Modeling the Fluid Phase Behavior of Carbon Dioxide in

Ind. Eng. Chem. Res. 2010, 49, 1883–1899

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Modeling the Fluid Phase Behavior of Carbon Dioxide in Aqueous Solutions of Monoethanolamine Using Transferable Parameters with the SAFT-VR Approach N. Mac Dowell, F. Llovell, C. S. Adjiman, G. Jackson, and A. Galindo* Department of Chemical Engineering and Centre for Process Systems Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, U.K.

The current method of choice for large-scale carbon dioxide (CO2) capture is amine-based chemisorption, typically in packed columns, with the benchmark solvent being aqueous solutions of a primary alkanolamine: monoethanolamine (MEA). In this contribution, we use the statistical associating fluid theory for potentials of variable range (SAFT-VR) to describe the fluid phase behavior of MEA + H2O + CO2 mixtures. The physical chemistry of CO2 in aqueous solutions of amines is highly complex owing to the chemical equilibria between the various species that are formed in solution at ambient conditions. We explicitly consider the multifunctional nature of MEA and, in so doing, are able to represent accurately the thermodynamic properties and phase equilibria of this highly nonideal mixture over a wide range of temperatures, pressures, and compositions. MEA is modeled as an associating chain molecule formed from homonuclear spherical segments with six distinct association sites incorporated to mediate the asymmetric hydrogen bonding interactions exhibited by this molecule. The models for H2O and CO2 are taken from previous work. In order to describe the chemisorption, which is the key to the CO2 capture process, two additional effective sites are incorporated on the otherwise nonassociating CO2 molecule to describe the chemical interaction between the MEA and CO2, so that the correct maximal stoichiometry of two amine molecules per CO2 molecule is retained. The vapor-liquid phase equilibria of the various binary mixtures and of the MEA + H2O + CO2 ternary mixture are accurately described with our approach, including the degree of absorption of CO2 in the solvent for wide ranges of temperature and pressure. This suggests that the underlying complexity of the chemical equilibria associated with this system are correctly captured by the model and provides great promise for the modeling of the overall process of CO2 capture. I. Introduction Alkanolamines have a long history of industrial use, where they have been deployed in aqueous solution for carbon dioxide (CO2) capture in the context of natural gas “sweetening” and for applications in enhanced oil recovery.1,2 The first patent for the use of alkanolamines as absorbents for acidic gases was granted in 1930.3 Due to their technological maturity, aminebased processes represent a low-risk technology and, as a consequence, a promising near-term option for large-scale CO2 capture. In addition, the flexibility of operation and ease of retrofitting these processes reduces the economic risk of stranded assets. It is therefore expected that amine chemisorption will be employed on a large scale in the near future for the purpose of capturing CO2 from power plant flue gases. The addition of CO2 capture processes to power plants, both as a retrofit or as new-build plants, results in a large energy penalty, an associated reduction in plant efficiency, and a rise in the cost of electricity, which has a negative impact on the economic viability of the power plant. There is hence great interest, both industrial and academic, in finding alternative solvents to capture CO2 in order to improve the viability of such processes. Currently, monoethanolamine (MEA) is considered to be the benchmark solvent, to which alternative solvents are to be compared.2 In this context, predictive models for the phase behavior and thermophysical properties of aqueous mixtures of MEA in particular, and of alkanolamines in general, with CO2 are of great topical interest. Here, we describe the use of the statistical associating fluid theory for potentials of variable range (SAFT-VR)4-7 to * To whom correspondence should be addressed. E-mail: [email protected].

calculate the thermodynamic properties and fluid phase equilibria of CO2 in aqueous MEA as it has previously been shown to model complex associating and reactive mixtures successfully for a wide range of conditions, particularly when hydrogen bonding and other types of chemical association are involved. Accurate models for water8 and carbon dioxide9,10 are already available for use within the SAFT-VR framework. In this work, we develop detailed molecular models that take into account the key interactions in these mixtures, including those due to the different hydrogen bonding groups of MEA (hydroxyl and amine), which are treated separately. The reactive nature of the MEA + CO2 + H2O system is well-known, and there is a large body of experimental and theoretical work in place detailing the mechanism and rates of these reactions (see, for example, refs 11-16 and references therein for details). Only a short summary of the relevant reactions is provided here. In addition to the ionic speciation equilibria due to the association of CO2 and MEA in aqueous solution, the principal reaction of interest between CO2 and a primary amine (in aqueous media) is the formation of carbamate, which is typically considered to occur via the formation of a zwitterion, as Zwitterion formation CO2+RNH2 h RNH2+CO2-

(1)

and subsequent base (amine in this case) catalyzed deprotonation of the zwitterion such that Base catalysis RNH2+CO2- + RNH2 h RNHCO2- + RNH3+

(2) 14,15

In combination, these two reactions can be represented as

10.1021/ie901014t  2010 American Chemical Society Published on Web 12/21/2009

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Carbamate formation CO2 + 2RNH2 h [RNHCO2- + RNH3+]

(3)

where, in the case of MEA, R ) HO-CH2-CH2- and it can be seen that the overall stoichiometry of the reaction is such that each molecule of CO2 is eventually associated with two of MEA; the carbamate and protonated amine can be considered as a fairly tightly bound ion pair (denoted by the square brackets) particularly at higher temperatures. Other reactions that contribute to the overall reaction rate are those related to the reversion of carbamate to bicarbonate via a hydrolysis reaction, Carbamate reversion RNHCO2- + H2O h RNH2 + HCO3-

(4)

Bicarbonate formation CO2 + OH- h HCO3-

(5)

and carbonic acid, Carbonic acid formation CO2 + H2O h HCO3- + H+

(6)

The formation of carbonic acid from CO2 and H2O by reaction 6 is very slow in comparison to reactions 3-5 and is therefore considered to have a negligible contribution to the overall reaction rate,16 while the reversion of carbamate to bicarbonate by reaction 4 is considered to be more important only at higher concentrations of CO2 in the liquid phase. There have been numerous efforts to model the thermophysical properties and phase behavior of CO2 in MEA and H2O. Given the chemical equilibria involved, the system is most commonly treated as a weak electrolyte solution. Early treatments were based on empirical approaches involving the determination of the equilibrium constants for the various reactions (see the work of Austgen et al.17 and references therein). In the late 1980s, Austgen et al.17 presented one of the first thermodynamically consistent models by using the electrolyte nonrandom two liquid (eNRTL) model of Chen et al.18,19 (a modification of the NRTL model of Renon and Prausnitz20) for the activity coefficients of the various ionic species at equilibrium in the liquid phase and the SoaveRedlich-Kwong (SRK) equation21 for the fugacities of the vapor phase. The eNRTL approach has at its heart the quasichemical theory of Guggenheim22-25 corresponding to a lattice model of the liquid phase. The excess Gibbs energy is considered to be a sum of the contributions to the free energy of the short- and the long-range interactions. The long-range ion-ion contribution is treated using Pitzer’s26 reformulation of the Debye-Hu¨ckel expression; in order to account for the excess contribution of the transfer of charged species into the solvent, the Born expression27 is used. The short-range interactions (local composition contribution) are simply accounted for with the standard NRTL equation.20 Very recently, Faramarzi et al.28 have presented a study where the extended UNIQUAC model of Thomsen and coworkers29,30 is used to represent the absorption of CO2 in aqueous solutions of alkanolamines. The extended treatment uses the original UNIQUAC model of Abrams and Prausnitz31 and of Maurer and Prausnitz32 with the incorporation of the Debye-Hu¨ckel term to account for the contribution of the electrostatic interactions to the Gibbs free energy. The thermodynamic model of Faramarzi et al. uses the extended UNIQUAC approach to calculate liquid phase activity coefficients and the Soave-Redlich-Kwong21 model to calculate vapor phase fugacities. Using this framework, Faramarzi et al. provide a

detailed treatment of the speciation equilibria and the phase equilibria exhibited by this system. A total of thirteen adjustable interaction parameters (eleven of which are temperature dependent) are used to describe the thermophysical properties of these mixtures. Faramarzi et al. also present an accurate representation of the phase behavior of the CO2 + MEA + H2O mixture for temperatures relevant to typical operating conditions for alkanolamine-based CO2 capture processes. The % AAD is of the order of 1-2% in terms of absolute system pressure. While successful for the treatment of liquid phases, an important limitation of lattice-based (activity coefficient) approaches such as NRTL in describing fluid phase equilibria is that they are not suitable for the gas phase, and as a consequence, a different model is required. The properties of the vapor phase (the fugacity coefficients or chemical potentials, and the pressure) are usually calculated with cubic equations of state.17,19 More importantly, in chemical approaches of this type, it is necessary to assume a priori the reaction equilibria of the system, so that empirical expressions for the chemical equilibrium constants need to be proposed based on relevant experimental data.17,19,33 This can prove highly impractical and cumbersome in the case of complex equilibria and is only strictly appropriate for conditions where experimental data are available. In a departure from such an approach, Gabrielsen et al.34 have proposed a simplified method, concentrating only on carbamate formation, reaction 3, instead of treating in detail the chemical and phase equilibria. They combine Henry’s law for the solubility of CO2 in the solvent and the chemical reaction equilibrium for the formation of the carbamate into one empirical constant, and obtain an explicit expression for the partial pressure of CO2 over aqueous solutions containing MEA, diethanolamine (DEA), or n-methyldiethanolamine (MDEA). Using four parameters regressed to experimental data, they are able to correlate accurately the partial pressure of CO2 in the solutions of interest, albeit over a relatively limited range of temperatures, pressures, and compositions. More recently, equations of state that can take into account chemical equilibria in the liquid phase and are also appropriate for the vapor phase have been used to model this type of reacting system. Furst and co-workers35,36 have employed the electrolyte equation of state of Furst and Renon37 to study the absorption of CO2 and H2S in aqueous DEA and MDEA. Of direct relevance to our approach is the work of Button and Gubbins38 who have used the statistical associating fluid theory (SAFT)39,40 to model the vapor-liquid equilibria of mixtures of CO2 + MEA + H2O. The SAFT approach is based on the thermodynamic perturbation theory (TPT) of Wertheim41-44 where the free energy of an associating (or reacting) fluid is obtained from an intermolecular potential model that incorporates a number of associating (or reacting) sites that mediate the formation of aggregates (or complexes); a key advantage of this type of “physical” treatment is that the nature of the chemical equilibria present in a system does not need to be specified a priori. Furthermore, the SAFT approach takes the form of an equation of state and can be used to treat the liquid and vapor phases on an equal footing. Button and Gubbins38 used the original SAFT expressions, describing the molecules as chains of bonded Lennard-Jones segments with the dispersion term obtained from a correlation of the appropriate simulation data.45 Water is treated in the usual SAFT manner with a four-site model, and in order to account for the strong quadrupole moment of CO2, they also proposed a model with four association sites for CO2. MEA is modeled with five identical association sites corresponding to the -OH

Ind. Eng. Chem. Res., Vol. 49, No. 4, 2010

and -NH2 groups. Despite explicitly recognizing the multifunctional nature of the alkanolamines, they do not include this feature (the asymmetry of the association of MEA) in their model. They model the MEA + H2O mixture using a single adjustable binary interaction parameter to describe the unlike dispersion interactions, and describe the unlike association interactions by assuming the cross-association parameters to be the geometric mean of the association parameters for each of the pure components. The deviation between experimental and calculated mole fractions at given temperatures and pressures is calculated. They correlate the phase behavior of MEA + H2O with an average absolute deviation in the liquid phase mole fraction of 0.02. They propose a fully predictive model and treat the ternary mixture assuming that the unlike hydrogen bonding interactions can be described as the geometric mean of the purecomponent values (a Berthelot-like treatment). Comparisons of the experimental and predicted values are presented for CO2 loading (xCO2/xMEA) at a CO2 partial pressure of 2.2 MPa in a temperature range of 353-413 K. The CO2 loading (vapor-liquid equilibria) is found to be very sensitive to small errors in the predicted mole fractions; overall, this leads to a relatively large average error of 62% in the pressure or composition for the MEA mixtures. Avlund et al.46 have also taken advantage of the capability of treating reacting systems with the association theory of Wertheim. They have applied the cubic-plus-association (CPA) approach to study the phase behavior of MEA, DEA and MDEA, and their mixtures in water. The CPA equation combines the cubic SRK equation of state21 with the contribution to the free energy (and pressure) due to the formation of associated species or aggregates as described by the theory of Wertheim (and used in SAFT approaches). They follow the general association schemes proposed by Huang and Radosz47 to model MEA; they model MEA with a symmetric four-site association scheme originally proposed for H2O, as opposed to one of the asymmetric schemes more suitable for primary amines or alkanols. The MEA + H2O mixture is modeled using a geometric mean for the unlike association strength (in terms of the like association energies of each molecule) and a rule suggested by Folas et al.48 for the unlike mean-field attractive interaction parameters. Avlund et al. present results for the MEA + H2O mixture comparing the suitability of these two combining rules; they use a single temperature independent binary parameter (termed kij) to minimize the error between experimental and calculated values of pressure and vapor phase composition. The accuracy of their results varies considerably with the choice of the association scheme. However, without fitting kij to experimental data, the description is quite poor, regardless of the combining rule used: the % AAD in pressure ranges between 41% and 143%. On adjusting the binary interaction parameter, a much greater accuracy is achieved with a range of 5%-10% in the bubble point pressure. More impressively, they present results for the calculation of bubble point temperatures and of vapor-phase compositions for the MEA + H2O mixture which are on the order of 0.5% and 0.02-0.08 in temperature and vapor-phase composition, respectively. In the study of Avlund et al.,46 as in the work of Button and Gubbins,38 the multifunctional nature of the alkanolamines is recognized, but not taken into account explicitly (a decision made, most likely, in favor of reducing the complexity of the model). The goal of our current work is to develop a model for studies of the phase behavior of CO2 + MEA + H2O mixtures, explicitly addressing the multifunctional nature of the interactions of MEA. We use the SAFT-VR4,5 approach, following

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from the idea of treating the reactions involved in solutions of CO2 in water and MEA through association schemes mediated via short-ranged associating sites. Although the SAFT-VR approach has been extended to describe electrolyte solutions,49,50 in this work we do not consider ionic speciation explicitly as it adds an extra level of complexity we do not consider necessary at this point; we discuss this issue more thoroughly in a later section when details of the models are given. Here, we present a model of MEA that explicitly considers that the hydroxylhydroxyl interaction, the amine-amine interaction, the hydroxyl electron lone-pair-amine hydrogen, and the hydroxyl hydrogen-amine electron lone-pair interactions all have different hydrogen bond energies. Inevitably, this increases the number of intermolecular parameters required to model the multifunctional nature of MEA, but one can exploit the molecular nature of the theory to reduce the number of parameters that have to be determined by transferring parameters from other molecules with the same functional groups: SAFT-VR models of ethanol and ethylamine. In this way, we present a general methodology for the development of accurate, predictive models of complex, multifunctional, associating molecules, and their mixtures with other associating fluids. Our long-term goal is to integrate the thermodynamic description developed and tested in this work within a process design environment in search of better processes and solvents for CO2 capture. II. Theory, Models, and Methodology A. The SAFT-VR Equation of State. The Helmholtz free energy A of a model mixture of associating chain molecules can be written in the usual SAFT form as4,5,39,40,51 A AMONO ACHAIN AASSOC AIDEAL + + + ) NkT NkT NkT NkT NkT

(7)

where N is the number of molecules, k the Boltzmann constant, and T the absolute temperature. The term AIDEAL corresponds to the ideal free energy of the mixture, and AMONO, ACHAIN, and AASSOC are residual contributions to the free energy due to monomer-monomer repulsive and attractive (dispersion) interactions, to the formation of chains, and to site-site intermolecular association, respectively. The free energy of an ideal gas mixture is given by52 AIDEAL ) NkT

n

∑ x ln(F Λ i

i

)-1

3 i

(8)

i)1

where xi ) Ni/N is the mole fraction, Fi ) Ni/V is the number density, and Λi is the thermal de Broglie wavelength of species i, which contains all of the kinetic (translational, rotational, and vibrational) contributions to the partition function of the molecule. The precise form of the function can be obtained from experimental ideal heat capacity data. In the SAFT-VR4,5 approach, the monomer contribution is obtained from a Barker-Henderson53-56 high-temperature perturbation expansion up to second order, i.e., A1 A2 AMONO AHS + + ) NkT NkT NkT NkT

(9)

The free energy of the reference hard-sphere mixture is obtained from the expressions of Boublı´k57 and Mansoori et al.,58 A1 is the mean-attractive energy, and the second-order term A2 describes the fluctuation of the attractive energy.59 For further details of the approach and of the specific expressions used, the reader is directed to the original papers.4,5

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The chain contribution to the free energy due to the formation of a chain of mi monomers is given by4,40,51 n

ACHAIN )xi(mi - 1) ln gSW ii (σii) NkT i)1

∑

(10)

where gSW ii (σii) is the contact radial distribution function of the monomer square-well (SW) fluid. In the SAFT-VR approach, an expression for this function is obtained through a selfconsistent method using the pressure from the Clausius virial theorem and the volume derivative of the monomer free energy (which corresponds to the pressure of the monomers). The contribution due to association for s sites on the molecules is obtained, as in other SAFT approaches, from the theory of Wertheim.41-44 It can be written as60 ASSOC

A ) NkT

∑ x ∑ [( si

n

i

i)1

a)1

) ]

Xai si ln Xai + 2 2

(11)

where the first sum is over the species i, and the second is over all si sites of type a on a molecule of species i. Xai is the fraction of molecules of species i not bonded at sites of type a, which can be obtained from a solution of the following mass-action equation: 1

Xa,i )

n

1+

(12)

s

∑ ∑ Fx X

j bj∆ab,ij

j)1 b)1

In the case of square-well association sites, the specific site-site functions can be approximated by4,60 ∆ab,ij ) Kab,ij fab,ij gSW ij (σij)

(13)

so that ∆ab,ij is characterized by the contact value gSW ij (σij) of the radial distribution function of the monomer fluid, the Mayer f function of the site-site association, and the site-site bonding volume Kab,ij. Though the degree of hydrogen bonding in the system is fully characterized by the strength of the sitesite interaction and the overall bonding volume, it is often more convenient and physically intuitive to describe the volume accessible to bonding in terms of the square-well range (cutoff parameter) r*c,ab,ij ) rc,ab,ij/σij and the distance r *d ) rd/σij ) 0.25 from the center of the segment, σij being the interaction diameter of the i and j segments. The other thermodynamical properties can be obtained from the Helmholtz free energy using the standard relationships: the pressure is obtained from the partial derivative with respect to the volume P ) -(∂A/∂V)N,T and the chemical potential from the partial derivative with the number of particles µi ) (∂A/ ∂Ni)T,V,Nj*i. The fluid phase equilibria between coexisting phases I and II require that the temperature, pressure, and chemical potential of each component in each phase are equal, i.e., T I ) T II, PI ) PII, and µIi ) µIIi ∀ i. These conditions for phase equilibria are solved numerically with Maxwell’s equal area construction using a steepest-descent method61 in the case of pure-component phase equilibria, and with the numerical solvers available in the gPROMS software package62 in the case of the binary and ternary mixtures. We also present predictions of the heat of vaporization (the enthalpy is easily obtained from the Helmholtz free energy following H ) A - (∂A/∂V)T,NV (∂A/∂T)V,NT) and the vapor-liquid surface tension, which is obtained from the partial derivative with respect to the surface area using a density functional treatment.63-65 B. Molecular Models. In this work, a molecule i is modeled as a homonuclear chain of mi bonded square-well segments of hardcore diameter σii. The square-well interactions are further character-

ized by a well depth εii and a range λii. In addition, a number of off-center, square-well association sites are used to mediate the association interactions. The sites are placed at a distance r *d ) 0.25 from the center of a segment, and the cutoff range between a site a on a segment i and a site b on a segment j is denoted by r *c,ab,ij ) rc,ab,ij/σij. These two parameters define the volume Kab,ij available for site-site bonding.60 The relationship between the reduced position and reduced cutoff value of the site-site interaction and the bonding volume Kab,ij is given by60 *3 *2 *3 Kab,ij ) 4πσij3[ln(r *c + 2r *)(6r d c + 18r c r * d - 24r d ) + *2 (r *c + 2r *d - 1)(22r *2 d - 5r *r c * d - 7r * d - 8r c +

r*c + 1)]/(72r *2 d ) (14) When two sites are within a distance of rcab,ij, they interact with HB . The sites are commonly labeled as e or H, a well depth εab,ij representing either an electronegative atom (or its lone pairs of electrons) or the hydrogen atoms in a molecule, respectively; only e-H bonding is allowed. In all of the models considered in this paper, one e site is allocated for each electron lone pair and one H site for each hydrogen atom. Following this general scheme, MEA (HO-CH2CH2-NH2) is modeled using two tangentially bonded spherical segments (mMEA ) 2). Association interactions are mediated via six association sites, three to treat the -OH group and three for the -NH2 group. In the -OH group, two of the sites are of type e and one is of type H, and in the -NH2 group, one site is of type e* and two are of type H*. We propose two models for MEA. One in which the e and e* and H and H* sites are identical, and as a result, only one type of interaction occurs (i.e., the e-H, e*-H*, e*-H, and e-H* hydrogen bonding is equivalent). We refer to this model as “symmetric”. In other words, we do not explicitly consider the difference between the hydroxyl and the amine functional groups. In a second more sophisticated model, each type of site-site interaction is considered to be different, acknowledging the fact that the OH-OH, NH2-NH2, and NH2-OH interactions are different. Hence, the e-H, e*-H*, e-H*, and e*-H interactions are all considered separately. We refer to this model as “asymmetric”. Intramolecular hydrogen bonding between the hydroxyl and amine groups of the same MEA molecule is also possible on geometric grounds. This type of association into ringlike structures66-68 (and even double bonding69) can be taken into account with a more complex Wertheim-like treatment. There is, however, experimental evidence from a comparison of the boiling points of MEA and related compounds that intermolecular association is the dominant feature for MEA,70 and we, therefore, do not include bonding between groups on the same molecule in our description. For water, the model developed in previous work8 is adopted. The molecule is modeled as a single spherical segment (mH2O ) 1) with four association sites: two sites of type e corresponding to the lone pairs of electrons, and two of type H corresponding to the hydrogen atoms (only e-H bonding is allowed). Four-site models for water have been used previously by a number of authors (see the work of Clark et al.8 and Nezbeda71 and references therein for details); it is seen as the most physically intuitive, as it preserves the tetrahedral character of the molecular geometry. The shape anisotropy of carbon dioxide is modeled by representing the molecule by two spherical segments (mCO2 ) 2) following previous work.9,10 Pure CO2 is treated as nonassociating, but in order to take into account the formation of carbamate in the reaction with MEA (cf. reaction 3), two association sites are incorporated which only interact with the amine group of MEA.

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These sites are both labeled R in order to designate them as “acceptor” sites, in keeping with the nature of the amine-CO2 reaction. In this way, we explicitly consider the interaction of the amine electron lone-pair with the electron-depleted carbon in CO2 by permitting e*-R interactions. We do not permit R-R interactions since CO2 does not self-associate. In the case where the symmetric model of MEA is considered, the acceptor sites of CO2 interact with all electron donating sites (e and e*) of MEA. At this point, it is also important to reiterate, that though the SAFT-VR approach has been extended to describe electrolyte systems,49,50 we do not consider ionic speciation explicitly in our current study as this would add to the complexity of the treatment. Instead, we assume that the reactions involve an association of the various species as aggregates with no net overall charge. In such an assumption, one is essentially treating the ionic RNHCO2- and RNH3+ species of the carbamate (reaction 3) as a bound ion pair. The dielectric constant of MEA in aqueous solution is expected to be somewhere between the values of the pure components (40 and 80) at ambient conditions and is expected to drop below 20 at the higher temperatures; the lower values of the dielectric would certainly be consistent with conditions where one would expect ion pairing. There is also evidence that ionic speciation is less prominent in MEA than would be expected from its polarity,70 which would support the validity of a simplified neutral model of the type we employ. In order to model the mixtures, a number of unlike intermolecular potential parameters also need to be specified. The arithmetic mean is used to obtain size-related intermolecular parameters, so that the unlike contact diameter between two molecules i and j is given by σij )

σii + σjj 2

(15)

the unlike square-well range by λij )

λiiσii + λjjσjj σii + σjj

(16)

and the unlike bonding volume by Kab,ij )

[

Kab,ii1/3 + Kab,jj1/3 2

]

3

(17)

These parameters are not readjusted at any point. The unlike dispersion and hydrogen bonding energetic parameters are defined in terms of the geometric mean of the like interactions and a correction factor, so that the unlike dispersion energy between two components i and j is given by εij ) (1 - kij)√εiiεjj

(18)

and the unlike hydrogen bonding energy between two sites a and b is given by HB HB HB εHB ab,ij ) (1 - kab,ij)√εab,iiεab,jj HB kab,ij

(19)

The adjustable parameters kij and are determined by comparison to mixture experimental data (cf. section II.C). As in previous work,72-74 no association between CO2 and H2O is considered. A single adjustable parameter, kij, is used to capture the fluid phase behavior of the mixture. In the MEA + H2O mixture, we consider both unlike dispersion and unlike association HB have to be interactions; hence values for both kij and kab,ij determined. As we will show later in the case of the asymmetric model of MEA, it is possible to treat the MEA + H2O hydrogen bonding interactions in a transferrable manner from separate studies of aqueous solutions of ethanol and of ethylamine. In order to model the mixture of CO2 + MEA, both the unlike dispersion

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interactions (via the parameter kij) and the unlike association energy used to represent the reaction leading to the formation of carbamate need to be determined. There are, to our knowledge, no experimental fluid phase equilibrium data for this binary system. Instead, we use ternary data for CO2 in aqueous solutions of MEA. A discussion of the values of the parameters and the techniques used to determine them is given in section II.C. C. Parameter Estimation. Appropriate values for the SAFTVR intermolecular model parameters are determined by fitting the theoretical calculations to experimental phase equilibrium data. As is common practice, experimental vapor pressure PV and saturated liquid density Fl data are used in the determination of pure component parameters. The task involves a minimization of a relative least-squares objective function consisting of the appropriate sum of individual residuals: min FObj θ

NP

∑

1 ) NP

i)1

[

exp calc PV,i (Ti) - PV,i (Ti ;θ) exp PV,i (Ti)

1 NF

NF

∑ j)1

[

]

2

+

calc Fexp l,j (Tj) - Fl,j (Tj ;θ)

Fexp l,j (Tj)

]

2

(20)

HB where θ is the vector of parameters θ ) (m, σii, λii, εii, εab,ii , Kab,ii), and NP and NF are the number of pressure and density data points, respectively. The superscripts exp and calc refer to experimental data points and calculated values. Equal weight is given to every data point in this objective function. We use temperatures from the triple point to 90% of the critical point Tc, i.e., T/Tc ) 0.9. The upper cutoff in temperature is chosen to avoid including critical and near-critical data in the estimation, as this region is known to be poorly represented with meanfield equations of state such as SAFT. Methods that account for critical fluctuations, such as the SAFT-VRX equation,75,76 based on universal scaling functions,77 or the renormalization method of White and co-workers,78,79 used by Llovell et al. for soft-SAFT,80,81 are well suited to model this region. The least-squares function is chosen as it is continuous and mathematically well behaved and is one of the most widely used in the estimation of equation of state parameters. We use a combined annealing and simplex method61 to solve for phase equilibria and to minimize the function expressed in eq 20. The multidimensional objective function surface is characterized by large valleys of near-optimal solutions, which can be attributed to correlation between the parameters (e.g., εii and λii). It is therefore desirable to identify several low-lying minima and to use any additional information available for the compound to discriminate between parameter sets. In this work, we discretise the energy parameter space as proposed in previous work8 to reduce the dimensionality of the optimization problem and to explore fully the parameter space in order to ensure that we have an optimal parameter set for our model. In order to determine the adjustable unlike binary interaction HB parameters kij (or εij) and kHB ab,ij (or εab,ij) needed to model the binary mixtures of interest, a least-squares objective function of the following form is used:

minFObj φ

1 ) NP 1 Nx

NP

∑ i)1

Nx

[

∑ [x

I calc I I Pexp i (T, xi ) - Pi (T, F , xi ;θ, φ)

II,exp (T, (xIi )) j

I Pexp i (T, xi )

]

2

+

- xII,calc (T, FII, (xIi );θ, φ)]2 (21) j

j)1

in the case where isothermal mixture data is used. Here, Nx is the number of compositional data points used in the parameter estimation. In this expression, φ represents the vector of adjustable

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Figure 1. Schematic representation of the molecular models used in this work. Molecules are modeled as chains of m bonded square-well segments of hard-core diameter σii with dispersive interactions characterized by a well depth εii and range λii. The hydrogen-bonding interactions are mediated through square-well bonding sites of types e (electron lone pairs) or H (hydrogen) located halfway between the center and surface of the molecular core; only e-H bonding is considered in the HB pure component models, and multiple bonding at any given site is forbidden. When an e and H sites come within a cutoff range rc,eH,ii of each other, there is a site-site hydrogen-bonding associative interaction of energy εHB . (a) Symmetric model of MEA. Two spherical segments are used in order to treat the nonsphericity eH,ii of the molecule. Six sites in total are incorporated, with no distinction made between the association behavior of the different functional groups: the NH2 group is modeled with one site e and two sites H, and the OH group, with two sites e and one H; e and H sites are identical regardless of the group they mimic. (b) Asymmetric model of MEA. One e* site and two H* sites are used for NH2, and two e sites with one H site, for the OH group. (c) Water treated as spherical with four association sites: two of type e and two type H.8 (d) Carbon dioxide modeled with two tangential segments.9 Two additional acceptor R sites are incorporated to account for the chemical reaction between the amine and CO2.

parameters for the mixture, and we have indicated as (xIi) the implicit dependence of the composition of the second phase xIIi on the composition of the first, since they must satisfy equilibrium conditions and are thus not independent. In the case of isobaric data, an equivalent function is formulated min FObj φ

1 ) NT 1 Nx

NT

∑

Nx

i)1

[

I Texp i (P, xi )

∑ [x

II,exp (P, (xIi )) j

]

I I 2 - Tcalc i (P, xi , F ;θ, φ) I Texp i (P, xi )

In the case of the mixtures, we report either the error in the calculated equilibrium pressure of the mixture, at a given temperature and liquid composition, given by 100 % AAD P ) NP

- xII,calc (P, FII, (xIi );θ, φ)]2 j

(22)

As in the determination of the intermolecular parameters of the pure components, these expressions are chosen since they are continuously differentiable. Here, an absolute error is used for mole fractions to avoid placing undue emphasis on the low values of the compositions often encountered for coexisting phases. In reporting the performance of our models, we use the average absolute deviations AAD. For the pure components, we use three descriptors of the quality of the fit: an overall percentage AAD, 100 % AAD ) NP + NF

{∑|

Pexp v,i (Ti)

i)1

|

NF

∑ j)1

-

Pcalc v,i (Ti ;θ)

Pexp v,i (Ti)

|

% AAD Fl )

100 NF

| ∑| NP

∑ i)1 NF

i)1

+

calc Fexp l,j (Tj) - Fl,j (Tj ;θ)

Fexp l,j (Tj)

exp PV,i (Ti) - Pcalc v,i (Ti ;θ)

Pexp v,i (Ti) calc Fexp v,i (Ti) - Fv,i (Ti ;θ)

Fexp v,i (Ti)

i)1

|}

| |

I calc I I Pexp i (T, xi ) - Pi (T, F , xi ;θ, φ) I Pexp i (T, xi )

|

(26)

or the error in the calculated equilibrium temperature at given pressures and liquid compositions % AAD T )

100 NT

NT

∑ i)1

|

calc I I I Texp i (Pi, xi ) - Ti (Pi, F , xi ;θ, φ) I Texp i (Pi, xi )

|

(27)

and, if available, the error in the composition of the other equilibrium (vapor or liquid) phase at each Ti or Pi and phase I composition. As mole fractions are constrained to be between zero and one, an absolute measure of error is more appropriate, AAD xII )

1 Nx

Nx

∑ |x

II,exp i

- xII,calc | i

(28)

i)1

III. Results and Discussion

(23)

and separate percentage AADs for vapor pressure and liquid density, 100 % AAD P ) NP

∑

+

j)1

NP

|

NP

(24)

(25)

A. Pure Components. We first develop intermolecular models (symmetric and asymmetric) for MEA. A set of 376 data points82 from 64 separate sources, comprising data from the triple point to 90% of the critical point, is used in the objective function, eq 20. The symmetric model proposed (see Figure 1a) is characterized by six intermolecular parameters: mMEA, σMEA, εMEA, λMEA, εHB eH,MEA, and rc,eH,MEA. The chain length mMEA is fixed at mMEA ) 2.0 following a detailed study on the effect of its value on the model. The energy parameter space is discretized in a manner similar to that presented in the work of

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Table 1. Parameters Characterizing the Pure Component Intermolecular Potential Models (the Number of Segments mii, the Diameter of the HB Spherical Core σii, the Depth εii and Range λii of the Dispersive Square Well, the Depth εab,ii of the Hydrogen-Bonding Site-Site Interaction, HB and its Range rc,ab,ii (Corresponding to the Bonding Volume KeH,ii of the Site-Site Interaction)) of Molecule i Optimized to Vapor-Liquid Equilibrium Data from the Triple Point to 90% of the Critical Temperaturea i b

MEA C2H5OH C2H5NH2 H2O CO2c

e-sites H-sites HB (a) (b) R-sites εab,ii /k (K) rc,ab,ii (Å) % AAD Pi % AAD Fl % AAD Pi + Fl

mii

σii (Å)

εii/k (K)

λii

2.0 1.533 1.7 1.0 2.0

3.58714 3.71500 3.67397 3.03420 2.78640

325.000 244.417 270.000 250.000 179.270

1.56098 1.67300 1.53136 1.78890 1.51573

3 2 1 2 0

3 1 2 2 0

0 0 0 0 2

1300.00 2357.79 960.000 1400.00 0000.00

2.34511 2.17328 2.39523 2.10822 0.00000

3.66 6.75 1.08 0.69 0.61

0.27 0.40 0.22 0.98 1.18

2.47 5.04 0.84 0.78 0.68

ref this work 130 87 8 9

a HB HB HB ) εHe,ii . Where no interaction energy is reported, it is set to zero (e.g., εee,MEA-MEA ) 0.0 or The interaction matrix is symmetric, i.e., εeH,ii HB εRR,CO -CO ) 0.0). The percentage absolute average deviation (% AAD) as defined in eqs 23-25 is used to assess the quality of the description. b This 2 2 c is the symmetric model of MEA (Figure 1a). Two effective sites are included on the CO2 model. This is done solely to mediate the interaction between CO2 and MEA; in mixtures, CO2 does not self-associate, nor does it associate with water or the alkanol.

Table 2. Optimal Parameter Set for the Asymmetric Model of Pure MEA (Figure 1b)a i

mii

σii (Å)

εii/k (K)

λii

e-sites

H-sites

e*-sites

H-sites

% AAD Pi

% AAD Fl

% AAD Pi + Fl

MEA

2.0

3.52779

305.000

1.58280

2

1

1

2

3.58

0.26

2.41

a

See Table 1 for details. The corresponding values of the association parameters are given in Table 3.

HB Table 3. Site-Site Association Energies εab,ii and Range Parameter rc,ab,ii for the Asymmetric Model of Pure MEA (Figure 1b) HB εab,MEA /k (K)

rab,MEA (Å)

b\a

e

H

e*

H*

e

H

e*

H*

e H e* H*

000.000 2357.79 000.000 900.000

2357.79 000.000 550.000 000.000

000.000 550.000 000.000 960.000

900.000 000.000 960.000 000.000

0.00000 2.08979 0.00000 2.65064

2.08979 0.00000 2.65064 0.00000

0.00000 2.65064 0.00000 2.32894

2.65064 0.00000 2.32894 0.00000

Clark et al.8 in order to carry out a “global” optimization of the intermolecular model parameter set (see also ref 83). Here, we HB /k e discretise the parameter space in terms of 600 K e εeH,MEA 2000 K for the association interaction and 200 K e εMEA/k e 800 K for the dispersive interaction. The space was divided into 1,425 discrete points, in intervals of 25 K, and at each point, the hard-core diameter (σMEA), square-well range (λMEA), and rc,eH,MEA are obtained by optimizing the description of the vapor-liquid equilibria data from the triple point to 90% of the critical temperature using eq 20. The final SAFT-VR parameters obtained for this symmetric model of MEA together with the % AAD are presented in Table 1. Though a good description of the phase behavior of MEA can be obtained for this relatively simple model (as can be observed from the overall % AAD of 2.47%), it is important to preserve the multifunctional nature of MEA with an asymmetric model of MEA which, as we will show, is more suitable for an adequate description of the phase behavior of mixtures. While a symmetric model of MEA will give a good prediction of the phase behavior of the MEA + H2O mixture, it fails to give an adequate description of the phase behavior of MEA + CO2. In ternary mixtures of MEA + CO2 + H2O, we observe that the interaction of the three e sites on the symmetric MEA model with the two R sites on the CO2 model provides such a strong impetus for the absorption of CO2 into the liquid phase that the vapor phase will then consist almost entirely of H2O, which is not in line with experimental evidence. Furthermore, it can be seen from the stoichiometry of reaction 3 that each CO2 will bond with two MEA molecules; it is impossible to preserve this stoichiometry of the reaction using the symmetric model of MEA. As our long-term view is to implement these molecular models within a process and solvent design environment, where small errors in the phase behavior can lead to an important under- or overestimation of equipment requirements,84 the symmetric model is therefore abandoned in favor of its asymmetric analogue.

As discussed briefly in section II.B, the asymmetric model of MEA is characterized by twelve parameters: mMEA, σMEA, HB HB HB , rc,eH,MEA, εe*H*,MEA , rc,e*H*,MEA, εeH*,MEA , εMEA, λMEA, εeH,MEA HB rc,eH*,MEA, εe*H,MEA, and rc,e*H,MEA, which results in a parameter estimation problem of much higher dimensionality than is usual in SAFT-VR studies of associating systems. At this point, we take advantage of the physical basis and transferability of parameters in SAFT (see, for example, the studies reported in refs 85 and 86) and propose to transfer the association parameters describing the interaction between the hydroxyl groups of the MEA molecules (represented by the e-H site-site HB , rc,eH,MEA) from those obtained in a separate interaction: εeH,MEA study for ethanol (see Table 1). Similarly, the parameters related to the interaction between the amine groups of MEA (represented by the e*-H* site-site interaction: εHB e*H*,MEA, rc,e*H*,MEA) are determined from a separate study for ethylamine87 (see Table 1). When these parameters for ethanol and ethylamine are transferred for the corresponding interactions in MEA, the only association interactions that remain to be specified for the MEA molecule are those for the cross amine-hydroxyl group association interactions. These are represented by e*-H and e-H* site-site interactions characterized by εHB e*H,MEA, rc,e*H,MEA, HB , and rc,eH*,MEA. To reduce further the number of εeH*,MEA parameters, we set the value of the range of the association potential for the e-H* and e*-H interactions to be the same such that rc,eH*,MEA ) rc,e*H,MEA. The % AAD is not improved by using two different values for rc,eH*,MEA and rc,e*H,MEA. The proposed procedure has allowed us to reduce the number of HB HB , εe*H,MEA , and parameters to six (σMEA, εMEA, λMEA, εeH*,MEA rc,eH*,MEA), no more than for other SAFT-VR models. To ensure that we gain an understanding of the nature of the objective function surface (eq 20) with respect to the six parameters, we discretise the parameter space for the asymmetric HB model of MEA in terms of εMEA, εHB e*H,MEA, and εeH*,MEA. Initially, HB a parameter space of dimension 600 K e εe*H,MEA/k e 2000 K, HB /k e 2000 K, and 200 K e εMEA/k e 800 K 600 K e εeH*,MEA

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Figure 2. Contour plot for the relative average absolute deviation (% AAD) of the vapor pressure and saturated liquid density determined using the SAFTHB VR equation of state with the asymmetric model of MEA. At each point on the surface, the dispersion εMEA/k and self-cross-association εeH,MEA /k and HB /k energies are fixed, and the remaining size (σMEA) and range (λMEA) parameters are optimized by minimizing the least-squares objective function εe*H*,MEA (eq 20) for 376 points between the triple-point temperature to 90% of the critical point. The optimal model on this surface corresponds to % AAD Psat + Fl ) 2.41%. Only the relevant section of the entire parameter space explored is depicted. The final set of parameters are collected in Tables 2 and 3.

is investigated. This space is divided into 75 264 discrete points, in intervals of 25 K, and at each point, the hard-core diameter (σMEA) and square-well range (λMEA) are obtained by optimizing the description of the vapor-liquid equilibria data from the triple point to 90% of the critical temperature using eq 20; the association range parameter is fixed to an average value (cf. Table 3) obtained during a series of preliminary optimisation runs. The region of near optimal intermolecular parameter sets is determined by inspection of the % AAD, and within this region, a second discretization is then carried out, in intervals of 5 K. After carrying out this procedure we find that the asymmetric model, which takes into account details of the different hydrogen bond interactions that are present in MEA and which is based on a number of parameters transferred from other pure components, provides an excellent description of the experimental phase behavior. A second conclusion is that a large number of parameter sets can lead to similar representations of the experimental phase behavior in terms of the % AAD. The degeneracy in the values of the intermolecular parameters in models of associating fluids has been observed previously8 and simply choosing the model with the lowest value of the % AAD is not necessarily the same as selecting the best physical model. This is because the % AAD only takes into account vapor pressure and saturated liquid density; these data alone do not provide sufficient information for model discrimination. Given HB HB > εe*H,MEA , so these facts, we focus on models where εeH*,MEA as to mimic the differences in electronegativities of the oxygen and nitrogen atoms in the hydroxyl and amine functional groups. On this basis, a further search of the parameter space is HB performed with εHB eH*,MEA > εe*H,MEA selecting for each combination the value of the dispersion interaction εMEA resulting in the lowest % AAD. The relevant region of the % ADD surface HB HB > εe*H,MEA and εMEA is in the parameter space of εeH*,MEA presented in Figure 2. Several near-optimal parameter sets are then assessed in terms of their adequacy in the description of the vapor-liquid equilibria, the enthalpy of vaporization in the region T e 0.9Tc, and the vapor-liquid interfacial tension of MEA. The enthalpy of vaporisation is a second derivative property of the Helmholtz

free energy (related to the slope of the vapor pressure with temperature) and as such represents a stringent test of the model. Similarly, the analysis of the surface tension is helpful in establishing that one has the correct partitioning between the enthalpic and entropic contributions to the free energy (the temperature dependence of the tension is related to the excess surface entropy). The performance of the best overall model (with a corresponding overall % AAD ) 2.41 in the vapor pressure and saturated liquid density), which is distinct from the global minimum on the surface given by eq 20, can be seen in Figures 3-6. The predictions obtained for the enthalpy and the surface tension in particular are in excellent agreement with the experimental data.88-91 It is striking to see how the set of selected molecular parameters is able to quantitatively predict the surface tension values over a wide range of temperatures and pressures. These results give added confidence in the adequacy of the model developed for the complex MEA molecule. The intermolecular model parameters for this asymmetric model of MEA are summarized in Tables 2 and 3. Both water and CO2 have been thoroughly studied within the SAFT-VR platform,8-10 and the reader is directed to the original papers for details; for completeness, the SAFT-VR parameters for the models of pure water and CO2 used here are also reported in Table 1. In common with other studies,9,10 we do not consider CO2 to be self-associating, despite its strong quadrupole; indeed the low solubility of CO2 in H2O clearly suggests that the intermolecular interactions between CO2 and H2O are of insufficient strength to be regarded as hydrogen bonds. On the other hand, as can be seen from reaction 3, CO2 and MEA react readily (in aqueous solution) to form carbamate, and corresponding strong specific interactions are active. More specifically, it is known that there is a strong interaction between the lone-pair of electrons on the amine nitrogen and the electron depleted carbon in CO2. Chemical equilibrium is quickly achieved, and this reaction is not considered to be kinetically limited,11 i.e., in aqueous solution, the rate-determining factor is the mass transport of CO2 to the amine, not the actual rate of reaction between the CO2 and the amine. This suggests that the equilibrium reaction can be treated within the SAFT formalism

Ind. Eng. Chem. Res., Vol. 49, No. 4, 2010

Figure 3. (a) Experimental data82 for the pressure-temperature (PT) phase diagram of MEA compared with the SAFT-VR description for the asymmetric model of MEA (continuous curve). (b) Vapor pressure shown in the Clausius-Clapeyron representation, where the low temperature region is better appreciated. The vapor-pressure curve exhibits the concave curvature that is typically associated with strongly polar fluids.

in a manner analogous to association interactions. In order to do so, we incorporate two effective, electron acceptor R sites onto the CO2 model proposed in earlier studies.9,10 The choice of two sites ensures that the stoichiometry of the reaction is preserved. For simplicity, we assume that the interaction range is the same as that of the e* site of MEA (i.e., r*c,e*H*,MEA ) r*c,e*R,MEA-CO2) corresponding to rc,e*R,MEA-CO2 ) 2.05354 Å and a bonding volume of Ke*R,MEA-CO2 ) 0.491797 Å3. Like-like HB ) 0.0. The (R-R) interactions are not allowed, i.e., εRR,CO 2 energy associated with this interaction is determined by comparison with experimental data for mixtures of CO2 and aqueous MEA. These results are presented in section III.C. B. Binary Mixtures. A number of unlike (or binary mixture) intermolecular model parameters need to be determined in order to describe the thermodynamics of mixtures. In this section, we examine the fluid phase behavior of H2O + MEA and H2O + CO2, for which experimental data are readily available, and use these data to determine the unlike interaction energy HB parameters: εij and εab,ij . All other unlike parameters characterizing the binary mixtures (σij, λij, and Kab,ij) are calculated using combining rules of the Lorentz type92 (cf. eqs 15-17). A detailed description of the combining rules used in this work can be found in the work of Galindo et al.5 1. MEA + H2O. A mixture of MEA and H2O modeled using the asymmetric model of MEA presented in section III.A requires the determination of three adjustable unlike energy interaction parameters: the hydrogen bonding energy between HB HB ) εHe,MEA-H ) and amine water and the hydroxyl (εeH,MEA-H 2O 2O HB HB (εe*H,MEA-H2O ) εH*e,MEA-H2O) groups of MEA and the unlike

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Figure 4. Experimental data82 for the vapor-liquid coexistence densities, F, and molar volumes, V, of MEA compared with the SAFT-VR description for the asymmetric model of MEA (continuous curve). (a) Coexistence densities and (b) coexistence volumes are shown.

Figure 5. Experimental data82 for the enthalpy of vaporisation ∆Hvap of MEA compared with SAFT-VR predictions for the asymmetric model (continuous curve).

dispersion interactions between MEA and water εMEA-H2O. In order to reduce the number of mixture parameters, a transferable approach is proposed. The hydrogen-bonding interaction between the hydroxyl group of MEA and water is transferred from that of a mixture of ethanol and water, and similarly, the hydrogen-bonding interaction between the amine group and water is transferred from a study of ethylamine and water. The intermolecular model parameters for pure ethanol and ethylamine are determined as described in section II.C. The parameter values of the final models and the associated % AADs are reported in Table 1. The optimized unlike parameters for

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Figure 6. Experimental data82 for vapor-liquid interfacial tension of MEA compared with SAFT-VR predictions for the asymmetric model (continuous curves).63-65

the CH3CH2OH + H2O and CH3CH2NH2 + H2O are presented in Table 4. In the case of CH3CH2OH + H2O, the unlike interaction parameters are determined by comparison to 106 experimental data points comprising six isobars in a pressure range of 0.12-2.068 MPa.82,93-101 The overall agreement in terms of the AAD in the vapor phase mole fraction is 0.006, while the % AAD in the temperature is also excellent at 0.11%. A representative sample of these results are presented in Figure 7, where the agreement between theory and the experiment is evident. The characteristic low boiling azeotrope is described quantitatively by this model. The unlike interaction parameters for CH3CH2NH2 + H2O are determined by comparison to 36 experimental data points comprising three isobars in a pressure range of 0.0799-0.1067 MPa.82,102,103 The overall description is characterized by an AAD ) 0.011 in the vapor phase mole fraction and a % AAD ) 1.11% in the temperature. An example of the description of the phase behavior is shown in Figure 8, where the SAFT-VR theory is seen to provide a good representation of the experimental data. Once the unlike interaction parameters for CH3CH2OH + H2O and CH3CH2NH2 + H2O have been determined, they are transferred to the corresponding parameters characterizing the hydrogen bonding interactions of water and MEA (i.e., the association energy and range between the hydroxyl group of MEA and water is 1780.71 K and 2.14374 Å, and the association energy between the amine group of MEA and water is 1517.11 K and 2.25215 Å). The remaining energetic parameter (εMEA-H2O) which characterizes the strength of the MEA-water dispersion interaction is determined by comparison with experimental phase equilibrium data for this mixture. In determining the value of this parameter, 97 data points comprising 6 isotherms covering the temperature range 298.15 e T e 364.15 K and 105 data points comprising 8 isobars covering the

Figure 7. Isobar of the temperature-composition (Tx) vapor-liquid equilibria for the C2H5OH + H2O mixture compared with SAFT-VR calculations at (a) constant pressure P ) 0.1013 MPa; (b) Isotherm of the pressure composition (Px) vapour-liquid equilibria at constant temperature T ) 298.15 K. The continuous curves represent the SAFT-VR description, and the symbols represent the corresponding experimental data.82,94,95,98-100

pressure range 0.06 e P e 0.686 MPa have been used.82,104-109 We find, in accordance with the results of other workers employing a Wertheim-like treatment of MEA,38,46 that a symmetric model of MEA can be used to accurately model mixtures of MEA + H2O. We obtain values for the unlike binary HB ) for the symmetric model interaction parameters (εij and εab,ij of MEA with H2O as described previously, using the same experimental data as for the asymmetric model. In Figure 9, three isotherms of the vapor-liquid equilibrium for MEA + H2O at T ) 298.15, 343.15, 364.15 K are presented; the adequacy of the description can be clearly seen from the figure. The continuous lines represent calculations performed with the asymmetric model of MEA, and the dashed lines represent calculations performed with the symmetric model. As shown in Table 5, the accuracy of the models in describing the MEA + H2O mixture is % AAD ) 2.03% in temperature and pressure and AAD ) 0.027 in vapor phase composition when using the asymmetric model of MEA, and % AAD ) 4.39% in

Table 4. Binary Interaction Parameters for the Mixtures Studied in This Worka i C2H5OH C2H5NH2 MEAb CO2 a

+ + + + +

j H2O H2O CO2 H2O

εij/k 252.870 277.690 209.324 224.404

HB εeH,ij /k (K)

1780.71 1517.11 0000.00 0000.00

HB εe*R,ij /k (K)

0000.00 0000.00 4300.00 0000.00

rc,eH,ij (Å) 2.14374 2.25215 0.00000 0.00000

rc,e*R,ij (Å) 0.00000 0.00000 2.05354 0.00000

% AAD T or P 0.112 1.096c

AAD x 6.0 1.1 1.0 2.0

× × × ×

data

-3

10 10-2 10-2 10-3

d

94, 95, 98-100 102, 103 82, 124-126 72-74

HB and rc,ab,ij are the strength and range of Here, εij characterizes the strength of the dispersion interaction between molecules of types i and j, and εab,ij HB HB HB the association between sites a and b. The unlike association between sites of the same type is assumed to be symmetric, i.e., εeH,ij ) εHe,ij ) εeH,ji ) HB HB HB HB HB HB HB εHe,ji , and εe*H,ij ) εH*e,ij ) εeH*,ji ) εHe*,ji . Where no interaction energy is reported, it is set to zero (e.g., εee,MEA-MEA ) 0.0). The εe*R,ij /k and rc,e*R,ij b interactions pertain only to the interactions between the e* site on the asymmetric MEA model and the R sites on the CO2 model. Asymmetric MEA model (Figure 1b). c Parameters for C2H5NH2 + H2O are estimated only with isobaric data. Hence, the % AAD reported here corresponds to eq 27. d Parameters for MEA + CO2 are estimated only with isothermal data. Hence, the % AAD reported here corresponds to eq 28.

Ind. Eng. Chem. Res., Vol. 49, No. 4, 2010

Figure 8. Isobars of the temperature-composition (Tx) vapor-liquid equilibria for the C2H5NH2 + H2O mixture compared with SAFT-VR calculations at P ) 0.1067 MPa (squares and dashed curves) and P ) 0.07999 MPa (triangles and continuous curves). The symbols correspond to experimental data82,102,103 and curves to the corresponding SAFT-VR description.

Figure 9. Isotherms of the pressure-composition (Px) vapor-liquid equilibria of MEA + H2O compared with SAFT-VR calculations for both the symmetric and asymmetric models of MEA. The continuous curves are the calculations with the asymmetric model of MEA, and the dashed line curves are those with the symmetric model of MEA. Three representative temperatures are shown: 0, T ) 298.15 K; O, T ) 343.15 K; ) T ) 363.15 K. The symbols correspond to the experimental data82,104-109 and the curves to the corresponding SAFT-VR description.

temperature and pressure and AAD ) 0.008 in vapor phase composition when using the symmetric model of MEA. 2. MEA + CO2. To our knowledge, there is unfortunately no experimental data available for mixtures of carbon dioxide and MEA. It is useful however to discuss briefly the available evidence on the nature of the different intermolecular interactions contributing to the phase and chemical equilibrium in this mixture. As mentioned in the introduction (see reaction 3), MEA and CO2 react readily via the amine group and the electron depleted oxygen of CO2 to form a carbamate. As stated in the previous sections, we take this into account in our proposed model by adding two acceptor sites of type R on the model for CO2.

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Figure 10. SAFT-VR predictions for the isobaric temperature-composition (Tx) vapor-liquid equilibria of MEA + CO2 at a pressure of 0.1 MPa.

There is a significant amount of theoretical and experimental evidence which suggests a specific, anisotropic interaction between CO2 and hydroxyl groups, with energies consistent with hydrogen bonding.110,111 Saharay and Balasubramanian111 report an interaction energy between CO2 and CH3CH2OH of approximately 11 kJ/mol. This is an energy consistent with a weak hydrogen bond.112 When interacting with ethanol, CO2 can be treated both as a Lewis acid (it can form an electron donor-acceptor complex with ethanol), as well as a Lewis base (it can also form a hydrogen-bonded complex with ethanol111). We have however not incorporated these interactions in our model as the phase behavior is found to be dominated by the amine-CO2 interaction that leads to the formation of carbamate. We use ternary mixture data to assess the validity of this assumption and determine the unlike parameters associated with these interactions. Kassenbrood113 and Lemkowitz and coworkers114-120 have presented a detailed investigation of the phase behavior of the NH3 + CO2 mixture, and some limited experimental data for the vapor-liquid equilibria of the mixture is reported. From this body of work, it is clear that the NH3 + CO2 mixture exhibits positive azeotropy. Azeotropic behavior may therefore be expected in the CO2 + MEA system, as represented in Figure 10 (which is obtained with parameters estimated to the CO2 + H2O + MEA ternary system as will be explained in section III.C). 3. H2O + CO2. The vapor-liquid equilibria of aqueous solutions of CO2 have been examined in numerous studies including with the SAFT-VR approach (see the work of dos Ramos et al.72,73 and Valtz et al.74 and references therein), though much of the previous emphasis was on the supercritical properties of the system due to the suitability of supercritical CO2 as an inexpensive and benign alternative to conventional organic solvents. Additionally, applications in the areas of enhanced oil and gas recovery as well as CO2 sequestration call for a detailed knowledge of the phase behavior of these systems. The binary mixture of water and carbon dioxide exhibits type III phase behavior according to the Scott and van Konynenburg classification,121-123 which is characterized by extensive

Table 5. Binary Interaction Parameters for MEA and H2Oa +

i b

MEA MEAc

+ +

j H2O H2O

εij/k 273.373 285.044

HB εeH,ij /k (K)

1780.71 1450.00

HB εe*H,ij /k (K)

1517.10 0000.00

rc,eH,ij (Å) 2.14374 2.22705

rc,e*H,ij (Å) 2.25215 0.00000

% AAD T and P 2.03 4.39

AAD xII -2

2.7 × 10 7.9 × 10-3

data 82, 104-109 82, 104-109

a These binary interaction parameters are estimated from both isobaric and isothermal data. The quality of the description is assessed from a measure of the percent absolute average deviation (% AAD) of the coexistence temperature/pressure and the average deviation (AAD) of the vapour composition (cf. eqs 26-28). See Table 4 for details. b Asymmetric MEA model (Figure 1b). c Symmetric MEA model (Figure 1a).

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Figure 11. Isotherms of the pressure-composition (Px) vapor-liquid equilibria for CO2 + H2O at temperatures relevant to amine-based CO2 capture compared with the SAFT-VR calculations. (a) CO2-rich vapor phase and (b) H2O-rich liquid phase. The symbols correspond to the experimental data72-74,82 and the continuous curves to the corresponding SAFT-VR description: /, T ) 288.15 K; O, T ) 298.15 K; ×, T ) 308.15 K; +, T ) 323.15 K; 0, T ) 348.15 K; ∆, T ) 353.15 K; ), T ) 373.15 K.

liquid-liquid immiscibility up to temperatures almost as high as the critical point of water. Although binary interaction parameters have already been proposed for H2O + CO2, a new parameter set is developed in our current study to better represent the conditions relevant to amine-based CO2 capture. The unlike-interaction parameter εH2O-CO2 is adjusted by comparison to seven sets of experimental isothermal data72-74 over a temperature range of T ) 273-373 K, corresponding to a pressure range of 0.007 e P e 10 MPa, by minimization of eq 21 in the gPROMS software package. An optimal value εH2O-CO2/k ) 224.404 K with associated AAD ) 0.002 in the equilibrium vapor phase composition is found (see Table 4). As we are specifically concerned with the application of the models developed here in the context of modeling CO2 capture, we present in Figure 11 the phase behavior at pressures and temperatures of relevance for amine-based CO2 capture processes. Additionally, we emphasize the fact that the SAFT intermolecular parameters are independent of the thermodynamic state by calculating the high-pressure phase behavior of this mixture at T ) 473.15 K, which is outside the range where the parameters are adjusted; quantitative agreement with the experimental data is obtained at this elevated temperature. These results are depicted in Figure 12. The SAFT-VR model is also assessed in terms of its ability to predict the excess properties of the mixture. It has been shown in previous work73 that the SAFT-VR approach is able to provide a good description of the phase behavior and of the excess properties of H2O + CO2 mixtures. In Figure 13, we confirm that our proposed model also results in a good representation of the excess enthalpies of the mixture. One should again note that the temperature and pressure conditions at which these predictions are performed are significantly different to those used to determine the binary interaction parameters. The description of excess properties constitutes a very stringent test of any theory and molecular model. It is therefore particularly gratifying to see that our models and approach provide a quantitative prediction of this type of property. C. MEA + CO2 + H2O. Armed with the molecular models for pure component and binary mixtures developed in the previous sections, we now come to the main goal of our work: the accurate representation of the fluid phase behavior of carbon dioxide in aqueous MEA. As mentioned in the introduction,

Figure 12. Isotherm of the pressure-composition (Px) vapor-liquid equilibria at T ) 473.15 K for CO2 + H2O compared with the SAFT-VR calculations. The symbols correspond to the experimental data,72-74,82 and the continuous curves, to the corresponding SAFT-VR description.

Figure 13. Excess enthalpies ∆HE for CO2 + H2O compared with SAFTVR predictions. The continuous curves correspond to SAFT-VR calculations, and the symbols, to experimental data. (a) T ) 498.15 K: +, P ) 10.4 MPa; O, P ) 11.0 MPa; and /, P ) 12.4 MPa. (b) T ) 523.15 K: +, P ) 10.4 MPa; O, P ) 12.4 MPa; and /, P ) 15.0 MPa. (c) T ) 573.15 K: +, P ) 11.0 MPa; O, P ) 12.4 MPa; and /, P ) 13.8 MPa.

numerous studies of the thermophysical properties of the MEA + CO2 + H2O mixture have been reported to date. There are also a substantial number of correlations which describe the vapor-liquid equilibria of this system. The majority of these expressions are however applicable only over a limited range of compositions and/or temperature and pressure. Outside the recommended range, these expressions are typically inapplicable and are therefore of limited use in the design and optimization of novel processes incorporating these components.

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Figure 14. Isotherms of projections of the pressure-composition (Px) vapor-liquid equilibria of the ternary mixture MEA + CO2 + H2O compared with the SAFT-VR description: (a) T ) 313.15 K, (b) T ) 333.15 K, and (c) T ) 353.15 K. The thick continuous curves correspond to SAFT-VR calculations with the asymmetric model of MEA, and the thick dashed curve in part a, to SAFT-VR calculations with the symmetric model of MEA. In all plots, the thin continuous curves correspond to a correlation presented by Aboudheir et al.,131 and the thin dashed curves correspond to a correlation presented by Gabrielsen et al.34 The symbols denote the experimental data: square, data of Jou et al.125 diamond and right-pointing triangle, data of Dugas;126 circle, data of Lee et al.124

One major advantage of the SAFT approach is that the parameters used in the models are temperature and pressure independent, and thus there is in principle no region in the fluid range beyond description (with due caution taken in the critical and near-critical regions). A caveat, however, in the context of the MEA + CO2 + H2O system, is that our models do not fully capture the various reaction mechanisms (we focus on the formation of carbamate), so that use of the model far outside the region where the models are developed may not be as reliable (e.g., in the limit of low water concentration). In modeling MEA + CO2+ H2O, we examine data over a temperature range from 298.15 to 373.15 K, a pressure range from 0.001 to 10 MPa, and a liquid phase CO2 concentration of 0.01 e xCO2 e 0.12.124-126 We have used the data at 313.15 HB K to estimate the MEA-CO2 association energy εe*R,MEA-CO 2 62 using the gPROMS software package assuming that εMEA-CO2 is given by the Berthelot rule, i.e., kMEA-CO2 ) 0 in eq 18. Using these parameters, we are able to obtain and excellent description of the ternary system at these conditions and excellent quantitative predictions of the ternary phase behavior at 333.15 and 353.15 K, with an AAD over the three isotherms of 0.010 in liquid mole fraction of CO2, for MEA represented as the asymmetric model. This level of accuracy is in line with that presented in other contributions, for example the recent work of Faramazi et al.28 We note that, unlike the many correlations

that are currently available, our model captures the behavior of the data over the entire composition range for which data is available. The results of our SAFT-VR calculations for the vapor-liquid phase equilibria of MEA + CO2 + H2O are summarized in Figure 14. As can be seen, a complex, nonlinear behavior is seen for the partial pressure of CO2 of the coexisting gas phase as a function of the liquid phase CO2 mole fraction (the latter is a direct measure of the extent of absorption of CO2 in the amine solvent). It is noted that this behavior is due to a complex system of competing interactions, and it is very encouraging to see this behavior reproduced so accurately with our simple physical models of the chemical association. From Figure 14, one can also see that, though the various correlations can be used to provide a good description of the absorption, their use is not appropriate over wide ranges of conditions. Further, in Figure 14a, we compare the results of using both the symmetric and asymmetric models of MEA to predict the phase behavior of this mixture. It can be seen that, while the asymmetric model fully captures the complex fluid phase behavior, the symmetric model does not. This is because, as stated in section III.A, a fully symmetric model of MEA completely misrepresents the stoichiometry of the corresponding reactions of this system and results in a vapor phase consisting almost entirely of water. Finally, we have found that the inclusion of nitrogen (an

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essentially inert gas, chemically speaking) in our SAFT-VR description does not modify the phase behavior of the liquid phase appreciably. The accurate representation of the fluid phase behavior of MEA + CO2 + H2O (+ N2) within our SAFT-VR platform is of paramount importance for use in a detailed description of the CO2 capture process. IV. Concluding Remarks We have used the SAFT-VR approach to examine the fluid phase behavior of MEA + CO2 + H2O. This system is of much interest in the context of CO2 capture processes, and as such, a detailed understanding of its properties is crucial. A key to the design of new, more energy-efficient processes and to solvent design is the ability to predict thermophysical properties accurately. This was the overall aim of the work presented in our current paper. With this in mind, we have proposed a new molecular model for MEA which takes into account the multifunctional nature of the molecule. In our model, hydroxyl-hydroxyl, amine-amine, and aminehydroxyl hydrogen bonding interactions are treated explicitly, and differences in the energies of the interactions that can be expected in the system are taken into account. A key advantage of the SAFT approach is its molecular basis, which means that features of the intermolecular interactions in MEA can be obtained from molecules of related compounds, namely ethanol and ethylamine. In all of our models, the molecules have been modeled as chains of fused square-well segments, with short-range squarewell association sites to mediate hydrogen-bonding and other specific interactions. The pure component models are developed by minimizing least-squares objective functions incorporate experimental data for the vapor pressure and saturated liquid density, and when available, previous SAFT-VR models from the literature are used. In modeling MEA, we have been able to transfer the hydrogen bonding parameters for the OH-OH interaction from those of ethanol, and the parameters for the NH2-NH2 interaction from ethylamine. In this way, only the strength of the NH2-OH hydrogen bonding interaction for MEA needs to be determined from pure component data for this substance (in addition to the square-well parameters characterizing the segment diameters and dispersion energy). An excellent description of the fluid phase behavior, the enthalpy of vaporization, and the vapor-liquid surface tension is provided by the SAFT-VR approach with such a model. Following the same ideas, this model of MEA has been used to study MEA + H2O. The unlike MEA-water association interaction parameters have been transferred from those obtained from aqueous mixtures of ethanol and of ethylamine. The remaining MEA-water dispersion interaction parameter has been determined by comparison with experimental data to ensure an optimal description of the vapor-liquid equilibrium of the mixture. The ability to quantitatively predict the phase behavior of this mixture is of great practical importance. In our study, two additional sites are included in the model of CO2 to account for its interaction with MEA in order to describe the reactions between the two molecules; there is of course no association between carbon dioxide molecules in the pure state so the sites are inactive in this case. We have revisited the phase behavior and thermodynamic properties of the H2O + CO2 mixture. The simple model for carbon dioxide used in this work, which does not take into account explicitly the quadrupolar nature of the molecule, can nevertheless provide an accurate description of the thermodynamic properties of these mixtures. An unlike adjustable parameter for the dispersion energy has been

determined by comparison with experimental data at conditions of interest for CO2 capture processes. This model has been used to determine the phase behavior of the mixture over a wide range of conditions and assessed by comparison with excess property data. Good agreement has been found throughout. The key system of our study is the ternary mixture MEA + H2O + CO2. We have found that our proposed asymmetric model for MEA and our methodology for treating the reactive nature of the interaction between MEA and CO2 is well suited to deal with such systems, and our predictions provide an accurate representation of the fluid phase behavior. As has already been mentioned in the introduction, this ternary mixture has been the subject of much theoretical and experimental attention over the years. It is well-known that a failure to adequately account for the changes in free energy associated with chemical equilibria will result in a large over prediction of vapor pressures.127 This being the case, it is most satisfying that a simple approach of the type outlined in our paper can be used to model such systems, without deviating from the traditional SAFT formalism. In the context of the simulation of postcombustion CO2-capture processes with amine solvents, given the low physical solubility of N2 and O2 in aqueous systems, it is expected that the model presented here will provide an excellent description of the entire system. The development of a transferable model based on the contributions to the free energy of each individual functional group and their interactions is one of the particular strengths of our approach; this can be seen as an intermediate step toward a full group contribution treatment of the type described in recent work.128,129 Our transferable model parameters for MEA and MEA + H2O provide us with a very convenient platform from which to investigate the phase behavior of other aqueous alkanolamine mixtures of practical and scientific interest, to start tackling challenging problems in solvent and process design. Acknowledgment N.M.D thanks the British Coal Utilisation and Research Association (BCURA) for the funding of a Ph.D. studentship, and we are very grateful to Nick Booth of e.ON for very useful discussions and suggestions. Financial support from the Engineering and Physical Sciences Research Council (EPSRC) of the UK (Grant number: EP/E016340/1) to the Molecular Systems Engineering group is also acknowledged. Literature Cited (1) Astarita, G.; Savage, D. W.; Biso, A. Gas Treating With Chemical SolVents; John Wiley and Sons: New York, 1983. (2) Kohl, A. L.; Riesenfeld, F. C. Gas Purification, second ed.; Gulf Publishing Company: Houston, 1974. (3) Bottoms, R. R. Reissued U.S. Patent 1.783.901, 1933, 18958. (4) Gil-Villegas, A.; Galindo, A.; Whitehead, P. J.; Mills, S.; Jackson, G.; Burgess, A. N. Statistical associating fluid theory for chain molecules with attractive potentials of variable range. J. Chem. Phys. 1997, 106, 4168– 4186. (5) Galindo, A.; Davies, L.; Gil-Villegas, A.; Jackson, G. The thermodynamics of mixtures and the corresponding mixing rules in the SAFT-VR approach for potentials of variable range. Mol. Phys. 1998, 93, 241–252. (6) Paricaud, P.; Galindo, A.; Jackson, G. Recent advances in the use of the SAFT approach in describing electrolytes, interfaces, liquid crystals and polymers. Fluid Phase Equilib. 2002, 194, 87–96. (7) Tan, S. P.; Adidharma, H.; Radosz, M. Recent Advances and Applications of Statistical Associating Fluid Theory. Ind. Eng. Chem. Res. 2008, 47, 8063–8082. (8) Clark, G. N. I.; Haslam, A. J.; Galindo, A.; Jackson, G. Developing optimal Wertheim-like models of water for use in Statistical Associating Fluid Theory (SAFT) and related approaches. Mol. Phys. 2006, 104, 3561– 3581.

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ReceiVed for reView June 23, 2009 ReVised manuscript receiVed November 10, 2009 Accepted November 11, 2009 IE901014T