Modeling CO2 Solubility in Aqueous N-methyldiethanolamine Solution

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Modeling CO2 Solubility in Aqueous N-methyldiethanolamine Solution by Electrolyte Modified Peng−Robinson Plus Association Equation of State Ali T. Zoghi,†,‡ Farzaneh Feyzi,*,† and Mohammad R. Dehghani† †

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Thermodynamics Research Laboratory, School of Chemical Engineering, Iran University of Science and Technology, Tehran 16846-13114, Iran ‡ Research Institute of Petroleum Industries, Tehran 14665-1998, Iran ABSTRACT: In the present work, the electrolyte equation of state proposed by Huttenhuis et al. [Fluid Phase Equilibria 2008, 264, 99−112] is improved to describe the solubility of carbon dioxide in aqueous solutions of N-methyldiethanolamine (MDEA) in wide ranges of concentration, pressure, temperature, and acid gas loading. The molecular part of the equation is based on the modified Peng−Robinson Plus Association equation of state (mPR-CPA EoS) proposed by Zoghi et al. [J. Pet. Sci. Eng. 2011, 78, 109−118]. To account for the presence of ions, three contributions are added to the mPR-CPA EoS to describe short-range interactions, long-range interactions, and the Born term. The same EoS is used for both vapor and liquid phases. A consistent database including 567 experimental data points is utilized in this study. In the first step of modeling the parameters of the EoS have been tuned by regression to the vapor pressure and saturated liquid density experimental data for associating pure components (i.e., water and MDEA). In the next step, the vapor−liquid equilibrium calculations were carried out for adjusting the molecular binary interaction parameters. These parameters are optimized for binary subsystems including H2O−CO2, CO2− MDEA, and H2O−MDEA. Finally, the binary interaction parameters between ionic and molecular species are tuned via the simultaneous vapor−liquid and chemical reaction equilibrium calculations. The results show that the proposed model is able to improve the precision of prediction of the solubility of CO2 in aqueous MDEA solution by more than 6.7% in comparison with that of Huttenhuis et al. [Fluid Phase Equilibria 2008, 264, 99−112] in a wide range of pressures, temperatures, acid gas loadings, and aqueous MDEA concentrations.

1. INTRODUCTION Carbon dioxide (CO2) and hydrogen sulfide (H2S) are the most important impurities in natural and industrial gases and must be removed in order to avoid industrial and environmental problems. The most common industrial method for removing these gases is absorption in aqueous alkanolamine solutions. These solutions are weak bases that react with acid gases. At high pressures and low temperatures, acid gases are absorbed by alkanolamine aqueous solutions, and the desorption process occurs in the reverse conditions of pressure and temperature. Among alkanolamines, N-methyldiethanolamine (MDEA) is the most widely used in industrial applications due to some of its favorable properties such as low vapor pressure, low thermal degradation, and low corrosion rate. The wide applicability of alkanolamine solutions in gas sweetening and CO 2 capturing processes makes their thermodynamic modeling a vital demand in process simulation calculations. Absorption of acid gases in aqueous alkanolamine solutions produces ionic species which makes their vapor− liquid equilibrium calculation very complex and requires sophisticated thermodynamic models. The proposed models in literature can be divided into three categories. The first is empirical models in which the activity coefficients of all the species present in equilibrium reactions are assumed to be equal to unity and the equilibrium constants are treated as adjustable parameters. One of the well-known models in this category is Kent−Eisenberg.1 The main weakness of these types © 2012 American Chemical Society

of models is poor extrapolation applicability outside the validity range. This type of model is mostly used by process engineers because of their low complexity and relatively high speed of computation. The second category is the γ−φ approach, in which, an equation of state (EoS) accounts for the nonidealities of the vapor phase and an activity coefficient model is used to describe the liquid phase nonideality. Since in electrolyte solutions activity coefficients are estimated for both molecular and ionic species, these models usually consist of two or three terms. For the contribution of long-range interactions, the Debye−Huckle model and its extensions are commonly used. For the contribution of short-range interactions, different activity coefficient models, such as NRTL and UNIQUAC, are usually preferred. Finally, the Born term is added to represent the contribution of mixed solvent effects. This approach has been well established and implemented by numerous authors. A brief review of the published works in this category is presented below: Deshmukh and Mather2 used an extension of the Debye− Huckel model for long-range interactions and the simplified version of Pitzer model to consider short-range interactions for modeling the solubility of CO2 and H2S in mono ethanol amine Received: Revised: Accepted: Published: 9875

November 12, 2011 June 17, 2012 June 18, 2012 June 18, 2012 dx.doi.org/10.1021/ie2026053 | Ind. Eng. Chem. Res. 2012, 51, 9875−9885

Industrial & Engineering Chemistry Research

Article

(MEA). Austgen et al.3 adjusted the parameters of electrolyte NRTL model for obtaining the solubility of CO2 and H2S in aqueous solutions of MEA and diethanolamine (DEA) in the temperature range from 293 to 413 K. Posey and Rochelle4 have also used electrolyte NRTL model for the solubilities of acid gases in MDEA solution. They adjusted the model parameters as a function of temperature and introduced a new function for equilibrium reaction of hydration of MDEA. Kamps et al.5 and Ermatchkov et al.6 adjusted the Pitzer’s activity model interaction parameters for modeling the solubility of CO2 in aqueous MDEA solution. Faramarzi et al.7,8 have used extended UNIQUAC model for the solubility of carbon dioxide in MEA and MDEA solutions in wide ranges of pressure and temperature. They also predicted the quaternary system (CO2−MDEA−MEA−H2O) by using the adjusted parameters of the ternary subsystems. Haghtalab and Dehghani9 used UNIQUAC-NRF model for (CO2−MEA− H2O) and (CO2−MDEA−H2O) systems. Haghtalab and Shojaeian10 used N-Wilson-NRF model for prediction of solubilities of acid gases in different alkanolamine solutions in a wide range of pressure and temperature. The most important weakness of these types of models is that the effect of pressure on the activity coefficients is not taken into account and density cannot be calculated. In addition, despite the parameters of the activity coefficient model, Henry’s law constants for the solubility of volatile components, such as acid gases, are needed. Finally, the last category, the so-called φ−φ approach, deals with using an electrolyte EoS (eEoS). In this approach, the same EoS is used for both vapor and liquid phases. Since at high pressures (i.e., in absorbers of natural gas plants), the difference between the densities of liquid, and vapor phases becomes smaller, and may even disappear, the EoS approach is superior to activity coefficient models. The application of a suitable EoS for computation of vapor−liquid equilibrium of alkanolamine systems is a highly interesting topic and has received great attention in recent years; however, the published papers on this approach are more limited than the works on γ−φ approach. A brief review of this category of models is explained in the following: Kuranov et al.11 used a modified hole quasichemical model for chemical reactions and electrostatic interactions in liquid phase. They used their model for CO2−H2O system in a wide range of temperature and pressure. Vallee et al.12 studied the solubility of acid gases (CO2 and H2S) in aqueous DEA solution by using the eEoS developed by Fürst and Renon.13 The same eEoS has been also used by Chunxi and Fürst14 to represent the solubility of acid gases in aqueous MDEA mixtures. The Fürst and Renon eEoS is also used by Derks et al.15 for modeling the solubility of CO2 in aqueous piperazine (PZ) solution. Huttenhuis et al.16,17 added the Born term to the proposed model by Fürst and Renon13 for vapor−liquid calculation of CO2−H2O−MDEA−CH4 systems. They18 have also extended their eEoS for representation of the solubility of mixed CO2, H2S, and CH4 in the aqueous solutions of MDEA. Haghtalab and Mazloumi19 have developed an electrolyte equation of state in which the nonelectrolyte part of the eEoS is expressed by a cubic square-well (CSW) EoS. They have used the explicit version of the Mean Spherical Approximation (MSA) theory for long-range electrostatic interactions of ions, and the Born equation for contribution of ionic species. They adopted the eCSW-EoS to model the solubility of CO2 and H2S in aqueous MDEA solution and, without any additional parameter, they predicted the solubilities of mixed acid gases in

aqueous MDEA solution. Nasrifar and Tafazzol20 have used the PC-SAFT EoS to model the solubility of acid gases in aqueous solutions of MEA, DEA, and MDEA. They first tuned the model parameters for pure compounds and binary subsystems and then, carried out the calculations for ternary systems. In calculating the chemical reaction equilibrium constants, they assumed that the activity coefficients of the species are equal to one. Following Kontogeorgis et al.,21 Zoghi et al.22 have recently extended the modified Peng−Robinson23 (mPR) EoS to associating compounds and have developed a cubic plus association (CPA) EoS, which they call it mPR-CPA EoS, and have predicted the solubility of light gases in water. In this work, since alkanolamines are considered as associative substances,24 a new combination of the mPR-CPA EoS and the electrolyte part of the Fürst and Renon13 model plus the Born term, is applied to systems of aqueous acid gas alkanolamine solutions. We call the proposed model emPRCPA EoS. Since, the aqueous MDEA solutions are widely used in treating natural gas and fuel gases, the emPR-CPA EoS is applied for vapor−liquid calculation of CO2 solubility in this solution in a wide range of acid gas loading, temperature, and pressure. To proceed with this idea we have presented the thermodynamic framework in section 2 followed by the results and discussions in section 3. Conclusion is brought in section 4.

2. THERMODYNAMIC FRAMEWORK 2.1. Chemical Equilibrium. Carbon dioxide is absorbed by alkanolamine solutions via chemical equilibrium reactions. The following parallel reversible reactions take place. Dissociation of water K1

2H 2O ↔ H3O+ + OH−

(1)

Formation of bicarbonate K2

CO2 + 2H 2O ↔ HCO−3 + H3O+

(2)

Formation of carbonate K3

HCO−3 + H 2O ↔ H3O+ + CO=3

(3)

Dissociation of protonated amines K4

MDEAH+ + H 2O ↔ MDEA + H3O+

(4)

The chemical equilibrium constants of the above reactions are expressed as Kx , j =

∏ (xiγi)ν

i

(2) (3) = exp(C(1) j + C j / T + C j ln(T )),

i

j = 1, ..., 4

(5)

where xi, γi νi, and T are mole fraction, activity coefficient (mole fraction scale), reaction stochiometry coefficient of species i, and temperature, respectively. The subscript j denotes the reaction number. The mole fraction based equilibrium constants of these reactions are correlated as a function of temperature in eq 5 and the numerical values of coefficients C(1), C(2), and C(3) for each reaction are given in Table 1. The symmetrical activity coefficient for water is defined by γwater = 9876

φ(T , P , x water) 0

φ (T , P , x water → 1)

(6)

dx.doi.org/10.1021/ie2026053 | Ind. Eng. Chem. Res. 2012, 51, 9875−9885


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⎛ Ar ⎞ ⎛ Ar ⎞ ⎛ Ar ⎞ ⎛ Ar ⎞ Ar ⎟ +⎜ ⎟ +⎜ ⎟ ⎟ =⎜ +⎜ ⎝ RT ⎠RF ⎝ RT ⎠SR1 ⎝ RT ⎠ Assoc ⎝ RT ⎠SR2 RT

Table 1. Coefficients of Temperature Dependent Reaction Equilibrium Constants of Equation 517 constant

C(1)

C(2)

C(3)

T (K)

ref

Kx,1

132.899

−13445.9

−22.4773

273−498

Kx,2

231.465

−12092.1

−36.7816

273−498

Kx,3

216.049

−12431.7

−35.4819

273−498

Kx,4a

−77.262

−1116.5

10.06

278−423

Posey and Rochelle4 Posey and Rochelle4 Posey and Rochelle4 Huttenhuis et al.16

⎛ Ar ⎞ ⎛ Ar ⎞ ⎟ +⎜ ⎟ +⎜ ⎝ RT ⎠LR ⎝ RT ⎠Born

In eq 8, the subscripts RF and SR1 represent repulsive forces and short-range interactions related to molecular part. Assoc, SR2, LR, and Born are the contributions of association interactions, short-range ionic interactions, long-range ionic interactions, and the Born term, respectively. The molar residual Helmholtz energy for the mPR EoS is23

a

Huttenhuis et al. have correlated MDEA protonation reaction using experimental data at reference state of infinite dilution for MDEA.17

⎛ Ar ⎞ ⎛ Ar ⎞ Ar ⎟ +⎜ ⎟ =⎜ ⎝ RT ⎠RF ⎝ RT ⎠SR1 RT

P is pressure and φ is the fugacity coefficient. For other molecular and ionic species, the unsymmetrical activity coefficients are given by eq 7: γi* =

(8)

⎛ ⎛ v + 2.4142b ⎞ b⎞ a ⎟ ln⎜ = −ln⎜1 − ⎟ − ⎝ v⎠ 2 2 RTb ⎝ v + 0.4142b ⎠

(9)

where v is the molar volume and a and b are defined by eqs 10 and 11:

φi(T , P , xi) φi∞(T , P , xi → 0)

i ≠ water, i = ionic, molecular species

(7)

The fugacity coefficients of the ionic and molecular species (φi) are calculated by the emPR-CPA EoS. 2.2. Electrolyte emPR-CPA EoS. The proposed model has two main parts. The first part is the nonelectrolyte contribution, which is a combination of the mPR EoS23 and the association contribution based on the theory proposed by Wertheim.25 The second part deals with the electrolyte contribution composed of the Fü rst and Renon13 eEoS and the Born term.17,18 Consequently, the molar residual Helmholtz energy is expressed as:

⎛ 0.4572R2T 2 ⎞ c ⎟α ′ a = α⎜ P ⎝ ⎠ c

(10)

⎛ 0.0778RTc ⎞ b = β⎜ ⎟β ′ Pc ⎝ ⎠

(11)

Parameters α and β are functions of reduced temperature for which the details are given by Feyzi et al.23 Parameters α′ and β′ are equal to one for nonassociating compounds and are defined as functions of temperature for associating compounds.22 These parameters are presented below:

Table 2. Pure Component Parameters of the emPR-CPA EoS −1

MW (kg·kmol ) TC (K) PC (× 102 kPa) ω δ (× 10−10 m)a d(0) d(1) d(2) d(3) d(4) no. assoc sites εAiBj/k (K) θAiBj α′0 α′1 α′2 α′3 β′0 β′1 β′2 β′3 AAD% Psat AAD% ρliq range of Tr a

MDEAH+

MDEA

120.16

119.16 677 38.8 1.242 4.5 −8.17 8.99 × 103

4.5

4 1840.1 0.04 0.7402 0.2491 −1.1435 0.9683 2.4087 −4.0060 3.6716 −0.9700 0.047b 0.013b 0.55−.90

H3O+

2.52

H2O

CO2

18.02 647.3 220.9 0.344 2.52 −19.29 2.98 × 104 −1.97 × 10−2 1.32 × 10−4 −3.11 × 10−7 2 2610.21 0.04201 0.6664 −1.0412 1.581 −0.5876 1.2761 −1.7209 1.8336 −0.4983 0.03c 0.43c 0.42−0.98

44.01 304.2 74 0.224 3.94 2

CO3=

OH−

61

59.98

17

3.12

3.7

3.52

HCO3−

All parameters are based on the work of Huttenhuis et al.17 bData source.24 cExperimental data source.26 9877



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α′ = α0′ + α1′Tr + α2′Tr 2 + α3′Tr 3

(12)

β′ = β0′ + β1′Tr + β2′Tr 2 + β3′Tr 3

(13)

where zion is the charge number of ionic species. The shielding parameter (Γ), the parameter αLR, and the system’s dielectric constant D, are defined as follows

The coefficients of eqs 12 and 13 are determined by data regression of pure component vapor pressure and saturated liquid density experimental data to the model22 and are introduced in Table 2. The ordinary van der Waals mixing rules defined by eqs 14 and 15 are used in this work: amix =

ion

αLR 2 =

∑ bixi

The association contribution is defined by eq 16. ⎛ Ar ⎞ ⎜ ⎟ = ⎝ RT ⎠ Assoc

⎡ ⎤ Mj X Aj ⎥ Aj ⎢ ∑ xj⎢∑ ln X − ⎥ + 2 ⎦ 2 ⎣ Aj

25

Ds = (16)

X A = (1 + ρ ∑ X BΔAB)−1

1 1 − 1.9η

NAπ 6

∑ i

xiδi 3 v

(19)

xiφi l = yi φi v

(20)

(27)

(28)

(29)

where xi and yi are, respectively, the liquid and vapor phase mole fractions of species i. In addition to phase and chemical equilibrium equations, mass balance equations are required to completely determine the governing system of equations. These equations are presented below. Water mole balance

(21)

n w0 = n w + nHCO3− + nCO32− + nOH−

In eq 21, the summation is carried out over all the species present, δi is the molecular or ionic diameter, and NA is Avogadro’s number. The long-range ion−ion contribution is defined by the simplified MSA13 model. ⎛ x z 2 Γ ⎞ Γ 3υ ⎛ Ar ⎞ α 2 ⎜ ⎟ = − LR ∑ ⎜ ion ion ⎟ + ⎝ RT ⎠LR 4π ion ⎝ 1 + Γδion ⎠ 3πNA

(26)

2.3. Phase Equilibria. The emPR-CPA EOS is used to perform vapor−liquid equilibrium calculations for molecular species. Furthermore, it is assumed that ionic species are only present in liquid phase. Because of low vapor pressure of MDEA in the temperature range from 298 to 413 K, it is assumed that this component is not present in the vapor phase,28 and, therefore, the vapor phase contains only CO2 and water molecules. The equilibrium relations are then expressed by eq 29:

where at least one of the i or j is an ion and wij is an ion−ion or ion−molecule interaction parameter. The packing factor ξ3 is obtained from the following equation. ξ3 =

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

⎞ ⎛ Ar ⎞ xz 2 NA e 2 ⎛ 1 ⎜ ⎟ = ⎜ − 1⎟ ∑ i i ⎝ RT ⎠Born 4πε0RT ⎝ Ds ⎠ i δi

(18)

where η = 0.25bρ is the packing fraction. The short-range ionic interaction term is calculated by the following relation:13 xixjwij ⎛ Ar ⎞ ⎜ ⎟ = −∑ ∑ ⎝ RT ⎠SR2 v(1 − ξ3) i j

(25)

The coefficients of this equation are introduced in Table 2. The Born27 contribution to the molar residual Helmholtz energy is obtained from eq 28:

where k, εAiBj, and θAiBj are the Boltzmann’s constant, association energy, and association volume, respectively. The simplified radial distribution function, g(ρ), is given by21 g(ρ) =

∑ xmDm ∑ xm

Dm = d(0) +

(17)

In eq 17, ρ is the molar density and ΔAB is the association strength estimated by eq 18. ⎤ ⎡ ⎛ ε A iBj ⎞ ΔA iBj = g (ρ)⎢exp⎜ ⎟ − 1⎥bijθ A iBj ⎦ ⎣ ⎝ kT ⎠

(24)

In eq 26, the summation is over the molecular pure components present. The pure component dielectric constant is assumed to be temperature dependent and is defined by eq 27:

where XAj and Mj are the mole fraction of the molecules not bonded at site A and number of associating sites per molecule j, respectively. XAj is rigorously defined as B

e 2NA ε0DRT

(23)

where ξ3″ is calculated similarly to ξ3, except that the summation should be over the ionic species only. The solvent dielectric constant is given by

(15)

i

2 x ion ⎛ z ion ⎞ ⎜ ⎟ υ ⎝ 1 + Γδion ⎠

⎛ ⎞ 1 − ξ3″ ⎟ ⎜ D = 1 + (Ds − 1) ⎜ 1 + ξ″3 ⎟ ⎝ 2 ⎠

(14)

j

2

4Γ = αLR NA ∑

∑ ∑ xixj(aiaj)0.5 (1 − kij) i

bmix =

2

(30)

MDEA mole balance 0 nMDEA = nMDEA + nMDEAH+

(31)

CO2 mole balances 0 0 nCO = LCO2nMDEA = nCO2 + nHCO3− + nCO32− 2

(22) 9878

(32)



Article

Table 3. Literature References Used For the Data of MDEA−CO2−H2O System author

MDEA (wt %)

T (K)

loading (mol gas/mol amine)

np

Lemoine et al.31 Sidi-Boumedine et al.35 Ma’mun et al.37 Austgen and Rochelle3 Kuranov et al.28 Rho et al.38 Kamps et al.5 Rogers et al.39

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

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

0.02−0.26 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 total

13 86 32 16 81 81 33 28 370

Boumedine et al.35 The database used in this work is summarized in Table 3. The number of experimental data points used for the solubility of CO2 in aqueous solutions of MDEA is 370. The distribution of experimental points in this database is as follows: the maximum experimental data points are used in the range of 0.1−1 of acid gas loading which makes 246 out of 370 (66%), 32% of the experimental data points belong to the temperature of 313.15 K, and 48% and 33% of the experimental data points for the concentration of aqueous MDEA solutions are in the range of 18−26 wt % and >33 wt %. 3.2. Pure Component Parameters. The adjustable parameters of the emPR-CPA EOS for pure associating compounds are the coefficients of eqs 12 and 13 and the association parameters (εAiBj and θAiBj). The number of association site schemes for MDEA and water are considered to be four24 and two,22 respectively. The adjusted parameters are presented in Table 2. The error of prediction of vapor pressure and saturated liquid density data for H2O and MDEA are also reported in this table. The ionic species diameter for MDEAH+, HCO−3, CO=3, OH−, and H3O+ are assumed to be the same as those proposed by Huttenhuis et al.17 3.3. Binary Subsystems. Before adjusting the model parameters for the solubility of CO2 in aqueous MDEA solution, the model should be tested for the binary subsystems. The binary subsystems are CO2−H2O, MDEA−H2O, and CO2−MDEA. This procedure is carried out by adjusting the binary interaction parameters (kij) in eq 14. Since there is always trace amounts of water in pure MDEA, the physical solubility of CO2 in MDEA cannot be measured directly; and therefore, no published data are available17 for the CO2− MDEA binary solution. Consequently, different alternatives may be considered to obtain the binary interaction parameters for this system. First, the binary interaction parameters can be determined simultaneously with other ternary parameters of the model by regression of the solubility experimental data of CO2 in ternary systems.14 Second, the N2O analogy may be applied.17 In this approach, the experimental data of physical solubility of N2O in aqueous MDEA solution are converted to the physical solubility data of CO2 in aqueous MDEA solution, as explained by eq 34.

Charge balance nMDEAH+ + n H3O+ = nHCO3− + 2nCO32− + nOH−

(33)

In these equations, LCO2 is loading (moles of acid gas absorbed per mole of amine) and n is the number of moles. For chemical equilibrium reactions 1−4, four equations are generated due to the chemical reaction equilibrium constants presented by eq 5; therefore, these equations together with eqs 29−33 represent a system of nonlinear equations that must be solved simultaneously to obtain the equilibrium concentrations of all of the species present in the liquid phase. To solve this system of nonlinear equations, we used the proposed procedure introduced by Smith and Missen.29

3. RESULTS AND DISCUSSIONS 3.1. Database. Accurate and consistent experimental data is a vital demand for validating any model. Unfortunately, there is some discrepancy in a number of available experimental data for the solubility of acid gases in aqueous alkanolamine solutions in published literature. A number of authors have recognized this problem and have tried to collect a consistent database. Weiland et al.30 first analyzed the consistency of the published data for the solubility of CO2 and H2S in several aqueous alkanolamine solutions. Chunxi and Fürst14 have performed self and mutual consistency tests to establish the database. The self-consistency tests were performed at specified temperatures and alknolamine solution concentrations graphically and presented the variation of acid gas partial pressure as a function of acid gas loading.14 They performed mutual consistency tests when considering very similar experimental values at the same experimental conditions by various authors.14 They also found three general variations.14 First, at very low loadings, a linear relationship between the logarithm of the partial pressure and the gas loading exists. Second, at fixed values of loading and temperature, the acid gas partial pressure increases with alkanolamine concentration. Finally, at specified loading and alkanolamine concentration, the acid gas partial pressure increases with temperature. Lemoine et al.31 followed the procedure proposed by Weiland et al.30 and performed the consistency tests for aqueous MDEA solutions. Huttenhuis et al.16 performed extensive investigations for the consistency of the database that have already been proposed by Chunxi and Fürst14 and Solbraa.32 Recently, Haghtalab and Mazloumi19 used a similar database used by Huttenhuis et al.,16 and the recent data of Haji-Sulaiman et al.,33 Park and Sandall,34 Sidi-Boumedine et al.,35 and Ma'mun et al.36 In the present work, we have used the proposed database by Haghtalab and Mazloumi19 but we have omitted the data of Haji-Sulaiman et al.33 because the reported values are not consistent with those that have been reported by Sidi-

HCO2,aqMDEA =

HCO2,water HN2O,water

× HN2O,aqMDEA

(34)

In this equation, H is the Henry’s law constant. The binary interaction parameter of MDEA−CO2 system is obtained in an indirect way by using the physical solubility data of CO2 in aqueous MDEA solution derived from the above equation and the already determined binary interaction parameters of the MDEA−H2O and CO2−H2O systems.17 Finally, it may be 9879



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Table 4. Coefficients of Equation 35 For Temperature-Dependent Binary Interaction Parameters and the AAD% Values of the Prediction of Bubble Point Pressure kij = a′T 2 + b′T + c′ + d′/T binary system

temp (K)

nP

a′

b′

c′

CO2−H2O MDEA−H2O

313−393 349−459 298−393 288−308 293−333 293 303−313

39 34 50 74

1.69 × 10−5 0

−5.97 × 10−3 1.15 × 10−3

7.44 × 10−1 −6.35 × 10−1

MDEA−CO2a

a

0

0

d′

1.98

AAD%

ref

0 0

2.1 1.58

7.38 × 101

1.87

Kiepe et al.41 Voutsas et al.42 Chang et al.40 Haimour and Sandall43 Versteeg and Swaalj44 Pawlak and Zarzycki45 Li and Mather46

The experimental data are related to MDEA−N2O system that are converted to MDEA−CO2 by eq 34.

Table 5. Optimum Binary Interaction Parameters between Ion−Ion and Ion−Molecule for the MDEA−CO2−H2O System wij = c1T + c 2 scenario I wij wMDEAH −MDEA wMDEAH+−H2O wMDEAH+−CO2 wMDEAH+−HCO3− wMDEAH+−CO3= +

scenario II

c1

c2 −7

c1 −6

2.14 × 10 −5.73 × 10−7 0 −1.3 × 10−6 0

−7.46 × 10 2.72 × 10−4 0 5.05 × 10−4 0

−6.81 × 10−4 2.67 × 10−4 4.39 × 10−5 6.93 × 10−4 −7.71 × 10−4

1.72 × 10 −5.68 × 10−7 −9.45 × 10−8 −1.93 × 10−6 −3.51 × 10−6

AAD% = 18.22

AAD% = 17.32

simply set equal to zero.19 In this work, the second approach is applied and almost the same database proposed by Huttenhuis et al.17 is used for the solubility of N2O in MDEA. Plentiful data are reported in literature for the binary system CO2−H2O; however, one should be careful to choose the data set for which the pressure and temperature are consistent with the nature of the ternary system under consideration. As discussed in our previous work,22 the reported pressures are usually more than atmospheric while in the solubility calculation it is needed that the model be able to predict the solubility of CO2 in water in low partial pressures of CO2, which happens for low values of loading. We should mention that bubble-P calculation is used for determination of the binary interaction parameters in eq 14 for all the binary subsystems. For MDEA−H2O system, two types of experimental data are available. The first type is the vapor−liquid equilibrium (VLE) experimental data at intermediate and high temperatures in terms of the mole fraction of MDEA, and the second is the freezing point depression data. Chang et al.40 used both data sets to determine the NRTL model parameters. Using the interaction energy parameters of the NRTL model allows generating the activity coefficient data of water against mole fraction of MDEA ranging from 0 to 0.2, and at temperatures ranging from 298 to 393 K. For the binary and ternary systems, pure water is used as the reference state. This range of MDEA mole fraction and temperature is suitable for application of CO2 solubility calculation in aqueous MDEA solutions. To model the solubility data for the binaries in the whole range of temperature, the following general equation for the binary interaction coefficients is obtained as a function of temperature. kij = a′T 2 + b′T + c′ + d′/T

c2 −6

binary subsystems with good accuracy. The obtained values of AAD% for the bubble point pressure of the three binary subsystems are 2.1, 1.58, and 1.87, respectively. AAD% =

1 np

np

⎛ |exp − calci| ⎞ i ⎟⎟ × 100 expi ⎝ ⎠

∑ ⎜⎜ i=1

(36)

3.4. Modeling the Ternary CO2−MDEA−H2O System. In this section, the results of modeling the solubility of CO2 in aqueous MDEA solution is presented. As described in the Introduction section, the φ−φ approach using emPR-CPA EoS is applied and the equality of fugacities and the chemical equilibrium equations are solved simultaneously. The pure components and the molecular binary interaction parameters have already been determined in the previous section using the binary subsystems data. Therefore, only the ionic interaction parameters should be optimized using the solubility data of the ternary systems. In this work, the approach proposed by Haghtalab and Mazloumi19 has been applied. The proposed algorithm is based on the reactive bubble pressure calculation that consists of two main loops. In the inner loop, the set of nonlinear chemical equilibrium equations together with both mass and charge balance equations are solved by the Smith and Missen29 method. The mole fractions of the ionic and molecular species in the liquid phase are calculated at the given temperature and CO2 loading in the inner loop, and then, the VLE calculation is carried out in the external loop. The iterative procedure continues until convergence is achieved. Outputs of the algorithm are the total bubble pressure and the mole fractions of water and CO2 in the vapor phase. As discussed in section 2.3, the presence of MDEA in the vapor phase is neglected. This procedure is used to optimize the ionic interaction parameters (wij), defined in eq 20. In order to evaluate the effect of short-range ionic forces (i.e., SR2 term in eq 8), all the wij parameters were set equal to zero

(35)

The coefficients of this equation are introduced in Table 4. As it is observed from this table, the emPR-CPA EoS describes 9880



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in the first step of calculations. The obtained AAD% of the bubble point pressure for the experimental data points, introduced in Table 3, was 51.8; which is an indication of the strong effect of SR2 contribution. Next, the ion−ion and ion− molecule parameters related to SR2 term were adjusted by using the database. There exist eight ionic and molecular species in the liquid phase as the products of the reactions described by eqs 1−4, and therefore, 64 binary interaction parameters should be adjusted. In order to reduce the number of adjustable parameters we have made some assumptions. We set self-interaction parameters equal to zero. As stated by Chunxi and Fürst,14 the solvation effect of the anion is less than that of the cation, and as a result, the interaction between anions and other species present in the liquid phase are neglected. In this way, only the interactions of the cationic species with other ionic and molecular species in the liquid phase are taken into account. In the SR2 term at least one of the i or j species is an ion, this leads to the fact that all the molecule−molecule interaction parameters can be set equal to zero. Moreover, because of the low concentration of H3O+, its interaction parameters with other species are ignored. Consequently, only five parameters remain to be adjusted: wMDEAH+−MDEA, wMDEAH+−H2O, wMDEAH+−CO2, wMDEAH+−HCO3−, and wMDEAH+−CO3=. In order to further reduce the parameters, two scenarios were considered as is indicated in Table 5. In the first scenario, only three interaction parameters, and in the second, five interaction parameters, are considered. Using all of the 370 experimental data points simultaneously, the selected binary ionic interaction parameters were fitted for both scenarios. The resulting AAD% for each scenario is reported in Table 5. As it can be seen, the resulting values of AAD% are very close; however, its value for scenario II is smaller. On the basis of the various aspects such as amine concentration, gas loading, temperature, and the works of other authors for the ternary systems, the detailed results for the two scenarios are shown in Table 6. As it can be seen, the highest deviations for both scenarios are obtained for concentration of MDEA less than 15 wt %. The lowest deviations for scenarios I and II are observed for the aqueous MDEA concentration of 32 wt %. The highest deviations are reported for both of the scenarios for the CO2 loading less than 0.01. It should be noted that the accuracy of the reported data is always questionable.14,17 The lowest deviation is observed for the CO2 loading values more than 1.0 for both scenarios. In addition, the highest deviations were found at 323.15 K for both scenarios, and the lowest deviations are at 343.15 and 353.15 K for scenarios I and II, respectively. Finally, the results presented by different authors show that the best AAD% values belong to the data of Ma’mun et al.36 and Kuranov et al.,28 a result that is also confirmed by Haghtalab and Mazloumi.19 Our experience in modeling also shows that their reported data has high accuracy and consistency. On the basis of scenario II, Figure 1 shows the effect of temperature on acid gas loading as a function of total pressure for 32.2 wt % of aqueous MDEA solution. Moreover, in Figure 2, the effect of MDEA concentration on the calculated and experimental partial pressure of CO2 for various acid gas loadings is investigated. Very good agreement between the calculated and experimental pressure is observed in both Figures 1 and 2. In Figure 3, the ratio of Pcalc/Pexp based on scenario II is plotted against CO2 loading. As can be seen in this figure, for loading values less than 0.01, the model prediction is poor.

Table 6. Calculation Results in Predicting the Bubble Pressure of MDEA−CO2−H2O Systems for the Two Scenarios Considered AAD% aqueous MDEA (wt %)

np

45 loading 1.0 temp (K) 298.15 313.15 323.15 328.15 333.15 343.15 348.15 353.15 358.15 373.15 393.15 413.15 author Lemoine et al.31 Sidi-Boumedine et al.35 Ma’mun et al.37 Austgen and Rochelle3 Kuranov et al.28 Rho et al.38 Kamps et al.5 Rogers et al.39 a

BIAS%a

scenario I scenario II scenario I scenario II

23 177 50 120

28.41 14.95 13.98 22.84

27.57 12.54f 12.95 24.17

23.89 −7.64 12.24 17.63

26.19 −5.14 11.56 20.88

22 57 246 44

37.08 23.87 16.96 10.75

28.74 23.97 16.23 10.66

20.64 9.28 2.44 9.67

27.30 12.90 4.51 9.83

32 116 35 10 16 13 57 8 9 40 21 13

14.89 16.22 31.10 4.75 8.88 4.12 22.24 4.13 3.58 24.55 28.20 11.12

14.78 16.10 28.10 2.23 7.01 2.19 21.93 1.95 2.25 23.93 27.88 6.83

10.80 8.59 −2.92 −4.07 1.16 −2.65 3.92 −2.33 3.58 5.66 12.80 1.93

10.56 8.11 21.59 0.04 4.32 0.26 4.59 −0.05 0.91 5.43 11.52 −3.52

13 86

10.83 16.68

10.85 16.21

5.94 9.54

5.11 9.37

32 14

4.16 17.08

2.22 18.29

−1.34 −8.77

0.37 −10.24

81 81 33 28

11.02 25.54 23.45 37.36

10.11 26.93 22.42 27.97

1.34 3.54 19.15 7.03

1.29 10.93 19.85 15.44

p BIAS% = 1/np∑ni=1 (expi − calci)/(expi) × 100.

Table 6 shows that the BIAS% for the acid gas loading values less than 0.01 is 27.3, while the best BIAS% is obtained for the range of loading between 0.1 and 1.0. On the basis of scenario II, the ratio of Pcalc/Pexp is presented as a function of temperature in Figure 4. The highest BIAS% is related to the temperature of 323.15 K, that means that the model underpredicts the experimental data. The minimum and maximum AAD% values are related to 353.15 and 323.15 K, respectively. The performance of the model for prediction of concentration of various ionic species in the liquid phase at different values of acid gas loading, based on scenario II, is also investigated. In Figure 5, the results of the model is compared with NMR studies,47 which are reported for 23 wt % of MDEA at 293 K. Good agreement between the experimental results and calculated values obtained by emPR-CPA EOS is evident. Finally, the emPR-CPA EOS is compared with other electrolyte EoSs based on the work of Fürst and Renon.13 Since different databases have been used by other authors, it is difficult to make exact comparisons; however, it is possible to make comparison between this work and the results obtained by Huttenhuis et al.17 and Derks et al.48 As shown in Table 7, 9881



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Figure 1. Comparison of calculated (based on scenario II) and experimental28 total pressure as a function of CO2 loading for aqueous MDEA (32.2 wt %) solution at various temperatures.

Figure 3. Ratio of calculated pressure (based on scenario II) to experimental pressure as a function of CO2 loading for the CO2− MDEA−H2O system.

Figure 2. Comparison of calculated (based on scenario II) and experimental partial pressure of CO2 in the CO2−H2O−MDEA system at various amine concentrations: (⧫) ref 28, (*) ref 37, (■) ref 5, (●) ref 5.

Figure 4. Ratio of calculated pressure (based on scenario II) to experimental pressure as a function of temperature for CO2−MDEA− H2O System.

4. CONCLUSION In the present work, a combination of the mPR-CPA22 EoS and the electrolyte part of the Fürst and Renon13 EoS plus the Born term has been applied to modeling the solubility of CO2 in aqueous MDEA solutions. The study has been performed in wide ranges of temperature, pressure, acid gas loading, and MDEA concentration. For the associative components (i.e., MDEA and H2O), the parameters of the mPR-CPA EoS have been adjusted which has resulted to the prediction of the pure component properties with high accuracy. In the next step, the binary interaction parameters were correlated for CO2−H2O, MDEA−H2O, and MDEA−CO2 binary subsystems with AAD% values equal to 2.1, 1.58, and 1.87, respectively, for the prediction of bubble point pressure of binary solutions. Then, the ionic interaction parameters were correlated by the reactive bubble point calculation procedure

the main differences between the databases are the following: the reported data of Sidi-Boumedine et al.35 and Ma'mun et al.37 are used in this work, while the reported data by Huang and Ng49 is used by the other authors. Despite the database, the better AAD% is obtained by emPR-CPA EoS in comparison with those of Huttenhuis et al.17 and Derks et al.48 The employed electrolyte EoS used by Huttenhuis et al.17 and Derks et al.48 are very similar, but Huttenhuis et al.17 have used the Born term, which may be responsible for lower AAD%. Considering our results, we may conclude that, addition of the association contribution to the EoS is responsible for the improved accuracy of the model about 6.7% compared with the work of Huttenhuis et al.17 9882



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Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS Financial support from the Research Institute of Petroleum Industry (RIPI) is greatly appreciated.

Figure 5. Comparison of the calculated mole fractions of different species (based on scenario II) with those obtained by NMR study for CO2 solubility in 23 wt % aqueous MDEA at 293 K.47

Table 7. Comparison of the Results of Bubble Point Pressure Obtained in This Work (Based on Scenario II) and Those Obtained by Huttenhuis et al.17 and Derks et al.48 for CO2− MDEA−H2O System For the Data Produced By Different Authors Huttenhuis et al.17

Derks et al.48

author

np

AAD%

np

Lemoine et al.31 Sidi-Boumedine et al.35 Ma’mun et al.37 Austgen and Rochelle3 Kuranov et al.28 Rho et al.38 Kamps et al.5 Rogers et al.39 Huang and Ng49 overall

13

17

13

14 78 65 14 34 65 283

28 20 19 25 43 27 24

14 81 58 28 34 66 294

AAD% 28

24.4 17.8 23.7 30.6 38.7 33.2 26.8

this work (scenario II) np

AAD%

13 86 32 16 81 81 33 28

10.9 16.2 2.2 18.3 10.1 26.9 22.4 28.0

370

17.3

Greek Letters

εAB = association energy of interaction between sites A and B θ = parameter in the association term of CPA EoS ξ3 = parameter defined in eq 21 η = packing fraction γ = activity coefficient φ = fugacity coefficient α = parameter of eq 10 β = parameter of eq 11 α′i = parameters of eq 12, i = 1 ... 3 βi′ = parameters of eq 13, i = 1 ... 3 ΔAB = strength of interaction between sites A and B Γ = shielding parameter (m−1) δi = ionic/molecular diameter (m) ρ = molar density (mol m−3) ε0 = vacuum electric permittivity (C2 J−1 m−1) αLR = long-range parameter in ionic interaction term (m) κ = Boltzmann’s constant (1.38066 × 10−23) (J K−1)

for 370 experimental data points. Two scenarios were considered for correlating the ionic binary interaction parameters. The first scenario considers three binary ionic interaction parameters, while the second considers five. The results show that the second scenario is more accurate with AAD% = 17.32. The accuracy of prediction of the emPR-CPA EoS for the calculation of concentration of the species in the liquid phase has been compared with NMR study results from literature. Very good agreement is observed. Finally, the comparison results of the present work with similar eEoS models proved that the contribution of association term improves the accuracy of prediction of the model in wide ranges of temperature, pressure, acid gas loading, and amine concentration.

■

NOMENCLATURE Ar = molar residual Helmholtz free energy (J mol−1) a = attraction parameter of mPR-EoS (J m3 mol−1) a′ = coefficient of temperature dependent kij in eq 35 AAD% = average absolute percent deviation BIAS% = mean BIAS percent deviation b = covolume parameter of mPR-EoS (m3 mol−1) b′ = coefficient of temperature dependent kij in eq 35 C(i) = coefficient in eq 5, i = 1 ... 3 c′ = coefficient of temperature dependent kij in eq 35 c1 = coefficient of temperature dependent wij in Table 5 c2 = coefficient of temperature dependent wij in Table 5 D = dielectric constant of solution Ds = dielectric constant of solvents Dm = molecular pure component dielectric constant d(i) = coefficients in eq 27 d′ = coefficient of temperature dependent kij in eq 35 e = electronic charge (1.60219 × 10−19) (C) g(ρ) = radial distribution function Kx = equilibrium constant in mole fraction scale kij = binary interaction parameter between species i and j LCO2 = CO2 loading (moles of acid gas per mole of amine) Mj = number of associating sites per molecule j n = the number of moles np = number of data points NA = Avogadro’s number (6.02205 × 1023) (mol−1) P = pressure (kPa) R = gas constant (8.314 J mol−1 K−1) T = temperature (K) v = molar volume (m3 mol−1) xi = mole fraction of component i zi = charge number of ionic species i

Subscripts

AUTHOR INFORMATION

c = critical property i = component i j = component j m = molecular component

Corresponding Author

*Tel.: +98 21 77240496. Fax: +98 21 77240495. E-mail address: [email protected]. 9883



Article

(15) Derks, P. W. J.; Dijkstra, H. B. S.; Hogendoorn, J. A.; Versteeg, G. F. Solubility of Carbon Dioxide in Aqueous Piperazine Solutions. AIChE J. 2005, 51 (8), 2311. (16) Huttenhuis, P. J. G.; Agrawal, N. J.; Hogendoorn, J. A.; Versteeg, G. F. Gas Solubility of H2S and CO2 in Aqueous Solutions of Nmethyldiethanolamine. J. Pet. Sci. Eng. 2007, 55 (1−2), 122. (17) Huttenhuis, P. J. G.; Agrawal, N. J.; Solbraa, E.; Versteeg, G. F. The Solubility of Carbon Dioxide in Aqueous N-methyldiethanolamine Solutions. Fluid Phase Equilib. 2008, 264 (1−2), 99. (18) Huttenhuis, P. J. G.; Agrawal, N. J.; Versteeg, G. F. Solubility of Carbon Dioxide and Hydrogen Sulfide in Aqueous N-Methyldiethanolamine Solutions. Ind. Eng. Chem. Res. 2009, 48 (8), 4051. (19) Haghtalab, A.; Mazloumi, S. H. Electrolyte Cubic Square-Well Equation of State for Computation of the Solubility CO2 and H2S in Aqueous MDEA Solutions. Ind. Eng. Chem. Res. 2010, 49 (13), 6221. (20) Nasrifar, K.; Tafazzol, A. H. Vapor-Liquid Equilibria of Acid Gas Aqueous Ethanolamine Solutions Using the PC-SAFT Equation of State. Ind. Eng. Chem. Res. 2010, 49 (16), 7620. (21) Kontogeorgis, G. M.; Voutsas, E. C.; Yakoumis, I. V.; Tassios, D. P. An Equation of State for Associating Fluids. Ind. Eng. Chem. Res. 1996, 35 (11), 4310. (22) Zoghi, A. T.; Feyzi, F.; Zarrinpashneh, S.; Alavi, F. Solubility of Light Reservoir Gasses in Water by the Modified Peng-Robinson Plus Association Equation of State Using Experimental Critical Properties for Pure Water. J. Pet. Sci. Eng. 2011, 78 (1), 109. (23) Feyzi, F.; Riazi, M. R.; Shaban, H. I.; Ghotbi, S. Improving Cubic Equations of State For Heavy Reservoir Fluids and Critical Region. Chem. Eng. Commun. 1998, 167, 147. (24) Avlund, A. S.; Kontogeorgis, G. M.; Michelsen, M. L. Modeling Systems Containing Alkanolamines with the CPA Equation of State. Ind. Eng. Chem. Res. 2008, 47 (19), 7441. (25) Wertheim, M. S. Fluids with Highly Directional Attractive Forces. III. Multiple Attraction Sites. J. Stat. Phys. 1986, 42 (3), 459. (26) Smith, J. M.; Van Ness, H. C. Introduction of Chemical Engineering Thermodynamic, 5th ed.; McGRAW-HILL: New York, 2005. (27) Born, M. Volumen und Hydrationswarme der Ionen. Z. Phys. 1920, 1, 45. (28) Kuranov, G.; Rumpf, B.; Smirnova, N. A.; Maurer, G. Solubility of Single Gases Carbon Dioxide and Hydrogen Sulfide in Aqueous Solutions of N-Methyldiethanolamine in the Temperature Range 313−413 K at Pressures up to 5 MPa. Ind. Eng. Chem. Res. 1996, 35 (6), 1959. (29) Smith, W. R.; Missen, R. W. Strategies for Solving the Chemical Equilibrium Problem and an Efficient Microcomputer-Based Algorithm. Can. J. Chem. Eng. 1988, 66, 591. (30) Weiland, R. H.; Chakravarty, T.; Mather, A. E. Solubility of Carbon Dioxide and Hydrogen Sulfide in Aqueous Alkanolamines. Ind. Eng. Chem. Res. 1993, 32 (7), 1419. (31) Lemoine, B.; Li, Y.-G.; Cadours, R.; Bouallou, C.; Richon, D. Partial Vapor Pressure of CO2 and H2S Over Aqueous Methyldiethanolamine Solutions. Fluid Phase Equilib. 2000, 172 (2), 261. (32) Solbraa, E. Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing. Ph.D. Thesis, Norwegian University of Science and Technology, 2002. (33) Haji-Sulaiman, M. Z.; Aroua, M. K.; Benamor, A. Analysis of Equilibrium Data of CO2 in Aqueous Solutions of Diethanolamine (DEA), Methyldiethanolamine (MDEA) and Their Mixtures Using the Modified Kent Eisenberg Model. Chem. Eng. Res. Des. 1998, 76 (8), 961. (34) Park, M. K.; Sandall, O. C. Solubility of Carbon Dioxide and Nitrous Oxide in 50 mass Methyldiethanolamine. J. Chem. Eng. Data 2000, 46 (1), 166. (35) Sidi-Boumedine, R.; Horstmann, S.; Fischer, K.; Provost, E.; Furst, W.; Gmehling, J. Experimental Determination of Carbon Dioxide Solubility Data in Aqueous Alkanolamine Solutions. Fluid Phase Equilib. 2004, 218 (1), 85. (36) Ma’mun, S.; Nilsen, R.; Svendsen, H. F.; Juliussen, O. Solubility of Carbon Dioxide in 30 mass % Monoethanolamine and 50 mass %

r = residual s = saturated t = total Born = Born in eq 8 LR = long-range in eq 8 RF = repulsive force in eq 8 SR1 = nonelectrolyte short-range in eq 8 SR2 = ionic short-range in eq 8 Superscripts

l = liquid r = residual s = saturated v = vapor

■

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Modeling CO2 Solubility in Aqueous N-methyldiethanolamine Solution

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