Rogers et al., 1997)

 

 

 

 

 

 

 

 

-10.90

18.56

112

(Jong Il Lee et al., 1973a)

 

 

-1.40

18.23

166

(Jong Il Lee et al., 1973b)

-15.80

20.04

 

 

89

(Lawson & Garst, 1976)

 

 

 

 

673

Total

 

 

 

 

Figure 5. Comparison of Calculated and Experimental (Fang-Yuan Jou et al., 1995)  Partial Pressure of the  System in 30 wt % Alkanolamine at Various Temperatures.

 

 

Figure 6. Comparison of Calculated and Experimental (Lawson & Garst, 1976) Partial Pressure of the  System in 15.2 wt % Alkanolamine at Various Temperatures.

 

Figure 7. Comparison of Predicted and Experimental *(Bhairi, 1984; Lawson & Garst, 1976)** Partial Pressure of the System in 2.5 M and 15.2 wt % Alkanolamine at Various Temperatures and Sources.

 

 

Figure 8. Comparison of Calculated and Experimental (Jong Il Lee et al., 1972) Partial Pressure of the  System in 0.5 M Alkanolamine at Various Temperatures.

 

Figure 9. Comparison of Calculated and Experimental (Jong Il Lee et al., 1973a) Partial Pressure of the  System in 3.5 M Alkanolamine at Various Temperatures.

 

Figure 10. Comparison of Calculated Mole Fraction of Various Species with those Obtained by NMR Study (Bottinger et al., 2008) for Solubility   in 30 wt %  at 313 K.

 

For the solubility of  and  in aqueous , , , , and  solutions, the calculations are same as previous procedure. So that, the number of  one and/or two references have been used to correlate, then the other references were used in order to predict the solubility of acid gases in alkanolamine solutions, except  and , that all of the experimental data of these systems were correlated. Table 13, shows the AAD% and BIAS% of the EoS model for the solubility of acid gases in aqueous , , , , and  solutions. Also, in table 14 and 15, the ionic interaction parameters that were calculated by using eCSW, have been shown.

 

Table 13. Percent of Absolute Average Deviation in Predicting and Correlating the Bubble Pressure of the Solubility of Acid Gases in Aqueous , , ,  and  Solutions for Ternary Systems

Pred.

Corr.

np

Author

BIAS%

AAD%

BIAS%

AAD%

 

 

 

 

 

 

 

 

 

 

3.09

15.42

40

(Tontiwachwuthikul et al., 1991)

 

 

7.10

17.00

51

(Kundu et al., 2003)

8.73

24.56

 

 

66

(Silkenbaumer et al., 1998)

11.17

21.28

 

 

30

(Jamal, 2002)

3.22

21.32

 

 

20

(Haji-Sulaiman & Aroua, 1996)

0.93

5.40

 

 

8

(Yang et al., 2010)

0.99

5.14

 

 

8

(Jane & Li, 1997)

10.66

18.22

 

 

36

(Roberts & Mather, 1988)

5.45

10.09

 

 

24

(Teng & Mather, 1990)

 

 

 

 

 

 

-1.45

8.97

-1.45

8.97

41

(M.-H. Li & Chang, 1994)

-0.75

3.67

 

 

9

(Jane & Li, 1997)

1.14

12.38

 

 

27

(Roberts & Mather, 1988)

 

 

 

 

360

Total

 

 

 

 

 

 

 

 

-9.75

23.95

45

(Isaacs et al., 1977)

 

 

 

 

 

 

4.60

10.27

 

 

26

(Isaacs et al., 1977)

 

 

2.52

7.91

23

(Mazloumi et al., 2012)

10.49

11.14

 

 

77

(Uusi-Kyyny et al., 2013)

 

 

 

 

171

Total

 

 

 

 

 

 

 

 

-1.12

22.04

92

(A. P.-S. Kamps et al., 2003)

-22.43

24.47

 

 

52

(P. W. Derks et al., 2005)

-20.86

21.35

 

 

33

(Ermatchkov et al., 2006)

 

 

 

 

 

 

 

 

2.66

9.08

82

(Xia et al., 2003)

-11.36

12.61

 

 

25

(Speyer & Maurer, 2011)

 

 

 

 

284

Total

 

 

 

 

 

 

 

 

-11.47

17.36

30

(Cheng et al., 2010)

 

 

 

 

 

 

 

 

12.38

14.19

17

(Atwood et al., 1957)

 

 

 

 

47

Total

 

 

 

 

 

 

 

 

10.78

12.25

46

(Martin et al., 1978)

 

 

-0.13

16.37

43

(Chen, 1991)

 

 

 

 

 

 

 

 

7.23

11.52

36

(Martin et al., 1978)

 

 

 

 

125

Total

Table 14. Adjustable Binary Parameters Obtained by Correlation of the Bubble Pressure of the Ternary Aqueous Acid Gas-Alkanolamine Systems for , ,  and  Solutions

Parameters

 

 

 

 

 

 

 
   

 

   

 

   

 

   
 

0.7807

-172.00

 

0.3090

-0.11

 

0.3062

0.08

 

0.1625

-0.02

 

0.2113

-43.63

 

-0.0544

0.25

 

-0.1411

-0.06

 

0.2106

0.09

 

0.8811

-0.13

 

-0.4782

-0.23

 

-0.1592

-0.33

 

-0.1374

-0.8

 

-0.1720

52.02

 

-0.0381

0.22

 

-0.0336

0.01

 

0.0328

0.11

 

-0.0379

-0.01

 

0.1790

-0.28

 

0.1996

-0.04

 

-0.1163

-0.04

 

-0.3212

103.91

 

-0.1219

0.06

 

0.1364

0.21

 

0.1445

0.06

 

0.1467

-22.16

 

0.3054

0.29

 

0.0049

0.05

 

-0.4252

0.06

 

-0.5603

1.85

 

-0.2163

0.08

 

-0.0779

0.01

 

-0.0584

-0.00

 

0.1720

-52.02

 

-0.0613

0.15

 

-0.2167

0.09

 

-0.1200

-0.01

 

--

--

 

-0.3336

0.14

 

-0.0870

0.00

 

0.0528

0.01

Table 15. Adjustable Binary Parameters Obtained by Correlation of the Bubble Pressure of the Ternary Aqueous Acid Gas-Alkanolamine Systems for , ,  and  Solutions

Parameters

 

 

 

 

 

 

 
   

 

   

 

   

 

   
 

0.0132

0.05

 

0.8811

-0.13

 

-0.0226

-0.01

 

0.1566

0.07

 

0.0171

0.04

 

-0.0379

-0.01

 

-0.1070

-0.33

 

-0.2789

-0.10

 

0.0231

0.03

 

-0.5603

1.78

 

0.0740

0.30

 

0.0813

-0.02

 

-0.0084

0.01

 

0.6494

-53.83

 

-0.1566

0.09

 

0.0256

0.03

 

0.0422

0.01

 

-0.1683

-16.36

 

0.1741

-0.16

 

-0.0229

-0.03

 

-0.0510

0.04

 

-0.6144

-7.40

 

0.0689

-0.10

 

0.0140

-0.03

 

-0.1473

0.17

 

0.8573

-13.91

 

0.9501

0.02

 

0.1900

0.07

 

0.0264

-0.31

 

0.2104

-0.59

 

0.0448

0.03

 

-0.0601

0.37

 

-0.0160

-0.03

 

-0.3084

0.35

 

0.2014

-0.55

 

0.1853

-0.22

 

0.0267

0.06

 

--

--

 

0.9353

0.07

 

0.0008

0.07

 

 

In Figure 11, using the ratio of calculated and experimental pressure, the deviation versus the  loading for the  system was observed. As one can see, the most of the points are below the horizontal line. It means the results of the eCSW EoS model are under correlated. Also, Figure 12 shows the ratio of calculated and experimental partial pressure of  against the temperature for  system. Also in this figure, an under-correlation is observed in the most data points.

Figure 13 shows the predicted of partial pressure of  by eCSW EoS in aqueous  solution against temperature in various acid gas loading. The predicted values are in good agreement with experiment (Isaacs, Otto, & Mather, 1977), but a little deviation is evident in low temperatures. A comparison between the experimental (Ermatchkov, Kamps, Speyer, & Maurer, 2006) and calculated partial pressure of in the  system by 14.57 wt % of at various temperatures is shown in Figure 14. It can be seen that, except high acid gas loadings and temperatures, the results are in very good agreement with experiment.

 

 

Figure 11. Ratio of Calculated Pressure to the Experimental Pressure for each Data point Against Loading of  in the  Ternary System.

 

 

Figure 12. Ratio of Calculated Pressure to the Experimental Pressure at Different Temperatures in the  Ternary System.

 

Figure 13. Comparison of Predicted and Experimental (Isaacs et al., 1977) Partial Pressure of the  System in 2.5 M Alkanolamine Against Temperature at Various  Loading.

 

Figure 14. Comparison of Calculated and Experimental (Ermatchkov et al., 2006) Partial Pressure of the  System in 14.57 wt % Alkanolamine at Various Temperatures.


3.5. The Quaternary Systems

In order to show the predictability of the eCSW EoS model for the quaternary systems, without adjusting any new interaction parameters, the solubility of mixed acid gases in aqueous , , , and solutions is computed. As shown in table 16, 370 number of experimental data points are used in various amine concentrations, acid gas loadings, and partial pressures for modeling of quaternary systems by present EoS model. Also, in table 17, the AADs and BIASs of modeling are observed. These results seem to be acceptable. In Figures15, 16 and 17, the predicted pressure against experimental pressure are plotted in various temperatures and amine concentrations, respectively, for the quaternary , and  systems. It can be observed that the results of model are in line with the experiments.

 

Table 16. Specifications of the Experimental Data Sources Used for the Solubility of Acid Gases in Aqueous Alkanolamine Solutions for Quaternary Systems

np

Pressure (kPa)

Loading

(mole/mole)

Amine

(Wt%)

T(K)

System

 

       

 

 

 

 

 

 

 

 

34

2.068

0.068

0.0-0.3

0.116-1

30.43

313

(J. I. Lee, Otto, & Mather, 1974)

 

 

 

 

 

 

 

 

58

0.8-1505

0.21-5764

0.012-1.0

0.04-1.22

20.67

323

(J. I. Lee et al., 1974)

84

0.8-2199

1.4-2293

0.0056-1.0

0.07-0.93

25

310-394

(Lawson & Garst, 1976)

25

0.0001-0.5

0.0003-0.5

0.001-0.56

0.006-0.2

20

322

(Rogers et al., 1997)

 

 

 

 

 

 

 

 

106

0.032-196

0.005-529

0.0-0.88

0.0-0.788

35

373, 313

(Fang-Yuan Jou, Carroll, Mather, & Otto, 1993)

22

0.002-2.65

0.004-1.67

0.0-0.20

0.0-0.102

23, 50

313, 323

(Rogers et al., 1998)

 

 

 

 

 

 

 

 

15

0.53-1050

0.40-5650

0.001-1.0

0.07-1.37

28.63

323

(Fang-Yuan Jou, Otto, & Mather, 1996)

 

 

 

 

 

 

 

 

30

2.240-74.5

1.17-8.38

0.14-0.55

0.11-0.56

30

313, 353

(Jane & Li, 1997)

372

Total

 

 

 

 

 

 

 

Table 17. Percent of Absolute Average Deviation in Predicting of the Bubble Pressure of the Solubility of Mixed Acid Gases in Aqueous , , ,  and  Solutions for Quaternary Systems.

BIAS%

AAD%

np

System

 

 

 

 

11.48

26.17

34

(J. I. Lee et al., 1974)

 

 

 

 

-25.63

26.74

58

(J. I. Lee et al., 1974)

24.64

31.11

84

(Lawson & Garst, 1976)

7.54

7.63

25

(Rogers et al., 1997)

 

 

 

 

19.49

26.80

106

(Fang-Yuan Jou et al., 1993)

-12.20

12.20

22

(Rogers et al., 1998)

 

 

 

 

-12.79

23.21

15

(Fang-Yuan Jou et al., 1996)

 

 

 

 

15.08

27.00

30

(Jane & Li, 1997)

 

 

372

Total

 

 

 

 

 

Figure 15. Comparison of the Predicted Total Pressure by eCSW and the Experimental Data for the  Quaternary System.

 

 

 

Figure 16. Comparison of the Predicted Total Pressure by eCSW and the Experimental Data for the  Quaternary System.

 

 

Figure 17. Comparison of the Predicted Total Pressure by eCSW and the Experimental Data for the  Quaternary System.

 

No

 

Input of data

 

Initial guess of kij

 

Initial guess of P and vapor phase mole fractions

 

Calculate

 

 

Calculate

 

Calculate

 

 

 

change ?

 

Yes

 

 

 

No

 

 

 

 

Converge? 

 

 

No

 

Print

 

Yes

 

Set , calculate liquid mole fractions

 

  Calculate  and

 

 

Calculate mole fractions of liquid phase

 

 

 

Yes

 

No

 

Yes

 

Optimization tool

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Figure B.1. Flowchart of Simultaneously Calculation of Chemical and Physical Equilibrium.

     


4. Conclusions

In this work, over 3000 experimental data points were used in order to correlate and predict the solubility of  and  in alkanolamine solutions by eCSW EoS model. A comparison between this work and the work of (Ali Haghtalab & Mazloumi, 2010) was carried out. The decreases of 2.1 and 1.28 percents, respectively, for AAD% and BIAS% were achieved in modeling the  and  systems. Then, the eEoS systematically was applied to describe the solubility of acid gases in various alkanolamine solutions, i.e. , , , , , ,  and .The results of the eCSW were in good agreements with the experiment. After that, to investigate the accuracy of the modeling, the simultaneous solubility of mixed  and in aqueous , , ,  and  solutions were predicted, and the acceptable results were achieved for the quaternary systems. The results show that eCSW EoS can be used successfully for correlating and predicting the solubility of  and  in various alkanolamines in wide range of temperature, acid gas loading and pressure.

Appendix A. The Electrolyte Cubic Square-Well (eCSW) EoS.

The basic equation of the model is based on a Helmholtz free energy expression. This equation can be written by three contributions as:

                                                                         (A.1)

Where subscript "CSW" and "MSA" stand for the cubic square well EoS and mean spherical approximation theory, respectively. The Born equation is used for discharging and charging processes as (Ali Haghtalab & Seyed Hossein Mazloumi, 2009):

                    (A.2)

where  is the unit of elementary charge, is permittivity of the free space, is the dielectric constant,  is the charge number of ions and is Avogadro's number.
The pressure and chemical potential equations of the Born equation are given as:

                                                (A.3)

                                                          (A.4)

where  and are calculated as (Ali Haghtalab & Mazloumi, 2010):

                                                      (A.5)                                                                                                    (A.6)

where subscript s denotes pure solvent. It should be pointed out that for the other species, i.e., acid gases and ions, =0. The dielectric constants for pure solvents are given in table 1.For the long range contribution of the ions, the explicit version of  MSA is applied as (Ali Haghtalab & Seyed Hossein Mazloumi, 2009):

                                                                                        (A.7)

where  is the MSA screening parameter are computed as:

                             (A.8)

                                                                                          (A.9)

In the above relations, is the Debye screening length, is the average diameter of ions that is computed using linear mixing rule as:

                                                                                                       (A.10)

The pressure and chemical potential equations of the MSA contribution are expressed as:

                                                                    (A.11)

                                                          (A.12)

The contribution of the molar Helmholtz energy from the square well potential, following (A. Haghtalab & S. H. Mazloumi, 2009), is presented as:

                                                  (A.13)

The first term of Eq. (A.13) represents the Van der Waals repulsive force and the second term denotes the attractive force, base on square well potential. is absolute temperature, is molar volume and is a constant value.
The following mixing rules are used to generalize calculations for mixture as:

                                (A.14)

                                                             (A.15)

                                                                                                    (A.16)

                                                                                                       (A.17)

                                                                                           (A.18)

                                                                                                     (A.19)

                                                                                                 (A.20)

also the combining rules as:

                                                                                              (A.21)

                                                                                               (A.22)

where  is the CSW potential depth,  is the diameter of the species ,   is the potential range, and the coupling parameter,   is the binary interactions parameter. In above equations, the variable  is maximum attainable coordination number, is the orientional parameter and  is the closed packed volume and the note is that the summations is over all components, i.e. ions, solvents, and acid gases.

The pressure and chemical potential equations of the CSW EoS were illustrated as:

                                                   (A.23)                                                    (A.24)

So, having the chemical potential express, the fugacity coefficient for each component in a mixture is expressed as:

                                                   (A.25)

 

Appendix B.

To do the calculations of Vapor-Liquid Equilibria (VLE) of acid gases-alkanolamine-water systems, simultaneous calculations of physical and chemical equilibrium are required. Fig. B.1 shows the flowchart for such calculations.

Nomenclature

 

Coefficient in Eq. (34)

 

Molar Helmholtz free energy

 

Coefficient in Eq. (34)

 

Coefficients in Eq. (44)

 

Coefficient in Eq. (34)

 

Coefficient in Eq. (34) and dielectric constant of solution

 

Dielectric constant of solvent

 

Coefficient in Eq. (7)

 

Electronic charge

 

Equilibrium constant 

 

Boltzmann's constant

 

Coupling interaction parameter between species and

 

Orientatioal parameters defined in Eq. (14)

 

Number of mole

 

Number of data points

 

Avogadro's number

 

Pressure

 

Gas constant

 

Temperature

 

Molar volume

 

Van der Waals

 

Close-packed volume  defined in Eq. (14)

 

Mole fraction of component

 

Maximum coordination defined in Eq. (14)

 

Charge number of ionic species

 

A function of temperature defined in Eq. (14)

Greek Letters

 

MSA screening parameters

 

Activity coefficient

 

Square-well potential parameter

 

Square-well potential depth

 

Vacuum permittivity

 

Size parameter

 

Fugacity coefficient

 

Debye screening length

 

Constant

 

Stoichiometric number

Subscripts

 

Born contribution

 

Cubic square-well

 

Calculated properties

 

Experimental properties

 

Component

 

Binary pair of and

 

Component

 

Mean Spherical Approximation theory

 

Solvent

Superscripts

*

Unsymmetrical normalization

 

Pure state

 

Infinite dilution

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