Part 5c: Solvent chemistry: solubility of CO₂ in reactive solvents for post-combustion CO₂

Abstract

Concerns about climate change have propelled research efforts to develop affordable and environmentally benign technologies to capture CO₂ from large emission sources, which can subsequently be used either for enhanced oil recovery or stored in other geological storage sites. The study of the solubility of CO₂ in solvents is therefore of great interest, both from the theoretical and practical points of view. To screen solvents or to design CO₂ capture processes, knowledge of the equilibrium solubility of CO₂ in the solvents is necessary. A large body of solubility data of CO₂ in aqueous and non-aqueous solutions of prominent industrial amines are available in literature. We present such data along with a description of the experimental techniques and thermodynamic models used. Innovations made to obtain an optimum solubility of CO₂ and to minimize the energy cost of a desired CO₂ capture system by adopting different kinds of solvents are also reviewed.

Figure 1.  High-pressure solubility data for CO₂ in high concentrated chemical solvents at 40°C.

Red: primary amines; turquoise: sterically hindered amines; gray: secondary amines; blue: diamines.

1-MPZ: 1-methyl piperazine; AEEA: 2-((2-aminoethyl)amino)ethanol; AEPD: 2-amino-2-ethyl-1,3-propanediol; AHPD: 2-amino-2-(hydroxymethyl)-1, 3-propanediol; AMP: 2-amino-2-methyl-1-propanol; AMPD: 2-amino-1-methyl-1,3-propanediol; DEA: Diethanolamine; DGA: Diglycolamine; MDEA: Methyldiethanolamine; MEA: Monoethanolamine; MIPA: Monoisopropanolamine; PE: 2-piperidineethanol; PZ: Piperazine; TIPA: Triisopropanolamine.

Data taken from [17,19,29–42].

Figure 2.  Low-pressure solubility data for CO₂ in chemical solvents (low concentrated) at 40°C.

Red: primary amines; turquoise: sterically hindered amines; gray: secondary amines; blue: diamines; black: tertiary amines.

3AP: 3-aminopyridine-2-carboxaldehyde thiosemicarbazone; 4DEA2B: 4-(diethylamino)-2-butanol; AEEA: 2-((2-aminoethyl)amino)ethanol; AEPD: 2-amino-2-ethyl-1,3-propanediol; AHPD: 2-amino-2-(hydroxymethyl)-1, 3-propanediol; AMP: 2-amino-2-methyl-1-propanol; DEA: Diethanolamine; DGA: Diglycolamine; DIPA: Diisopropanolamine; HXDD: 1,6-hexanediamine; MAE: 2-methylamino ethanol; MDEA: Methyldiethanolamine; MEA: Monoethanolamine; MO: Morpholine; PZ: Piperazine; TEA: Triethanolamine; TIPA: Triisopropanolamine.

Data taken from [19,33,41–54].

Figure 3.  Change in the solubility of CO₂ in aqueous methyldiethanolamine after addition of other amines at 40°C.

AMP: 2-amino-2-methyl-1-propanol; DEA: Diethanolamine; DIPA: Diisopropanolamine; MDEA: Methyldiethanolamine; MEA: Monoethanolamine; PZ: Piperazine.

Data taken from [46,55–58].

Figure 4.  Change of solubility of CO₂ in piperazine after the addition of other amines at 40°C.

AHPD: 2-amino-2-(hydroxymethyl)-1, 3-propanediol; AMP: 2-amino-2-methyl-1-propanol; DEA: Diethanolamine; DIPA: Diisopropanolamine; MDEA: Methyldiethanolamine; PZ: Piperazine; TEA: Triethanolamine; TIPA: Triisopropanolamine.

Data taken from [22,55,58–63].

Figure 5.  Change in the solubility of CO₂ in aqueous diglycolamine by addition of morpholine at 25°C.

DGA: Diglycolamine; MO: Morpholine.

Data taken from [52].

Figure 6.  Change in the solubility of CO₂ at 100 kPa.

3AP: 3-aminopyridine-2-carboxaldehyde thiosemicarbazone; AEEA: 2-((2-aminoethyl)amino)ethanol; AEPD: 2-amino-2-ethyl-1,3-propanediol; AHPD: 2-amino-2-(hydroxymethyl)-1, 3-propanediol; AMP: 2-amino-2-methyl-1-propanol; AMPD: 2-amino-1-methyl-1,3-propanediol; DEA: Diethanolamine; DGA: Diglycolamine; DIPA: Diisopropanolamine; MAE: 2-methylamino ethanol; MDEA: Methyldiethanolamine; MEA: Monoethanolamine; PZ: Piperazine; TEA: Triethanolamine; TIPA: Triisopropanolamine.

Data taken from [17,30,31,33–36,41,42,53,54,56,60,61,64].

Figure 7.  Comparison of the solubility of CO₂ in different mixtures of ionic liquids and amines.

[BMIM][BF₄]: 1-butyl-3-methylimidazolium tetraflluoroborate; BHEAA: Bis(2-hydroxyethyl)ammonium acetate; MDEA: Methyldiethanolamine; MEA: Monoethanolamine.

Data taken from [65–67].

Figure 8.  CO₂ capture capacity of aqueous ionic liquids, amines and their mixtures.

[BMIM][BF₄]: 1-butyl-3-methylimidazolium tetraflluoroborate; IL: Ionic liquid; MDEA: Methyldiethanolamine; MEA: Monoethanolamine; PZ: Piperazine; TEA: Triethanolamine.

Data taken from [68].

Figure 9.  Comparison of the experimental data for CO₂ partial pressure of the methyldiethanolamine–H₂O–CO₂ system and the model results.

Methyldiethanolamine concentration is ∼8 M.

e-NRTL: Electrolyte nonrandom two-liquid; MDEA: Methyldiethanolamine; T: Temperature.

Reproduced with permission from [69] © American Chemical Society (2011).

The reduction and control of atmospheric CO₂ has received considerable attention due to its contribution to climate change. Post-combustion capture of CO₂ from large stationary sources such as power plants and subsequent storage could reduce anthropogenic CO₂ emissions considerably. The process of separating CO₂ from flue gas through chemical absorption with a suitable reactive solvent is considered to be the most viable technology in the short and medium terms. The selection of a solvent for commercial post-combustion CO₂ capture is a complex process and requires laboratory-scale and pilot plant data, as well as the use of accurate process simulators. Preliminary screening of such solvents has been carried out in many laboratories all over the world. One of the key components of solvent screening is the determination of the equilibrium solubility of CO₂ as a function of temperature and pressure. Such information is used to determine the solvent circulation rate to achieve a certain degree of CO₂ removal. Recent screening solubility studies were published by Singh et al.[1,2], Puxity et al.[3], Chowdhury et al.[4,5] and Porcheron et al.[6,7]. In this present article, we report on the available experimental techniques and data for the solubility of CO₂ in the most common and promising solvents of interest to CO₂ capture operations. The latest reviews on the solubility of CO₂ in amine solutions were published in 2000 by Rochelle et al.[8] and in 2007 by Anufrikov et al.[9].

Vapor–liquid equilibrium or equilibrium solubility

Data gathered in this review provides a comprehensive database of vapor–liquid equilibrium (VLE) data, which can be used for testing and developing theoretical models and correlations, and are of interest to process design software developers and researchers working on solvent screening studies. The overall cost of the CO₂ capture plant is determined partially by the thermophysical properties of the solvent. Incorrect estimates of the absorber size can lead to large columns, and failure to meet product specifications are quite often the result of inaccurate VLE data [10]. Although VLE data are of great importance, the reported literature data for the solubility of CO₂ in aqueous solvents are scattered [11,12]. Therefore, there is a need for obtaining good quality and internally consistent VLE data in order to prove the extent and the accuracy of existing thermodynamic databases for solvent–CO₂ systems [13].

Experimental methods

The selection of the experimental method for VLE depends not only on the thermodynamic conditions, but also on the type of system, properties of the individual components, the required amount of material, the analytical amenities of measuring the composition of the equilibrium phases, the demand for accuracy of the measurement and many other factors. In CO₂ capture research, the existing experimental set-ups can be classified in several ways [14,15]. They can be classified as closed- or open-circuit methods or as analytical (or direct sampling method) and synthetic (indirect methods). In the analytical method, both liquid and vapor phases are sampled and analyzed. For example, the vapor phase composition is determined by chromatography, whereas the liquid phase is analyzed by titration (or chromatography). In the synthetic method, a mass balance is used for calculating the amount of acid gas absorbed by the solvent. The acid gas quantity introduced in the equilibrium cell is determined based on the knowledge of the pressure–volume–temperature conditions [16]. Three different types of VLE cells have been used extensively to obtain equilibrium solubility data. These cells are used to bring the vapor and liquid phases into thermal and composition equilibrium at known temperatures and pressures. The cells differ in the way they bring together (mix) the two phases. The compositions of the equilibrium phases are then determined by withdrawing samples and analyzing them.

▪ Static analytic method

Static analytical methods involve the establishment of a thermodynamic equilibrium in the cell followed by the analysis of solution samples. The constraints of the static analytical methods are those of the applied analysis technique such as spectroscopy or chromatography. It is important to use a reliable sampling technique, which allows withdrawing samples that are small enough not to perturb the established equilibrium. A known amount of solvent is placed in the cell and a required amount of CO₂ is introduced. The system is kept until equilibrium is established and then the pressure and mole fractions of components in both vapor and liquid phases are measured. A typical example of static analytical method, shown in Supplementary Figure 1, was used by Ma’mun et al.[16].

Noncirculation method

Rocking design was used by Lawson and Garst (Supplementary Figure 2)[17]. Severe corrosion to the point of failure in the weld of the sample port was the major disadvantage observed for this kind of equipment. An internal/mechanical stirrer (Supplementary Figure 3) was used by Tong et al.[13]. Reliable and repeatable results were obtained by this method for a wide range of temperatures. A variable-volume static cell was used by Addicks and Owren (Supplementary Figure 4)[18]. A major disadvantage of this method is that the mass transport over the small vapor–liquid surface in the equilibrium cell is so slow that without stirring, pressure, volume and temperature can become constant without equilibrium being reached [18].

Circulation method

In the circulation method, a known amount of solvent is placed in the equilibrium cell, nitrogen is introduced into the cell for CO₂ batching after the temperature is equilibrated, and the equilibrium pressure due to the amine and water vapor pressures and the nitrogen pressure are recorded. CO₂ is then introduced into the cell and the change in the pressure of the batching vessel is recorded. Equilibrium is considered to be attained if the total pressure in the cell remains constant for a long interval of time. The equilibrium partial pressure of CO₂ is the difference between the total pressure and the nitrogen equilibrium pressure recorded before. Both liquid and vapor phases were sampled for analysis. A circulation method (Supplementary Figure 5)[18] was used by Kadiwala et al.[19]. Although this kind of apparatus is used for a wide range of pressures and temperatures, their accuracy at low pressures is less compared with noncirculation static synthetic methods.

Static synthetic method

Static synthetic methods do not require sampling devices, but visualize the VLE process of a known composition. The equipment is simple, but the preparation of the solution to be studied has to be done adequately. The solubility is measured at a fixed temperature and a complete data set for multisolute solutions is calculated by linking with an analytical technique. Sidi-Boumedine et al. used computer-operated static apparatus (Supplementary Figure 6)[12]. The obtained data were high in accuracy and reproducibility with the data obtained by the analytical method.

▪ Flow method

Partial pressure of CO₂ in the gas flow is fixed in the course of an experiment and the composition of the liquid solution through which the gas flow is passed changes until the solution comes to equilibrium with the gas. The quantities set in the experiment are the temperature, number of moles of water and amine in the solution, and the partial pressure of CO₂. A typical example of flow system is shown in Supplementary Figure 7[20]. A series of equilibrium samples were necessary to check the reproducibility and accuracy. Detailed discussion of these experimental techniques was published by Anufrikov et al.[9]. There are two types of methods available to approach equilibrium.

The static method (closed circuit) is where gas mixtures are bubbled and recirculated through the solvent. After equilibrium is reached, circulation is stopped and samples are withdrawn for analysis. A closed circuit cell used by Ma’mun et al. is shown in Supplementary Figure 8[21].

The dynamic method (open circuit) is where gas mixtures are passed continuously through an absorber and the solubility is continuously measured. This method allows the gas to be analyzed without disturbing the equilibrium, but it is more difficult to operate. An absorption cell used by Daneshvar et al. is shown in Supplementary Figure 9[22]. CO₂ content in the liquid is usually analyzed with the following methods:

	▪ Titration method: BaCO3 precipitation and titration with an acid [11];
	▪ Knorr method: evolving CO2 from the solution by addition of acid and absorbing it in ascarite [23];
	▪ Chittck apparatus [24];
	▪ Calibrated gas chromatography [11];
	▪ Infrared CO2 analyzer [16];
	▪ Fourier infrared spectroscopy [25];
	▪ 13C nuclear magnetic resonance spectroscopy: used to evaluate carbamates stability constant, distribution of CO2 species and individual ionic concentrations [26];
	▪ Raman spectroscopy: to evaluate carbamates stability constant, distribution of CO2 species and individual ionic concentrations [27];
	▪ Material balance [28].

Supplementary Table 1 summarizes the experiments conducted during the past eight decades (1936–2012) with the developments made in phase analysis.

Analysis of the published solubility data

Solubility of CO₂ in aqueous monoethanolamine (MEA), diethanolamine (DEA), methyldiethanolamine (MDEA), 2-amino-2-methyl-1-propanol (AMP), piperazine (PZ) and amine blends have been reported by many researchers at different temperatures, pressures and amine concentrations (Supplementary Tables 2–7). In order to analyze the solubility data available for different solvents, the change in the solubility (loading, α = mol_CO2/mol_amine) with respect to pressures and temperatures were studied in the same concentration ranges. Flue gases resulting from combustion processes are available at low-pressure conditions. The concentration of CO₂ in the flue gas stream is rather low and can vary in general from 5 to 14% by volume, depending on the type of fuel used. The low concentration of CO₂ combined with the low pressure of the gas stream reduces the partial pressure of CO₂. Since the absorption process is driven by partial pressure gradient, the absorption of CO₂ by chemical solvents is favored under high-pressure conditions. The challenge is to find a solvent that would be effective in absorbing CO₂ under low partial pressure conditions. The partial pressure of CO₂ varies from 100 kPa (blast furnace) to 4 kPa in the case of turbine exhaust gas (14 kPa in coal-fired power plant). The partial pressure of CO₂ increases in the stripper at 120°C [29]. As solubility data are, in general, not available at very low pressures for a wide range of solvents, a range of partial pressures from 10 kPa to 500 kPa was used to compare different solvents in terms of CO₂ capacity and demonstrate that the choice of ‘best’ solvent depends on the partial pressure of CO₂.

▪ Change in the solubility of CO₂ in solvents by changing pressures

Figure 1 represents the high-pressure solubility of CO₂ available in the literature in highly concentrated chemical solvents (10–60 wt%) at 40°C [17,19,29–42]. As well known, when the pressure increases the solubility of CO₂ in the solvent increases. At 500 kPa, a maximum solubility (1.2 mol_CO2/mol_amine) occurs for an aqueous sterically hindered amine diamine, 2-amino-2-(hydroxymethyl)-1, 3-propanediol (AHPD, 10 wt%) followed by an aqueous cyclic diamine, PZ (10 wt%), and low solubility (0.6 mol_CO2/mol_amine) occurs for the primary amine, diglycolamine (DGA, 60 wt%). From the structure of these chemicals, it can be concluded that the increase in hindrance to the amino groups increases the loading capacity; the solubility of CO₂ in amines follows, in general, an order such that: primary amines < hindered amines < secondary amines < tertiary amines < diamines. Figure 2 represents the low-pressure solubility data from the literature for chemical solvents at low concentration (<30 wt%) at 40°C [19,33,41–54]. At 100 kPa, triethanolamine (30 wt%) has the lowest solubility (0.4 mol_CO2/mol_amine) and 1,6-hexadiamine (10 wt%) has the highest solubility (1.4 mol_CO2/mol_amine) at 40°C.

Figure 3 represents the change in solubility of a tertiary amine (MDEA) when mixed with other amines [46,55–58]. Adding a hindered amine with a tertiary amine could make a better solvent blend to achieve a maximum loading, as well as an increase in the reaction rate with CO₂. Figure 4 shows the change in the solubility of CO₂ in aqueous PZ solutions by adding other amines [22,55,58–63]. It can be concluded that the addition of sterically hindered amine with aqueous PZ (promoter) will yield a better mixed solvent with high absorption capacity and absorption rate for CO₂. Figure 5 is a good representation of the change in the solubility of CO₂ in aqueous DGA (a primary amine) with the addition of morpholine (a cyclic amine) [52]. It can be observed that the addition of morpholine enhances the solubility of CO₂ in aqueous DGA (0.23–0.26). At low pressures, the enhancement is low (≈0.001) but is higher at higher pressures (≈0.03).

▪ Changes in the solubility of CO₂ in solvents by changing temperatures

The solubility of CO₂ in different solvents with respect to temperatures is very important to estimate the amount of heat required to regenerate the solvent for the absorption/regeneration cycle in CO₂ capture operations, and in the energy balances involved in the design calculations. As the temperature increases, the solubility of CO₂ in the solvent decreases and the slope of this linear change indicates the amount of heat at which the solvent can be regenerated from undesirable products such as the carbamates. The solubility of CO₂ in the solvent has to be more at lower temperature (40°C) and less at a higher temperature (120°C). Therefore, the solvent with the higher slope will be the desired one for CO₂ capture studies. Figure 6 shows the change in the solubility of some proposed amines for CO₂ capture studies with respect to temperature [17,30,31,33–36,41,42,53,56,60,61,64]. It can be observed that the sterically hindered amines have higher slopes, followed by aqueous PZ (cyclic diamine). The general trend of the slopes is sterically hindered amines > tertiary amines > secondary amines > primary amines.

▪ Effect of co-solvent on the solubility of CO₂

Figure 7 shows data of mixtures of ionic liquids (ILs) and amines to produce better solvents for CO₂ capture operations [65–67]. The maximum loading (1.14) is achieved for the mixed solvent with 20 wt% MEA and 20 wt% 1-butyl-3-methylimidazolium tetraflluoroborate at 40°C and 1500 kPa. It shows that the increase in amine concentration increases the solubility of CO₂ in the mixed solvent, and that the solubility of CO₂ in this IL mixture is more than the task-specific IL with an amine added to the cation. Although this kind of mixed solvent involving ILs looks profitable in CO₂ capture loading capacity, they have high viscosity and are expensive [67]. Zhao et al. reported the changes in the physical properties (densities, viscosities and CO₂ capture capacity) during the addition of amines and water in ILs [68]. It was concluded from their work that PZ added to aqueous IL had a good CO₂ capture capacity, and did not decrease after four capture and regeneration cycles. Figure 8 shows the CO₂ capture capacities of these systems at 40°C and 1500 kPa [68]. Industrially attractive hybrid solvent for effective CO₂ capture could be developed by integrating the desirable properties of both ILs as well as amines through the combination of the targeted ILs with selective amines.

VLE modeling

Theoretical modeling of the VLE of the CO₂–alkanolamine system is challenging due to the highly non-ideal nature of the liquid phase arising from the complex interactions such as hydrogen bonding among polar molecules, long-range interaction between ions and short-range interaction among molecule–molecule, ion–ion and ion–molecules, lack of accurate model parameters, and availability and quality of the solubility data in the region of operating conditions. A thermodynamically consistent and rigorous model correlates available experimental data, facilitates process modeling and simulation in wider a range of thermodynamic conditions, and guides in screening out questionable data [69].

▪ Thermodynamic framework & modeling approach

The chemical reaction in the liquid phase drives the dissolution of CO₂ from vapor to liquid phase. The VLE of CO₂–alkanolamine is typically represented as a combination of phase (diffusion) equilibrium between vapor and liquid phase and chemical equilibrium in the liquid phase. Edwards et al. developed the basic thermodynamic framework to treat aqueous solution of weak electrolytes such as CO₂, which couples VLE, dissociation balances, mass balances, electroneutrality and deviations from ideality [70]. The phase and chemical equilibrium equations typically used in modeling for a general monoamine are summarized in Supplementary Table 8. At low pressure, the vapor phase is usually treated as ideal, but at higher pressure, the fugacity coefficient is calculated using an equation of state (EoS). The liquid phase non-ideality is thermodynamically quantified by the activity coefficients. The equilibrium constants relate the species concentration with the activity coefficients. In rigorous modeling, the activity coefficients are calculated from an expression of excess Gibbs energy model (Equation 6 in Supplementary Table 8), which are developed from solution theory of electrolytes (e.g., the model of Deshmukh–Mather [DM] [71], Pitzer’s excess Gibbs energy-based models [72], electrolyte nonrandom two-liquid [e-NRTL] model [73–76] and extended universal quasichemical [e-UNIQUAC] model [77,78] or from an expression of residual Helmholtz free energy obtained from an EoS [79–81]. Such rigorous thermodynamic models have emerged in the last few decades and some were further refined or modified. Different researchers have chosen different models for the same system, which shows the comparative predictive power of these models. The models used for solubility of CO₂ (or a mixture of gases including CO₂) in industrially important amines such as MEA, DEA, MDEA, AMP, PZ and their mixtures and blends with physical solvents are given in Supplementary Tables 2–6, respectively. A brief overview of the popular rigorous models is also given in the Supplementary Information. We summarize the general features of rigorous thermodynamic models in the section titled ‘General features of rigorous thermodynamic models’ and highlight some of the recent applications of popular thermodynamic models in the following sections. Details of these models can be found in Newman et al.[82], and a recent review of thermodynamic modeling of CO₂–amine system published by Georgios and Georgios [83].

▪ General features of rigorous thermodynamic models

Representation of species interactions

At the fundamental level, the models differ in their viewpoints in attributing the liquid phase non-idealities to the type of interactions between species which determines the subsequent modeling approach. Long-range ion–ion interactions are invariably considered by all rigorous models through either one of the forms of modified Debye–Hückel expression or mean spherical approximation. However, the treatment of short- or medium-range interactions is usually different in different modeling approaches:

	▪ DM model: only the molecule–molecule, molecule–ion binary interaction, Bij: Equation 1
	▪ Pitzer model: binary, ternary or many-body interactions between the solute and ionic species;
	▪ e-NRTL: binary interactions between molecule–molecule, molecule–electrolyte, electrolyte–electrolyte interactions only;
	▪ e-UNIQUAC: molecule–molecule and molecule–ion interaction; in some variations (molecule–molecule and molecule–ion pair interaction);
	▪ Furst and Renon EoS: ion–ion and ion–molecule interaction (usually cation–molecule and cation–anion) interaction.

Physical property requirement

A number of thermodynamic parameters/properties are required to solve these equations, and in general are taken from the literature:

	▪ Some equilibrium constants are available in the literature as a function of temperatures. Kim et al. have presented different expressions for the equilibrium constants of the reactions from literature [84];
	▪ Solubility of N2O data in pure amine are used to estimate the solubility of CO2 in pure or blended amines. Penttilä et al.[85] have presented a new correlation for Henry’s law constant for CO2 using the N2O analogy and by regression of a large number of solubility data points taken from literature. Henry’s law constants for mixed solvents are estimated from Henry’s law constants in pure solvents. Henry’s law constant for CO2 in water is usually taken from the literature;
	▪ Vapor pressure, molar volume and dielectric constants of solvents are also taken from the literature;
	▪ Partial molar volume of CO2 at infinite dilution in solvent is computed from correlations.

Interaction parameter regression requirement

Regression of the interaction parameters will depend on the particular model in hand. To enhance the accuracy, additional thermodynamic data (pure component data, e.g., vapor pressure and calorimetric data for binary system: excess enthalpy and VLE of binary system) are used in regression in addition to the VLE data of the actual ternary (CO₂–amine–H₂O) or quaternary system with blended amines.

▪ Rigorous thermodynamic models & recent applications

Applications of the DM model

Application to 2-((2-aminoethyl)amino)ethanol

Recently, Zoghi et al. applied the DM method to correlate and predict the CO₂ solubility in aqueous 2-((2-aminoethyl)amino)ethanol (AEEA) solutions [33]. For correlation purposes, 96 data points for CO₂ solubility in 30 wt% of AEEA at temperatures ranging from 313.2 to 368.2 K and CO₂ partial pressures ranging from above atmospheric to 4400 kPa were considered. AEEA is a diamine and 14 species are considered to be present at equilibrium participating in ten chemical reactions in the liquid phase. The activity of water is set to its mole fraction in the liquid phase. They imposed the following assumptions and a sensitivity analysis that left only eight binary interaction parameters to be considered:

	▪ Symmetry Bij = Bji;
	▪ Interaction between like-charged ions are neglected;
	▪ Self interaction between molecular species are neglected;
	▪ All interactions of molecular and ionic species associated with low concentration species (H+, OH-, +HAEEH+, -OOCAEEACOO- and CO3--) are ignored.

Correlation of data was successful with a percentile absolute average deviation (AAD%) for all the experimental data points of 8.2. Finally, the enthalpy of solution was calculated using the Gibbs–Helmholtz equation at different loading with an average uncertainty of approximately 4.6%. Ma’mun et al. considered 14 B_ij values allowing for solute interaction with water, and found the prediction was qualitatively satisfying (data ranged from 0.01 to 220 kPa) [21].

Application to AMP

We cite another example (Pahlavanzadeh et al.) where the application of the DM model was found to be unsatisfactory [86]. Only seven temperature-dependent B_ij parameters were considered (B_ij = a_ij + B_ijT). The average absolute relative error is equal to 30.35%.

Application to diethylenetriamine & MDEA

The diethylenetriamine–H₂O–CO₂ system consists of 22 species due to the three amine functionalities and, therefore, Harnoto et al. attempted to model the system with all binary interaction parameters equal to zero and the prediction was successful up to loading of 1.0 [87]. They fitted 12 equilibrium constants as functions of first order polynomials (total 24 coefficients) setting all B_ij to zero. With B_ij equal to zero, the model represents the experimental data reasonably well up to a loading of approximately 1.0; however, at loadings above 1.0 the discrepancies are large. For further agreement, consideration of binary interaction parameters was necessary as shown by a sensitivity test, but they did not do so due to insufficiency of data. The estimated value for the differential heat absorption using the Gibbs–Helmholtz equation of aqueous 2.5 M diethylenetriamine solution deviated greatly in the low loading range up to a loading of approximately 0.6 while the agreement is reasonable for loadings between 0.6 and 1.2. The deviation in the low loading region was attributed to the presence of very few experimental data points in the low loading region.

Dicko et al. found that the DM model was in good agreement correlating solubility data up to a total CO₂ + H₂S loading of 1.0 in 50 wt% MDEA [88]. Kumar et al. used a thermodynamic framework by employing the virial EoS and the extended Debye–Hückel equation (Equation 1) to address the vapor and liquid phase nonideality to model the CO₂ solubility data at temperatures of 303.1, 313.1 and 323.1 K and in the CO₂ pressure range of 1 to 350 kPa [89]. A total of 12 binary pairs of the CO₂ + DEA + AMP + H₂O system, and 12 binary pairs of CO₂ + DEA + MDEA + H₂O were correlated with AADs% of 5.3 and 8, respectively.

Applications of Pitzer model

Application to PZ

Bougie and Iliuta presented a new set of interaction parameters for the Pitzer model for the CO₂ + PZ + H₂O system by regressing 354 experimental data to cover a wider range of temperature (286.1–395.1 K), pressure and amine concentrations (0.1–8 mol/kg) with an average deviation of 26.1% [90]. Eleven dissolved species are considered to be present in the liquid phase (two molecular species [CO₂ and PZ], three cations [PZH⁺, PZH₂⁺ and H⁺] and six anions [HCO₃^-, CO₃^-- , PZCOO^-, PZ(COO^-)₂, PZH⁺COO^- and OH^-]. All ternary interaction parameters were assumed to be zero in order to reduce the binary interaction parameters from a possible total 66 (allowing symmetry); they invoked the following assumptions:

	▪ Interaction parameters associated with H+, OH-, PZH2+ and CO3-- are set to zero due to low concentration;
	▪ Interaction with species with same sign of charge (including neutral solute–solute) are neglected.

Finally, from the remaining parameters only those which have significant influence on the data are kept, which are a total of eight binary interaction parameters. They were expressed as first order polynomial of temperature (total 16 coefficients).

Application to the AHPD system

Bougie and Iliuta also modeled the solubility of CO₂ in an aqueous AHPD system covering a large range of amine concentrations (between 0.0125 and 4 mol kg^-1), temperature (between 283.15 and 333.15 K) and total pressure (between 1.85 and 2640.8 kPa) [63]. Using seven temperatures dependent binary interaction parameters (14 coefficients) plus two temperature-independent ternary interaction parameters, they correlated 177 selected experimental data points with an average relative deviation of 22.7%. Generally, higher deviations were obtained at very high amine concentration and very high pressures. Speciation in an aqueous AHPD based on the equilibrium model was also presented.

Application to AMP

Silkenbäumer et al. correlated the solubility of CO₂ in aqueous solutions containing AMP in the temperature range from 313 to 353 K at total pressures up to 2.7 MPa, with the Pitzer excess Gibbs energy model mostly within the experimental uncertainty [46].

Applications of e-UNIQUAC model

Application to MEA, MDEA & blend

Faramarzi et al. have applied the e-UNIQUAC model for CO₂ absorption in the MEA + H₂O, MDEA + H₂O and MDEA + MEA + H₂O systems [91]. Water was considered the only solvent and all other species are considered solute. Mole fraction-based symmetric and asymmetric convention is adopted for solvent and solute species, respectively. Standard chemical potential was calculated from data taken from the literature or estimated from the thermodynamic relationship (e.g., Gibbs–Helmholtz equation), equilibrium constants and assumptions (heat capacity of some ions are set to zero). Fugacity coefficients were calculated using the Soave–Redlich–Kwong EoS, using the standard mixing rule, and no additional parameters were needed. No adjustable parameters were required for as water was the only solvent and density and dielectric constant of water was required as in the DM or Pitzer models presented above. Evaluation of the term requires size and shape-related pure species properties; that is, UNIQUAC volume parameters (r) and surface area parameters (q). The volume and surface area parameters for MEA, MEAH⁺, MEACOO^-, MDEA and MDEAH⁺ are determined by fitting to experimental data, and parameters for other species are taken from the literature. Finally, the enthalpic contribution requires energy interaction parameters (and ) among the species present in the system (molecule–molecule, molecule–ion and ion–ion). Due to the like-ion repulsion assumption, only ion–ion parameters with opposite signs were considered. A wide range of data set was used to fine-tune the model parameters, for example:

	▪ Excess enthalpy;
	▪ Freezing point of the water–MEA system;
	▪ CO2–MEA–water and CO2–MDEA–water VLE data;
	▪ CO2–MEA–MDEA–H2O VLE data.

Thirteen binary interaction parameters (26 coefficients) were regressed for both MEA and MDEA systems and good agreement was found across a wide number of thermodynamic properties such as excess enthalpy, vapor pressure and speciation for a wide range of condition.

Application to MEA

Aronu et al. represented solubility of CO₂ in 15, 30, 45 and 60 wt% MEA from 40 to 120°C using an extended UNIQUAC framework [92]. The Soave–Redlich–Kwong EoS was used to calculate the gas-phase properties. Chemical equilibria in the liquid phase was represented by five chemical reactions involving nine species (three molecular: H₂O, CO₂ and RNH₂; two cations: H₃O⁺ and RNH₃⁺; and four anions: OH^-, HCO₃^-, CO₃^-- and RNHCOO^-). Model parameters were either taken from literature or regressed:

	▪ Mole fraction-based temperature-dependent equilibrium constants and Henry’s law constant for CO2 were taken from the literature;
	▪ Volume and surface area parameters, ri and qi, for H2O, MEA, CO2, H3O+ and OH- were taken from literature and those of MEAH+, HCO3-, CO3-- and MEACOO- were regressed;
	▪ The binary energy interaction parameters are assumed to be symmetric, therefore considering interaction between all species, a maximum of 81 parameters and 81 is required. Many of them were taken from the literature and the remaining ones were found from regression;
	▪ Experimentally determined CO2 partial pressures, total pressures and loadings, as well as N2O solubility data, were used in regression.

The thermodynamic properties of the H₂O–MEA system was represented well: total pressure in 2%, activity coefficient and excess enthalpy in 11%, freezing point depression in 3%. The partial pressure of CO₂, total pressure and physical CO₂ solubility were correlated with an average absolute relative deviation of 24.3, 11.7 and 2.7%, respectively. The estimated heat of absorption and the amine volatility were also found to be satisfactory.

Application to NH₃

Thomsen and Rasmussen modeled the NH₃ + CO₂ + H₂O system in the temperature range 0–110°C, pressure up to 10 MPa and the concentration range up to 80 M ammonia [78]. In a later work by Darde et al., the validity of the e-UNIQUAC model was extended up to 150°C by refitting 43 model parameters with a larger experimental database [93].

Applications of the e-NRTL model

Application to MDEA

Zhang et al. used the symmetric e-NRTL model to correlate a wide variety of thermodynamic properties of the system MDEA–H₂O–CO₂ at temperatures from 313 to 393 K, MDEA concentrations up to 8 M (∼50 wt%), and CO₂ loadings up to 1.32 mol_CO2/mol_amine[69]. The vapor phase is assumed to be a ternary mixture of water, CO₂ and MDEA and the fugacity coefficients of these species were calculated using the perturbed chain statistical associating fluid theory EoS. Eight species (molecular: MDEA, H₂O and CO₂; cations: H₃O⁺ and MDEAH⁺; anions: OH^-, HCO₃^- and CO₃^--) and four chemical reactions are considered in modeling the liquid phase. The activity coefficient of the species in the liquid phase was calculated from the symmetric e-NRTL model [76]. In VLE calculations, the asymmetric mixed-solvent reference state for the molecular solute CO₂ was applied. The reference states for aqueous phase chemical equilibrium calculations were pure liquid for the solvents (water and MDEA) and aqueous-phase infinite dilution for the solutes (ionic and molecular). Standard-state chemical potentials as a function of temperature are calculated from physical property data mostly taken from the literature and using thermodynamic relationships. Physical properties of MDEAH⁺ were obtained from data regression. All molecule–molecule binary parameters and electrolyte–electrolyte binary parameters were defaulted to zero. All molecule–electrolyte binary parameters were defaulted to 8 and -4 for the NRTL model. The nonrandomness factor (R) was fixed at 0.2. The dominant binary NRTL parameters were obtained by regression from the experimental data. Experimental and e-NRTL prediction of CO₂ partial pressure of the MDEA–H₂O–CO₂ system at an MDEA concentration of approximately 8 M are shown in Figure 9[69]. Prediction using the same model parameters was obtained from Zhang and Chen [69]; the 1986 framework is also shown. The two versions of the model yield similar results at low MDEA concentrations with the difference increasing with increasing MDEA concentration. Slight discrepancy in the prediction of partial pressure of CO₂ over MEA + CO₂ + H₂O by the refined e-NRTL and the original e-NRTL was found by Hessen et al.[94]. Earlier, Austgen et al. applied the unsymmetrical e-NRTL model to MDEA and in blends (MDEA + MEA or DEA) with a thorough discussion of modeling details [20].

Application to AMP, PZ, MEA & NH₃

Dash et al. modeled CO₂ + AMP + H₂O using the unsymmetrical e-NRTL model [34]. Nonrandomness factors for molecule–molecule and molecule–electrolyte have been fixed at 0.2 [34]. The ion-pair–ion-pair parameters were assigned a default value of zero. Molecule–ion-pair, ion-pair molecule and one molecule–molecule parameters were regressed as a function of temperature. The modeling results were compared with the solubility data of their own and those from the literature. Their own data at 2.5, 3.4 and 4.9 M AMP concentration in a temperature range of 298 to 328 K were correlated within 10.5%. This model also predicts the speciation, heat of absorption, pH of CO₂-loaded AMP solution and the amine volatility.

The high-pressure CO₂ + PZ + H₂O system was modeled with the unsymmetrical e-NRTL model by Kadiwala et al.[19] and Dash et al.[60]. Dash et al. adjusted the Henry’s law constants in aqueous solution of PZ for a better prediction of the CO₂ partial pressure over aqueous PZ solution. Kadiwala et al. set the ion-pair–ion-pair parameters to zero, took molecule–molecule binary interaction parameters from the literature and regressed three water–electrolyte and five electrolyte–water temperature-independent interaction parameters [19]. A number of data sets including their own high-pressure data were correlated with AAD deviation less than 3% in partial pressure of CO₂. The AAD% deviation reported in the work of Kadiwala et al. and Dash et al. in partial pressure of CO₂ for data from various literature sources is less than the overall AAD (26%) reported by Bougie et al., who used the Pitzer’s excess model for the same system using selected literature data [90].

Vivier et al. correlated a variety of literature data on the MEA + CO₂ + H₂O system with the unsymmetric e-NRTL model with a differential evolution algorithm [95]. The symmetric e-NRTL model was used by Que and Chen to satisfactorily represent the thermodynamic properties (VLE, SLE, speciation, heat of solution and heat capacity) of the NH₃ + CO₂ + H₂O system with a temperature up to 473 K, pressure up to 7 MPa, NH₃ concentration up to 30 wt% and CO₂ loading up to unity [96].

▪ Application of nonrigorous models

The nonrigorous model of Kent and Eisenberg is attractive due to its limited input information requirement, mathematical simplicity and ability to well correlate the partial pressure of CO₂ in a limited range of experimental conditions [97]. The equilibrium constants were treated as apparent equilibrium constants:

Equation 2

The non-ideality of the system was overcome by fitting two equilibrium constants (one of them was for carbamate reversion) to the solubility data while the other equilibrium constants are usually taken from the literature as function of temperature. In the original approach, all equilibrium constants were expressed only as function of temperature. Later, one or more equilibrium constants were expressed as function of temperature, amine concentration, loading or partial pressure of CO₂ to add further flexibility.

The modified Kent and Eisenberg model from Li and Shen was applied [98], in more recent works, to the CO₂ + H₂O + MIPA system by Rebolledo-Morales et al.[38], 2-amino-2-methyl-1-propanol + PZ + water + CO₂ and by Yang et al.[62], and aqueous 4-(diethylamino)-2-butanol by Sema et al.[99], where the two equilibrium constants are expressed as a function of temperature, amine concentration and loading and, subsequently, the constants a_i and b_i are obtained from fitting to experimental data:

Equation 3

In the work of Haider et al. for the modeling of the CO₂ + H₂O + 2-(methylamino)-ethanol system, only one equilibrium constant (carbamate reversion) was expressed as function of temperature, partial pressure and amine concentration, and the rest of the equilibrium constants were considered as function of temperature only [100]. The correlation of partial pressure was deemed to be satisfactory. Gabrielsen et al. considered only one reaction in the aqueous amine system (carbamate formation for MEA and DEA and bicarbonate formation for MDEA) and the partial pressure of CO₂ is expressed as a function of mole fraction CO₂, loading of CO₂ and a combined Henry’s law and equilibrium constant [101]. The parameters in the expression of the equilibrium constant were regressed to experimental data and accurate representation of partial pressure was obtained, although in a limited range of pressure and concentration.

Conclusion

In terms of solubility at low and high pressures, and a low concentration of aqueous sterically hindered amine, AHPD seems to be one of the best solvents. At low pressure and high concentration, an aqueous diamine, AEEA, has higher solubility than other amines but is subject to high rates of degradation. At low pressure and low concentration, an aqueous diamine, 1,6-hexanediamine, has more CO₂ capacity than other available aqueous amines. Unfortunately, the environmental impact of these amines remains questionable.

Considering only the flue gas conditions (low-pressure solubility data), it was observed that 1,6-hexanediamine has the highest loading capacity followed by a mixed solvent with 40 wt% MDEA and a task-specific IL (tetramethylammonium glycinate [N1111Gly]). Mixed solvents with sterically hindered amines have the advantages of maximum CO₂ loading capacity at lower temperatures and low loading at higher temperatures. Adding physical solvents enhances the solubility at high pressures and reduces the solubility at high temperatures, which is desirable for the absorption/stripping cycle.

Rigorous thermodynamic modeling of a reactive CO₂–aqueous alkanolamine system is a challenging task. While the long-range interaction is usually taken care of by an extended Debye–Hückel equation, great varieties exist in modeling the array of short-range interactions.

The nonlocal composition-based models such as the DM model, Pitzer’s excess Gibbs energy model, and local composition-based models such as e-UNIQUAC and e-NRTL and the modified (still nonrigorous) Kent–Eisenberg model are frequently chosen. The nonrigorous models perform well in a limited range of temperature, pressure and loading. The performance of the DM model may deteriorate at higher amine concentration.

The e-NRTL model has been applied to numerous systems. A recently proposed symmetric e-NRTL is thermodynamically consistent for treating an aqueous or non-aqueous system and mixed solvent system. It has also been applied to model VLE, liquid–liquid equilibrium and solid–liquid equilibrium in a single (ammonia) system. Prediction using the unsymmetrical and symmetrical e-NRTL may vary slightly for some systems.

The e-UNIQUAC requires ion-specific parameters (size and shape parameters) in addition to binary interaction parameters and can model complex systems including VLE, liquid–liquid equilibrium and solid–liquid equilibrium. Many assumptions are introduced to reduce the theoretically possible hundreds of binary interaction parameters to a manageable number in the applications of the DM, Pitzer, e-UNIQUAC, e-NRTL, and Fürst and Renon EoS models. Extensive experimental data on pure component property and binary subsystems (H₂O + CO₂, H₂O + amine) are required to enhance the capability of the model. Nuclear magnetic resonance speciation data are useful to verify the model predictive ability for speciation.

Binary interaction parameters are usually transferable from previous work or from similar systems and can be used as an initial guess. EoS models require molecule-specific and ion-specific parameters.

Future perspective

Large-scale carbon capture for flue gases is still not available commercially. The first CO₂ capture plant for a 110 MW coal power plant unit is being built in Saskatchewan, Canada, in 2012 for Saskpower. The process is still quite costly and, therefore, there is much room for potential improvement in the design of new solvents. It is for this reason that we have left the door open in our review to some solvents that for now are not considered probable candidates for flue gas application. Many researchers have focused their efforts on mixed or blended amines to overcome the deficiencies of single solvents. Some recent screening studies show the potential of finding aqueous single monoamines, diamines or task-specific ILs for industrial applications. However, the optimal solvent has to pass the test of kinetics, cyclic capacity, energy of regeneration, volatility, degradation, corrosion, toxicity, cost and pilot plant demonstration studies. Future research work is expected to continue to further optimize the currently promising solvents, focused on overcoming their limitations. Research is expected to intensify in dealing with novel cyclic and tertiary amines, amine blends with ILs, amine functionalized ILs or amino acids, in order to find an economical solvent for CO₂ capture.

Equilibrium solubility

Study of the solubility of a gas in a liquid when temperature, pressure and concentration of vapor and liquid have no net change over time.

CO₂ loading

Ratio of mole of CO₂ absorbed per mole of solvent.

Executive summary

Desired properties of a CO₂ capture solvent

	▪ High specific absorption capacity for the acid gases.
	▪ High boiling point and consequently low vapor pressure to prevent solvent loss.
	▪ High degree of stability of the molecule in order to prevent decomposition.
	▪ Reduced corrosion.

Vapor–liquid equilibrium or equilibrium solubility

	▪ Vapor–liquid equilibrium (VLE) data are required for the design and operation of the plants.
	▪ VLE data can be used for testing and development of theoretical models, correlations and process design software.

Experimental methods

	▪ In CO2 capture research, the existing experimental set-up can be classified into two main experimental methods: analytical and synthetic.
	▪ Three different types of VLE cells are used extensively to obtain equilibrium solubility data. Supplementary Table 1 summarizes the experiments conducted during the past decades with the development made in phase analysis.

Experimental data on the solubility of CO₂

	▪ General advantages and disadvantages of different industrial solvents are reviewed.
	▪ Solubility data in a number of industrially important solvents monoethanolamine, diethanolamine, methyldiethanolamine, 2-amino-2-methyl-1-propanol, piperazine and their mixtures and blends with physical solvents are reviewed.

Analysis of the published solubility data

	▪ Trends in the effect of pressure and temperature on solubility are analyzed.
	▪ Pure, mixed and blended solvents are compared in terms of capacity.

VLE modeling

	▪ Both rigorous and nonrigorous models are applied in data correlation of CO2–alkanolamine systems.
	▪ Thermodynamic models used by different researchers for different systems are tabulated.
	▪ Overview of the models and recent applications are highlighted.

Supplementary data

To view the supplementary data that accompany this paper please visit the journal website at: www.future-science.com/doi/suppl/10.4155/CMT.12.47

Financial & competing interests disclosure

The authors have no relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript. This includes employment, consultancies, honoraria, stock ownership or options, expert testimony, grants or patents received or pending, or royalties.

No writing assistance was utilized in the production of this manuscript.