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May 26, 2010 - The electrolyte cubic square-well (eCSW) equation of state [ Haghtalab , A. ; Mazloumi , S. H. Fluid Phase Equilib. 2009 , 285 , 96−1...
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Ind. Eng. Chem. Res. 2010, 49, 6221–6230

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Electrolyte Cubic Square-Well Equation of State for Computation of the Solubility CO2 and H2S in Aqueous MDEA Solutions Ali Haghtalab* and Seyed Hossein Mazloumi Department of Chemical Engineering, Tarbiat Modares UniVersity, P.O. Box 14115-143, Tehran, Iran

The electrolyte cubic square-well (eCSW) equation of state [Haghtalab, A.; Mazloumi, S. H. Fluid Phase Equilib. 2009, 285, 96-104] is applied to study the solubility of CO2 and H2S in aqueous Nmethyldiethanolamine (MDEA) solutions in the wide range of concentration, pressure, temperature, and acid gas loading. This electrolyte equation of state is composed of the mean spherical approximation (MSA) theory, the Born equation, and a cubic square-well equation of state (SWEOS). Using eCSW EOS, calculations of the vapor-liquid equilibria are performed for the binaries of water-alkanolamine and acid gas-water systems so that the binary molecular interaction parameters, kij in the combing rule of the EOS, are optimized for the CO2-H2O, H2S-H2O, and MDEA-H2O systems. Having the binary interaction parameters between the molecular species, the solubility of CO2 and H2S in the aqueous solution of MDEA is calculated by the use of the simultaneous vapor-liquid equilibria and chemical equilibria algorithm. Also, to improve the calculation of the solubility of the acid gases in the ternary CO2-MDEA-H2O, H2S-MDEA-H2O systems, some of the binary interaction parameters among ionic and molecular species are optimized using the same EOS approach. Influence of the binary interaction parameters on the performance of the SWEOS is investigated using a large number of experimental data points of the acid gas-aqueous MDEA solutions. Moreover, the solubilities of mixed H2S and CO2 gases in aqueous MDEA solution are predicted. The results demonstrate that the eCSW EOS is able to represent the solubility data of both ternary and quaternary aqueous alkanolamine systems with very good accuracy. 1. Introduction Thermodynamic modeling of the solubility of the acid gases in the alkanolamine solutions is a vital step in the design of many chemical processes such as natural gas treatment and capturing CO2 from flue gases. Also computation of vapor-liquid equilibria for the acid gas-alkanolamine systems is theoretically complex because of nonideality of such systems that involve the speciation reactions with formation of the complex ions in the aqueous phase. Calculation of the solubility of acid gases in alkanolamines is carried out by using the two basic approaches as follows. In the first method, the activity coefficient models such as the Clegg-Pitzer equation1 and local composition models: electrolyte-NRTL,2 UNIQUAC-NRF,3 and Wilson-NRF4 are adopted for representating the nonideality of molecular and ionic species in the liquid phase. On the other hand, in the φ-approach, the equation of state is used for calculation of the phase equilibrium in both vapor and liquid phases. The former approach has been well established and implemented by numerous authors;5–8 however, in this method the pressure effect on the activity coefficient has not usually been taken into account, and Henry’s constants for solubility of the volatile components such as acid gases should be available. The EOS approach, which is rather new for alkanolamine solutions, is not subjected to the mentioned weaknesses, so the thermodynamic modeling of those subsystems involved in the alkanolamine systems, such as solubility of an acid gas in a solvent, can be well represented by this approach. As a result, the application of a suitable EOS for computation of vapor-liquid equilibrium of the alkanolamine systems is a highly interesting topic and has been widened in recent years, but it should be noted that the thermodynamic modeling of such systems using the φ-approach is rather more difficult than the * Corresponding author. Telephone: (09821)82883313. Fax: (09821)82883381. E-mail: [email protected].

activity coefficient models. Moreover, the simple approach such as the Kent and Eisenberg model,9 which is usually used in the engineering design, is approximation and does not take into account the nonideality of the ionic species and is only valid at the fitted range that presents uncertain prediction results. Using EOS, several works have been used for calculation of the solubility of the acid gases in aqueous alkanolamine solutions. Fu¨rst and Planche10 have applied two different EOSs, one for liquid phase and another one for vapor phase, to compute solubility of the acid gases in the alkanolamine mixtures. The hole model and SRK EOSs have been adopted for representation of the VLE in the alkanolamine solutions by Kuranov et al.,11 and Smirnova et al.12 Vallee et al.13 have studied the solubility of CO2 and H2S in aqueous DEA solutions using the electrolyte EOS which was developed by Fu¨rst and Renon.14 Chunxi and Fu¨rst15 have also used the same eEOS to represent the solubility of the acid gases in aqueous MDEA mixtures. Derks et al.16 have adopted the Fu¨rst and Renon eEOS14 to model the solubility of CO2 in aqueous piperazine solutions. For calculation of the VLE of the CH4-CO2-MDEA-H2O systems, Huttenhuis et al.17,18 added the Born term to the Fu¨rst and Renon eEOS.14 They also extended the eEOS for representation of the solubility of the mixed CO2, H2S, and CH4 in the aqueous solutions of the MDEA.19 Haghtalab and Mazloumi20 have recently developed an electrolyte equation of state in which the nonelectrolyte part of the eEOS is expressed by a cubic square-well, CSW, EOS.21 The explicit version of the MSA theory was used for long-range electrostatic interactions of ions, and the Born equation, for discharge and charging processes of the ionic species. The eCSW EOS has been successfully applied to correlation and prediction of the activity and osmotic coefficients of the strong aqueous electrolyte solutions at a wide range of electrolyte concentration and temperature. The aim of the present work is

10.1021/ie901664k  2010 American Chemical Society Published on Web 05/26/2010

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Table 1. Coefficients of Chemical Equilibrium Constants of the Reactions

a

equilib. const.

A

B

C

T (K)

ref

Kx1 Kx2 Kx3a

231.465 214.582 -77.262

-12092.1 -12995.4 -1116.5

-36.7816 -33.5471 10.06

273-498 273-498 278-423

Posey et al.39 Posey et al.39 Huttenhuis et al.17

Huttenhuis et al. have correlated MDEA protonation reaction using experimental data at reference state of infinite dilution for MDEA.

to extend the eCSW for representation of the solubility of the acid gases in alkanolamine solutions. Since the aqueous Nmethyldiethanolamine (MDEA) solution is widely used in treating natural gas and fuel gases, so the eCSW is applied for the VLE calculation of CO2 and H2S solubility in this aqueous alkanolamine solution in a wide range of acid gases loading, temperature, and pressure. 2. Thermodynamic Framework

ares(T, V, xi) ) a - aid ) aCSW + aMSA + aBorn

where subscript “CSW” and “MSA” stand for the cubic squarewell EOS and mean spherical approximation theory, respectively. Following Haghtalab and Mazloumi,20 the contribution of the molar Helmholtz energy from the square-well potential is written as aCSW ) RT ln

2.1. Chemical Equilibrium. Depending on the type of alkanolamine, the various speciation reactions take place in aqueous phase that produces several ionic species. In this work, as in that of Chunxi and Fu¨rst,15 the second dissociation of CO2 and H2S are neglected, so that the concentration of CO-2 3 and S2- are ignored. Also due to very low concentration of H3O+ and OH-, these species have not been taken into account in the model development. Thus, for simplicity, it is common to neglect some reactions, and for the CO2-MDEA-H2O and H2S-MDEA-H2O systems the following reactions are considered. Kx1

CO2 + 2H2O 798 H3O+ + HCO3

(1)

Kx2

(2)

(

(

)

)

mV + V0w V zRT ln (8) V - 4τV0 2 mV + V0(1 - m)

where the first term illustrates the van der Waals repulsive part and the second term represents the attractive part based on square-well potential. R is gas constant, T is absolute temperature, V is molar volume andτ ) 2π/6. For a mixture, the following mixing rules are used as m)

∑ ∑xxm i j

i

w)

∑ ∑xxw

i j ij

i

H2S + H2O 798 H3O+ + HS-

(7)

(9)

ij

j

∑ ∑ x x (exp( kT ) - m ) εij

)

i j

j

i

V0 )

ij

(10)

j

∑xV

(11)

∑xz

(12)

i 0i

i

Kx3

H2O + MDEAH+ 798 H3O+ + MDEA

(3)

∏ (x γ )

Vi

i i

where xi, γi, and Vi are mole fraction, activity coefficient, and reaction stoichiometry of the species i, respectively. The coefficients A, B, and C are the numeric constants that are given in Table 1. In this work, the symmetrical activity coefficient for water is used as γwater )

0 φwater (T, P, xwater f 1)

φi(T, P, x) ∞ φi (T, P, xi f

0)

; i * water

4√2πλ3ij - 3 4√2π(λ3ij - 1)

(13)

V0i )

zi )

NAσ3i

√2

4√2π 3 λ -1 3 ii

(14)

(15)

with the combining rules as:

(5)

and unsymmetrical activity coefficient for the other species with the reference state of infinite dilution in water16 is written as γ*i )

mij )

(4)

i

φwater(T, P, x)

i i

i

On the basis of the mole fraction scale, the chemical equilibrium constant of the above reactions is expressed as Kx ) eA+B/T+Cln T )

z)

(6)

The fugacity coefficients of the ionic and molecular species (φi) are computed using the electrolyte cubic square-well (eCSW) equation of state.20 2.2. The Electrolyte Cubic Square-Well (eCSW) EOS. The molar residual Helmholtz energy for the electrolyte cubic squarewell (eCSW) EOS20 is expressed as

εij ) √εiεj(1 - kij) λij )

σiλi + σjλj σi + σj

(16) (17)

where ε is the square-well potential depth, σ is the diameter of the species, λσ is the potential range, the coupling parameter, kij ) kji, is the binary interaction parameter. The variable “z” is maximum attainable coordination number, V0 is the closed packed volume, NA is Avogadro’s number, and m is the orientational parameter. It should be pointed out that in the above equations the summation is over all ionic and nonionic species. The explicit version of MSA22 is implemented for the longrange contribution of ions in the eCSW EOS is presented as

Ind. Eng. Chem. Res., Vol. 49, No. 13, 2010

aMSA ) Γ)

3

2Γ RTV 3 1 + σΓ 3πNA 2

(

)

(18)

1 [√1 + 2σκ - 1] 2σ

(19)

e2NA2 x Z2 Dε0RTV ions i i

(20)

κ2 )

∑

where Γ is the MSA screening parameter, κ is the Debye screening length, “e is the unit of elementary charge, ε0 is permittivity of the free space, Z is the charge number of ion, V is molar volume, σ is the average diameter of ions that is calculated using linear mixing rule, σ ) Σxiσi/Σxi, where summation is over ions. Ds is the dielectric constant of the pure solvent, so the dielectric of the alkanolamine solution is calculated as D)

∑x D ∑x s

s

(21)

s

where subscript “s” denotes pure solvent. The dielectric constant for a pure solvent in terms of temperature is calculated as Ds ) d0 +

d1 + d2T + d3T2 + d4T3 T

(22)

where the coefficients of eq 22 for the molecular solvents are given in Table 2. The dielectrics of water and MDEA are given in the literature.20,15 The Born23 contribution to the molar residual Helmholtz energy is written as aBorn ) -

NAe2 1 14πε0 D

(

xiZ2i σi ions

)∑

(23)

It should be noted that the Born term has no influence on the pressure equation of eCSW EOS because the dielectric constant calculated by eq 21 is volume independent; however, it contributes to the chemical potential equation. The expression of the pressure EOS and the chemical potential for the three contributions of eCSW EOS are given in the Appendix A. 3. Results and Discussions 3.1. The Database. The first step in validating any model is to use precise and consistent experimental data. One of the problems associated with the study of the solubility of the acid gases in aqueous alkanolamine solutions is some discrepancy in a number of experimental data available in the literature. Several authors have recognized this issue and have tried to collect a consistent database in their data treatment. Weiland et al.24 have analyzed the deviation in the published data of the solubility of the acid gases in several of the aqueous alkanolamine solutions. Chunxi and Fu¨rst,15 Lemoine et al.,25 and Huttenhuis et al.17 have followed an approach similar to that of Weiland et al.24 to assemble a consistent database for the CO2 and H2S solubilities in the aqueous MDEA solutions. Thus, in this work a similar database has been assigned that is shown in Table 3. For the CO2-MDEA-H2O system, the recent data of Haji-Sulaiman et al.,26 Park and Sandall,27 Sidi-Boumedine et al.,28,29 and Mamun et al.30 are added to the database of Huttenhuis et al.17 The same references are used for the data of the H2S-MDEA-H2O system, so that the number of experi-

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mental data points that are used for the CO2-MDEA-H2O and H2S-MDEA-H2O systems are 413 and 189, respectively. In the parameter fitting, the distribution of the experimental data used is the following: at 313 K, the maximum experimental data points of 213 out of 602 points (35%) are used for both systems. Also, about 42% and 39% of the total experimental data of aqueous MDEA are at the concentration range of 18-26 wt % and >45 wt %, respectively. Moreover, 60% of the total experimental points were used in the range of 0.1-1 of acid gases loading. 3.2. Pure Component Parameters. The adjustable parameters of the eCSW EOS for pure components are σ, ε, and λ that are calculated by simultaneous optimization of the saturated vapor pressure and the liquid density of the pure components.21 These parameters for the molecular species present in the aqueous MDEA solution, i.e. H2O, MDEA, CO2, and H2S, are given in Table 2. The parameters of CO2 were taken from previous work.20 One should note that for water the new parameters are fitted in the wider range of temperature31 than in previous work21 so that the new parameters of eCSW EOS presented here are different from those of previous work for water. The parameters of the CSW EOS for H2S have been fitted using the saturated liquid density and vapor pressure data32 simultaneously, however for MDEA the data of saturated vapor pressure33 has been used alone. The parameters of the eCSW EOS for the ionic species such as MDEAH+, HS-, HCO3- are assumed to be the same as those of the corresponding molecular species, i.e., MDEA, H2S, and CO2 except for the diameter of HCO3-. Since the diameter of H+ is small, it is assumed that adding H+ to the molecular species does not influence the diameter of the species; however, HCO3-, because of addition of O2-, is larger than CO2; thus, its value is taken from the literature.18 3.3. Binary Subsystems. Before correlation of the solubility of acid gases in aqueous MDEA solutions, it is necessary to determine the adjustable binary interaction parameter, i.e. kij in eq 16, for the binaries of CO2-H2O, MDEA-H2O, H2S-H2O, CO2-MDEA and H2S-MDEA. On the other hand, no experimental data are available for the solubility of the acid gases in the pure MDEA,12,15 so the three alternatives may be considered to obtain the binary interaction parameters of CO2 and H2S with MDEA. In the first method, by optimization of the solubility experimental data of acid gases in the ternary systems these parameters are calculated. In the second approach, one may apply N2O analogy.18 So using this approach, the experimental data of physical solubility of N2O in aqueous MDEA are converted to the physical solubility data of CO2 in aqueous MDEA as a nonreactive ternary system so that the interaction parameter between CO2 and MDEA can be obtained by fit of these pseudo data if one has already obtained the interaction parameters for the CO2-H2O and MDEA-H2O systems.17,18 Finally one may simply assume zero values for these parameters. In this work, for simplicity and to show the predictability of the EOS, the third alternative is adopted, i.e., kij, is assumed to be zero for the molecular binaries. The data of the solubility of the acid gases in water are available, so that in this work, the solubility data of CO2 and H2S in water are used as given by Kiepe et al.,34 Capoy et al.,35 and Selleck et al.36 It should be noted that the high-pressure data points, i.e. pressures >100 bar reported by Selleck et al.,36 are not reliable,37,38 and as a result, such data points have not been considered in the fitting of kij for the H2S-H2O system. Thus, the selected data from Selleck et al.36 are 10, 6, and 6 at 344.3 K, 377.6 K, 410.9 K, respectively, i.e. a total of 22, and

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Table 2. Parameters of the eCSW Equation of State and the Dielectric Constants of the Species

ε/k (K) λ σ (0A) Tr range (ref) AAD% Pa AAD% F d0 d1 d2 d3 d4 a

AAD% )

H2O

MDEA

CO2

H2S

MDEAH+

HCO3

HS-

772.657 1.4641 2.317 0.44-0.9431 5.8 3.5 -19.291 2.9815 × 103 -1.9678 × 10-2 1.3189 × 10-4 -3.1144 × 10-7

1261.451 1.4270 1.692 0.44-0.9533 2.3 8.16976 8.9893 × 103

462.655 1.3090 2.819 0.72-0.9521 0.6 2.2

524.895 1.3330 2.885 0.73-0.9632 2.6 1.9

1261.451 1.4270 1.692

462.655 1.3090 3.120

524.895 1.3330 2.885

100 |Pexp -Pcal| ∑ np Pexp

Table 3. Specifications of the Experimental Data Sources Used for the CO2-MDEA-H2O and H2S-MDEA-H2O Systems author

MDEA(wt%)

temp (K)

loading (mol gas/mol amine)

np

23.63 23.3, 45.8 50 25.73, 46.88 50 23.4 18.8, 19.2, 32.1 20.5, 50 32.1, 48.8 23, 50 23.3

298 303, 313, 323 298, 323, 348, 373 298, 313, 348 328, 343, 358 313 313, 333, 373, 393, 413 323, 348, 373 313, 353, 393 313, 323 313

0.02-0.26 0.01-0.88 0.0087-0.4923 0.008-1.303 0.1658-0.8133 0.006-0.65 0.105-1.157 0.0087-0.8478 0.126-1.243 0.000591-0.1177 0.124-1.203

13 42 30 77 34 14 78 58 28 34 5 413

CO2 + MDEA + H2O Lemoine et al.25 Haji-Sulaiman et al.26 Park and Sandall27 Sidi-Boumedine et al.28 Mamun et al.30 Austgen and Rochelle41 Kuranov et al.42 Rho et al.43 Kamps et al.44 Rogers et al.45 MacGregor and Mather46 total H2S + MDEA + H2O Lemoine et al.25 Sidi-Boumedine et al.29 Kuranov et al.42 Kamps et al.44 Rogers et al.45 MacGregor and Mather46 total

11.83, 23.63 46.78 18.7, 32.2 48.8 23, 50 23.3

298 313, 373 313, 333, 373, 393, 413 313, 353, 393 313 313

0.0151-0.2299 0.039-1.116 0.480-1.933 0.153-1.428 0.00627-0.313 0.382-1.725

27 25 71 26 22 18 189

Table 4. Percent of Absolute Average Deviation in Correlation of the Bubble Pressure and in Predicting of Activity Coefficient of Binary Subsystems kij T range (K) CO2-H2O H2S-H2O MDEA-H2O

np

313-393 298-411 298-393

39 53 50

a

b

0.3415 0.2607 0

-76.56 -43.87 0

by using 31 data points of Chapoy et al.35 that makes 53 total data points for the H2S-H2O system. To model the solubility data of the binaries in the whole range of temperature, the following relation is used: kij ) b0 +

b1 T

(24)

where T is absolute temperature in Kelvin. The coefficients of eq 24 for the binaries and the percent of average absolute deviation (AAD%) are given in Table 4. As one can see, with the use of only one adjustable parameter, the results are in good agreement with the experiment. The VLE data of the MDEA-H2O system are available at intermediate and high temperatures in terms of the mole fraction of MDEA, and also the freezing point depression data for this system are used for determination of reliable interaction parameters of this binary system. Using the NRTL activity coefficient equation, Chang et al.40 have correlated both the VLE and the freezing point

AAD% 2.6 2.3 1.8

ref 34

Kiepe et al. Capoy et al.,35 Selleck et al.36 Chang et al.40

data of the various alkanolamine-water systems with good accuracy. In this work, following Chunxi and Fu¨rst,15 using the interaction energy parameters of the NRTL allows one to generate the activity coefficient data of the water against the mole fraction of MDEA, 0-0.2, and at ranges of 298-393 K. So for this binary system, pure water is used for the reference state as well as in the ternary systems. As shown in Table 4 using the CSW EOS, the activity coefficient of water is calculated for the MDEA-H2O system with good accuracy, i.e. AAD% is 1.8, demonstrating that the values of the parameters of the CSW EOS for this binary system are reasonable. 3.4. Modeling the CO2-MDEA- H2O and H2S-MDEAH2O Systems. In this section the results of modeling the solubility of acid gases in aqueous MDEA solution are presented. Using the φ-approach with eCSW EOS, the VLE and chemical equilibrium calculations are performed to correlation of the CO2 and H2S solubilities in aqueous MDEA solution. The molecular binary interaction parameters have already been obtained as explained in the previous section so

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Table 5. Adjustable Binary Parameters to Correlation of the Bubble Pressure of the Ternary Aqueous Acid Gas-Alkanolamine Systems Using the Different Regressions with the Total Percent of Absolute Average Deviation kMDEA-MDEAH+

kH2O-MDEAH+

kCO2-MDEAH+

kHCO3--MDEAH+

kH2S-MDEAH+

kHS--MDEAH+

Fit

a

b

a

b

a

b

a

b

a

b

a

b

AAD%

I II III IV V

0.1850 0.1952 0.2031 0.1534 0.1720

-59.26 -58.20 -60.87 -46.07 -52.02

-0.1830 -0.1952 -0.2031 -0.1534 -0.1720

52.68 58.20 60.87 46.07 52.02

0 0 0.9173 0 0.7807

0 0 -214.61 0 -172.00

0 0 0 0.3381 0.2113

0 0 0 -76.24 -43.63

0 0 -0.2694 0 -0.3212

0 0 88.94 0 103.91

0 0 0 0.2864 0.1467

0 0 0 -72.29 -22.16

13.8 16.0 13.7 14.0 11.6

that the ionic interaction parameters should be optimized using the solubility data of the ternary systems. The algorithm that is used here is based on the reactive bubble pressure calculation that consists of two main loops: a step of the chemical equilibrium calculation as an inner loop and the second step of the vapor-liquid equilibria computation as an outer loop. The mole fractions of ionic and molecular species in the liquid phase are calculated at the given temperature and pressure by simultaneous solving the mass and electroneutrality equations together with the equation of the chemical equilibrium constant. By optimizing the binary interaction parameters and using an iteration procedure the chemical equilibrium calculation is used for finding the mole fractions of molecular species in liquid phase so that the bubble pressure calculation is performed until the convergency is achieved. The outputs are the bubble pressure and the mole fractions of acid gases and water in the vapor phase. It should be noted that, because of low vapor pressure of MDEA in the temperature range of 298-413 K, its presence in the vapor phase is negligible.42 In the beginning, using only the kij of molecular species from the data of the binary systems, calculation of the bubble pressure for the CO2-MDEA-H2O and H2S-MDEA-H2O systems is carried out so that the AAD%’s of 33.9% and 19.3% have been obtained for these two systems, respectively, that seems to be fairly good. Using the solubility data of the ternary systems, the binary interaction parameters between the ionic and molecular species in both ternary alkanolamine systems are calculated and optimized. As it was stated by Chunxi and Fu¨rst15 that the solvation effect of the anion is less than that of the cation, the interaction between anions and other species present in the liquid phase is negligible. Thus, it has been assumed that the interaction of the cationic species has more influence than does the interaction of the anions with the other species. Thus, for the VLE modeling of the CO2-MDEA-H2O system, the binary interaction parameters consist of the pair of interactions of the MDEAH+ -CO2, MDEAH+-MDEA, MDEAH+-H2O, and MDEAH+-HCO3- and for the H2S-MDEA-H2O system are MDEAH+-H2S, MDEAH+-MDEA, MDEAH+-H2O, and MDEAH+-HS-. On the other hand, since the species of MDEA, MDEAH+, H2O are common between these ternary systems, it will be reasonable to have fewer adjustable parameters so that the same values for the binary parameters kMDEA-MDEAH+ and kH2O-MDEAH+ are considered in both ternary systems. Therefore, all of the 602 solubility data points of both ternary systems were used simultaneously, and the six new binary parameters were fitted for the interaction among the ionic and molecular species as: kMDEA-MDEAH+, kH2O-MDEAH+, kCO2-MDEAH+, kHCO3--MDEAH+, kH2S-MDEAH+, and kHS--MDEAH+. To investigate the influences of these new parameters, the various scenarios have been studied that are given in Table 5. It should be noted that kMDEA-MDEAH+ is the common adjustable parameter and the binary parameters are temperature dependent through eq 24. As one can see from Table 5, in the first case denoting by the label I, the two common parameters are optimized while

the four remaining parameters set to zero. For this case the overall AAD% is 13.8 that show very good result. As one can see in the Fit I, the absolute values of the adjusted parameters are almost the same. In the Fit II, only the parameter kMDEA-MDEAH+ was fitted and it is empirically assumed that kH2O-MDEAH+ ) -kMDEA-MDEAH+. So in fact, only one parameter is adjusted, and a 2% increase in AAD% is observed that shows the deviation is still acceptable. In the Fit III, the two binary interaction parameters between acid gases and MDEAH+ are added to the parameters of the Fit II so that a value of 13.7 is obtained for the AAD%. By comparison of these three Fits, one may conclude that the interactions between the acid gases molecules and the cations have less influence than the interaction between the molecular solvents and the cations. In the Fit IV, the interactions among the two anions and MDEAH+ have been taken into account so that a value of 14.0 is resulted for the AAD%. In the Fit V the five interaction parameters, assuming kH2O-MDEAH+ ) -kMDEA-MDEAH+, have been adjusted so that a value of 11.6 is obtained for AAD%. Therefore, as one can observe the results of all the scenarios are in good agreement with the experiment. Based on the various aspects such as concentration, temperature, gas loading and the works of the authors for the two ternary systems, the details of the AAD% of the Fits I and V are shown in Table 6. As one can see for the CO2-MDEA-H2O system, in spite of not using the experimental data at low MDEA concentration, the highest deviation was obtained in the concentrations more than 45 wt % of MDEA, however for the H2S-MDEA-H2O system, the highest AAD% was found in 11.83 wt % of MDEA. For this system the number of data points at this concentration is low as reported by Lemoine et al.25 The highest deviation was resulted in the lower acid loading less than 0.01 in which the both ternary systems present less accuracy of the data in these ranges of loadings.15,17 Also a relative high deviation is seen at higher loading more than 1.0 for the case of CO2 in Fit I. Moreover, the highest deviation was found at the temperatures less than 323 K for the both ternary systems. Finally, as shown at Table 6, the results by the different authors show that the best AADs% belong to the data of Mamun et al.30 and Kuranov et al.42 So as Table 3 shows the data of these authors are at the gas loading more than 0.1 and mostly at the temperatures higher than 323 K. Based on Fit V, Figure 1 shows the comparison of the calculated and experimental total pressure36 against acid gas loading for the CO2-MDEA-H2O system by 32.2 wt % of alkanolamine at various temperatures. Also based on Fit V, Figure 2 presents the calculated and experimental26 partial pressure of CO2 versus the acid loading for the CO2-MDEA-H2O system at various concentrations and temperatures. As one can see the results of the eCSW EOS are in good agreement with experiment. Similarly based on Fit V, Figures 3 and 4 show the results of the present eEOS for the solubility of H2S in the aqueous MDEA solution at various concentrations and temperature. As we can observe, using the

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Table 6. Percent of Absolute Average Deviation in Predicting and Correlation of the Bubble Pressure of the Ternary Aqueous Acid Gas-Alkanolamine Systems Based on Various Variables and Using the Regressions I and V CO2-MDEA-H2O category MDEA concn (wt %) 45

H2S-MDEA-H2O

AAD%

BIAS%

AAD%

BIAS%

np

Fit I

Fit V

Fit I

Fit V

np

Fit I

Fit V

Fit I

Fit V

184 44 185

14.1 12.5 16.2

11.4 4.8 14.5

6.9 12.5 8.2

4.0 4.7 6.9

14 79 36 60

40.9 13.0 4.6 6.4

39.9 12.8 1.2 6.5

40.9 -7.2 -4.2 -0.4

39.9 -6.9 -0.4 -0.5

24 76 272 41

26.0 20.9 10.6 25.7

25.4 21.3 9.2 6.2

6.4 16.5 3.2 25.7

4.0 16.1 2.8 3.8

3 33 87 66

30.9 24.3 9.1 7.0

35.7 25.1 9.0 4.3

-30.9 9.8 -1.0 -4.7

-35.7 7.6 -1.2 -1.0

35 14 124 50 10 16 14 59 8 10 42 20 11

17.9 22.5 17.8 18.2 8.7 11.7 7.3 10.0 8.9 4.7 15.9 10.4 12.0

15.7 26.1 12.0 17.4 9.1 3.7 7.7 9.1 1.4 6.1 14.6 6.5 9.9

16.2 20.9 9.0 0.1 7.0 11.6 -7.1 2.9 8.6 -4.3 15.7 10.4 12.0

14.9 23.4 3.2 0.7 9.1 3.3 -7.5 2.2 -0.8 -5.0 14.6 5.7 9.9

14 89 14 10 28 22 12

40.9 13.3 3.6 8.7 4.9 4.2 3.7

39.9 13.8 1.5 4.9 2.8 2.3 2.1

40.9 -5.3 -3.2 -5.3 -3.3 -2.8 -2.5

39.9 -6.1 -0.2 -1.8 -1.6 0.4 0.3

28.4 3.2 -2.4 -2.7 -16.5 -22.9 -0.9

27.1 2.8 0.5 -0.8 -19.8 -22.8 -0.2

Loading (mol/mol) 1 Temp (K) 298 303 313 323 328 333 343 348 353 358 373 393 413 Author Lemoine et al.25 Haji-Sulaiman et al.26 Park and Sandall27 Sidi-Boumedine et al.28 Mamun et al.30 Austgen and Rochelle41 Kuranov et al.42 Rho et al.43 Kamps et al.44 Rogers et al.45 MacGregor and Mather46 OVerall

13 42 30 77 34 14 78 58 28 34 5 413

14.8 14.3 22.1 11.5 7.0 17.0 13.1 17.7 14.7 22.8 20.7 14.9

12.7 15.2 22.3 7.0 7.6 14.7 6.3 17.7 4.9 22.4 17.6 12.1

14.0 10.6 10.0 6.3 -2.1 -6.7 13.1 9.7 13.8 1.2 15.1 8.1

11.6 12.0 12.1 2.4 -1.9 -6.6 6.2 10.7 2.1 -1.5 12.1 5.4

27 25 71 26 22 18 189

28.4 7.2 3.4 6.1 16.9 23.6 11.4

27.1 7.3 1.4 4.8 20.0 23.5 10.6

various data sources, the calculated values are in very good agreement with experiment. Using the ratio of calculated pressure based on Fit I to the experimental pressure, Figure 5 shows the deviation versus the CO2 loading for the CO2-MDEA-H2O ternary system. It can

be seen that most of the points are below the horizontal line which means the results of the model are under correlated. A similar scheme is plotted for the H2S-MDEA-H2O system that is shown in Figure 6. As one can observe, a different scattering deviation is observed for this system so that most of the points are above the horizontal line. The values of the BIAS% ) (100/

Figure 1. Comparison of calculated (based on Fit V) and experimental42 total pressure of the CO2-MDEA-H2O system (32.2 wt %) at various temperatures.

Figure 2. Comparison of calculated (based on Fit V) and experimental26 partial pressure of CO2 in the CO2-MDEA-H2O system at various concentrations and temperatures.

Ind. Eng. Chem. Res., Vol. 49, No. 13, 2010

6227

Figure 3. Comparison of calculated (based on Fit V) and experimental42 total pressure of the H2S-MDEA-H2O system (32.2 wt %) at various temperatures.

Figure 6. Ratio of calculated pressure (based on Fit I) to the experimental pressure for each data point against loading of H2S in the H2S-MDEA-H2O ternary system.

Figure 4. Comparison of calculated (based on Fit V) and experimental partial pressure of H2S in the H2S-MDEA-H2O system at various concentrations and temperatures.

Figure 7. Ratio of calculated pressure (based on Fit V) to the experimental pressure at different temperatures in the CO2-MDEA-H2O ternary system.

Figure 5. Ratio of calculated pressure (based on Fit I) to the experimental pressure for each data point against loading of CO2 in the CO2-MDEA-H2O ternary system.

Figure 8. Ratio of calculated pressure (based on Fit V) to the experimental pressure at different temperatures of the H2S-MDEA-H2O ternary system.

n) · Σ(Pexp-Pcal)/Pexp are 8.1 and -0.9 for the CO2-MDEA-H2O and H2S-MDEA-H2O systems, respectively. Figures 7 and 8 show the pressure deviation, Pcal/Pexp, obtained by Fit V for the two ternary systems at various temperatures. As one can see, the deviation of the pressure at

low temperatures is more than that at high temperatures. Also, an under-correlation, i.e. Pcal/Pexp < 1, is observed at 298 K for both ternary systems. The BIAS%’s are 5.4 and -0.2 for the CO2-MDEA-H2OandH2S-MDEA-H2Osystems,respectively.

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Ind. Eng. Chem. Res., Vol. 49, No. 13, 2010

Figure 9. Comparison of calculated mole fraction (based on Fit V) of various species with those obtained by NMR study for CO2 solubility in 23 wt % MDEA at 293 K.48 Table 7. Comparison of the Results of This Work (Fit I) and Those Obtained by Huttenhuis et al.18 for CO2-MDEA-H2O System Fu¨rst, Renon17

a

this work

author

np

AAD%

np

AAD%, Fit I

Lemoine et al.25 Haji-Sulaiman et al.26 Park and Sandall27 Sidi-Boumedine et al.28 Mamun et al.30 Austgen and Rochelle41 Kuranov et al.42 Rho et al.43 Kamps et al.44 Rogers et al.45 MacGregor and Mather46 Huang and Ng47 OVerall

13 14 78 65 14 34 65 283

17 28 20 19 25 43 27 24

13 42 30 77 34 14 78 58 28 34 5 413

14.8 14.3 22.1 11.5 7.0 17.0 13.1 17.7 14.7 22.8 20.7 14.9

a

This model was modified by Huttenhuis et al.18

To investigate the accuracy of the results of the concentration of the species in the liquid phase, a comparison is performed with the NMR studies. Based on Fit V, Figure 9 shows this comparison for the CO2-MDEA-H2O system with those results obtained by NMR study at 23 wt % of MDEA and 293 K.48 As one can see a good agreement between the results of the eCSW EOS calculation and the results of NMR are obtained. Since the different databases have been used by several authors, the exact comparison between the results of this work and the others are unattainable; however for the CO2-MDEA-H2O system, it is possible to give a fair comparison between this work and the work of Huttenhuis et al.18 As shown in Table 7, some of the data sources such as Haji-Sulaiman et al.,26 Park and Sandall,27 Sidi-Boumedine et al.,28 Mamun et al.,30 and MacGregor and Mather46 were used in this work, but not used by Huttenhuis et al.18 However, the data of Huang and Ng47 and Rho et al.43 at 5 wt % of MDEA are not included in our data sources because the data of Rho et al.43 at 5 wt % of MDEA cannot be validated by applying the

Figure 10. Comparison of the predicted partial pressure (based on Fit I) of CO2 and H2S by eCSW and the experimental data45 for the CO2 + H2S + MDEA + H2O quaternary system.

simplifications of the present model such as neglecting CO32and OH- concentrations.17 Finally based on Fit I as one can observe, the present EOS with the two binary parameters results better agreement with experiment than those obtained by Huttenhuis et al.18 using the modified Fu¨rst and Renon EOS. The reasons of the superiority of the present EOS respect to the Fu¨rst and Renon18 EOS may be explained as follows. The backbone of the present eCSW EOS is a theoretical basis since it could represent the simulation data of square-well potential fluids accurately as show in Haghtalab and Mazloumi.21 Moreover, the eCSW EOS has one term less than Fu¨rst and Renon18 EOS since the second short-range term in the present EOS not included. Finally, in Fu¨rst and Renon EOS18 the critical properties of the pure components were used in calculation of the attractive and repulsive parameters a and b, however in the eCSW EOS the parameter of size is used simultaneously with the same value in all terms of repulsive, the short-range force, Born and MSA that this is an advantage of the present EOS. As a last word, the eCSW EOS has already applied to pure fluids such as hydrocarbon, CO2, N2, etc21 and aqueous strong electrolyte20 systems successfully. In this work, application of the eCSW EOS is extended to industrial systems such as solubility of acid gases in alkanolamines. To show the predictability of the present model for the quaternary system, the simultaneous solubility of CO2 and H2S in aqueous MDEA solution is calculated without adjusting any new interaction parameters. As shown in the Table 8, since the experimental data of Rogers et al.45 are already used for the solubility of single acid gases in the aqueous MDEA, so the same source of data is used here to predict the solubility of the mixed acid gases in the aqueous MDEA solution. Using the parameters of Fits I and V, the results of prediction for the CO2-H2S-MDEA-H2O system are given in Table 8. Based on Fit I, Figure 10 shows the prediction results of eCSW for the quaternary system. It can be seen the results of the eCSW EOS are in good agreement with the experiment with acceptable and good accuracy. It should be noted that the superiority of

Table 8. Specifications of the Experimental Data of Rogers et al.45 Used for the CO2-H2S-MDEA-H2O System and the Prediction Results Based on Fits I and V AAD% (prediction) P (kPa) wt %

np

T (K)

CO2

loading H2S

CO2

Fit I H2S

Fit V

CO2 H2S CO2 H2S

BIAS% (prediction) Fit I CO2

H2S

Fit V CO2

H2S

23 19 313,323 0.00476-1.441 0.0028-2.675 0.00500-0.1020 0.00135-0.2082 15.7 42.7 17.1 44.6 -15.5 -42.5 -17.8 -44.7 20.6 -10.8 16.4 -15.9 50 6 313 0.0009-1.671 1.599-1.889 2.97 × 10-5-0.0487 0.0795-0.08205 20.6 10.8 18.1 15.1 OVerall 25 16.9 35.0 17.3 37.5 -6.8 -34.9 -8.5 -37.5

Ind. Eng. Chem. Res., Vol. 49, No. 13, 2010

( )

the results of Fit I with respect to Fit V is due to better accuracy of Fit I in the ternary systems as seen from Table 6.

∂D ∂ni

) T,V,nj*i

1 Ds - D i ) s ) H2O&MDEA (A.5) nt xs

∑ s

4. Conclusion The electrolyte CSW EOS has been successfully applied to correlation of the solubility of the acid gases in aqueous MDEA solutions. Using one adjustable parameter, in the attractive part of eCSW EOS, the experimental data of bubble pressure of the CO2-H2O and H2S-H2O systems were correlated with the AAD% of 2.6 and 2.3, respectively. Using the molecular adjustable parameters for binaries, the bubble pressure of the 602 data points of the both CO2-MDEA-H2O and H2S-MDEA-H2O systems were predicted with the AAD% of 33.9 and 19.3, respectively. To improve the accuracy of the present EOS and to investigate the effects of the interactions between the ionic and molecular species, the solubility data were correlated simultaneously for the both ternary systems so that the five cases were investigated by changing the number of interaction parameters from one to five. It has been shown that the very good results were obtained by adjusting the common binary parameters between molecular solvents and MDEAH+ in the both ternary systems. The results presented in all of the cases were in good agreement with the experiment, so with the one and five binary interaction parameter(s) the AADs% were 16.0 and 11.6, respectively. To verify the predictability of the model, the eCSW EOS was extrapolated to the solubility data of the mixed CO2-H2S systems. So for the CO2-H2S-MDEA-H2O system the values of AADs% were about 17% and 35% for the CO2 and H2S partial pressures, respectively. Finally, the comparison of the results demonstrated that the eCSW EOS can be used successfully for good representation of the solubility of the acid gases in the aqueous MDEA solutions. Acknowledgment We are grateful to NIGC (National Iranian Gas Company) for financial support under the contract number 087162. Appendix A. The Pressure and Chemical Potential Equations of eCSW The pressure and chemical potential equations of the CSW EOS were obtained as:19 PCSW )

µi,CSW

(

) ln

(∑

RT

2V

-

z 2

(1 - m - w)mV0 zRT RT + V - 4τV0 2 (mV + V0w)(mV + V0(1 - m)) (A.1)

V V - 4τV0

)

+

4τV0i V - 4τV0

xjmij + wV0i + 2V0

j

-

∑xw

zi 2

ln

mV + V0w

mV + V0w mV + V0(1 - m)

2(V - V0)

j ij

j

(

)

∑ x m + (1 - m)V j

ij

0i

+ 2V0

j

-

mV + V0(1 - m)

)

(A.2)

The pressure and chemical potential equations of the MSA contribution were expressed as: PMAS )

Γ 2Γ3RT 3 RTκ2 1 + σΓ 3πNA 2 4πNA 1 + σΓ

(

)

(

µi,MSA e2NA Γ 1 ∂D ) -Z2i + RT 4πDε0RT 1 + σΓ D ∂ni where

6229

∑nZ

2 i i

ion

(A.3)

)

(A.4)

It should be noted that for the other species, i.e., acid gases and ions, ∂D/∂ni ) 0 and consequently, only the first term on right hand side of eq A.4 is considered for these species. The pressure and chemical potential equations of the Born equation were given as: PBorn ) 0

(

(A.6)

µi,Born NAe2 Z2i niZ2i 1 ∂D 1 ) - 2 1RT RT4πε0 D ∂ni ions σi σi D

∑

(

)) (A.7)

So having the chemical potential expression, the fugacity coefficient for each component in a mixture is obtained as: φi )

( )

(

)

µi,MSA µi,Born µres µi,CSW i RT RT exp exp + + ) PV RT PV RT RT RT (A.8)

Nomenclature A ) coefficient in eq 4 a ) molar Helmholtz free energy (J mol-1) B ) coefficient in eq 4 bi ) coefficients in eq 24 C ) coefficient in eq 4 D ) dielectric constant of solution Ds ) dielectric constant of solvents di ) coefficients in eq 22 e ) electronic charge (1.60219× 10-19 C) Kx ) equilibrium constant in mole fraction base k ) Boltzmann’s constant (1.38066 × 10-23J K-1) kij ) coupling interaction parameter between species i and j m ) orientational parameter defined in eq 13 np ) number of data points NA ) Avogadro’s number (6.02205 × 1023 mol-1) P ) pressure (Pa) R ) gas constant (8.314 J mol-1 K-1) T ) temperature (K) V ) molar volume (m3 mol-1) vdW ) van der Waals V0 ) close-packed volume (m3 mol-1) defined in eq 14 xi ) mole fraction of component i z ) maximum coordination number defined in eq 15 Zi ) charge number of ionic species i w ) a function of temperature defined in eq 10 Greek Letters Γ ) MSA screening parameters (m-1) γ ) activity coefficient λ ) square-well potential parameter ε ) square-well potential depth (J) ε0 ) vacuum permittivity (8.85419× 10-12 C2 J-1 m-1) σ ) size parameter (m) φ ) fugacity coefficient κ ) Debye screening length (m-1) τ ) constant (0.7405) υ ) stoichiometric number Subscripts Born ) Born contribution CSW ) cubic square-well cal ) calculated properties exp ) experimental properties

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Ind. Eng. Chem. Res., Vol. 49, No. 13, 2010

i ) component i ij ) binary pair of i and j j ) component j MSA ) Mean Spherical Approximation theory s ) solvent Superscripts id ) ideal gas res ) residual properties * ) unsymmetrical normalization 0 ) pure state ∞ ) infinite dilution

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ReceiVed for reView October 26, 2009 ReVised manuscript receiVed April 24, 2010 Accepted May 5, 2010 IE901664K