Thermodynamic Modeling of Acidic Gas Solubility in Aqueous

Thermodynamics and Transport Phenomena Laboratory, School of Chemical Engineering, National Technical. UniVersity of Athens, 9 Heroon Polytechniou Str...
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Ind. Eng. Chem. Res. 2006, 45, 5148-5154

Thermodynamic Modeling of Acidic Gas Solubility in Aqueous Solutions of MEA, MDEA and MEA-MDEA Blends Athanassios Vrachnos,† Georgios Kontogeorgis,‡ and Epaminondas Voutsas*,† Thermodynamics and Transport Phenomena Laboratory, School of Chemical Engineering, National Technical UniVersity of Athens, 9 Heroon Polytechniou Str., Zographou Campus, 157 80 Athens, Greece, and IVC-SEP, Instituttet for Kemiteknik, Technical UniVersity of Denmark, DK 2800 Lyngby, Denmark

The thermodynamic framework that was developed in a previous work [Vrachnos et al. Ind. Eng. Chem. Res. 2004, 43, 2798] for the description of chemical and vapor-liquid equilibria of carbon dioxide, hydrogen sulfide, and their mixtures in aqueous methyldiethanolamine (MDEA) solutions is revised and extended in this study to the absorption of carbon dioxide into aqueous monoethanolamine (MEA) solutions and aqueous MDEA-MEA blends. The results of the model are compared with experimental data taken from the literature. Very satisfactory predictions of acidic gas vapor-liquid equilibrium over MDEA, MEA, and their blends at various concentrations, acidic gas loadings, and temperatures are obtained. Introduction The removal of acidic gas impurities from gas streams is of great importance nowadays for the chemical industry because such industrial processes as the purification of the natural gas and the sweetening of gas streams in petrochemical plants should be carried out in compliance with environmental directives requirements. The absorption of carbon dioxide into aqueous alkanolamine solutions is the most favorable technique during the last few years, and a number of primary, secondary, and tertiary alkanolamines have been used in order to obtain the maximum absorption capacity and rate accompanied with the minimum energy consumption. The fact that each alkanolamine has its own advantages and disadvantages led Chakravarty et al.1 to propose the addition of a primary or secondary amine to an aqueous solution of a tertiary one, to enhance the absorption rate without considerably affecting the absorption capacity and the energy requirements for stripping. Today, the use of alkanolamine blends gains ground in the industry, assisted by an improved understanding of the phase equilibria and the rate of the reactions occurring in these systems. Thus, by adjusting the analogy between the two or three amines in the solution, the specifications required can be met. The properties of different classes of alkanolamines are wellknown, so they are only briefly discussed here. Primary alkanolamines such as monoethanolamine (MEA) and secondary alkanolamines such as diethanolamine (DEA) react rapidly with CO2 and form carbamates. Although the formation of carbamates enhances the reaction rate, it limits the absorption capacity because of the reaction mechanism and stoichiometry. Moreover, the relatively high heat of absorption caused by the formation of carbamates leads to a higher cost of amine regeneration. On the other hand, tertiary amines as N-methyldiethanolamine (MDEA) cannot react directly with CO2 to form carbamates. Therefore, the reaction, which enhances the hydrolysis of CO2, is slow and helps the selective absorption of H2S in gas streams where H2S and CO2 are both present. In the case of tertiary amine, the products are bicarbonate and protonated amine, and since the reaction stoichiometry is 1:1, high equilibrium loadings * Corresponding author. Phone: +30 210 7723971. Fax: +30 210 7723155. E-mail: [email protected]. † National Technical University of Athens. ‡ Technical University of Denmark.

are allowed. Moreover, the regeneration costs for tertiary amines are lower, because the heat of formation of bicarbonate is significantly lower than that of carbamate. In our previous work,2 a thermodynamic framework that accounts for both the chemical and phase equilibria of acidic gases over aqueous solutions of N-methyldiethanolamine was developed. This model, referred to as electrolyte-LCVM (e-LCVM), is an extension of the LCVM EoS/GE model of Boukouvalas et al.3 to electrolyte solutions. The advantage of the e-LCVM model is that, because it is basically an equation of state (EoS) approach, it describes all phases at equilibrium consistently with the same equation. Other researchers have used different methods to calculate the phase equilibrium of alkanolamine containing systems. Kent and Eisenberg4 presented a simple model that shows good accuracy at loadings > 0.1, assuming ideal vapor and liquid-phase behavior. Austgen et al.5,6 developed a model based on the γ-φ approach, where the activity coefficients were calculated by the electrolyte-NRTL model. Recently, Liu et al.7 modified the model by Austgen et al.5 in order to provide a better representation of the vaporliquid equilibrium for the CO2-MEA-H2O system. They also performed a critical evaluation of the chemical equilibrium constants, the Henry’s constant, and the phase equilibrium experimental data, and they proposed a new correlation for the equilibrium constant of the carbamate reversion reaction as well as new interaction parameters for the electrolyte-NRTL model. Finally, Gabrielsen et al.8 developed a simple model which obtains good results for a limited loading, temperature, and pressure range that is useful in modeling CO2 capture from coalfired power plants. The objectives of this work are as follows: (a) the modification of the originally developed e-LCVM model and its consequent revision for MDEA-containing solutions and (b) the extension of e-LCVM in MEA-containing solutions as well as blends of MDEA and MEA. The modification made in the original model concerns the GE model (extended UNIQUAC) that is used in the e-LCVM, which leads to the reduction of the parameters needed for the application of the model. So, first, a new set of parameters for MDEA-containing systems is regressed, and then, the e-LCVM model is extended to MEAcontaining solutions and mixtures of MDEA and MEA. In all cases, the results of the model are compared with experimental data taken from the literature. All calculations with the e-LCVM

10.1021/ie0600792 CCC: $33.50 © 2006 American Chemical Society Published on Web 06/10/2006

Ind. Eng. Chem. Res., Vol. 45, No. 14, 2006 5149 Table 1. Temperature-Dependent Equilibrium Constants for Reactions 1-8 reaction

A

B

C

D

1 -9.416 5 -4 234.98 0.0 2 2.121 1 -8 189.38 0.0 -0.007 484 3 231.465 -12 092.10 -36.781 6 4 216.049 -12 431.70 -35.481 9 5 214.582 -12 995.4 -33.547 1 6 -32.0 -3 338.0 0.0 7 132.899 -13 445.9 -22.477 3 8 1.282 562 -3 456.179 0.0 ln KX ) A + B/T + C ln T + DT, KX based on mole fraction, T (K)

ref 6 6 6 6 6 6 6 7

model were performed with a computer program written in Visual Fortran that was developed in-house. Thermodynamic Framework Chemical Equilibria. The gas absorption mechanism consists of two steps: First, the molecules of the acidic gas dissolve into the liquid, and then, they react with the amines. MEA is a primary amine, which reacts directly with carbon dioxide and forms stable carbamates, while MDEA, as a tertiary amine, cannot react directly with CO2. The chemical equilibria taking place in the liquid phase can be written as follows:

1. Dissociation of the protonated MDEA MDEAH+ + H2O a MDEA + H3O+

(1)

2. Dissociation of the protonated MEA MEAH+ + H2O a MEA + H3O+

(2)

3. Dissociation of carbon dioxide CO2 + 2H2O a HCO3- + H3O+

(3)

4. Dissociation of bicarbonate HCO3 - + H2O a CO32- + H3O+

(4)

5. Dissociation of hydrogen sulfide H2S + H2O a HS- + H3O+

(5)

6. Dissociation of bisulfide HS- + H2O a S2- + H3O+

(6)

7. Ionization of water 2H2O a OH- + H3O+

(7)

8. Carbamate reversion to bicarbonate MEACOO- + H2O a MEA + HCO3-

(8)

In Table 1 the equilibrium constants of the reactions are presented. By solving the equations describing the reaction equilibria, along with the amine mass balance, the CO2 or H2S mass balance, the electroneutrality, and the summation of all mole fractions that equals unity, the mole fractions of all species are determined. The equilibrium constants for reactions 1-7 were taken from Austgen et al.,6 while the one for the carbamate reversion (reaction 8) was taken from Liu et al.7 The latter was preferred, because Liu et al.7 did not simultaneously fit the equilibrium constant and the interaction parameters of the NRTL model on the vapor-liquid equilibrium (VLE) data of the CO2MEA-H2O system as Austgen et al.6 did. Instead, they used a

two-step procedure, avoiding, at least partly, the introduction of the uncertainty of the VLE data into the equilibrium constant. Phase Equilibrium. Phase equilibria for all molecular species (CO2, water, and MEA) of the system are determined by solving the equality of fugacities in the vapor and liquid phase,

fVk ) fLk

(9)

where fVk and fLk are the vapor- and liquid-phase fugacities, respectively, which are both calculated by the e-LCVM model. e-LCVM Model Electrolyte-LCVM (e-LCVM) has been presented in detail in our previous paper.2 It is actually an extension of the LCVM EoS/GE model3 to electrolyte solutions and combines the translated and modified Peng-Robinson (t-mPR) EoS9 with an extended UNIQUAC equation for electrolytes.10 The mixing rule for the attractive-term parameter of the EoS is a linear combination of Vidal11 and Michelsen12 mixing rules, while for the repulsive-term parameter of the EoS, a conventional linear mixing rule is used. The activity coefficient of the electrolyteUNIQUAC model, which is incorporated into the mixing rule for the attractive-term parameter, is given as the sum of two terms: one related to the long-range electrostatic interactions, which are present in electrolyte solutions, and the other related to short-range interactions between all species. The long-range interactions, which are most important at low concentrations, are calculated by a Debye-Hu¨ckel type term, and the shortrange interactions are calculated by the UNIQUAC combinatorial and residual expressions. The algebraic expressions of the e-LCVM model are briefly presented in the Appendix. The modification made here with respect to the original e-LCVM model refers to the extended UNIQUAC model that is used in the e-LCVM. More specifically, the concentration dependency of the UNIQUAC interaction parameters has not been taken into account, and consequently, the combinatorial and the residual terms are identical to those of the traditional UNIQUAC equation. This leads to a reduction of the number of adjustable parameters of the model. The application of e-LCVM in phase equilibrium calculations for the mixtures involved in this study requires a number of input parameters. When such parameters were available, they were taken from the literature. More specifically, the purecomponent critical properties and the acentric factors were taken from DIPPR;13 the Mathias-Copeman14 parameters (ci) for water were taken from Boukouvalas et al.;3 the van der Waals volume (r) and area parameters (q) for CO2 were taken from Voutsas et al.15 and those for MDEA, MEA, and water were taken from DIPPR;13 the van der Waals volume parameters of all ions were calculated from group increments presented by Bondi;16 the dielectric constants of MDEA, MEA, and water were taken from Austgen et al.6 and Chunxi and Fu¨rst;17 and the UNIQUAC interaction parameters for the CO2-H2O and H2S-H2O pairs were taken from Voutsas et al.15 and that for the MDEA-H2O pair was taken from Voutsas et al.18 On the other hand, the parameters estimated in this work are as follows: the Mathias-Copeman14 parameters for MDEA and MEA that were fitted to vapor pressure data taken from Daubert and Danner13 and Daubert and Hutchison;19 and the interaction parameters for MEA-H2O that were fitted to the binary VLE data of Touchara et al.,20 Nath and Bender,21 and Cai et al.22 Finally, the remaining binary interaction parameters and the q values of the ionic species, which are needed for the representation of aqueous MDEA solutions containing CO2 or H2S, were

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Table 2. List of Pure-Component Properties component

CO2

H2S

MDEA

MEA

H2O

Tc (K) Pc (bar) ω c1 c2 c3 d(0) d(1) d(2) d(3) × 10-2 d(4) × 10-5

304.19 73.815 0.2276

373.55 90.070 0.0814

677.79 38.760 1.240 0 2.469 4 -3.814 7 2.871 7 -8.169 76 8 989.3 0 0 0

638.0 68.70 0.796 6 1.881 8 -3.451 6 5.840 9 -18.554 14 836

647.13 220.55 0.344 9 0.923 6 -0.379 4 0.442 4 -19.290 5 29 814.5 -0.019 678 0.013 189 0.031 144

Table 3. van der Waals Volume (r) and Area (q) Parameters species

r

q

species

r

q

CO2 H2S H2O MDEA MEA MDEA+ MEAH+

1.296 0 1.166 5 0.920 0 4.944 1 2.573 6 5.167 8 2.800 3

1.261 1.163 1.400 4.268 2.360 8.043 0.572

H3O+ HCO3CO32MEACOOHSS2OH-

1.146 7 2.296 0 2.069 3 3.421 5 0.939 8 0.713 1 1.000 0

1.000 0.102 0.048 6.451 0.497 1.189 3.331

fitted to the VLE data of Jou et al.,23 and the corresponding ones required for the representation of aqueous MEA solutions containing CO2 were taken from Lee et al.24 All binary interaction parameters in the residual part of the UNIQUAC model are assumed to be linearly temperature dependent. The Ψ function is given by the following expression

(

Ψkl ) exp -

)

akl + bklT T

(10)

All parameters needed for the application of e-LCVM model are listed in Tables 2-4. It should be noted that all calculations made with the e-LCVM model in mixed gas and mixed amine systems are straight predictions, without adjusting any additional parameters. Results and Discussion Mixtures Containing MDEA. Liquid-phase speciation of aqueous MDEA solutions for both acidic gases is well-

documented in our previous paper.2 The correlation of e-LCVM model parameters was performed using the experimental data from Jou et al.23 at temperatures from 40 to 120 °C and MDEA concentrations of 2 M (23.3 wt %) and 4.28 M (48.9 wt %). Figures 1 and 2 present a comparison between e-LCVM correlations and experimental results23 for CO2 and H2S partial pressures over MDEA solutions versus acidic gas loading. In two cases, the Kent-Eisenberg4 model (KE), which uses Henry’s law to relate the partial pressure of the acidic gas to its loading, is also presented for comparison purposes. Very good results are obtained by the e-LCVM model, which are better than those of the KE model. In Figure 3, e-LCVM predictions are compared against the experimental data of Jou et al.25 and Baek and Yoon,26 which were not included in the database used for the evaluation of the model parameters, while Figure 4 presents e-LCVM total pressure predictions over 46.78 wt % MDEA solutions loaded with H2S.27 Especially, the fact that the model predicts satisfactorily both the partial and total pressures indicates that the e-LCVM model predicts successfully the vapor-phase composition of these systems, too. Finally, Figure 5 shows e-LCVM predictions against experimental data28 for a system in which both acidic gases, CO2 and H2S, are present, which also represents a successful test of the predictive capabilities of the model. Mixtures Containing MEA. Figure 6 demonstrates the liquid-phase speciation of an aqueous MEA (30.2 wt %) solution at 313 K. The mole fractions of H2O (very high), H3O+ and OH- (very small), and CO32- (almost constant at a magnitude of 10-5) are not included in this figure. At low loadings, when absorption begins, carbon dioxide reacts with MEA and forms carbamate, bicarbonate, and carbonate. Carbamate is the main product, while bicarbonate and carbonate are present in very small quantities. Because of the 1:2 stoichiometry of the reaction, the amine is almost totally consumed for a loading of ∼0.5, and at this point, the mole fraction of carbamate starts to decrease. At higher loadings, carbamate partially reverts to bicarbonate and the mole fraction of CO2 increases as a result of physical absorption. The correlation of e-LCVM model parameters was performed

Table 4. Binary Interaction Parameters of the Extended UNIQUAC Expression (First Row akl (K), Second Row bkl) CO2 CO2 H2S H2O MDEA MEA MDEAH+ MEAH+ H30+ HCO3CO32MEACOOHSS2OH-

H2S

H2O

MDEA

MEA

MDEAH+ MEAH+ H30+

0.0 -1280.13 1320.51 2750.40 2504.64 0.0 0.0 2.39 -2.22 1.89 1.59 0.0 587.54 0.0 1721.87 3511.96 0.0 0.0 -5.17 0.0 -3.20 -0.40 0.0 0.0 -353.12 -171.68 0.0 416.43 175.25 0.0 2.21 1.72 0.0 -1.14 -0.81 0.0 2558.89 -55.87 -670.16 0.0 0.0 0.0 2.19 0.74 1.61 0.0 0.0 0.0 276.11 0.0 -555.46 0.0 0.0 0.0 -1.81 0.0 1.16 0.0 0.0 0.0 -10.13 60.99 287.15 0.0 0.0 0.0 0.08 1.32 0.89 0.0 0.0 0.0 86.55 0.0 -781.86 0.0 -309.48 0.0 -0.09 0.0 2.16 0.0 -25.06 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3324.22 0.0 -2903.73 0.0 0.0 -4457.19 -12.60 0.0 0.45 0.0 0.0 -0.08 -1630.34 0.0 0.0 0.0 0.0 0.0 -1.55 0.0 0.0 0.0 0.0 0.0 375.19 0.0 -243.09 0.0 0.0 0.0 0.34 0.0 0.51 0.0 0.0 0.0 0.0 3256.51 -522.73 0.0 0.0 -2728.88 0.0 3.83 -0.12 0.0 0.0 -1.26 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -116.81 0.0 0.0 0.0 0.0 0.0 -10.25 0.0 0.0 0.0

0.0 0.0 0.0 0.0 48.39 -0.62 0.0 0.0 346.46 -8.92 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

HCO3-614.56 -4.68 0.0 0.0 1879.22 -2.09 0.0 0.0 0.0 0.0 -57.39 -1.59 -681.63 -0.13 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

CO32- MEACOO0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

33.47 -1.25 0.0 0.0 -231.82 0.07 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

HS0.0 0.0 -880.44 -2.78 3208.04 -1.16 0.0 0.0 0.0 0.0 38.12 -2.81 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

S2- OH0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

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Figure 1. (a) Comparison of e-LCVM correlation results with experimental data,23 for CO2 equilibrium partial pressures over 2 M (23.3 wt %) MDEA solutions. Dashed lines represent KE model predictions. (b) Comparison of e-LCVM correlation results with experimental data,23 for CO2 equilibrium partial pressures over 4.28 M (48.9 wt %) MDEA solutions.

using the experimental data from Lee et al.24 at temperatures from 40 to 120 °C and MEA concentrations of 2.5 M (15.2 wt %) and 3.75 M (22.7 wt %). Figures 7 and 8 show e-LCVM correlation results for CO2 partial pressures over MEA solutions versus CO2 loading, while Figure 8 also presents the results obtained with the KE model. The results obtained with the e-LCVM model are in good agreement with the experimental data. Figure 9 presents e-LCVM model predictions of CO2 partial pressures over 5 M (30.2 wt %) MEA solutions. Given that these data were not included in the model parameter evaluation, the results can be considered satisfactory. Mixtures Containing MDEA and MEA Blends. A final test of the model’s predictive capabilities and accuracy is its application in the case of mixtures containing amine blends, since such mixtures are encountered in practice. Figure 10 presents the liquid-phase speciation of a 20 wt % MDEA and 10 wt % MEA blend at 313 K. At low loadings, the main reaction is the production of carbamate, and that causes a reduction in the CO2 partial pressure. At loadings of ∼0.6 (moles of CO2/total moles of amine), MEA is almost depleted and carbamate starts to revert to bicarbonate to such an extent determined by the equilibrium constant. Then, MDEA absorbs the remaining carbon dioxide, and more bicarbonate is produced until MDEA is consumed and physical absorption continues. More MDEA in the amine blend means a greater reduction of the partial pressure at high loadings. A number of experimental data for MDEA-MEA mixtures have been reported in the open literature. Shen and Li,29 Li and Shen,30 and Jou et al.25 report experimental data at various

Figure 2. (a) Comparison of e-LCVM correlation results with experimental data,23 for H2S equilibrium partial pressures over 2 M (23.3 wt %) MDEA solutions. Dashed lines represent KE model predictions. (b) Comparison of e-LCVM correlation results with experimental data,23 for H2S equilibrium partial pressures over 4.28 M (48.9 wt %) MDEA solutions.

Figure 3. Comparison of e-LCVM predictions with experimental data,25,26 for CO2 equilibrium partial pressures over 30 wt % MDEA solutions.

temperatures for mixtures with a total amine concentration of 30 wt %. Austgen et al.6 also report some experimental points at solutions of 2 M (23.3 wt %) MDEA and 2 M (12.2 wt %) MEA. A comparison between the different data sets shows that the data of Shen and Li29 and Li and Shen30 follow a different trend from those of the other researchers,6,25 and they were not included in our evaluation. Figures 11-13 present e-LCVM predictions against the experimental data of Austgen et al.6 and Jou et al.25 at various amine analogies and temperatures. The results indicate that e-LCVM is an accurate predictive tool for practical industrial applications. Conclusions The e-LCVM model is slightly modified here in a way that leads to the reduction of the adjustable parameters. New model

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Figure 4. Comparison of e-LCVM predictions with experimental data,27 for total equilibrium pressures over 46.78 wt % MDEA solutions.

Figure 5. Comparison of e-LCVM predictions with experimental data,28 for CO2 and H2S partial equilibrium pressures over 35 wt % MDEA solution at 313 K.

Figure 7. Comparison of e-LCVM correlation results with experimental data,24 for CO2 equilibrium partial pressures over 2.5 M (15.2 wt %) MEA solutions.

Figure 8. Comparison of e-LCVM correlation results with experimental data,24 for CO2 equilibrium partial pressures over 3.75 M (22.7 wt %) MEA solutions. Dashed lines represent KE model predictions.

Figure 6. Liquid-phase mole fractions of a CO2 loaded 30.2 wt % MEA aqueous solution at 313 K.

parameters have been evaluated, which enables the model’s application in vapor-liquid equilibrium calculations for aqueous MDEA solutions containing CO2 and H2S, aqueous MEA solutions containing CO2, and aqueous MDEA-MEA blends containing CO2. The e-LCVM results were found in all cases to be in good agreement with the experimental data, which cover a wide range of temperatures, pressures, amine concentrations, and acidic gas loadings. Especially, the very successful model predictions for the cases of solutions that contain mixed gases or amine blends indicate that e-LCVM is a powerful predictive tool for practical industrial applications. Acknowledgment The authors gratefully acknowledge Nordic Energy Research for the financial support of this work, especially the research stay of A.V. in Denmark, where part of this work was done.

Figure 9. Comparison of e-LCVM predictions with experimental data,24 for CO2 equilibrium partial pressures over 5 M (30.2 wt %) MEA solutions.

Appendix: The e-LCVM Model e-LCVM uses the translated and modified Peng-Robinson (t-mPR) equation of state, which is given by the following equation

P)

RT a (A1) V + t - b (V + t)(V + t + b) + b(V + t - b)

The mixing rules for the attractive-term parameter R (R ) a/bRT) and the repulsive-term parameter b are given by

R)

(

)

λ 1 - λ GE 1 - λ + + AV AM RT AM

()

∑xi ln bi b

+

∑ xiRi

(A2)

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Figure 10. Liquid-phase mole fractions of a CO2 loaded 20 wt % MDEA and 10 wt % MEA aqueous solution at 313 K.

Figure 13. Comparison of e-LCVM predictions with experimental data,25 for CO2 equilibrium partial pressures over 20 wt % MDEA and 10 wt % MEA solutions.

represent the UNIQUAC combinatorial and residual contributions, respectively. The Debye-Hu¨ckel contribution to the activity coefficient of solvent n is

ln γDH n )

Figure 11. Comparison of e-LCVM predictions with experimental data,6 for CO2 equilibrium partial pressures over 2 M (23.3 wt %) MDEA and 2 M (12.2 wt %) MEA solutions. Dashed lines represent KE model predictions.

[

2AMnds b3dn

1 + bxI -

1 1 + bxI

]

- 2 ln(1 + bxI)

(A5)

where A ) 1.327 757 × 105ds1/2/(DT)3/2, b ) 6.359 696ds1/2/ (DT)1/2, Mn is the molecular weight of pure solvent n (kg/mol), dn is the density (kg/m3) of pure solvent, ds is the density of the solvent mixture (kg/m3), and D the dielectric constant of the solvent mixture. The dielectric constant of a molecular species has the following temperature dependence:

Dn ) d(0) +

d(1) + d(2)T + d(3)T2 + d(4)T3 T

(A6)

The combinatorial term of the activity coefficient is given by

) ln ln γcomb n

(

)

φn φn φn φn + 1 - - 5qn ln +1xn xn θn θn

(A7)

where

φn ) Figure 12. Comparison of e-LCVM predictions with experimental data,25 for CO2 equilibrium partial pressures over 27 wt % MDEA and 3 wt % MEA solutions. Dashed lines represent KE model predictions.

b)

∑xibi

(A3)

where AV ) -0.623 and AM ) -0.53, which come from the Vidal and Michelsen mixing rules for the t-mPR EoS, and λ is a constant (λ ) 0.36) that determines the relative contributions of the Vidal and Michelsen mixing rules to the parameter R. GE (GE/RT ) ∑xi ln γi) is calculated by the extended UNIQUAC equation for electrolytes. The activity coefficient of a species n in solution is expressed by the following equation, C R ln γn ) ln γDH n + ln γn + ln γn

(A4)

where ln γDH ¨ ckel term and ln γCn and ln γRn n is the Debye-Hu

xnrn

∑j xjrj

and θn )

xnqn

∑j xjqj

The residual term of the activity coefficient is given by

(

ln γRn ) qn 1 - ln(

∑k

θkΨkn) -

θlΨnl

∑l ∑k θkΨkn

)

(A8)

The interaction parameter, Ψkl, is given by the following expression:

(

Ψkl ) exp -

)

akl + bklT T

(A9)

It should be noted that the concentration dependency of the

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UNIQUAC interaction parameters (eq A9) has not been taken into account here. Nomenclature a ) attractive term parameter of the EoS ((kPa m6)/mol2) b ) covolume parameter of the EoS (m3/mol) akl ) binary interaction parameter (K) in eq A10 bkl ) binary interaction parameter in eq A10 ci ) Mathias-Copeman parameter D ) dielectric constant (C m) f ) fugacity (kPa) GE ) excess Gibbs free energy (J) P ) pressure (kPa) q ) van der Waals area parameter r ) van der Waals volume parameter R ) universal gas constant (J K-1 mol-1) T ) temperature (K) x ) liquid-phase mole fraction Greek Symbols γ ) activity coefficient δij,m ) parameter for the concentration dependency of the UNIQUAC interaction energy parameters θ ) surface-area fraction φ ) volume fraction Ψkl ) UNIQUAC interaction energy parameter ω ) acentric factor Subscripts c ) critical value k ) component k r ) reduced property Superscripts L ) liquid phase V ) vapor phase AbbreViations EoS ) equation of state e-LCVM ) electrolyte-linear combination of the Vidal and Michelsen mixing rules t-mPR ) translated and modified Peng-Robinson EoS VLE ) vapor-liquid equilibrium Literature Cited (1) Chakravarty, T.; Phukan, U. K.; Weiland, R. H. Reaction of Acid Gases with Mixtures of Amines. Chem. Eng. Prog. 1985, 81, 32. (2) Vrachnos, A.; Voutsas, E.; Magoulas, K.; Lygeros, A. Thermodynamics of Acid Gas-MDEA-Water Systems. Ind. Eng. Chem. Res. 2004, 43, 2798. (3) Boukouvalas, C.; Spiliotis, N.; Coutsikos, P.; Tzouvaras, N.; Tassios, D. Prediction of Vapor-Liquid Equilibrium with the LCVM Model: A Linear Combination of the Vidal and Michelsen Mixing Rules Coupled with the Original UNIFAC and the t-mPR Equation of State. Fluid Phase Equilib. 1994, 92, 75. (4) Kent, R.; Eisenberg, B. Better Data for Amine Treating. Hydrocarbon Process. 1976, 55, 87. (5) Austgen, D. M.; Rochelle, G. T.; Peng, X.; Chen, C.-C. Model of Vapor-Liquid Equilibria for Aqueous Acid Gas-Alkanolamine Systems Using the Electrolyte-NRTL Equation. Ind. Eng. Chem. Res. 1989, 28, 1060. (6) Austgen, D. M.; Rochelle, G. T.; Chen, C. C. A Model of VaporLiquid Equilibria for Aqueous Acid Gas-Alkanolamine Systems. 2. Representation of H2S and CO2 Solubility in Aqueous Mixtures of MDEA with MEA and DEA. Ind. Eng. Chem. Res. 1991, 30, 543.

(7) Liu, Y.; Zhang, L.; Watanasiri, S. Representing Vapor-Liquid Equilibrium for an Aqueous MEA-CO2 System Using the Electrolyte Nonrandom-Two-Liquid Model. Ind. Eng. Chem. Res. 1999, 38, 2080. (8) Gabrielsen, J.; Michelsen, M. H.; Stenby, E. H.; Kontogeorgis, G. M. A Model for Estimating CO2 Solubility in Aqueous Alkanolamines. Ind. Eng. Chem. Res. 2005, 44, 3348. (9) Magoulas, K.; Tassios, D. Thermophysical Properties of n-alkanes from C1 to C20 and their Prediction for Higher Ones. Fluid Phase Equilib. 1990, 56, 119. (10) Macedo, E. A.; Skovborg, P.; Rasmussen, P. Calculation of Phase Equilibria For Solutions of Strong Electrolytes in Solvent-Water Mixtures. Chem. Eng. Sci. 1990, 45, 875. (11) Vidal, J. Mixing Rules and Excess Properties in Cubic Equations of State. Chem. Eng. Sci. 1978, 33, 787. (12) Michelsen, M. L. A modified Huron-Vidal Mixing Rule for Cubic Equations of State. Fluid Phase Equilib. 1990, 60, 213. (13) Daubert, T. E.; Danner, R. P. Data Compilation Tables of Properties of Pure Compounds. In Design Institute for Physical Property Data; American Institute of Chemical Engineers: New York, 1985. (14) Mathias, P. M.; Copeman, T. W. Extension of the Peng-Robinson Equation of State to Complex Mixtures: Evaluation of the Various Forms of the Local Composition Concept. Fluid Phase Equilib. 1983, 13, 91. (15) Voutsas, E.; Kalospiros, N. S.; Boukouvalas, C.; Tassios, D. The Performance of EoS/GE Models in the Prediction of Phase Equilibria in Asymmetric Systems. Fluid Phase Equilib. 1996, 116, 480. (16) Bondi, A. Physical Properties of Molecular Crystals, Liquids, and Glasses. Wiley: New York, 1968. (17) Chunxi, L.; Fu¨rst, W. Representation of CO2 and H2S Solubility in Aqueous MDEA Solutions Using an Electrolyte Equation of State. Chem. Eng. Sci. 2000, 55, 2975. (18) Voutsas, E.; Vrachnos, A.; Magoulas, K. Measurement and Thermodynamic Modeling of the Phase Equilibrium of Aqueous NMethyldiethanolamine Solutions. Fluid Phase Equilib. 2004, 224, 193. (19) Daubert, T. E.; Hutchison, G. Vapor Pressure of 18 Pure Industrial Chemicals. AIChE Symp. Ser. 1990, 86 (279). (20) Touchara, H.; Okazaki, S.; Okino, F.; Tanaka, H.; Ikari, K.; Nakanishi, K. Thermodynamic Properties of Aqueous Mixtures of Hydrophilic Compounds. 2. Amino-ethanol and its Methyl Derivatives. J. Chem. Thermodyn. 1982, 14, 145. (21) Nath, A.; Bender, E. Isothermal Vapor-Liquid Equilibria of Binary and Ternary Mixtures Containing Alcohol, Alkanolamine and Water with a New Static Device. J. Chem. Eng. Data 1983, 28, 370. (22) Cai, Z.; Xu, R.; Wu, Z. Binary Isobaric Vapor-Liquid Equilibria of Ethanolamines and Water. J. Chem. Eng. Data 1996, 41, 1101. (23) Jou, F.-Y.; Mather, A.; Otto, F. Solubility of H2S and CO2 in Aqueous Methyldiethanolamine solutions. Ind. Eng. Chem. Process Des. DeV. 1982, 21, 539. (24) Lee, J. I.; Otto, F. D.; Mather, A. E. Equilibrium Between Carbon Dioxide and Aqueous Monoethanolamine Solutions. J. Appl. Chem. Biotechnol. 1976, 26, 541. (25) Jou, F.-Y.; Otto, F.D.; Mather, A. E. Vapor-Liquid Equilibrium of Carbon Dioxide in Aqueous Mixtures of Monoethanolamine and Methyldiethanolamine. Ind. Eng. Chem. Res. 1994, 33, 2002. (26) Baek, J.-I.; Yoon, J.-H. Solubility of Carbon Dioxide in Aqueous Solutions of 2-Amino-2-methl-1,3-propanediol. J. Chem. Eng. Data 1998, 43, 635. (27) Sidi-Boumedine, R.; Horstmann, S.; Fischer, K.; Provost, E.; Fu¨rst, W.; Gmehling, J. Experimental Determination of Hydrogen Sulfide Solubility Data in Aqueous Alkanolamine Solutions. Fluid Phase Equilib. 2004, 218, 149. (28) Jou, F.-Y.; Carroll, J.; Mather, A.; Otto, F. Solubility of Mixtures of Hydrogen Sulfide and Carbon Dioxide in Aqueous N-Methyldiethanolamine Solutions. J. Chem. Eng. Data 1993, 38, 75. (29) Shen, K.-P.; Li, M.-H. Solubility of Carbon Dioxide in Aqueous Mixtures of Monoethanolamine and Methyldiethanolamine. J. Chem. Eng. Data 1992, 37, 96. (30) Li, M.-H.; Shen, K.-P. Densities and Solubilities of Solutions of Carbon Dioxide in Water + Monoethanolamine + N-Methyldiethanolamine. J. Chem. Eng. Data 1992, 37, 288.

ReceiVed for reView January 18, 2006 ReVised manuscript receiVed May 2, 2006 Accepted May 8, 2006 IE0600792