CO₂ solubility in aqueous N-methylcyclohexylamine (MCA) and N-cyclohexyl-1,3-propanediamine (CHAP) solutions

Abstract

N-methylcyclohexylamine (MCA) and N-cyclohexyl-1,3-propanediamine (CHAP) have been suggested, in mixtures with lipophilic amines, as potential phase change solvents for CO₂ capture applications, and subsequently studied as promising alternatives to monoethanolamine (MEA) for minimizing the desorber's energy requirements. In this study, new high pressure experimental data were obtained for the solubility of CO₂ in aqueous solutions containing MCA or CHAP at 313 and 333 K. The obtained data were used to parameterize the modified Kent–Eisenberg model. In this direction, CHAP was modeled assuming a “principle of independent reactivity,” that is, that the reactivity of each amine group does not depend on the potential reaction of the other one. It was shown that through this approach the model can be successfully applied to diamines using the relevant equations of amine mixtures.

1 INTRODUCTION

For post-combustion CO₂ capture many research activities are underway at present. These include solid sorbents, membranes, and new liquid absorbents.¹ Among such technologies, absorption/desorption processes have received significant attention, with several efforts observed worldwide regarding the scaling-up of capture plants.² The major limitation of such processes is the reboiler duty required for solvent regeneration, which poses significant energy penalties in the CO₂ emitting plants. To reduce the energy costs of absorption/desorption systems, it is imperative to search for solvents that can decrease the heat duty in the order of 2.0 GJ/ton of CO₂ captured or below.²

In this direction, numerous different solvents have been investigated at laboratory or pilot scale,^{3, 4} but few have been tested at larger capacity units. Among such solvents, mixtures such as 2-amino-2-methyl-1-propanol (AMP) and piperazine (PZ), methyldiethanolamine (MDEA) and PZ, or the proprietary solvent KS-1 appear to be promising as they indicated potential for regeneration energy around 3.0 GJ/ton of CO₂ captured, compared to the approximately 4.0 GJ/ton of CO₂ captured with the 30 wt.% MEA.^{5, 6} While these reductions have been attained in standard absorption/desorption flowsheets, solvents such as PZ exhibited reductions down to approximately 2.0 GJ/ton CO₂ in flowsheets that included internal energy recovery equipment.²

Recently, using computer aided molecular design (CAMD) coupled with Pareto optimization, Papadopoulos et al.⁷ suggested N-cyclohexyl-1,3-propanediamine (CHAP) as a novel promising solvent. Aqueous N-cyclohexyl-1,3-propanediamine (CHAP)—N,N-dimethyl-cyclohexylamine (DMCA) mixtures were investigated and it was shown that they exhibit high cyclic capacity and low regeneration energy requirements, around 2.3 GJ/ton of captured CO₂. These mixtures exhibit phase-change behavior, in which a second liquid phase is generated upon a change in processing conditions.⁸ The second liquid phase is lean in CO₂ and may be recycled directly to the absorber, thus enabling a reduction of the regeneration energy requirements due to the reduction of the CO₂-rich solvent that is thermally processed in the desorber. Phase-change solvents do not require additional equipment, other than a simple decanter. In a previous study,⁹ it was indicated that mixtures of cyclohexylamines, such as N-methyl-cyclohexylamine (MCA) and DMCA, can reduce the regeneration energy in the range of 2.0–2.5 GJ/ton CO₂. Another work¹⁰ further showed that MCA and CHAP/DMCA can result in up to 47% lower operating costs than MEA.

In this work, new experimental data and modeling results are presented for aqueous solutions of MCA and CHAP, since both were used in mixtures with DMCA as phase change solvents for CO₂ capture applications. The available literature data regarding the phase behavior of systems containing MCA, CHAP and their mixtures under CO₂ atmosphere are shown in Table 1.

TABLE 1. Literature studies reporting experimental data for the CO₂ loading and the phase behavior of aqueous solvents containing MCA or CHAP

Amine(s)	References
CHAP^a	Papadopoulos et al.^7
MCA	Zhang^9; Perdomo et al.,^11 Jeon et al.^12
DMCA + CHAP^a	Papadopoulos et al.^7; Tzirakis et al.^13
DMCA + MCA	Tzirakis et al.^14; Wang et al.^15; Ζhang^9
Screening experiments	Ye et al.^16

• ^a Mentioned as S₁N in Papadopoulos et al.⁷

In more detail, Perdomo et al.¹¹ presented experimental equilibrium results for DMCA and MCA aqueous solutions at CO₂ partial pressures up to approximately 80 kPa. It was shown that at MCA aqueous solutions, although biphasic in the absence of CO₂ and at ambient conditions, present a single liquid phase upon CO₂ dissolution at 40 and 60°C and for CO₂ partial pressures higher than approximately 15 kPa. At 90°C, they present liquid–liquid phase separation for CO₂ partial pressures lower than approximately 25 kPa, while they present a single liquid phase for high loading conditions (higher CO₂ partial pressures). The results were modeled using the SAFT-γ Mie group contribution approach.¹¹

The CO₂-DMCA-CHAP-H₂O system was experimentally investigated at 40–90°C, using an aqueous amine solution with total amine content of 44.3 wt.%, (app. 3 M) at a 2:1 DMCA to CHAP mole ratio.¹³ It was shown that upon liquid–liquid phase separation, the hydrophilic CHAP is accumulated in the CO₂ rich aqueous phase, while the hydrophobic DMCA is mainly found in the organic, CO₂ lean, phase. In addition, it was concluded that as the CO₂ partial pressure increases, more amine molecules, and mainly the lipophilic DMCA, are transformed in hydrophilic ionic species that end up in the aqueous phase.¹³

Another work¹⁵ investigated aqueous solutions of DMCA-MCA blends. The CO₂ solubility in the aqueous DMCA-MCA blends is high and significantly increases with the ratio of MCA in the amine mixture. Using NMR and theoretical analyses, the authors showed that the formed MCA carbamate is relatively unstable and it is easily transformed to bicarbonate, rendering bicarbonate as the main product. Finally, the regeneration energy of such aqueous solvent is very low and in the range of 2.3 GJ/ton CO₂. Considering such phase change solvents, another study¹⁷ applied NMR analysis and quantum calculations revealing the mechanism of CO₂ absorption. The performed analysis proved the occurrence of a two-stage interaction mechanism; the first stage was controlled by absorption kinetics, and the second stage was controlled by thermodynamics.

The rigorous thermodynamic modeling of the vapor–liquid equilibrium of aqueous amine systems under CO₂ atmosphere requires accounting for all ionic and intermolecular interactions in the liquid solution and the calculation of fugacities in both phases. This is usually performed using electrolyte equation of state (EoS) theories, or EoS/G^E models, considering also the equilibrium constants of all relevant chemical reactions.^18-20 Such approach, although rigorous, presents significant complexity and, consequently, several simplifications are often applied, for example, ionic interactions are not explicitly accounted for and are lumped into the hydrogen bonding term of the relevant EoS models.^{7, 21-24}

The thermodynamic approaches for modeling gas solubility in such systems were reviewed recently.²⁰ It was observed that several empirical or semi-empirical approaches which are considerably simpler than EoS models, present a good correlation and prediction ability. In this direction, the most popular one is the Kent–Eisenberg model,²⁵ which requires the knowledge of equilibrium constants of all chemical reactions, and Henry's constant for calculating the molecular CO₂ dissolution into the liquid phase. Kent and Eisenberg²⁵ used the literature values of ionization and Henry's law constants, except from those referring to the amine reactions (the amine ionization reaction and the carbamate hydrolysis one), which were fitted to the experimental solubility data. According to Jou et al.,²⁶ in this way all non-idealities of the system are absorbed by the effective values of the adjustable parameters. Due to its low computational complexity, the model found numerous applications in correlating the CO₂ and H₂S solubility in aqueous amine systems and several modifications were presented in published literature.²⁷

Based on previous works,^{7, 10} it is deemed interesting to examine further MCA and CHAP aqueous solutions. This is due to their excellent carbon capture capabilities and phase change behavior when blended with DMCA. In this study we use a pressure decay method to obtain new experimental data for the CO₂ loading of aqueous MCA and CHAP solutions. The new experimental data cover a wide range of pressures, in contrast with the existing data presented in Table 1, which are limited to low pressures. Thus, the obtained new data allow the rigorous parameterization of the modified Kent–Eisenberg model that was extended to systems containing diamines with both a carbamate- and a non-carbamate forming amine group.

2 EXPERIMENTAL

2.1 Materials

The materials used in this work are shown in Table 2. They are used as received without further purification. The molecular structure of both investigated amines is shown in Figure 1.

TABLE 2. Chemicals used in this work

Product name	Abbreviation	CAS-number	Purity	Supplier
Carbon dioxide	CO2	124-38-9	99.9 (vol%)	Air Liquide
Nitrogen	N2	7727-37-9	99.9 (vol%)	Air Liquide
Helium	He	7440-59-7	99.99 (vol%)	Air Liquide
N-methylcyclohexylamine	MCA	100-60-7	99%	Sigma Aldrich
N-cyclohexyl-1,3-propanediamine	CHAP	3312-60-5	98%	ITC

FIGURE 1

Molecular structure of N-methyl-cyclohexylamine (MCA) and N-cyclohexyl-1,3-propanediamine (CHAP), which consists of a secondary (a) and a primary amine group (b) part, with the secondary amine group part (a) resembling the structure of MCA.

2.2 Experimental apparatus and procedure

The CO₂ solubility in aqueous ΜCA and CHAP solutions was measured using a pressure decay method and a relevant apparatus that is shown in Figure 2. The experimental procedure is described in our previous works.^{23, 24} Briefly, the air is removed from the high-pressure cell and, subsequently, a known amount of the aqueous solvent (around 25 g, maximum error ±0.002 g) is added. Then, 3–5 g of CO₂, depending on the experiment, are added to the system. The added amount of CO₂ is estimated (maximum error ± 0.002 g) by measuring the mass (accuracy of ±0.001 g) of a high-pressure CO₂ containing flask, before and after the addition. The pressure and the temperature inside the equilibrium cell are continuously monitored, using a pressure transducer (WIKA A-10, ±0.5%) and a Pt-100 (±0.01 K) thermometer, respectively. It is assumed that equilibrium conditions are reached upon pressure stabilization for at least 1 h. Knowing the temperature and pressure conditions, as well as the volume of the vapor phase, the amount of the absorbed CO₂ is calculated using the mass balance equations.^{23, 24} The equilibrium high-pressure cell is immersed inside a water bath of constant temperature (stability of temperature in the bath equal to 0.1 K). As described previously,²⁴ the volume of the cell (152.2 ± 1.6 cm³ at 298.15 K) was estimated at various temperatures by measuring the pressure after the addition of known CO₂ amounts. In all experimental conditions, the needed CO₂ densities were obtained from NIST.²⁸

FIGURE 2

Experimental apparatus for VLE measurements consisting of a CO₂ gas flask (A), water bath (B), equilibrium high-pressure cell (C), magnetically stirred and equipped with temperature and pressure sensors, and temperature controller (D).

According to such experimental procedure,^{23, 24} the total pressure of the system is measured. In order to estimate the partial pressure of CO₂, the vapor pressure of the aqueous solution is subtracted from the total pressure. Since the investigated solutions are not volatile, such approximation, which is often used in similar studies,^{29, 30} results in an insignificant correction, especially at relatively high pressures. In all cases, the uncertainties in the reported values for the CO₂ loading denote the maximum error, estimated through a propagation of errors analysis, knowing the uncertainties of all experimental measurements (i.e., weight of the materials, volume of the cell, etc.).²⁴

2.3 A modified Kent–Eisenberg model

A modified Kent–Eisenberg model was used in this study to correlate the experimental data as shown next in this section. In contrast with the original model,²⁵ equations are not solved iteratively, but a polynomial equation is used for estimating the hydrogen ion concentration, as shown by Haji-Sulaiman et al.³¹

Although the relevant equations of such modified Kent–Eisenberg model for pure carbamate or non-carbamate forming amines are presented in many studies,^{27, 31} the relevant equations and approaches for mixtures are not always well documented. Suleman et al.²⁷ recently reviewed the use of such models and approaches in literature and mention three possible ways of developing a model for amine blends. According to the first and most simple approach, but also the most approximate one, the single amine models are solved and the resulting CO₂ solubilities in both single amine solutions are summed up to estimate the solubility in the blend. According to the second one, the polynomial equations of the single amine models (that are used for estimating the hydrogen ion concentration) are summed up and then the loading is estimated through a combined equation. However, the summation of such polynomial equations adds unnecessary empiricism to the model. Finally, according to the third and most rigorous one, the mass and charge balances for the multicomponent system are thoroughly set, resulting in a rigorous polynomial equation for the hydrogen ion concentration. According to this work,²⁷ all approaches result in similar estimations for the CO₂ solubility, despite that the first two of them are very approximate.

In this study, the third approach, as described by Suleman et al.,²⁷ is followed and the relevant equations are presented for a mixture of a carbamate forming amine (R_aR_bNH) and a non-carbamate forming amine (R_cR_dNH), that, as we will show, can be also used for diamines.

Assuming a mixture of a carbamate forming amine (R_aR_bNH) and a non-carbamate forming amine (R_cR_dNH), we can write the following chemical reactions and the relevant equilibrium constants^{27, 31}:

$${R_a{R}_b\mathit{NH}}_2^{+}\stackrel{k_{11}}{\leftrightarrow }{R}_a{R}_b\mathit{NH}+{{\rm H}}^{+},$$ (1)

$${R_c{R}_d\mathit{NH}}_2^{+}\stackrel{k_{12}}{\leftrightarrow }{R}_c{R}_d\mathit{NH}+{{\rm H}}^{+},$$ (2)

$${{\rm H}}_{2}O+{\mathit{C{\rm O}}}_2\stackrel{k_2}{\leftrightarrow }{{\rm H}}^{+}+{\mathit{HCO}}_3^{-},$$ (3)

$${\mathit{HCO}}_3^{-}\stackrel{k_3}{\leftrightarrow }{{\rm H}}^{+}{+\mathit{CO}}_3^{-2},$$ (4)

$${{\rm H}}_{2}O\stackrel{k_4}{\leftrightarrow }{{\rm H}}^{+}+{\mathit{O{\rm H}}}^{-},$$ (5)

$${R_a{R}_b\mathit{NCO}{O}^{-}+H_{2}O\stackrel{k_5}{\leftrightarrow }{R}_a{R}_b\mathit{NH}+\mathit{HCO}}_3^{-},$$ (6)

where ${R_a{R}_b\mathit{NH}}_2^{+}\text{and}{R_c{R}_d\mathit{NH}}_2^{+}$ are the protonated forms of the carbamate forming and the non-carbamate forming alkanolamine, respectively, while R_aR_bNCOO⁻ represents the carbamate anion.

The equilibrium constants for Equations 1-6 are written as follows²⁷:

$$\text{Alkanolamine deprotonation}:k_{11}=\left[R_a{R}_b\mathit{NH}\right]\left[{{\rm H}}^{+}\right]/\left[{R_a{R}_b\mathit{NH}}_2^{+}\right],$$ (7)

$$\text{Alkanolamine deprotonation}:k_{12}=\left[R_c{R}_d\mathit{NH}\right]\left[{{\rm H}}^{+}\right]/\left[{R_c{R}_d\mathit{NH}}_2^{+}\right],$$ (8)

$$\text{Bicarbonate formation}:k_2=\left[{\mathit{HCO}}_3^{-}\right]\left[{{\rm H}}^{+}\right]/\left[C{{\rm O}}_2\right],$$ (9)

$$\text{Carbonate formation}:k_3=\left[{\mathit{CO}}_3^{-2}\right]\left[{{\rm H}}^{+}\right]/\left[{\mathit{HCO}}_3^{-}\right],$$ (10)

$$\text{Water dissociation}:k_4=\left[{\mathit{{\rm O}{\rm H}}}^{-}\right]\left[{{\rm H}}^{+}\right],$$ (11)

$$\text{Carbamate hydrolysis}:k_5=\left[R_a{R}_b\mathit{NH}\right]\left[{\mathit{HCO}}_3^{-}\right]/\left[R_a{R}_b\mathit{NCO}{O}^{-}\right].$$ (12)

Equations (7-12) result in the following equations for the concentration of species:

$$\left[O{{\rm H}}^{-}\right]=k_4/\left[{{\rm H}}^{+}\right],$$ (13)

$$\left[{\mathit{HCO}}_3^{-}\right]=k_2\left[C{{\rm O}}_2\right]/\left[{{\rm H}}^{+}\right],$$ (14)

$$\left[{\mathit{CO}}_3^{-2}\right]=k_2{k}_3\left[C{{\rm O}}_2\right]/{\left[{{\rm H}}^{+}\right]}^2,$$ (15)

$$\left[\mathit{\text{RRNCO}}{O}^{-}\right]=k_{11}{k}_2\left[C{{\rm O}}_2\right]\left[{R_a{R}_b\mathit{NH}}_2^{+}\right]/\left(k_5{\left[H^{+}\right]}^2\right).$$ (16)

Moreover, we can write three mass balance equations and one for the charge balance of the solution.

Alkanolamine balances:

$$\left[R_a{R}_b\mathit{\text{NHtot}}\right]=\left[R_a{R}_b\mathit{NH}\right]+\left[{R_a{R}_b\mathit{NH}}_2^{+}\right]+\left[\mathit{\text{RRNCO}}{O}^{-}\right],$$ (17)

$$\left[R_c{R}_d\mathit{\text{NHtot}}\right]=\left[R_c{R}_d\mathit{NH}\right]+\left[{R_c{R}_d\mathit{NH}}_2^{+}\right],$$ (18)

$$\left[\mathit{\text{RRNHtot}}\right]=\left[R_a{R}_b\mathit{\text{NHtot}}\right]+\left[R_c{R}_d\mathit{\text{NHtot}}\right].$$ (19)

Carbon dioxide balance:

$$a\left[\mathit{\text{RRNHtot}}\right]=\left[C{{\rm O}}_2\right]+\left[{\mathit{HCO}}_3^{-}\right]+\left[{\mathit{CO}}_3^{-2}\right]+\left[\mathit{\text{RRNCO}}{O}^{-}\right].$$ (20)

Charge balance:

$$\left[{{\rm H}}^{+}\right]+\left[{R_a{R}_b\mathit{NH}}_2^{+}\right]+\left[{R_c{R}_d\mathit{NH}}_2^{+}\right]=\left[O{{\rm H}}^{-}\right]+\left[{\mathit{HCO}}_3^{-}\right]+2\left[{\mathit{CO}}_3^{-2}\right]+\left[\mathit{\text{RRNCO}}{O}^{-}\right],$$ (21)

where α is the carbon dioxide loading (expressed as mole of CO₂ per mole of amine), [RRNHtot] is the total concentration of amines and [CO₂] is the liquid phase carbon dioxide solubility, determined by Henry's law, as follows:

$$\left[C{{\rm O}}_2\right]=P_{\mathit{CO}2}/H_{\mathit{CO}2},$$ (22)

where $P_{\mathit{CO}2}$ and $H_{\mathit{CO}2}$ are the CO₂ partial pressure in the vapor phase and the Henry's constant, respectively.

For a mixture of a carbamate and a non-carbamate forming alkanolamine, Equations (7-21) reduce to a system of three equations with three unknowns, $\left[{{\rm H}}^{+}\right]$, $\left[{R_a{R}_b\mathit{NH}}_2^{+}\right]$ and $\left[{R_c{R}_d\mathit{NH}}_2^{+}\right]$, as follows:

$$\left[R_a{R}_b{\mathit{NH}}_{\mathit{tot}}\right]=\left(1+k_{11}/\left[{{\rm H}}^{+}\right]+k_{11}{k}_2\left[C{{\rm O}}_2\right]/\left(k_5{\left[{{\rm H}}^{+}\right]}^2\right)\right)\left[{R_a{R}_b\mathit{NH}}_2^{+}\right],$$ (23)

$$\left[R_c{R}_{d}N{H}_{\mathit{tot}}\right]=\left(1+k_{12}/\left[{{\rm H}}^{+}\right]\right)\left[{R_c{R}_d\mathit{NH}}_2^{+}\right],$$ (24)

$$\left[{R_a{R}_b\mathit{NH}}_2^{+}\right]\left(1-k_{11}{k}_2\left[C{{\rm O}}_2\right]/\left(k_5{\left[{{\rm H}}^{+}\right]}^2\right)\right)+\left[{R_c{R}_d\mathit{NH}}_2^{+}\right]=k_4/\left[{{\rm H}}^{+}\right]+k_2\left[C{{\rm O}}_2\right]/\left[{{\rm H}}^{+}\right]+2k_2{k}_3\left[C{{\rm O}}_2\right]/{\left[{{\rm H}}^{+}\right]}^2-\left[{{\rm H}}^{+}\right].$$ (25)

After some algebra, the following polynomial equation of 6th order is obtained:

$$A{\left[{{\rm H}}^{+}\right]}^6+B{\left[{{\rm H}}^{+}\right]}^5+\mathrm{C}{\left[{{\rm H}}^{+}\right]}^4+\mathrm{D}{\left[{{\rm H}}^{+}\right]}^3+E{\left[{{\rm H}}^{+}\right]}^2+\mathrm{F}\left[{{\rm H}}^{+}\right]+G=0,$$ (26)

where A, B, C, D, E, F and G are shown in Table 3.

TABLE 3. Parameters of Equation (26)

Parameters	Relation
A	$-k_5$
B	$-k_5\left[R_a{R}_b{\mathit{NH}}_{\mathit{tot}}\right]-k_5\left[R_c{R}_{d}N{H}_{\mathit{tot}}\right]-k_{11}{k}_5-k_{12}{k}_5$
C	$-k_{12}{k}_5\left[R_a{R}_b{\mathit{NH}}_{\mathit{tot}}\right]-k_{11}{k}_5\left[R_c{R}_{d}N{H}_{\mathit{tot}}\right]+k_4{k}_5+k_2{k}_5\left[C{{\rm O}}_2\right]-k_{11}{k}_2\left[C{{\rm O}}_2\right]-k_{11}{k}_{12}{k}_5$
D	$k_{11}{k}_2\left[R_a{R}_b{\mathit{NH}}_{\mathit{tot}}\right]\left[C{{\rm O}}_2\right]-k_{11}{k}_2\left[R_c{R}_{d}N{H}_{\mathit{tot}}\right]\left[C{{\rm O}}_2\right]+2k_2{k}_3{k}_5\left[C{{\rm O}}_2\right]+k_{11}{k}_4{k}_5+k_{11}{k}_2{k}_5\left[C{{\rm O}}_2\right]-k_{11}{k}_{12}{k}_2\left[C{{\rm O}}_2\right]+k_{12}{k}_4{k}_5+k_{12}{k}_2{k}_5\left[C{{\rm O}}_2\right]$
E	$k_{11}{k}_{12}{k}_2\left[R_a{R}_b{\mathit{NH}}_{\mathit{tot}}\right]\left[C{{\rm O}}_2\right]+2k_{11}{k}_2{k}_3{k}_5\left[C{{\rm O}}_2\right]+k_{11}{k}_2{k}_4\left[C{{\rm O}}_2\right]+k_{11}{k_2}^2{\left[C{{\rm O}}_2\right]}^2+2k_{12}{k}_2{k}_3{k}_5\left[C{{\rm O}}_2\right]+k_{11}{k}_{12}{k}_4{k}_5+k_{11}{k}_{12}{k}_2{k}_5\left[C{{\rm O}}_2\right]$
F	$2k_{11}{k_2}^2{k}_3{\left[C{{\rm O}}_2\right]}^2+k_{11}{k}_{12}{k}_2{k}_4\left[C{{\rm O}}_2\right]+k_{11}{k}_{12}{k_2}^2{\left[C{{\rm O}}_2\right]}^2+2k_{11}{k}_{12}{k}_2{k}_3{k}_5\left[C{{\rm O}}_2\right]$
G	$2k_{11}{k}_{12}{k_2}^2{k}_3{\left[C{{\rm O}}_2\right]}^2$

Only the root with physical meaning, that is, $\mathit{pH}\in \left[7,12\right],$^{27, 31} is kept from Equation (26), while the loading is calculated through the following equations:

$$\mathrm{\alpha }=\left(\left[C{{\rm O}}_2\right]+\frac{k_2\left[C{{\rm O}}_2\right]}{\left[{{\rm H}}^{+}\right]}+\frac{k_2{k}_3\left[C{{\rm O}}_2\right]}{{\left[{{\rm H}}^{+}\right]}^2}+\left[\mathit{\text{RRNCO}}{O}^{-}\right]\right)/\left(\left[\mathit{\text{RRNHtot}}\right]\right),$$ (27)

where

$$\begin{array}{l}\left[\mathit{\text{RRNCO}}{O}^{-}\right]=\left(k_{11}{k}_2\left[C{{\rm O}}_2\right]\left[R_a{R}_b{\mathit{NH}}_{\mathit{tot}}\right]\right)/(k_5{\left[{{\rm H}}^{+}\right]}^2+k_{11}{k}_5\left[{{\rm H}}^{+}\right]\\ +k_{11}{k}_2\left[C{{\rm O}}_2\right]).\end{array}$$ (28)

The above equations are sufficient for estimating the loading in any mixture of two amines, one carbamate forming and one non-carbamate forming one. If two different monoamines are considered, then their total concentrations, $\left[R_a{R}_b\mathit{\text{NHtot}}\right]$ and $\left[R_c{R}_d\mathit{\text{NHtot}}\right]$, refer to the initial composition of the unloaded aqueous solvent (i.e., denote moles of amine molecules in kg of water). Similarly, all other species concentrations refer to moles of molecules (or ions) per kg of water and the calculated loading through Equation (27) denotes the moles of absorbed CO₂ per mole of amine molecules.

However, CHAP is a diamine consisting of two amine groups (Figure 1), one that is sterically hindered, and, thus, considered as non-carbamate forming group, and one carbamate forming group. In such case, one can also use the aforementioned equations. However, in that case all amine species concentrations will denote moles of amine groups and not moles of molecules. In that case the calculated loading from Equation (27) denotes the moles of absorbed CO₂ per mole of amine groups (not molecules) and should be adequately converted to be compared to experimental data (which usually present loadings as moles of CO₂ per mole of amine molecules).

In case of MCA (Figure 1), which has a single amine (assumed as sterically hindered and, thus, non-carbamate forming) group in each molecule, $\left[R_a{R}_b{\mathit{NH}}_{\mathit{tot}}\right]$ and $\left[{R_a{R}_b\mathit{NH}}_2^{+}\right]$ in Equations (23-25) are set equal to zero. Thus, the system of Equations (23-25) reduces to the following one:

$$\left[R_c{R}_{d}N{H}_{\mathit{tot}}\right]=\left(1+k_{12}/\left[{{\rm H}}^{+}\right]\right)\left[{R_c{R}_d\mathit{NH}}_2^{+}\right],$$ (29)

$$\left[{R_c{R}_d\mathit{NH}}_2^{+}\right]=k_4/\left[{{\rm H}}^{+}\right]+k_2\left[C{{\rm O}}_2\right]/\left[{{\rm H}}^{+}\right]+2k_2{k}_3\left[C{{\rm O}}_2\right]/{\left[{{\rm H}}^{+}\right]}^2-\left[{{\rm H}}^{+}\right],$$ (30)

which after some algebra gives the following polynomial equation, as described in similar studies²⁷:

$$A^{\prime }{\left[{{\rm H}}^{+}\right]}^4+B^{\prime }{\left[{{\rm H}}^{+}\right]}^3+{\mathrm{C}}^{\prime }{\left[{{\rm H}}^{+}\right]}^2+{\mathrm{D}}^{\prime }\left[{{\rm H}}^{+}\right]+E^{\prime }=0,$$ (31)

where $A^{\prime }$, $B^{\prime }$, $C^{\prime }$, $D^{\prime }$ and $E^{\prime }$ are shown in Table 4.

TABLE 4. Parameters²⁷ of Equation (31)

Parameters	Relation
$A^{\prime }$	1
$B^{\prime }$	[$R_c{R}_d{\mathit{NH}}_{\mathit{tot}}]+k_{12}$
$C^{\prime }$	$-k_4-k_2\left[{\mathit{CO}}_2\right]$
$D^{\prime }$	$-k_{12}{k}_4-2k_2{k}_3\left[{\mathit{CO}}_2\right]-k_{12}{k}_2\left[{\mathit{CO}}_2\right]$
$E^{\prime }$	$-2k_{12}{k}_2{k}_3\left[{\mathit{CO}}_2\right]$

Also, by setting $\left[\mathit{\text{RRNCO}}{O}^{-}\right]=0$, Equation (27) reduces to:

$$\mathrm{\alpha }=\left(\left[C{{\rm O}}_2\right]+\frac{k_2\left[C{{\rm O}}_2\right]}{\left[{{\rm H}}^{+}\right]}+\frac{k_2{k}_3\left[C{{\rm O}}_2\right]}{{\left[{{\rm H}}^{+}\right]}^2}\right)/\left(\left[R_c{R}_d{\mathit{NH}}_{\mathit{tot}}\right]\right).$$ (32)

The equilibrium constants, k_i or k_ij, are estimated using empirical relations as follows²⁷:

$$\ln \left(k_i\right)=\frac{A_i}{T}+B_i\mathit{lnT}+C_{i}T+D_i.$$ (33)

Details on the parameters that are fitted in Equation (33), are presented in the modeling results section.

3 RESULTS AND DISCUSSION

3.1 Experimental results

Considering the aqueous CHAP solution, measurements were performed at 313 and 333 K for CO₂ partial pressures higher than 80 kPa, since the pressure decay method is not recommended at very low pressures or high temperatures due to potential solvent vaporization. All measurements were performed starting for a 32.5 wt.% aqueous amine solution. The experimental results are presented in Table 5. The obtained data are compared with available literature low pressure data,⁷ which were obtained using a chemical analysis experimental technique, in Figures 3 and 4. It is observed that both data sets are in very good agreement, despite the differences in the investigated pressure range. Furthermore, as shown in Figures 3 and 4, the investigated aqueous CHAP solution presents almost the double CO₂ solubility than 30 wt.% aqueous MEA solution, which is considered as a benchmark solvent, and which is currently used in CO₂ capture applications.

TABLE 5. Solubility of CO₂ in 32.5 ± 0.1 wt.% aqueous CHAP solution at 313 and 333 K

Temperature/K^a	CO2 partial pressure^b, P/kPa	CO2 loading, α/mole CO2 per mole of amine
313.15	80	1.297 ± 0.043
	187	1.380 ± 0.043
	532	1.544 ± 0.047
	792	1.596 ± 0.050
	1207	1.676 ± 0.048
	1640	1.719 ± 0.054
333.15	141	1.231 ± 0.044
	276	1.293 ± 0.044
	680	1.417 ± 0.049
	963	1.467 ± 0.052
	1880	1.606 ± 0.056

• ^a Standard uncertainty in temperature u(T) = 0.10 K.
• ^b Standard uncertainty in total pressure u(p) = 0.005∙P.

FIGURE 3

Solubility of CO₂ in 32.5 wt.% aqueous CHAP solution at 313 K. Experimental data from this work (solid circles) and Papadopoulos et al.⁷ (open circles) and model correlations (curve). Experimental data³⁰ for the CO₂ solubility in 30 wt.% aqueous MEA solution are also shown (solid squares) for comparison.

FIGURE 4

Solubility of CO₂ in 32.5 wt.% aqueous CHAP solution at 333 K. Experimental data from this work (solid circles) and Papadopoulos et al.⁷ (open circles) and model correlations (curve). Experimental data³⁰ for the CO₂ solubility in 30 wt.% aqueous MEA solutions are also shown (solid squares) for comparison.

Considering the MCA aqueous system, measurements were performed at 313 and 333 K. All measurements were performed starting from a 31.5 wt.% aqueous amine solution. It was observed that aqueous MCA mixtures, although biphasic at temperatures higher than approximately 283 K (MCA-water presents liquid–liquid phase separation with lower critical solution temperature, LCST, behavior), present one liquid phase upon CO₂ dissolution at the investigated conditions. Thus, the CO₂ loaded aqueous MCA solutions present one liquid phase at 313 and 333 K at all the investigated CO₂ partial pressures.

The experimental results are presented in Table 6. The obtained data are compared with available low pressure literature data,¹¹ which were obtained using a chemical analysis experimental technique, in Figures 5 and 6. It is observed that both data sets are in very good agreement, despite the differences in the investigated pressure range. Moreover, as shown in Figures 5 and 6, the investigated MCA aqueous solution presents considerably higher CO₂ solubility than 30 wt.% aqueous MEA solution, which is considered as a benchmark solvent, and which is currently used in CO₂ capture applications.

TABLE 6. Solubility of CO₂ in 31.5 ± 0.1 wt.% aqueous MCA solution at 313 and 333 K

Temperature/K^a	CO2 partial pressure^b, P/kPa	CO2 loading, α/mole CO2 per mole of amine
313	114	0.963 ± 0.024
	132	0.973 ± 0.025
	180	0.975 ± 0.031
	291	0.988 ± 0.024
	311	0.991 ± 0.033
	412	1.003 ± 0.028
	447	0.996 ± 0.026
	547	1.009 ± 0.028
	763	1.016 ± 0.030
	988	1.069 ± 0.031
	1225	1.061 ± 0.035
333	52	0.849 ± 0.029
	166	0.935 ± 0.024
	178	0.948 ± 0.025
	221	0.951 ± 0.032
	342	0.970 ± 0.024
	354	0.972 ± 0.033
	459	0.990 ± 0.029
	493	0.987 ± 0.026
	597	1.001 ± 0.028
	821	1.013 ± 0.030
	1084	1.054 ± 0.031
	1324	1.055 ± 0.035

• ^a Standard uncertainty in temperature u(T) = 0.10 K.
• ^b Standard uncertainty in total pressure u(p) = 0.005∙P.

FIGURE 5

Solubility of CO₂ in aqueous MCA solution at 313 K. Experimental data from this work (solid circles) and Perdomo et al.¹¹ (open symbols)) and model correlations (curve). Experimental data³⁰ for the CO₂ solubility in 30 wt.% aqueous MEA solutions are also shown (solid squares) for comparison.

FIGURE 6

Solubility of CO₂ in aqueous MCA solution at 333 K. Experimental data from this work (solid circles) and Perdomo et al.¹¹ (open symbols)) and model correlations (curve). Experimental data³⁰ for the CO₂ solubility in 30 wt.% aqueous MEA solutions are also shown (solid squares) for comparison.

3.2 Modeling results

In order to apply the modified Kent–Eisenberg model, one has to know the temperature dependence of all needed equilibrium constants of reactions (1-6) and the Henry's law constant (shown in Equation (22)), which is usually given through the empirical equation (33). The parameters of Equation (33) for the equilibrium constants of reactions (3-5), as well as the parameters for Henry's constant, are usually obtained from literature.²⁷ Such values, which were also used in this study, are presented in Table 7.

TABLE 7. Parameters of the empirical equation (33) obtained from literature³²

Parameter^a (T in K)	Units	A	B	C	D
HCO2	atm kg/mol	−6789.04	−11.4519	−0.010454	94.4914
k2	mol/kg	−12092.1	−36.7816	–	235.482
k3	mol/kg	−12431.7	−35.4819	–	220.067
k4	(mol/kg)^2	−13445.9	−22.4773	–	140.932

• ^a Temperature validity: 273–498 K.

Non-sterically hindered primary or secondary amines, react with CO₂ mainly through the carbamate formation mechanism, which imposes a maximum loading, due to the stoichiometry of the reactions, equal to 0.5 mole of CO₂ per mole of amine.³³ On the other hand, sterically hindered amines react through a different mechanism, since the produced carbamate is relatively unstable, and may present loadings around 1 mole of CO₂ per mole of amine, even at rather low CO₂ partial pressures.³³ However, the experimental loading may present higher values than such theoretical limits, especially at relatively high CO₂ partial pressures, due to molecular CO₂ dissolution and/or due to significant carbamate hydrolysis.

Thus, before the application of the Kent–Eisenberg model, one has to assume the appropriate mechanism for the investigated amine. In this study, MCA was modeled as a non-carbamate forming sterically hindered amine. Having in mind the aforementioned theoretical maximum loadings, such assumption is in line with the experimental loading values that are around 1 mole of CO₂ per mole of amine, as shown in Table 6, even at rather low pressures. Consequently, reactions (1) and (6) were not accounted for and the model was applied using Equations (31) and (32). The k₁₂ equilibrium constant for reaction (2) was given by Equation (33). The parameters of that equation were adjusted to the experimental data of this study and other literature data.¹¹ However, results showed that the use of more than one adjustable parameter in Equation (33) does not significantly improve the correlations. Consequently, only the parameter A was estimated, while parameters B, C and D were kept equal to zero, as shown in Table 8. Here it is worth mentioning that if B and C parameters of Equation (33) are set equal to zero, such equation better resembles the Arrhenius equation and unnecessary empiricism is avoided. Therefore, using only one adjustable parameter, the model rather satisfactorily correlates the experimental data, presenting an average absolute deviation equal to 5.5% from the experimental data of this work and the data of Perdomo et al.¹¹ (for 313, 333, and 363 K). The model calculations are presented in Figures 5-7.

FIGURE 7

Solubility of CO₂ in aqueous MCA solutions at 363 K. Experimental data¹¹ (symbols) and Κent–Eisenberg correlations (curve)

As mentioned in a previous section, CHAP is a diamine (Figure 1) consisting of two amine groups, one that is sterically hindered and, thus, may be considered as non-carbamate amine forming group and one carbamate forming, primary amine group.

In this study, in order to use a minimum number of adjustable parameters, CHAP was modeled assuming a “principle of independent reactivity,” that is, that the reactivity of each group does not depend on the potential reaction of the other one. This is an approximation that resembles the Flory's equal reactivity principle, used in polymer chemistry, according to which the reactivity of each group is independent of the chain length and is considered a good approximation for chain lengths higher than approximately four carbon atoms.

As shown in Figure 1, the secondary amine group of CHAP resembles that of MCA. Since the reactivity of each group was assumed independent of its neighbors, the reactivity of the sterically hindered secondary amine group of CHAP can be approximated as equal to the reactivity of MCA. Thus, the k₁₂ parameters, obtained for MCA and shown in Table 8, can also be used for the secondary amine group of CHAP. Consequently, in order to apply the model, one should estimate only the parameters of Equation (33) for k₁₁ and k₅. If those parameters are available, the model can be applied through Equations (26-28). If a mixture of two different monoamines is considered, then the calculated loading through Equation (27) denotes the moles of absorbed CO₂ per mole of amine molecules. However, in the case of CHAP, which is a diamine consisting of two amine groups, one carbamate forming and one non-carbamate forming group, such equations can also be used. Nevertheless, as mentioned in a previous section, in that case all amine species concentrations showing in Equations (1-28) will denote moles of amine groups and not moles of molecules. Also, the calculated loading from Equation (27) will denote the moles of absorbed CO₂ per mole of amine groups (not molecules). Thus, it must be multiplied by two in order to be compared with the experimental data (loading was experimentally measured as moles of CO₂ per moles of amine molecules).

TABLE 8. Parameters for the empirical equation (33) obtained in this study

Parameter^a (T in K)	Units	A	B	C	D	Amine
k12	mol/kg	−7123.29	–	–	–	MCA and CHAP
k11	mol/kg	−4772.54	–	–	−6.2122	CHAP
k5	mol/kg	−1517.05	–	–	2.1065	CHAP

• ^a Temperature validity: 313–363 K.

Using this approach, the model was applied and the parameters of Equation (33) for k₁₂ and k₅ were adjusted to the experimental data of this work and that of Papadopoulos et al.⁷ To avoid unnecessary empiricism, only two parameters of Equation (33), A and D, were optimized, while the remaining ones were set equal to zero. Therefore, using only two adjustable parameters per equilibrium constant (k₁₂ and k₅), the model rather satisfactorily correlates the experimental data, presenting an average absolute deviation equal to 2.9% from the used experimental data (for 313, 333, and 363 K). The model calculations are presented in Figures 3, 4, and 8.

FIGURE 8

Solubility of CO₂ in aqueous CHAP solutions at 363 K. Experimental data⁷ (symbols) and Κent–Eisenberg correlations (curve)

Having parameterized the model, the concentration of all species in the liquid phase can be predicted. Such calculations are illustrated in Figures 9 and 10, for MCA and CHAP loaded solutions at 313 K, respectively. It is revealed that the free amine concentration becomes very low and approaches zero at CO₂ partial pressures higher than approximately 100 kPa. At higher CO₂ partial pressures, the CO₂ solubility increases through molecular CO₂ dissolution, as indicated by the respective CO₂ curve, and the substantial carbamate hydrolysis, in the case of CHAP, as indicated by the maximum shown in the RRNCOO⁻ concentration curve.

FIGURE 9

Model predictions for the liquid phase content of a CO₂ loaded MCA solution (4.1 m) at 313.15 K

FIGURE 10

Model predictions for the liquid phase content of a CO₂ loaded CHAP solution (3.1 m) at 313.15 K

4 CONCLUSIONS

Aqueous MCA and CHAP solutions were experimentally studied regarding the CO₂ solubility at 313 and 333 K and at CO₂ partial pressures higher than 50 kPa, using a pressure decay technique. The new high pressure experimental data are in good agreement with the low pressure data, previously obtained from our group using a chemical analysis method. Subsequently, the modified Kent–Eisenberg model was parameterized and used to correlate the available data for such systems. CHAP was modeled assuming a “principle of independent reactivity,” that is, that the reactivity of each amine group does not depend on the potential reaction of the other one. Using this approach, the model can be applied to diamines using the relevant equations of amine mixtures. Overall, the model calculations present a satisfactory agreement with the experimental data, presenting an absolute average deviation equal to 5.7% and 2.9%, for MCA and CHAP solutions, respectively.

AUTHOR CONTRIBUTIONS

Fragkiskos Tzirakis: Conceptualization (equal); investigation (equal); methodology (equal); software (equal); validation (equal); visualization (equal); writing – original draft (equal); writing – review & editing (equal). Athanasios I. Papadopoulos: Conceptualization (equal); funding acquisition (equal); investigation (equal); project administration (equal); writing – original draft (equal); writing – review and editing (equal). Panos Seferlis: Conceptualization (equal); funding acquisition (equal); investigation (equal); project administration (equal); writing – original draft (equal); writing – review and editing (equal). Ioannis Tsivintzelis: Conceptualization (equal); investigation (equal); methodology (equal); software (equal); validation (equal); visualization (equal); writing – original draft (equal); writing – review and editing (equal).

ACKNOWLEDGMENTS

This research has been cofinanced by the European Union and Greek national funds through the Operational Program Competitiveness, Entrepreneurship and Innovation, under the call Research−Create−Innovate, Project T2EDK-01911.

Open Research

DATA AVAILABILITY STATEMENT

Data available on request from the authors.