Density, Viscosity and Free Energy of Activation for Viscous Flow of Monoethanol Amine (1) + H₂O (2) + CO₂ (3) Mixtures

Abstract

Densities and viscosities of aqueous monoethanol amine (MEA) and CO₂-loaded aqueous MEA are highly relevant in engineering calculations to perform process design and simulations. Density and viscosity of the aqueous MEA were measured in the temperature range of 293.15 K to 363.15 K with MEA mass fractions ranging from 0.3 to 1.0. Densities of the aqueous MEA were fitted for a density correlation. Eyring’s viscosity model based on absolute rate theory was adopted to determine the excess free energy of activation for viscous flow of aqueous MEA mixtures and was correlated by a Redlich–Kister polynomial. Densities and viscosities of CO₂-loaded MEA solutions were measured in the temperature range of 293.15 K to 353.15 K with MEA mass fractions of 0.3, 0.4 and 0.5. The density correlation used to correlate aqueous MEA was modified to fit CO₂-loaded density data. The free energy of activation for viscous flow for CO₂-loaded aqueous MEA solutions was determined by Eyring’s viscosity model and a correlation was proposed to represent free energy of activation for viscous flow and viscosity. This can be used to evaluate quantitative and qualitative properties in the MEA + H₂O + CO₂ mixture.

1. Introduction

Post-combustion CO₂ capture (PCC) using absorption and desorption has gained great attention in the last decades and several amines have been investigated for their absorption efficiency. In acid gas treatment, monoethanol amine (MEA, IUPAC name: 2-aminoethanol) has been used since 1930 [1]. It is the benchmark amine for the evaluation of other amines in CO₂ capture performance considering absorption efficiency, reaction rates, energy demand and corrosion resistance. A blend of 30% MEA with 70% H₂O by mass is a standard in PCC. Higher reaction rates of MEA with CO₂ compared to secondary and tertiary amines enables optimization of the dimensions and operational parameters of the absorber column. MEA’s low-absorption capacity and high-energy demand for desorption and poor corrosion resistance are arguments against the use of MEA at the commercial scale [2,3].

Density and viscosity of pure, aqueous and CO₂-loaded aqueous MEA have been studied and reported in the literature under different temperatures, MEA concentrations and CO₂ loadings [1,4,5,6,7,8,9,10,11,12]. These data are vital for development of empirical correlations that are useful in various aspects of process equipment design and process simulations. Density is important to determine the physical solubility of CO₂ in solvent, the solvent kinetics and mass transfer. Viscosity is frequently used in the modified Stoke–Einstein equation to estimate diffusivity that is necessary for calculating mass transfer and kinetic properties [13,14]. Many references are available for data of aqueous MEA solutions under different MEA concentrations and temperatures. There is a lack of measured data for physical properties of CO₂-loaded solutions at different CO₂ loadings under different MEA concentrations. In order to reduce the unmeasured regions and to check the validity of measured data, further experimental studies are necessary.

Amundsen, Øi and Eimer [6] have used the McAllister three-body model [15] to represent the kinematic viscosity. Weiland, Dingman, Cronin and Browning [9] and Hartono, Mba and Svendsen [10] measured both density and viscosity of CO₂-loaded aqueous MEA solutions and proposed correlations to fit the data. The approach of using a Redlich-Kister [16] type polynomial to predict excess volume for the aqueous MEA solutions in the density correlations is widely used. A similar approach to correlate excess viscosity is adopted by Islam, et al. [17] for aqueous MEA.

In this work, density and viscosity of aqueous MEA and CO₂-loaded aqueous MEA were measured. The density correlation proposed by Aronu, Hartono and Svendsen [14] for the aqueous amino acid salt and amine amino acid salt solutions was used to correlate the density data of aqueous MEA. The same correlation was modified to predict the density of CO₂-loaded aqueous MEA solutions. The parameters of the correlations were found through a regression analysis. Eyring’s viscosity model [18] was used to calculate the free energy of activation for viscous flow of the aqueous MEA solutions and parameters of the Redlich-Kister type polynomial were estimated by regression. For the viscosity of CO₂-loaded solutions, the difference of activation energy between CO₂-loaded aqueous MEA and aqueous MEA solutions were calculated, and a correlation was proposed.

2. Materials and Methods

2.1. Sample Preparation and CO₂ Loading Analysis

Descriptions of materials used in this study are given in

Table 1. Materials used in this study ^a,b.

Chemical Name	CAS Reg. No.	Mole Fraction Purity a	Source	Purification
monoethanol amine (MEA)	141-43-5	≥0.995 (GC b)	Sigma–Aldrich	no
carbon dioxide (CO2)	124-38-9	0.99999	AGA Norge AS	no
nitrogen (N2)	7727-37-9	0.99999	AGA Norge AS	no
sodium hydroxide (NaOH)	1310-73-2	-	Merck KGaA	no
hydrochloric acid (HCl)	7647-01-0	-	Merck KGaA	no
barium chloride dihydrate (BaCl2·2H2O)	10326-27-9	≥0.99	Merck KGaA	no

^a As mentioned by the supplier. ^b Gas-liquid chromatography.

. The Milli-Q water (resistivity 18.2 MΩ·cm) was degassed using a rotary evaporator connected to a vacuum pump to remove any dissolved gasses. The weights of liquids were measured through an electronic balance from Mettler Toledo (XS403S, Mettler Toledo, Greifensee, Switzerland) with a resolution of 1 mg. Aqueous MEA solutions with MEA to H₂O mass ratio $w_1$ = 0.3, 0.4, and 0.5 were prepared and fully loaded by bubbling CO₂ through the solution until the pH become steady over time. Then different CO₂-loaded solutions were prepared by diluting them with corresponding aqueous MEA. The amount of CO₂ loaded to the aqueous MEA was determined by a titration method in which CO₂ was fixed as BaCO₃ via adding 50 mL of each 0.1 M NaOH and 0.3 M BaCl₂ to 0.1–0.2 g of CO₂ loaded solution. All the samples were boiled for approximately 10 min to ensure the completion of chemical reactions and were cooled until the temperature reaches the room conditions. Eventually, BaCO₃ was separated by filtering using a hydrophilic polypropylene membrane filter (47 mm, 0.45 µm). The filtered BaCO₃ was put into 100 mL of distilled water and titrated with 0.1 M HCl until the solution reached pH of 2. Meanwhile, care needed to be taken to make sure all the BaCO₃ was dissolved during the titration. Then, the sample was boiled and cooled again before it was titrated with 0.1 M NaOH. Finally, the MEA concentration of mixtures was determined by titrating 1 g of CO₂-loaded solution with 1 M HCl.

2.2. Density Measurements

The density of aqueous MEA and CO₂-loaded aqueous MEA was measured by a DMA 4500 density meter from Anton Paar (Graz, Austria). The standard calibration procedure for DMA 4500 was performed using degassed water and air at 293.15 K occasionally, while density checks were performed frequently to check the validity of the previous calibration at 293.15 K. Samples were inserted into the U-tube with care to prevent the presence of air bubbles in the tube. Measurements were performed using a separate sample at each temperature and composition. A cleaning and drying process of the U-tube was performed every time before a new sample was introduced. Density measurements were performed for the aqueous MEA of $w_1$ from 0.3 to 1 for the temperature range from 293.15 K to 363.15 K and CO₂-loaded aqueous MEA of $w_1$ = 0.3, 0.4 and 0.5 under different CO₂ loading for the temperature range from 293.15 K to 353.15 K. Final density data are presented as an average of three density measurements at each temperature and composition.

2.3. Viscosity Measurements

The dynamic viscosity was measured using a double-gap concentric rheometer Physica MCR 101 from Anton Paar (pressure cell XL DG35.12/PR; measuring cell serial number 80462200) (Graz, Austria). The standard viscosity solution S3S from Paragon Scientific Ltd. was used to calibrate the rheometer at different temperatures. The calibration and the measurement were done by using 7 mL of liquid volume under the shear rate (γ) of 1000 s⁻¹. Having compared with the reference viscosity data, measured viscosities of standard viscosity solution were used to determine the viscosity deviations at different temperatures. For temperatures where the supplier did not specify any reference viscosities, expected viscosity deviations were obtained via interpolation. A temperature controlling system with standard temperature uncertainty of ±0.03 K is equipped with the rheometer. An external cooling system of Anton Paar Viscotherm VT2 (Graz, Austria) with standard temperature uncertainty of ±0.02 K is employed for better temperature control in the range from 293.15 K to 303.15 K. The solution in the rheometer was pressured by N₂ gas (p = 4 bar) to minimize the possible release of MEA and CO₂ into the gas phase. Viscosity measurements were performed for the aqueous MEA of $w_1$ from 0.3 to 1 in the temperature range from 293.15–363.15 K and CO₂-loaded aqueous MEA with w₁ = 0.3, 0.4 and 0.5 under different CO₂ loadings for the temperature range from 293.15 K to 353.15 K. The viscosity data presented in this study are the averaged measurements for minimum of three different measurements.

3. Experimental Uncertainty

The Guide to the expression of Uncertainty in Measurement (GUM) [19,20] approach was adopted for the uncertainty evaluations using the mathematical models defined for the instruments for density and viscosity measurements. Several uncertainty sources including purity of MEA, weight measurements, repeatability, CO₂ loading and temperature were considered in addition to the uncertainty sources in the model equations during the uncertainty evaluation. The temperature accuracy of DMA 4500 and Physica MCR 101 Anton Paar are both specified as ±0.03 K. Considered standard uncertainties u for the density measurements are $u\left(\alpha \right)$ = ±0.005 (CO₂ loading mol CO₂/mol MEA), $u\left(w\right)$ = ±2 × 10⁻⁴ kg (weight measurement), $u\left(p\right)$ = ±0.003 (MEA purity), $u\left(T\right)$ = ±0.012 K (temperature) and $u\left(rep\right)$ = ±0.13 kg·m⁻³ (repeatability). The gradient $\partial \rho /\partial T$ of density against temperature was found as 0.73 kg·m⁻³·K⁻¹ and the corresponding uncertainty in $\rho$ that is $\left(\partial \rho /\partial T\right) u\left(T\right)$ was calculated as ±0.009 kg·m⁻³. The gradient of density against CO₂ loading, $\partial \rho /\partial \alpha$, was found as 334 kg m⁻³ and the corresponding uncertainty in ρ, $\left(\partial \rho /\partial \alpha \right) u\left(\alpha \right)$ was found as ±1.67 kg·m⁻³. The standard combined uncertainty for density measurement $u\left(\rho \right)$ was found as $u\left(\rho \right)$ = ±3.90 kg·m⁻³. Accordingly the combined expanded uncertainty $U_c\left(\rho \right)$ for density of CO₂-loaded aqueous MEA is $U_c\left(\rho \right)$ = ±7.80 kg·m⁻³ (level of confidence = 0.95, where $k$ = 2).

The considered standard uncertainties $u$ for the viscosity measurements are $u\left(\alpha \right)$ = ±0.005 (CO₂ loading mol CO₂/mol MEA), $u\left(w\right)$ = ±2 × 10⁻⁴ kg (weight measurement), $u\left(p\right)$ = ±0.003 (MEA purity), $u\left(T\right)$ = ±0.012 K (temperature) and $u\left(rep\right)$ = ±0.008 mPa·s (repeatability). The standard combined uncertainty for viscosity measurement $u\left(\eta \right)$ was found as $u\left(\eta \right)$ = ±0.018 mPa·s. Accordingly the combined expanded uncertainty $U_c$ is $U_c\left(\eta \right)$ = ±0.036 mPa·s (level of confidence = 0.95, where $k$ = 2).

4. Results and Discussion

This section discusses the density, viscosity and free energy of activation for viscous flow in aqueous and CO₂-loaded aqueous MEA solutions. The correlations to represent density and viscosity data were evaluated using average absolute relative deviation and absolute maximum deviation (AARD and AMD) as given in Equations (1) and (2).

$$AARD(\%)=\frac{100\%}{N}{\displaystyle \sum }_{i=1}^N\left|\frac{Y_i^E-Y_i^C}{Y_i^E}\right|$$

(1)

$$AMD=MAX\left|Y_i^E-Y_i^C\right|$$

(2)

where N, $Y_i^E$ and $Y_i^C$ refer the number of data points, the measured property and calculated property respectively.

4.1. Density of MEA (1) + H₂O (2) + CO₂ (3) Mixtures

Many approaches in density correlations are based on suggesting a Redlich–Kister polynomial to fit the excess volume properties of the mixture. One of the drawbacks of the excess volume approach using a Redlich–Kister polynomial to calculate density is the complexity of the correlation due to a high number of parameters. The density correlation proposed by Aronu, Hartono and Svendsen [14] as given by Equation (3) was used to fit the measured aqueous density data. The estimated parameters are presented in

Table 2. Correlation parameters for density of aqueous MEA.

$\mathbf{MEA}/{\mathit{w}}_1$	T/K	No. Points	Parameters
0.3–0.9	293.15–363.15	56	$k_1$ = 683.5
			$k_2$ = 1.344 × 105
			$k_3$ = −1.089 × 104
			$k_4$ = 145.2
			$k_5$ = 567.9
AARD (%)			0.12
AMD (kg·m−3)			3.45

. The correlation was in good agreement with measured data with AARD = 0.12% for the $w_1$ range from 0.3 to 0.9. The same parameters were used to fit the density of CO₂-loaded solutions by introducing a function with new parameters for the temperature and CO₂ mole fraction as illustrated in Equation (4).

Correlation for the density of aqueous MEA:

$$\rho =\left(k_1+\frac{k_2{x}_2}{T}\right)exp\left(\frac{k_3}{T^2}+\frac{k_4{x}_1}{T}+k_5{\left(\frac{x_1}{T}\right)}^2\right)$$

(3)

where $\rho$, $T$, $x_1$, $x_2$ and $k_i$ are density, temperature, mole fractions of MEA, H₂O of the aqueous mixture and estimated parameter vector.

The measured densities of aqueous MEA solutions are listed in

Table 3. Measured density $\rho$/kg·m⁻³ of aqueous MEA ^a,b,c,d,e.

${\mathit{w}}_1$	${\mathit{x}}_1$	Measured Density ρ/kg·m−3
		293.15 K	303.15 K	313.15 K	323.15 K	333.15 K	343.15 K	353.15 K	363.15 K
0.3	0.1122	1012.6 1012.68 d	1008.2 1008.4 b 1008.31 d 1008.2 e	1003.3 1003.3 b 1003.4 c 1003.45 d 1003.3 e	997.9 998.1 b 998.1 c 998.07 d 998.1 e	991.6 992.3 b 992.23 d 992.3 e	986.0 986.1 b 985.8 c 985.96 d	979.4 979.4 b 979.4 c 979.27 d	972.3 972.5 b
0.4	0.1643	1018.4	1013.3 1013.8 b 1013.3 e	1007.8 1008.3 b 1007.7 c 1007.8 e	1001.8 1002.3 b 1001.8 c 1002.1 e	995.5 996.1 b 995.7 e	988.9 989.4 b 988.9 c	981.9 982.4 b 981.9 c	974.6 975.0 b
0.5	0.2278	1023.6	1017.8 1018.2 b 1017.8 e	1011.6 1012.1 b 1011.7 c 1011.8 e	1005.2 1005.6 b 1005.3 c 1005.4 e	998.4 999.0 b 998.7 e	991.4 991.9 b 991.5 c	984.1 984.5 b 984.2 c	976.4 976.9 b
0.6	0.3067	1027.7	1021.2 1021.4 b 1021.3 e	1014.5 1014.7 b 1014.6 e	1007.6 1007.8 b 1007.8 e	1000.4 1000.7 b 1000.6 e	993.0 993.2 b	985.4 985.6 b	977.4 977.7 b
0.7	0.4077	1029.3	1022.4 1022.8 b 1022.6 e	1015.2 1015.7 b 1015.5 c 1015.5 e	1007.9 1008.3 b 1008.2 c 1008.2 e	1000.4 1000.8 b 1000.6 e	992.7 993.1 b 993.0 c	984.8 985.2 b 985.0 c	976.4 977.1 b
0.8	0.5412	1028.1	1020.8 1021.0 b	1013.3 1013.5 b	1005.7 1005.9 b	997.9 998.2 b	990.0 990.2 b	981.9 982.1 b	973.6 973.9 b
0.9	0.7264	1023.5	1015.8 1016.2 b	1008.1 1008.5 b 1008.4 c	1000.3 1000.6 b 1000.6 c	992.4 992.7 b	984.3 984.6 b 984.6 c	976.1 976.5 b 976.4 c	967.8 968.1 b
1	1.0000	1015.9	1008.1 1008.0 b	1000.1 1000.0 b 1000.3 c	992.1 992.0 b 992.3 c	984.0 983.9 b	975.9 975.8 b 976.0 c	967.6 967.5 b 967.8 c	959.3 959.2 b

^a Standard uncertainties $u$ are $u\left(w\right)$ = ±2 × 10⁻⁴ kg, $u\left(p\right)$ = ±0.003, $u\left(T\right)$ = ±0.012 K, $u\left(rep\right)$ = ±0.13 kg·m⁻³. The combined expanded uncertainty $U_c$ is $U_c\left(\rho \right)$ = ±7.10 kg·m⁻³ (level of confidence = 0.95, where k = 2). ^b Han, Jin, Eimer and Melaaen [1], ^c Amundsen, Øi and Eimer [6], ^d Hartono, Mba and Svendsen [10], ^e Jayarathna, Weerasooriya, Dayarathna, Eimer and Melaaen [8].

. A comparison between correlations that are based on excess volume presented by Hartono, Mba and Svendsen [10] and Han, Jin, Eimer and Melaaen [1] with this work is shown in Figure 1. The accuracy of the correlation fit is acceptable compared to the literature [1,10]. The correlation deviates from measured density with AMD of 3.45 kg·m⁻³ at $w_1$ = 0.8 and T = 293.15 K. This deviation is less than the measurement uncertainty reported in this study for aqueous MEA.

Correlation for the density of CO₂-loaded aqueous MEA:

$$\rho =(a_1+a_2\left(T\right)+a_3{\left(T\right)}^2+a_4{x}_3)\left(k_1+\frac{k_2{x}_2}{T}\right)exp\left(\frac{k_3}{T^2}+\frac{k_4{x}_1}{T}+k_5{\left(\frac{x_1}{T}\right)}^2\right)$$

(4)

The measured density of CO₂-loaded aqueous MEA of $w_1$ = 0.3, 0.4 and 0.5 solutions are shown in

Table 4. Measured density $\rho$/kg·m⁻³ of CO₂-loaded (α/mol CO₂·mol MEA⁻¹) aqueous MEA ^a.

${\mathit{x}}_3$	$\mathit{\alpha }$	$\mathbf{Measured}\mathbf{Density}\mathit{\rho }/\mathbf{k}\mathbf{g}·{\mathbf{m}}^{-3}$
		293.15 K	303.15 K	313.15 K	323.15 K	333.15 K	343.15 K	353.15 K
$w_1=0.3$
0.0000	0.000	1012.6	1008.2	1003.3	997.9	991.6	986.0	979.4
0.0105	0.095	1032.0	1027.6	1022.8	1017.4	1011.6	1005.1	995.5
0.0193	0.175	1052.5	1048.1	1043.3	1038.1	1032.4	1026.4	1020.1
0.0355	0.328	1077.8	1073.4	1068.6	1063.4	1057.9	1052.0	1044.1
0.0476	0.445	1103.3	1097.7	1092.8	1087.6	1082.1	1075.7	1069.3
0.0574	0.543	1123.1	1118.4	1113.4	1107.9
$w_1=0.4$
0.0000	0.000	1018.4	1013.3	1007.8	1001.9	995.5	988.9	981.9
0.0170	0.105	1045.6	1040.7	1035.3	1029.6	1023.6	1017.3	1010.6
0.0341	0.215	1073.4	1068.5	1063.3	1057.8	1051.9	1045.8	1039.4
0.0507	0.325	1102.0	1097.2	1092.0	1086.5	1080.8	1074.9	1068.6
0.0669	0.436	1130.3	1125.4	1120.2	1114.7	1109.2	1103.2	1097.0
0.0826	0.548	1155.5	1150.4	1145.1	1139.5
$w_1=0.5$
0.0000	0.000	1023.6	1017.8	1011.6	1005.2	998.4	991.4	984.1
0.0205	0.092	1052.3	1046.7	1040.9	1034.7	1028.3	1021.7	1014.8
0.0406	0.186	1082.4	1077.0	1071.4	1065.5	1059.4	1053.0	1046.4
0.0620	0.290	1112.7	1107.4	1101.9	1096.2	1090.3	1084.2	1077.9
0.0825	0.395	1144.5	1139.2	1133.8	1128.3	1122.5	1116.6	1110.5
0.1013	0.495	1175.7	1170.4	1165.0	1159.4	1153.6	1147.5

^a Standard uncertainties $u$ are u(α) = ±0.005, $u\left(w\right)$ = ±2 × 10⁻⁴ kg, u(p) = ±0.003, $u\left(T\right)$ = ±0.012 K, $u\left(rep\right)$ = ±0.13 kg·m⁻³. The combined expanded uncertainty $U_c$ is $U_c\left(\rho \right)$ = ±7.80 kg·m⁻³ (level of confidence = 0.95, where $k$ = 2).

and the correlation described in Equation (4) used to fit the data. At higher CO₂ loadings (α > 0.5), formation of air bubbles was noticed in the U-tube beyond temperatures of 323.15 K in DMA 4500. This increases the uncertainty of the density measurements. Accordingly, densities at temperatures up to 323.15 K are shown for the solutions with $w_1$ = 0.3 and 0.4. The same was observed for the solution of w₁ = 0.5 with α = 0.495 at above T = 343.15 K. Figure 2 shows the comparison of correlations proposed by Hartono, Mba and Svendsen [10], Han, Jin, Eimer and Melaaen [1] with this work for MEA solution of $w_1$ = 0.3. Measured densities at $w_1$ = 0.4 and 0.5 are given in Figure 3 and Figure 4 with data from the literature. The correlation by Hartono, Mba and Svendsen [10] deviates positively from the measured data with AMD of 8.9 kg·m⁻³ while Han, Jin, Eimer and Melaaen [1] deviates negatively with AMD of 9.5 kg·m⁻³ at higher CO₂ loadings. The required parameters of Equation (4) for the CO₂-loaded solutions are listed in

Table 5. Density correlation parameters for CO₂-loaded aqueous MEA.

Parameters	${\mathit{w}}_1=0.3$	${\mathit{w}}_1=0.4$	${\mathit{w}}_1=0.5$
$a_1$	0.6802	0.7731	0.7506
$a_2$	0.001951	0.001354	0.001494
$a_3$	−2.97 × 10−6	−2.015 × 10−6	−2.237 × 10−6
$a_4$	2.346	2.164	2.015
AARD (%)	0.15	0.08	0.15
AMD (kg·m−3)	4.2	2	3.8

. The AMD from Equation (4) is lower than that from the other correlations.

4.2. Viscosity of MEA (1) + H₂O (2) + CO₂ (3) Mixtures

The Eyring’s viscosity model based on absolute rate theory is shown in Equation (5). Here, viscous flow is treated as a chemical reaction considering the elementary process as the motion of a single molecule from one equilibrium position to another over a potential energy barrier [21,22].

$$\eta =\frac{h{N}_A}{V}exp\left(\frac{\Delta G^{*}}{RT}\right)$$

(5)

where $\eta , V, h, N_A, \Delta G^{*}, R$ and $T$ are dynamic viscosity, molar volume, Planck’s constant, Avogadro’s number, free energy of activation for viscous flow, universal gas constant and temperature respectively. For binary liquid mixtures, Equations (5) and (6) were adopted to derive Equation (7) to calculate excess free energy of activation for viscous flow $\Delta G^{E*}$.

$$\frac{\eta }{{\eta }_{ideal}}=\frac{V_{ideal }}{V}exp\left(\frac{\Delta G^{E*}}{RT}\right)$$

(6)

$$\frac{\Delta G^{E*}}{RT}=ln\left(\eta V\right)-{\displaystyle \sum }_{i=1}^{i=2}{x}_{i}ln\left({\eta }_i{V}_i^0\right)$$

(7)

where $x_i, {\eta }_i$ and $V_i^0$ (i = 1 for MEA and i = 2 for H₂O) are the mole fraction of components in the mixture, dynamic viscosity and molar volume of pure liquids.

The $\Delta G^{E*}$ was evaluated via measured viscosity and density data of aqueous MEA for $w_1$ from 0.3 to 1 and MEA temperatures from 293.15 K to 363.15 K. Viscosity and density of pure water for this study were taken from Korson, et al. [23] and Kestin, et al. [24]. A Redlich–Kister type correlation was used to fit the derived term $\Delta G^{E*}/RT$ and estimated parameters are given in

Table 6. Parameters of the excess free energy of activation for viscous flow correlation.

${\mathit{w}}_1$	T/K	Parameters
0–1	298.15–363.15	$a_0$ = 16.2
		$b_0$ = −0.03473
		$a_1$ = −4.853
		$b_1$ = 0.008315
		$a_2$ = −6.433
		$b_2$ = 0.02065
R2 = 0.998

. The measured viscosities of aqueous MEA are tabulated with literature data in

Table 7. Measured viscosity $\eta$ of aqueous MEA ^a,b,c,d.

${\mathit{w}}_1$	${\mathit{x}}_1$	$\mathbf{Measured}\mathbf{Viscosity}\mathit{\eta }$/mPa·s
		293.15 K	303.15 K	313.15 K	323.15 K	333.15 K	343.15 K	353.15 K	363.15 K
0.3	0.1122	2.836 2.874 b 2.879 b	2.109 2.133 b 2.130 b	1.628 1.628 b 1.638 b 1.67 c	1.290 1.305 b 1.318 b 1.33 c	1.046 1.055 b 1.067 b	0.866 0.878 b 0.874 b 0.92 c	0.740 0.742 b 0.740 b 0.77 c	0.687
0.4	0.1643	4.285	3.080	2.305 2.28 c	1.782 1.75 c	1.417	1.154 1.14 c	0.960 0.95 c	0.808
0.5	0.2278	6.610	4.580 4.69 d	3.310 3.39 c 3.37 d	2.454 2.54 c 2.53 d	1.915 1.94 d	1.528 1.57 c 1.54 d	1.243 1.28 c 1.26 d	1.029 1.05 d
0.6	0.3067	10.217	6.769 6.92 d	4.736 4.77 d	3.444 3.45 d	2.602 2.62 d	2.031 2.04 d	1.620 1.62 d	1.319 1.34 d
0.7	0.4077	15.348	9.823 9.89 d	6.664 6.96 c 6.69 d	4.720 4.94 c 4.76 d	3.461 3.49 d	2.615 2.79 c 2.63 d	2.029 2.18 c 2.04 d	1.616 1.63 d
0.8	0.5412	20.521	12.840 13.38 d	8.534 8.82 d	5.937 6.11 d	4.295 4.41 d	3.217 3.26 d	2.483 2.49 d	1.962 1.97 d
0.9	0.7264	24.027	14.963 15.12 d	9.879 10.20 c 9.95 d	6.829 7.06 c 6.88 d	4.936 4.94 d	3.683 3.81 c 3.67 d	2.832 2.93 c 2.82 d	2.222 2.23 d
1	1.0000	23.376	14.748 14.77 d	10.108 9.61 c 9.84 d	6.935 6.72 c 6.87 d	5.067 4.98 d	3.834 3.69 c 3.72 d	2.974 2.85 c 2.85 d	2.364 2.26 d

^a The pressure was maintained by N₂ gas (p = 4 bar) during the experiments. Standard uncertainties $u$ are $u\left(w\right)$ = ±2 × 10⁻⁴ kg, $u\left(p\right)$ = ±0.003, $u\left(T\right)$ = ±0.012 K, $u\left(rep\right)$ = ±0.008 mPa·s. The combined expanded uncertainty $U_c$ is U_c(η) = ±0.016 mPa·s (level of confidence = 0.95, where k = 2). ^b Hartono, Mba and Svendsen [10], ^c Amundsen, Øi and Eimer [6], ^d Idris, et al. [26].

. Our previous work has reported viscosities of aqueous MEA from $w_1$ = 0.3 to $w_1$ = 0.5 in Karunarathne, et al. [25]. Figure 5 shows the calculated and fitted $\Delta G^{E*}$ and Figure 6 compares the measured with calculated viscosities using the proposed correlation in this work and correlations suggested in the literature.

$$\frac{\Delta G^{E*}}{RT}=x_1{x}_2{\displaystyle \sum }_{i=0}^{i=2}{C}_i{\left(1-2x_2\right)}^i$$

(8)

$$C_i=a_i+b_i\left(T\right)$$

(9)

The viscosities from the correlation were in good agreement with measured data as shown in Figure 6. The proposed correlation was able to calculate viscosities with AARD 1.4% and with AMD 0.79 mPa·s.

Table 8. Average absolute relative deviations and absolute maximum deviation of different suggested correlations for viscosity of aqueous MEA solutions from $w_1$ = 0 to $w_1$ = 1 and 293.15–363.15 K.

Source (s)	No. Parameters	AARD (%)	AMD (mPa·s)
This work	6	1.4	0.79
Hartono, et al. [10]	4	2.4	0.66
Arachchige, et al. [11]	7	3.5	1.1
Islam, et al. [17]	4	5.1	0.59

summarizes the AARD and AMD of different suggested correlations.

Figure 5 illustrates the variation of $\Delta G^{E*}$ over the whole range of concentrations at different temperatures. At a specific temperature, $\Delta G^{E*}$ increases with the increase of MEA concentration until it reaches a maximum at $x_{MEA}$ about 0.41 and then gradually decreases. The $\Delta G^{E*}$ decreases with the increase of temperature while composition for maximum ΔG^E* is almost constant. A similar effect was observed for other aqueous amine mixtures [27,28].

The excess volume V^E and excess viscosity ${\eta }^E$ of aqueous MEA was determined by Equations (10) and (11) to analyze the molecular interaction between MEA and H₂O.

$$V^E=V-(x_1{V}_1^0+x_2{V}_2^0)$$

(10)

$${\eta }^E=\eta -\left(x_1{\eta }_1+x_2{\eta }_2\right)$$

(11)

The $\Delta G^{E*}>0$ and $V^E<0$ for the considered MEA concentrations while ${\eta }^E$ is negative $(<0)$ for the water-rich region and gradually become positive $(>0)$ with the increase of MEA concentration. The $\Delta G^{E*}>0$ indicates that the viscosity of aqueous MEA solutions has greater viscosities than that of ideal mixtures [29]. The V^E can be negative as a result of the chemical or specific interaction and the structural contribution due to the difference in shape and size [30]. According to Eyring’s viscosity model, it can be argued that more energy is required to make necessary holes for molecules to jump in when they are closely packed. The sign of ${\eta }^E$ emphasizes strong specific interactions such as hydrogen bonding, which causes complex formations in the amine-rich region and weak interactions in the water-rich region [31].

The viscosity of CO₂-loaded aqueous MEA solutions is given by

Table 9. Measured viscosity of CO₂-loaded (α/mol CO₂ mol·MEA⁻¹) aqueous MEA ^a.

${\mathit{x}}_3$	$\mathit{\alpha }$	$\mathbf{Measured}\mathbf{Viscosity}$ (η/mPa·s)
		293.15 K	303.15 K	313.15 K	323.15 K	333.15 K	343.15 K	353.15 K
$w_1=0.3$
0.0000	0.000	2.836	2.109	1.628	1.290	1.046	0.866	0.740
0.0105	0.095	3.103	2.305	1.768	1.397	1.128	0.937	0.788
0.0193	0.175	3.338	2.476	1.910	1.511	1.228	1.021	0.865
0.0355	0.328	3.730	2.764	2.138	1.699	1.384	1.152	0.977
0.0476	0.445	4.164	3.105	2.403	1.913	1.562	1.308	1.118
0.0574	0.543	4.515	3.360	2.602	2.064	1.680	1.403	1.191
$w_1=0.4$
0.0000	0.000	4.285	3.080	2.305	1.782	1.417	1.154	0.960
0.0170	0.105	4.793	3.423	2.567	1.985	1.590	1.302	1.090
0.0341	0.215	5.524	3.944	2.968	2.308	1.851	1.526	1.286
0.0507	0.325	6.496	4.655	3.502	2.726	2.198	1.813	1.524
0.0669	0.436	7.639	5.442	4.084	3.177	2.556	2.111	1.781
0.0826	0.548	8.820	6.203	4.614	3.544	2.821	2.302	1.917
$w_1=0.5$
0.0000	0.000	6.610	4.580	3.310	2.454	1.915	1.528	1.243
0.0205	0.092	7.859	5.378	3.926	2.955	2.303	1.838	1.493
0.0406	0.186	9.518	6.529	4.756	3.594	2.813	2.269	1.866
0.0620	0.290	11.611	7.904	5.710	4.291	3.328	2.667	2.190
0.0825	0.395	14.854	10.073	7.247	5.422	4.227	3.409	2.809
0.1013	0.495	19.348	12.841	9.068	6.678	5.169	4.118	3.365

^a The pressure was maintained by N₂ gas (p = 4 bar) during the experiments. Standard uncertainties $u$ are $u\left(\alpha \right)$ = ±0.005, $u\left(w\right)$ = ±2 × 10⁻⁴ kg, $u\left(p\right)$ = ±0.003, u(T) = ±0.012 K, $u\left(rep\right)$ = ±0.008 mPa·s.

for w₁ = 0.3, 0,4 and 0.5 under different CO₂ loading in the temperature range from 293.15–353.15 K. The measured viscosities at $w_1$ = 0.3, $w_1$ = 0.4 and 0.5 are shown in Figure 7, Figure 8 and Figure 9 respectively with data from the literature. It was observed that the viscosity of solution increases with the increase of CO₂ dissolved in the mixture for all three different MEA concentrations and it decreases with the increase of temperature. The $\Delta G^{*}$ was calculated for both CO₂-loaded and CO₂-unloaded solutions and the difference was considered to develop a correlation as shown in Equations (12) and (13) to predict the viscosity of CO₂-loaded solutions.

The combined expanded uncertainty U_c is $U_c\left(\eta \right)$ = ±0.036 mPa·s (level of confidence = 0.95, where $k$ = 2).

$$ln{\left(V\eta \right)}_{CO2 loaded}=ln{\left(V\eta \right)}_{unloaded}+f\left(x_3,T\right)$$

(12)

$$f\left(x_3,T\right)=x_3\left(d_1+d_{2}T+d_3{x}_3\right)$$

(13)

The calculated AARD shows that the predicted and measured viscosities are in good agreement and parameters for the correlation are given in

Table 10. Parameters of viscosity correlation for CO₂-loaded solutions.

T/K	Parameters	${\mathit{w}}_1=0.3$	${\mathit{w}}_1=0.4$	w1 = 0.5
298.15–343.15	d1	4.536	2.554	8.533
	$d_2$	0.006765	0.01205	−0.0037
	$d_3$	12.08	19.46	17.79
AARD (%)		0.58	1.13	1.25
AMD (mPa·s)		0.03	0.22	1.04

. The molar volume of CO₂-loaded aqueous MEA solutions was calculated using the mole fraction of dissolved CO₂ that was determined via CO₂ loading analysis. In a real solution, CO₂ reacts with MEA to form carbamate and bicarbonate ions and the solution becomes an electrolyte. Here it is assumed as unreacted and molar volumes were calculated using Equation (14) [32]. This approach was taken to represent dissolved CO₂ in aqueous MEA [7,10,26] and used in the viscosity correlation by Hartono, Mba and Svendsen [10].

$$V_{loaded}=\frac{{{\displaystyle \sum }}_1^3{x}_i{M}_i}{{\rho }_{loaded}}$$

(14)

The variations of $\Delta G^{*}$ with CO₂ loading and temperature are shown in Figure 10a–c. For CO₂ loaded solutions, $\Delta G^{*}$ increases with the increase of dissolved CO₂ while it decreases with temperature. The amount of ions present in the solution due to the formation of carbamate and bicarbonate increases with the CO₂ loading, which results in higher ionic strength as discussed by Matin, et al. [33]. At higher ionic strengths, ions can create an ionic field that attract water molecules to form clusters, which leads to higher viscosity. The increase of $\Delta G^{*}$ implies the increase of potential barrier for the molecule transfer. The molecular interactions among the molecules in CO₂-loaded solutions may enhance the strength of energy barrier more than that of unloaded solutions. The correlation given in Equation (15) was proposed to fit $\Delta G^{*}$ for the CO₂-loaded aqueous MEA of w₁ = 0.3, 0,4 and 0.5. On the other hand, since the Eyring’s viscosity model is based on the motion of individual molecules from one equilibrium position to another; it does not explain the effect of hydrogen bond network on the bulk viscosity of the various CO₂-loaded aqueous [34] MEA solutions. Further, the model has molar volume as a parameter that needs to be known to calculate the viscosity. This can be done by using calculated molar volume from density data measured under the same conditions or from a correlation.

$$\Delta G_{CO2 loaded}^{*}= \Delta G_{ unloaded}^{*}+x_{3}RT\left(d_1+d_{2}T+d_3{x}_3\right)$$

(15)

The relationship between Rln(ηV/(hN_A)) vs. $1/T$ gives information about activation parameters in which enthalpy of activation for viscous flow $\Delta H^{*}$ is given by the gradient and entropy of activation for viscous flow ΔS^* is given by the intercept of the curve under different mole fractions of the components. The $\Delta G^{*}$, $\Delta H^{*}$ and $\Delta S^{*}$ are connected through the equation $\Delta G^{*}=\Delta H^{*}-T\Delta S^{*}$. Accordingly, Eyring’s viscosity model is given as follows.

$$\eta =\frac{h{N}_A}{V}exp\left(\frac{\Delta H^{*}}{RT}-\frac{\Delta S^{*}}{R}\right)$$

(16)

Table 11. Free energy of activation for viscous flow $\Delta G^{*}$/kJ·mol⁻¹ for CO₂-loaded aqueous MEA.

T/K		293.15	303.15	313.15	323.15	333.15	343.15	353.15
${\mathit{w}}_1$	${\mathit{x}}_3$	$\mathbf{Free}\mathbf{Energy}\mathbf{\Delta }{\mathit{G}}^{*}/\mathbf{kJ}·{\mathbf{mol}}^{-1}$
0.3	0.0000	12.375	12.062	11.798	11.564	11.358	11.177	11.060
	0.0105	12.571	12.262	11.988	11.753	11.539	11.376	11.222
	0.0193	12.721	12.413	12.159	11.931	11.740	11.583	11.451
	0.0355	12.970	12.667	12.428	12.220	12.044	11.900	11.783
	0.0476	13.210	12.931	12.702	12.507	12.347	12.228	12.150
	0.0574	13.382	13.105	12.883	12.685
0.4	0.0000	13.595	13.240	12.936	12.674	12.448	12.255	12.094
	0.0170	13.835	13.471	13.179	12.924	12.726	12.556	12.419
	0.0341	14.148	13.793	13.521	13.291	13.105	12.965	12.860
	0.0507	14.509	14.175	13.914	13.698	13.540	13.413	13.312
	0.0669	14.870	14.534	14.278	14.072	13.919	13.807	13.725
	0.0826	15.194	14.837	14.568	14.337
0.5	0.0000	14.891	14.489	14.137	13.802	13.560	13.344	13.148
	0.0205	15.275	14.853	14.538	14.255	14.022	13.819	13.631
	0.0406	15.701	15.299	14.992	14.733	14.526	14.366	14.230
	0.0620	16.147	15.741	15.426	15.165	14.945	14.779	14.648
	0.0825	16.707	16.309	16.002	15.747	15.559	15.427	15.325
	0.1013	17.311	16.879	16.543	16.262	16.069	15.918

and

Table 12. Free energy of activation for viscous flow $\Delta G^{*}$/kJ·mol⁻¹ for CO₂-loaded aqueous MEA.

${\mathit{w}}_1$	${\mathit{x}}_3$	ΔH*/kJ·mol−1	$\mathbf{\Delta }{\mathit{S}}^{*}/\mathbf{J}·{(\mathbf{mol}·\mathbf{K})}^{-1}$
0.3	0.0000	18.834	22.301
	0.0105	19.150	22.696
	0.0193	18.902	21.360
	0.0355	18.716	19.895
	0.0476	18.400	18.003
	0.0574	20.173	23.234
0.4	0.0000	20.897	25.215
	0.0170	20.688	23.742
	0.0341	20.377	21.642
	0.0507	20.266	20.026
	0.0669	20.379	19.209
	0.0826	23.540	28.578
0.5	0.0000	23391	29.339
	0.0205	23147	27.247
	0.0406	22773	24.566
	0.0620	23389	25.142
	0.0825	23381	23.248
	0.1013	25441	28.114

list the calculated $\Delta G^{*}$ directly from Eyring’s viscosity model, and $\Delta H^{*}$ and $\Delta S^{*}$ from the relation shown in Equation (16). It is observed that $\Delta G^{*}$, $\Delta H^{*}$ and $\Delta S^{*}$ are positive for all considered mixtures while $\Delta H^{*}$ is greater than $T\Delta S^{*}$. This reveals that the influence of enthalpy of activation to the free energy of activation is greater than entropy of activation for viscous flow. Further, this work shows how $\Delta G^{*}$ can be regarded as a parameter to regress and also can be regarded as a parameter with a physical meaning.

5. Conclusions

Densities and viscosities of MEA (1) + H₂O (2) mixtures have been measured for the mass fraction $w_1$ from 0.3 to 1 and temperatures in the range 273.15 K to 363.15 K. The density data were correlated using the correlation proposed by Aronu, Hartono and Svendsen for $w_1$ from 0.3 to 0.9. The accuracy of the measured density with correlation predictions are acceptable as the AARD is 0.12% and AMD is 3.45 kg·m⁻³. The viscosity data were correlated using a Redlich–Kister type polynomial fitted to the excess free energy of activation for viscous flow $\Delta G^{E*}$ obtained via the Eyring’s viscosity model for the $w_1$ from 0 to 1 and temperatures in a range from 273.15 K to 363.15 K. The developed correlation was able to represent the measured viscosities with AARD = 1.4% and AMD = 0.79 mPa·s, which is acceptable in engineering calculations.

The densities of CO₂-loaded aqueous MEA solutions were measured at temperatures ranging from 293.15 K to 353.15 K for $w_1$ of 0.3, 0.4 and 0.5. Density of CO₂-loaded solutions increases with the CO₂ loading and decreases with temperature. The density correlation proposed by Aronu, Hartono and Svendsen was modified to correlate the density data. The AMD between correlated and experimental densities are 4.2 kg·m⁻³, 2 kg·m⁻³ and 4.5 kg·m⁻³ for CO₂-loaded solutions with $w_1$ of 0.3, 0.4 and 0.5 respectively.

The viscosities of CO₂-loaded aqueous MEA solutions were measured at temperatures ranging from 293.15 K to 353.15 K for w₁ of 0.3, 0.4 and 0.5. As CO₂ loading increased, the viscosity increased and the viscosity decreased with the increase of temperature. A correlation was proposed for the free energy of activation for viscous flow using CO₂ mole fraction and temperature to correlate viscosity data. The AMD between correlated and experimental viscosities are 0.03 mPa·s, 0.22 mPa·s and 1.04 mPa·s for CO₂-loaded solutions with $w_1$ of 0.3, 0.4 and 0.5 respectively. The proposed correlation is recommended to use in engineering calculations.