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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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.

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

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.