Density, Viscosity, and Excess Properties of Ternary Aqueous Mixtures of MDEA + MEA, DMEA + MEA, and DEEA + MEA

Abstract

This study presents the measured densities and viscosities of three ternary aqueous mixtures of tertiary and primary amines. The tertiary amines of n-methyldiethanolamine (MDEA), dimethylethanolamine (DMEA), diethylethanolamine (DEEA), and the primary amine monoethanolamine (MEA) at different concentrations (mass%) were mixed to prepare the liquid mixtures. The excess molar volume $V^E$ of the mixtures was analyzed using measured densities to acquire a better understanding of the molecular packing and intermolecular interactions in the mixtures. The excess free energy of activation $\Delta G^{E\ast }$ and excess entropy of activation $\Delta S^{E\ast }$ for viscous flow were determined from the measured viscosities by implementing the theory of rate processes of Eyring. Correlations based on the Redlich–Kister type polynomial were adopted to correlate the excess properties $V^E$ and $\Delta G^{E\ast }$ as a function of the amine mole fraction and temperature. The results showed that the correlations were able to represent the measured data with satisfactory accuracies for engineering calculations.

1. Introduction

The chemical absorption of CO₂ into aqueous alkanolamines is a mature technology that has been used for decades in the natural gas industry. The solvent-based commercial scale post-combustion CO₂ capture plants are generally operated with 15–20 mass% aqueous monoethanolamine (MEA), 30 mass% aqueous MEA, KS-1 based on sterically hindered amines, and DC-103 from Shell Cansolv (50 mass% amine and 50 mass% H₂O) [1,2,3]. Bernhardsen and Knuutila [4] reviewed the potential amine solvents for CO₂ absorption process by considering the absorption capacity, cyclic capacity, and pKa. The studies performed on 3-amino-1-propanol (3A1P) [5,6] and diethylenetriamine (DETA) [7,8] stated the possibilities of using them as solvents in post-combustion CO₂ capture. The applicability of this technology to post-combustion CO₂ capture is challenging owing to the economic feasibility of the process due to the high-energy penalty in the CO₂ stripping. MEA is a primary amine that shows a high CO₂ absorption rate, which is promising for the process. The main disadvantage of MEA is that it requires a high amount of energy to release CO₂ during the stripping. Tertiary amines like N-methyldiethanolamine (MDEA), dimethylethanolamine (DMEA), and diethylethanolamine (DEEA) have a low heat of reaction, which lowers the energy requirement in the stripping process [9,10,11]. MDEA is traditionally used for CO₂ removal at high pressures. It is normally not used for CO₂ removal at atmospheric pressure [12]. The MDEA solutions are used for the selective removal of H₂S from gas streams like natural gases, synthesis gases from the gasification of coal and heavy oils, and tail gases from sulphur plants that contain both CO₂ and H₂S [13,14]. In addition to the selective removal of H₂S, several advantages of MDEA over primary and secondary amines were reported, such as low vapor pressure, high CO₂ absorption capacity, high resistance to degradation, and fewer corrosion problems [15,16]. The low CO₂ absorption rate of tertiary amines makes it inefficient to use them alone with H₂O as a solvent in the absorption–desorption process to deal with gas streams with low CO₂ concentrations. The work performed by Kim and Savage [17] on reaction kinetics of CO₂ absorption in aqueous DEEA claimed that DEEA has a higher reaction rate than MDEA. Alongside the results found by Henni et al. [18] on kinetics of DMEA, it was observed that DMEA and DEEA have a higher absorption performance compared to MDEA [9]. Chakravarty et al. [19] demonstrated that CO₂ absorption can be enhanced by adding a primary or secondary amine to the tertiary amine without changing the stripping characteristics. Studies have been performed to investigate the performance of aqueous blends of tertiary and primary amines in CO₂ absorption [9,20,21,22]. Conway et al. [21] showed improvements in the cyclic capacity of DMEA + MEA + H₂O and DEEA + MEA + H₂O mixtures compared to aqueous MEA mixtures.

Physical properties, such as the density and viscosity of solvents, are essential for engineering calculations when performing mathematical modelling and simulations for the sizing of process equipment. The density and viscosity are required in many mass and heat transfer correlations that are used in the designing of absorbers, strippers, and heat exchangers in the process. Further properties are useful in flow calculations to select material transfer equipment like pumps and valves. The density and viscosity data of some MDEA + MEA + H₂O mixtures have been reported in literature sources [23,24,25]. For the mixtures of DMEA + MEA + H₂O and DEEA + MEA + H₂O, literature for measured properties are scarce [21].

In this study, the measurements of density and viscosity of three different aqueous tertiary and primary amines mixtures of MDEA (1) + MEA (2) + H₂O (3), DMEA (1) + MEA (2) + H₂O (3), and DEEA (1) + MEA (2) + H₂O (3) at different amine concentrations and temperatures were performed. The excess properties of molar volume, viscosity, and free energy of activation and entropy for viscous flow were determined to examine the molecular structure and interactions in the mixtures. Finally, the data were fitted to the density and viscosity correlations available in the literature and parameters were determined via regression. The accuracy of the data fitting was examined through average absolute relative deviation (AARD (%)) and absolute maximum deviation (AMD).

2. Materials and Methods

2.1. Material Description

Table 1. Materials used in this study.

Chemical Name	CAS No.	Source	Purity
MDEA	105-59-9	Merck Schuchardt OHG, Hohenbrunn, Germany	≥98%
DMEA	108-01-0	Alfa Aesar, Kandel, Germany	≥99
DEEA	100-37-8	Sigma-Aldrich, Darmstadt, Germany	≥99.5%
MEA	141-43-5	Sigma-Aldrich, Darmstadt, Germany	≥99.5% (GC) a

^a GC: Gas chromatography.

lists the materials that were used in this study. Liquid mixtures of aqueous tertiary and primary amines of MDEA + MEA + H₂O, DMEA + MEA + H₂O, and DEEA + MEA + H₂O were prepared on the mass basis using a balance, model: XS-403S from Mettler Toledo (Greifensee, Switzerland) with a resolution of 1 mg. Amines were used without further purification and dissolved with deionized (resistivity: 18.2 MΩ⸳cm) and degassed water from a rotary evaporator (Rotavapor R-210, Buchi, Flawil, Switzerland).

2.2. Density Measurement

Density of the mixtures was measured using a density meter of DMA 4500 from Anton Paar (Graz, Austria) under atmospheric conditions. DMA 4500 has a temperature controller with an accuracy of ±0.03 K and the accuracy of the density measurement is ±0.05 kg⸳m⁻³. A liquid sample with a volume of approximately 5 mL was used to take the density reading and a new sample was fed into the U-tube for density measurements at each temperature and composition. In order to check the reliability of the instrument, a density check was performed frequently at 293.15 K using degassed deionized water. As suggested by the manufacturer, the density check is accepted when the deviations between the experimental and stored reference density data is smaller than 0.1 kg⸳m⁻³. For deviations greater than 0.1 kg⸳m⁻³, a calibration was performed using both air and degassed deionized water at 293.15 K as per the instruction given by the manufacturer. The density of water was measured at different temperatures and compared with the literature data from the International Association for the Properties of Water and Steam (IAPWS) [26]. The comparison showed that the deviation of the measured density of water was less than 0.01%, which was acceptable.

2.3. Viscosity Measurement

A double-gap rheometer (pressure cell XL, Anton Paar, Graz, Austria) Physica MCR 101 was used for the dynamic viscosity measurements of the aqueous amine mixtures. A liquid sample of 7 mL in volume was transferred using a syringe in the space occupied between the rotating and fixed cylinders in the pressure cell. For the viscosity measurements at temperatures higher than 303.15 K, the internal temperature controller with an accuracy of ±0.03 K was used to maintain different temperatures up to 363.15 K. An external cooling system Viscotherm VT 2 (Anton Paar, Graz, Austria) with an accuracy of ±0.02 K was adopted to acquire precise measurements for the temperature range from 293.15 K to 303.15 K. Following the instructions provided by Anton Paar, an air check and motor adjustment were performed prior to the experiments. The accuracy of the torque measurement is given by the manufacturer as max (0.2 µNm; 0.5%) and the repeatability of the viscosity measurements is ±0.008 mPa⸳s. Further, a standard viscosity solution S3S from Paragon Scientific Ltd. (Prenton, United Kingdom) was used to calibrate the measuring system. The viscosity of the standard viscosity fluid was measured at specific temperatures suggested by the supplier and was compared with the reference data to record deviations. The measured viscosities were corrected for these deviations obtained during the calibration. The experiments were conducted at atmospheric pressure (1 atm).

2.4. Experimental Uncertainty

Several uncertainty sources of material purity $u\left(p\right)$, temperature measurement $u\left(T\right)$, weight measurement $u\left(w\right)$, and repeatability $u\left(rep\right)$ were taken into account to determine the combined standard uncertainty of density and viscosity measurements of aqueous amine mixtures.

For the uncertainty of density measurement, the specified standard uncertainties were $u\left(p\right)$ = ±0.003, $u\left(T\right)$ = ±0.012 K, $u\left(w\right)$ = ±2 × 10⁻⁴ kg, and $u\left(rep\right)$ = ±0.13 kg⸳m⁻³. The maximum gradient of density against temperature, $\partial \rho /\partial T$, was found to be 0.88 kg⸳m⁻³⸳K⁻¹ and the corresponding uncertainty in $\rho$, $\left(\partial \rho /\partial T\right)·u\left(T\right)$, was determined to be ±0.0106 kg⸳m⁻³. The combined standard uncertainty for the density measurement was calculated as described in the Guide to the Expression of Uncertainty in Measurement [27,28] by considering all mentioned uncertainty sources to be $u\left(\rho \right)$ = ±2.97 kg⸳m⁻³. Then, the combined expanded uncertainty of the density measurement $U\left(\rho \right)$ was found to be ±5.94 kg⸳m⁻³ (level of confidence $=$ 0.95).

In the uncertainty of viscosity measurement, specified standard uncertainties for the uncertainty sources were $u\left(p\right)$ = ±0.003, $u\left(T\right)$ = ±0.012 K, $u\left(w\right)$ = ±2 × 10⁻⁴ kg, and $u\left(rep\right)$ = ±0.008 mPa⸳s. The combined standard uncertainty for the viscosity measurement was calculated to be $u\left(\eta \right)$ = ±0.008 mPa⸳s. Then, the combined expanded uncertainty of the viscosity measurement $U\left(\eta \right)$ was found to be ±0.016 mPa⸳s (level of confidence $=$ 0.95).

3. Results

3.1. Density and Excess Molar Volume

The density of pure MDEA, DEEA, DMEA, and MEA are available in the literature. The measured densities of pure amines over a temperature range from 293.15 K to 343.15 K are listed in

Table 2. Densities $\rho$/kg⸳m⁻³ of pure amines MDEA, DMEA and DEEA.

Amine	T (K)	This Work	Literature
			Pinto et al. [29]	Hawrylak et al. [30]	Maham et al. [31]
MDEA	293.15	1040.6	1040.12
	298.15	1036.8		1036.88	1035.9
	303.15	1033.2			1032.0
	308.15	1029.4		1029.01
	313.15	1025.6	1024.74		1024.45
	318.15	1021.8		1022.64
	323.15	1018.0	1017.27		1016.66
	328.15	1014.1
	333.15	1010.3	1009.56		1009.00
	338.15	1006.4
	343.15	1002.5			1001.24
	T/(K)	This Work	Literature
			Maham et al. [32]	Hawrylak et al. [30]	Bernal-García et al. [33]
DMEA	293.15	887.3			887.816
	298.15	883.0	882.57	883.34	883.578
	303.15	878.8	878.35		879.315
	308.15	874.5		875.46	875.017
	313.15	870.1	869.86		870.686
	318.15	865.8		867.28	866.316
	323.15	861.4			861.902
	328.15	856.9			857.460
	333.15	852.5	851.89		852.965
	338.15	847.9			848.423
	343.15	843.3			843.844
	T/(K)	This Work	Literature
			Zhang et al. [34]	Hawrylak et al. [30]	Pinto et al. [29]
DEEA	293.15	884.3	884.20
	298.15	879.7	879.54	879.52	879.47
	303.15	875.1	874.82
	308.15	870.4		871.40
	313.15	865.8	865.56		865.54
	318.15	861.1		861.82
	323.15	856.3			856.12
	328.15	851.5
	333.15	846.7			846.61
	338.15	841.9
	343.15	837.1			837.03

with the relevant literature data and references. The measured density in this work is in good agreement with values reported in literature, which indicates the density meter was properly calibrated during the experiments.

The measured densities of MDEA + MEA + H₂O, DMEA + MEA + H₂O, and DEEA + MEA + H₂O mixtures over different amine concentrations (mass% of amine) and temperatures from 293.15 K to 343.15 K are listed in

Table 3. Densities $\rho$ (kg⸳m⁻³) and excess molar volume $V^E$ (m³⸳mol⁻¹) of MDEA (1) + MEA (2) + H₂O (3) mixtures.

Mixtures	MDEA/MEA
(Mass%/Mass%)	15/15		20/10		25/5		30/0
a $x_1$/$x_2$	0.0296/0.0577		0.0398/0.0388		0.0502/0.0196		0.0609/0.0000
T (K)	$\rho$	$V^E$(×106)	$\rho$	$V^E$(×106)	$\rho$	$V^E$(×106)	$\rho$	$V^E$(×106)
293.15	1019.7	−0.292	1022.1	−0.321	1024.5	−0.351	1026.9	−0.382
298.15	1017.6	−0.288	1019.9	−0.317	1022.3	−0.347	1024.7	−0.377
303.15	1015.3	−0.284	1017.6	−0.313	1020.05	−0.342	1022.4	−0.371
308.15	1012.8	−0.282	1015.2	−0.310	1017.6	−0.339	1019.9	−0.367
313.15	1010.3	−0.281	1012.6	−0.308	1015.0	−0.336	1017.3	−0.364
318.15	1007.6	−0.280	1009.9	−0.306	1012.2	−0.332	1014.6	−0.361
323.15	1004.8	−0.278	1007.1	−0.304	1009.3	−0.329	1011.7	−0.357
328.15	1001.9	−0.277	1004.1	−0.302	1006.3	−0.324	1008.7	−0.354
333.15	998.8	−0.276	1000.9	−0.297	1003.2	−0.323	1005.6	−0.350
338.15	995.6	−0.273	997.5	−0.288	999.7	−0.312	1002.3	−0.346
343.15	991.7	−0.257	993.1	−0.261	995.4	−0.287	998.7	−0.336

^a x = mole fraction.

,

Table 4. Densities $\rho$ (kg⸳m⁻³) and excess molar volume $V^E$ (m³⸳mol⁻¹) of DMEA (1) + MEA (2) + H₂O (3) mixtures.

Mixtures	DMEA/MEA
(Mass%/Mass%)	15/15		20/10		25/5		30/0
a $x_1$/$x_2$	0.0391/0.0571		0.0525/0.0383		0.0660/0.0193		0.0797/0.0000
T (K)	$\rho$	$V^E$(×106)	$\rho$	$V^E$(×106)	$\rho$	$V^E$(×106)	$\rho$	$V^E$(×106)
293.15	1001.9	−0.463	998.4	−0.550	994.4	−0.626	990.9	−0.715
298.15	999.6	−0.460	995.9	−0.545	991.8	−0.620	988.1	−0.707
303.15	996.7	−0.448	993.2	−0.539	989.0	−0.613	985.2	−0.698
308.15	994.4	−0.453	990.5	−0.536	986.1	−0.608	982.3	−0.693
313.15	991.6	−0.452	987.6	−0.533	983.1	−0.603	979.2	−0.687
318.15	988.7	−0.450	984.6	−0.531	980.0	−0.600	975.9	−0.682
323.15	985.5	−0.444	981.4	−0.528	976.8	−0.596	972.6	−0.678
328.15	982.5	−0.447	978.0	−0.523	973.4	−0.594	969.2	−0.674
333.15	979.3	−0.448	974.6	−0.520	970.0	−0.591	965.7	−0.671
338.15	975.7	−0.442	971.1	−0.517	966.4	−0.589	962.0	−0.668
343.15	972.4	−0.445	967.4	−0.511	962.8	−0.589	958.4	−0.669

^a x = mole fraction.

and

Table 5. Densities $\rho$ (kg⸳m⁻³) and excess molar volume $V^E$ (m³⸳mol⁻¹) of DEEA (1) + MEA (2) + H₂O (3) mixtures.

Mixtures	DEEA/MEA
(Mass%/Mass%)	15/15		20/10		25/5		30/0
a x1/x2	0.0301/0.0577		0.0404/0.0388		0.0510/0.0196		0.0618/0.0000
T (K)	$\mathit{\rho }$	${\mathit{V}}^{\mathit{E}} (\times {10}^6)$	$\mathit{\rho }$	${\mathit{V}}^{\mathit{E}} (\times {10}^6)$	$\mathit{\rho }$	${\mathit{V}}^{\mathit{E}} (\times {10}^6)$	$\mathit{\rho }$	${\mathit{V}}^{\mathit{E}} (\times {10}^6)$
293.15	1002.3	−0.489	998.4	−0.575	994.2	−0.654	989.6	−0.724
298.15	999.8	−0.484	995.7	−0.568	991.4	−0.645	986.5	−0.711
303.15	997.1	−0.479	992.9	−0.561	988.4	−0.636	983.4	−0.702
308.15	994.3	−0.476	990.0	−0.556	985.3	−0.629	980.2	−0.693
313.15	991.4	−0.473	986.9	−0.551	982.1	−0.623	976.9	−0.684
318.15	988.5	−0.471	983.7	−0.547	978.8	−0.617	973.4	−0.677
323.15	985.1	−0.464	980.5	−0.544	975.3	−0.611	969.8	−0.669
328.15	981.8	−0.462	977.1	−0.541	971.8	−0.606	966.2	−0.663
333.15	978.5	−0.459	973.6	−0.538	968.2	−0.602	962.4	−0.657
338.15	974.4	−0.443	970.0	−0.535	964.3	−0.595	958.5	−0.651
343.15	971.1	−0.448	966.2	−0.529	960.4	−0.589	954.6	−0.645

^a x = mole fraction.

, respectively. For the density of MDEA + MEA + H₂O mixtures, the density increased with the increase of the MDEA concentration in the mixture. Moreover, for the DMEA + MEA + H₂O and DEEA + MEA + H₂O mixtures, the density increased with the decrease of the DMEA and DEEA concentration in the mixtures.

The excess molar volume $V^E$ of the mixtures were determined using the molar volume of the mixture and pure components as follows:

$$V^E=V-{\displaystyle \sum }_{i=1}^n{x}_i{V}_i^0,$$

(1)

where $V$, $V_i^0,$ $V^E$, and $x_i$ refer to the molar volume of the mixture, molar volume of the pure component, excess molar volume of the mixture, and mole fraction, respectively. Here, $n$ = 3 to represent the ternary mixture and subscripts are as follows: $i$ = 1 for the tertiary amine, $i$ = 2 for the primary amine (MEA), and $i$ = 3 for H₂O.

The calculated $V^E$ from Equation (1) for MDEA + MEA + H₂O, DMEA + MEA + H₂O, and DEEA + MEA + H₂O mixtures are given in Table 3, Table 4 and Table 5, respectively. The following correlation was adopted to correlate the density data at different amine concentrations and temperatures. Redlich–Kister [35] polynomials are one of the most common approaches toward correlating the excess properties of binary mixtures because polynomial expressions are simple and easy to understand. Here, it was assumed that excess molar volume of a ternary mixture as a sum of excess molar volumes from different binary pairs, as given in Equation (3). The binary mixture polynomial shown in Equation (4) was extended by adding ternary coefficients for the ternary mixture with a temperature dependency, as described in Equation (5). Finally, the density was determined as follows:

$$\rho =\frac{{{\displaystyle \sum }}_{i=1}^n{x}_i{M}_i}{V^E+{{\displaystyle \sum }}_{i=1}^n\frac{x_i{M}_i}{{\rho }_i}},$$

(2)

where $\rho$, ${\rho }_i$, $V^E$, $x_i$, and $M_i$ are the density of the mixture, density of the pure amine, excess molar volume of the mixture, mole fraction, and molecular weight of the pure component, respectively. The subscripts are as follows: $i$ = 1 for tertiary amine, $i$ = 2 for primary amine (MEA), and $i$ = 3 for H₂O.

$$V^E=V_{12}^E+V_{23}^E+V_{13}^E,$$

(3)

$$V_{jk}^E=x_j{x}_k{{\displaystyle \sum }}_{i=0}^n{A}_i{\left(x_j-x_k\right)}^i,$$

(4)

$$A_i=a+b\left(T\right)+c{\left(T\right)}^2,$$

(5)

where $A_i$ are pair parameters and are assumed to be temperature dependent.

Other correlations have been suggested for the excess molar volume of ternary mixtures were reported by Domínguez et al. [36] and Samanta and Bandyopadhyay [37]. References [38,39,40] suggested correlations for CO₂-loaded solutions, but in this work, emphasis is on non-loaded aqueous amine mixtures.

The accuracy of the proposed correlation for the fitting of measured densities was examined through the average absolute relative deviation (AARD (%)) and the absolute maximum deviation (AMD) as defined in Equations (6) and (7), respectively.

Average absolute relative deviation:

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

(6)

and the absolute maximum deviation:

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

(7)

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

Figure 1 shows a comparison between the measured versus correlated density data for aqueous amine mixtures. The study reveals that the proposed correlation fits the density data with an acceptable accuracy. The calculated parameters for the excess volume $V^E$ correlation are given in

Table 6. Binary parameters $A_0$, $A_1$, and $A_2$ of the equation $V_{jk}^E=x_j{x}_k{\displaystyle \sum }_{i=0}^n{A}_i{\left(x_j-x_k\right)}^i$ for the excess molar volume of MDEA (1) + MEA (2) + H₂O (3).

Parameters		Binary Pair
		MDEA + MEA	MEA + H2O	MDEA + H2O
$A_0$	$a$	−5740.7862	110.3506	0.7103
	$b$	−9.4267	0.5623	0.0984
	$c$	−6.0994	0.7119	0.6020
$A_1$	$a$	47,728.6381	−91.5628	0.5925
	$b$	82.8194	0.5242	0.3620
	$c$	70.3044	0.4374	0.6230
$A_2$	$a$	−41,5410.0557	70.3808	−0.2463
	$b$	−724.8059	0.3897	0.2846
	$c$	−601.8188	−0.0807	−0.0710

,

Table 7. Binary parameters $A_0$, $A_1$, and $A_2$ of the equation $V_{jk}^E=x_j{x}_k{\displaystyle \sum }_{i=0}^n{A}_i{\left(x_j-x_k\right)}^i$ for the excess molar volume of DMEA (1) + MEA (2) + H₂O (3).

Parameters		Binary Pair
		DMEA + MEA	MEA + H2O	DMEA + H2O
$A_0$	$a$	1236.6194	−29.4723	−0.2082
	$b$	1.2313	0.1074	0.3237
	$c$	−4.8869	0.1673	0.3986
$A_1$	$a$	−10,260.3999	24.7205	0.3942
	$b$	−18.2970	0.9283	0.5201
	$c$	36.5240	0.3256	0.7509
$A_2$	$a$	66,361.3723	−16.8614	0.7635
	$b$	110.1435	0.8558	0.1605
	$c$	−240.1085	0.4951	0.3292

and

Table 8. Binary parameters $A_0$, $A_1$, and $A_2$ of the equation $V_{jk}^E=x_j{x}_k{\displaystyle \sum }_{i=0}^n{A}_i{\left(x_j-x_k\right)}^i$ for the excess molar volume of DEEA (1) + MEA (2) + H₂O (3).

Parameters		Binary Pair
		DEEA + MEA	MEA + H2O	DEEA + H2O
$A_0$	$a$	1499.9879	−31.3131	−0.3593
	$b$	−7.4459	0.5442	0.2384
	$c$	1.3969	0.0633	0.3485
$A_1$	$a$	−12,608.1516	24.6564	−0.4664
	$b$	68.6619	0.4921	0.7533
	$c$	−19.8546	0.5935	0.6335
$A_2$	$a$	107,748.3754	−15.3309	−0.0644
	$b$	−588.5102	0.2714	0.5491
	$c$	156.7816	0.5154	0.2691

. The reported AARD and AMD for the density correlation of MDEA + MEA + H₂O, DMEA + MEA + H₂O, and DEEA + MEA + H₂O are listed in

Table 9. Average absolute relative (AARD) and absolute maximum (AMD) deviations calculated based on the correlation proposed from Equations (2)–(5).

Mixture	AARD (%)	AMD (kg⸳m−3)
MDEA + MEA + H2O	0.013	0.4
DMEA + MEA + H2O	0.004	0.3
DEEA + MEA + H2O	0.005	0.3

. The regression performed with a linear temperature dependency in Equation (5) revealed a 13% increase of AARD for MDEA + MEA + H₂O mixtures, as given in Table 9. This indicated that the proposed correlation gave a better fit for the density data.

The Supplementary Materials provide the information of the used MATLAB program for the calculation of parameters involve in density correlation.

The excess molar volume $V^E$ of the ternary mixtures showed a negative sign for the considered amine concentrations and temperatures. The negative sign of $V^E$ can be explained by the intermolecular packing effect and strong intermolecular interactions, such as H-bonding between unlike molecules. The relatively small structures of MEA and H₂O compared to MDEA, DMEA, and DEEA could help to pack molecules efficiently, which resulted in the decrease of the mixture volume. In addition, the formation of H-bonds among the tertiary amines, MEA, and H₂O could also lead the volume of tertiary mixtures to show a negative deviation of $V^E$. The highest negative values were reported in the mixtures with a 0 mass% MEA concentration. The $V^E$ increased with the increasing of MEA concentration in the mixtures. Further, $V^E$ increased with the increase of temperature. At high temperatures, the increase of the energy of molecular motion weakens the interaction strength of H-bonds and inhibits the packing effect by leading to an increase of volume [41,42].

3.2. Viscosity and Excess Free Energy of Activation for Viscous Flow

Table 10. Viscosities $\eta$ (mPa⸳s) of pure amines MDEA, DMEA, and DEEA.

Amine	T (K)	This Work	Literature
			Teng et al. [43]	Li and Lie [24]	Kummamuru et al. [44]
MDEA	293.15	100.630
	298.15	75.775	77.19		73.10
	303.15	57.658		57.860	55.89
	308.15	44.483			43.45
	313.15	34.786	34.11	34.309	34.15
	318.15	27.575			27.l5
	323.15	22.145		21.672	21.82
	328.15	18.024			17.79
	333.15	14.820	14.30	14.386	14.63
	338.15	12.319			12.20
	343.15	10.325	9.849	9.979	10.21
	348.15	8.735			8.60
	353.15	7.444	7.115	7.086	7.31
	358.15	6.395			6.29
	363.15	5.535			5.43
	T (K)	This Work	Literature
			Bernal-García et al. [33]	Chowdhury et al. [45]	DiGuilio et al. [46]
DMEA	293.15	3.879
	298.15	3.381
	303.15	2.959		2.835	2.849
	308.15	2.595		2.485
	313.15	2.288	2.238	2.186	2.194
	318.15	2.028		1.938
	323.15	1.807	1.756	1.723	1.734
	328.15	1.618
	333.15	1.455	1.413		1.394
	338.15	1.315
	343.15	1.190	1.156		1.140
	348.15	1.078
	353.15	0.981	0.963		0.916
	358.15	0.896
	363.15	0.820			0.773
	T/(K)	This Work	Literature
			Maham et al. [32]	Chen et al. [47]	Ma et al. [48]
DEEA	293.15	4.950		4.81	4.848
	298.15	4.174	4.022
	303.15	3.536	3.308	3.37	3.410
	308.15	3.010
	313.15	2.579	2.414	2.46	2.466
	318.15	2.230
	323.15	1.943		1.86	1.855
	328.15	1.704
	333.15	1.503	1.435	1.46	1.431
	338.15	1.337
	343.15	1.196
	348.15	1.076
	353.15	0.971	0.925
	358.15	0.881
	363.15	0.800

provides an overview of the measured viscosities of pure MDEA, DMEA, and DEEA from this study and literature at different temperatures from 293.15 K to 363.15 K. As shown in Figure 2, the measured viscosities in this work were in good agreement with data in the literature. It indicated that the measuring system was properly calibrated during the viscosity measurements. The measured viscosities for MDEA + MEA + H₂O, DMEA + MEA + H₂O, and DEEA + MEA + H₂O mixtures are listed in

Table 11. Viscosities $\eta$ (mPa⸳s) and viscosity deviation ${\eta }^E$ (mPa⸳s) of MDEA (1) + MEA (2) + H₂O (3) mixtures.

Mixtures	MDEA/MEA
(Mass%/Mass%)	15/15		20/10		25/5		30/0
a x1/x2	0.0296/0.0577		0.0398/0.0388		0.0502/0.0196		0.0609/0.0000
T/(K)	$\mathit{\eta }$	${\mathit{\eta }}^{\mathit{E}}$		${\mathit{\eta }}^{\mathit{E}}$	$\mathit{\eta }$	${\mathit{\eta }}^{\mathit{E}}$	$\mathit{\eta }$	${\mathit{\eta }}^{\mathit{E}}$
293.15	3.263	−1.976	3.436	−2.400	3.581	−2.863	3.712	−3.352
298.15	2.780	−1.337	2.917	−1.635	3.034	−1.961	3.136	−2.311
303.15	2.385	−0.900	2.496	−1.107	2.593	−1.334	2.673	−1.584
308.15	2.065	−0.599	2.156	−0.744	2.235	−0.904	2.301	−1.082
313.15	1.803	−0.390	1.879	−0.489	1.946	−0.601	1.995	−0.735
318.15	1.588	−0.243	1.654	−0.311	1.709	−0.391	1.748	−0.490
323.15	1.410	−0.141	1.467	−0.185	1.512	−0.244	1.544	−0.318
328.15	1.264	−0.065	1.314	−0.095	1.350	−0.138	1.376	−0.194
333.15	1.140	−0.012	1.184	−0.029	1.215	−0.061	1.236	−0.104
338.15	1.036	0.030	1.075	0.020	1.099	−0.007	1.117	−0.039
343.15	0.947	0.058	0.979	0.051	0.998	0.030	1.017	0.010
348.15	0.867	0.077	0.896	0.075	0.913	0.060	0.930	0.044
353.15	0.797	0.090	0.824	0.092	0.841	0.082	0.853	0.068
358.15	0.741	0.103	0.763	0.104	0.777	0.097	0.790	0.089
363.15	0.712	0.133	0.722	0.126	0.738	0.125	0.747	0.116

^a x = mole fraction.

,

Table 12. Viscosities $\eta$ (mPa⸳s) and viscosity deviation ${\eta }^E$ (mPa⸳s) of DMEA (1) + MEA (2) + H₂O (3) mixtures.

Mixtures	DMEA/MEA
(Mass%/Mass%)	15/15		20/10		25/5		30/0
a x1/x2	0.0391/0.0571		0.0525/0.0383		0.0660/0.0193		0.0797/0.0000
T/(K)	$\mathit{\eta }$	${\mathit{\eta }}^{\mathit{E}}$	$\mathit{\eta }$	${\mathit{\eta }}^{\mathit{E}}$	$\mathit{\eta }$	${\mathit{\eta }}^{\mathit{E}}$	$\mathit{\eta }$	${\mathit{\eta }}^{\mathit{E}}$
293.15	3.523	1.130	3.744	1.734	4.079	2.456	4.245	3.013
298.15	2.969	0.978	3.130	1.437	3.389	1.996	3.487	2.398
303.15	2.512	0.832	2.644	1.197	2.848	1.639	2.898	1.928
308.15	2.155	0.718	2.256	1.006	2.410	1.349	2.440	1.571
313.15	1.866	0.624	1.943	0.852	2.064	1.126	2.079	1.296
318.15	1.632	0.547	1.691	0.729	1.790	0.953	1.791	1.081
323.15	1.439	0.482	1.485	0.629	1.565	0.813	1.557	0.909
328.15	1.282	0.430	1.319	0.552	1.386	0.706	1.369	0.776
333.15	1.149	0.386	1.180	0.489	1.235	0.616	1.212	0.666
338.15	1.038	0.351	1.063	0.436	1.111	0.545	1.082	0.578
343.15	0.942	0.318	0.962	0.390	1.001	0.481	0.973	0.507
348.15	0.859	0.291	0.874	0.350	0.906	0.427	0.882	0.448
353.15	0.788	0.267	0.800	0.318	0.827	0.384	0.805	0.401
358.15	0.728	0.248	0.735	0.288	0.761	0.349	0.737	0.360
363.15	0.701	0.257	0.703	0.289	0.711	0.328	0.686	0.333

^a x = mole fraction.

and

Table 13. Viscosities $\eta$ (mPa⸳s) and viscosity deviation ${\eta }^E$ (mPa⸳s) of DEEA (1) + MEA (2) + H₂O (3) mixtures.

Mixtures	DEEA/MEA
(Mass%/Mass%)	15/15		20/10		25/5		30/0
a x1/x2	0.0301/0.0577		0.0404/0.0388		0.0510/0.0196		0.0618/0.0000
T/(K)	$\mathit{\eta }$	${\mathit{\eta }}^{\mathit{E}}$	$\mathit{\eta }$	${\mathit{\eta }}^{\mathit{E}}$	$\mathit{\eta }$	${\mathit{\eta }}^{\mathit{E}}$	$\mathit{\eta }$	${\mathit{\eta }}^{\mathit{E}}$
293.15	3.691	1.280	3.963	1.933	4.217	2.575	4.536	3.290
298.15	3.086	1.085	3.281	1.577	3.464	2.063	3.689	2.595
303.15	2.604	0.919	2.746	1.296	2.886	1.675	3.048	2.081
308.15	2.220	0.781	2.325	1.075	2.435	1.378	2.552	1.691
313.15	1.910	0.669	1.991	0.904	2.078	1.147	2.165	1.393
318.15	1.662	0.580	1.726	0.769	1.795	0.967	1.860	1.163
323.15	1.460	0.506	1.507	0.658	1.565	0.823	1.617	0.984
328.15	1.296	0.449	1.330	0.571	1.380	0.710	1.419	0.840
333.15	1.159	0.401	1.182	0.498	1.229	0.621	1.259	0.728
338.15	1.041	0.359	1.057	0.438	1.101	0.547	1.126	0.637
343.15	0.942	0.323	0.953	0.388	0.993	0.484	1.016	0.563
348.15	0.858	0.294	0.874	0.357	0.900	0.431	0.920	0.499
353.15	0.782	0.266	0.797	0.321	0.822	0.388	0.842	0.450
358.15	0.719	0.243	0.730	0.289	0.752	0.349	0.771	0.405
363.15	0.686	0.246	0.691	0.283	0.696	0.320	0.708	0.365

^a x = mole fraction.

, respectively, with the relevant concentrations and temperatures. For the mixtures, the viscosity increased with the increase of the tertiary amine concentration and the viscosity decreased with the increase of temperature.

The viscosity deviation of the mixtures was calculated as follows:

$${\eta }^E=\eta -{\displaystyle \sum }_{i=1}^n{x}_i{\eta }_i^0,$$

(8)

where $\eta$, ${\eta }_i^0$, ${\eta }^E$, and $x_i$ refer to the viscosity of the mixture, viscosity of the pure component, viscosity deviation of the mixture, and mole fraction, respectively. Here, $n$ = 3 represents the ternary mixture and the subscripts are as follows: $i$ = 1 for the tertiary amine, $i$ = 2 for the primary amine (MEA), and $i$ = 3 for H₂O.

The viscosity deviation ${\eta }^E$ is a property that provides a qualitative measure of intermolecular interactions between component molecules in a liquid mixture. A negative deviation (${\eta }^E$ < 0) indicates weak intermolecular interactions, while a positive deviation points out strong intermolecular interactions like H-bonding among unlike molecules in the mixture [42,49]. This method is widely used to analyze binary mixtures and the same analogy is adopted to study ternary mixtures [42]. The MDEA + MEA + H₂O mixtures showed a negative deviation for ${\eta }^E$ at temperatures <343.15 K, and ${\eta }^E$ gradually increased with increasing temperature. As described by Domínguez et al. [50], the ${\eta }^E$ can become negative when intermolecular interactions between the molecules are stronger for the pure compounds than for their mixtures. The gradual increase of ${\eta }^E$ with increasing temperature implies that the strength of the interactions between the component molecules in mixtures decreases, which may be attributed to the breaking of the cohesive force in like molecules [51]. The mixtures of DMEA + MEA + H₂O and DEEA + MEA + H₂O showed a positive deviation for ${\eta }^E$ for the considered concentrations and temperatures. This revealed the association of strong intermolecular interactions of H-bonds in the mixtures. The increase of temperature resulted in a decrease of ${\eta }^E$ owing to weakening of intermolecular interaction between unlike molecules.

Eyring [52] explained that in a liquid at rest, the molecules are constantly undergoing rearrangements. This was elaborated by Bird et al. [53] in terms of one molecule at a time escaping from its cage into an adjacent hole. A cage is an available space for a molecule to vibrate due to the surrounding closely packed neighboring molecules. An energy barrier of height $\Delta G^{\ast }/N_A$ represents the cage in which $\Delta G^{\ast }$ and $N_A$ are the free energy of activation for viscous flow and Avogadro’s number, respectively.

The dynamic viscosity model for liquids found by Eyring [52] is given as follows:

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

(9)

where $\eta$, $V$, $h$, $N_A$, $R$, $T$, and $\Delta G^{\ast }$ refer to the viscosity, molar volume, Planck’s constant, Avogadro’s number, gas constant, temperature, and free energy of activation for viscous flow, respectively.

Equations (10) and (11) enable the determination of the excess free energy of activation for viscous flow $\Delta G^{E\ast }$ in terms of the viscosity and molar volume of the pure components:

$$ln\left(\eta V\right)=ln{\left(\eta V\right)}_{ideal}+\frac{\Delta G^{E\ast }}{RT},$$

(10)

$$ln\left(\eta V\right)={\displaystyle \sum }_{i=1}^n{x}_{i}ln\left({\eta }_i{V}_i^0\right)+\frac{\Delta G^{E\ast }}{RT},$$

(11)

where $\eta$, ${\eta }_i$, $V$, $V_i^0$, $x_i$, $R$, $T$, and $\Delta G^{E\ast }$ refer to the viscosity of the mixture, viscosity of pure component, molar volume of the mixture, molar volume of the pure component, mole fraction, gas constant, temperature, and excess free energy of activation for viscous flow, respectively. The subscripts are as follows: $i$ = 1 for the tertiary amine, $i$ = 2 for the primary amine (MEA), and $i$ = 3 for H₂O.

A Redlich–Kister-type [35] polynomial, as given by Equations (12)–(14), was proposed to fit the calculated $\Delta G^{E\ast }$ for the considered amine mixtures:

$$\Delta G^{E\ast }=\Delta G_{12}^{E\ast }+\Delta G_{23}^{E\ast }+\Delta G_{13}^{E\ast },$$

(12)

$$\Delta G_{jk}^{E\ast }=x_j{x}_k{{\displaystyle \sum }}_{i=0}^n{A}_i{\left(x_j-x_k\right)}^i,$$

(13)

$$A_i=a+b\left(T\right)+c{\left(T\right)}^2.$$

(14)

The correlation proposed for $\Delta G^{E\ast }$ was adopted to represent the measured viscosities, as illustrated in Figure 3. Due to the non-availability of measured density data beyond 343.15 K, the correlation represents viscosities only in the temperature region of 293.15 K–343.15 K. The calculated parameters of correlation for $\Delta G^{E\ast }$ are given in

Table 14. Binary parameters $A_0$, $A_1$, and $A_2$ of the equation $\Delta G_{jk}^{E\ast }=x_j{x}_k{\displaystyle \sum }_{i=0}^n{A}_i{\left(x_j-x_k\right)}^i$ for the excess free energy of activation for the viscous flow of MDEA (1) + MEA (2) + H₂O (3).

Parameters		Binary Pair
		MDEA + MEA	MEA + H2O	MDEA + H2O
$A_0$	$a$	793,598.3561	29,742.8180	88,484.8967
	$b$	−4103.0875	−151.4883	−415.9737
	$c$	0.0695	0.9416	1.1885
$A_1$	$a$	−24,596,691.6004	−34,368.3693	−100,459.5203
	$b$	144054.1895	176.3634	472.7640
	$c$	−147.3226	0.1721	−0.0422
$A_2$	$a$	−992,156,463.1846	39,623.1737	114,056.3754
	$b$	6,459,639.6117	−202.4417	−536.0680
	$c$	−11,029.3913	0.2259	0.6852

,

Table 15. Binary parameters $A_0$, $A_1$, and $A_2$ of the equation $\Delta G_{jk}^{E\ast }=x_j{x}_k{\displaystyle \sum }_{i=0}^n{A}_i{\left(x_j-x_k\right)}^i$ for the excess free energy of activation for the viscous flow of DMEA (1) + MEA (2) + H₂O (3).

Parameters		Binary Pair
		DMEA + MEA	MEA + H2O	DMEA + H2O
$A_0$	$a$	408,836.2339	23,045.8957	121,961.3271
	$b$	−2025.9328	−111.1510	−594.2230
	$c$	−1.7551	0.3358	1.2015
$A_1$	$a$	−7,605,815.8343	−26,647.3964	−142,650.2697
	$b$	30,647.5124	129.8558	695.9285
	$c$	7.3689	0.1302	−0.18829
$A_2$	$a$	200,073,604.4909	30,794.61597	166,795.8337
	$b$	−1,158,470.4621	−148.3353	−812.9574
	$c$	1738.2732	0.7219	1.4276

and

Table 16. Binary parameters $A_0$, $A_1$, and $A_2$ of the equation $\Delta G_{jk}^{E\ast }=x_j{x}_k{\displaystyle \sum }_{i=0}^n{A}_i{\left(x_j-x_k\right)}^i$ for the excess free energy of activation for the viscous flow of DEEA (1) + MEA (2) + H₂O (3).

Parameters		Binary Pair
		DEEA + MEA	MEA + H2O	DEEA + H2O
$A_0$	$a$	25,126.2870	6568.5853	187,358.9813
	$b$	1235.2155	6.8875	−956.1233
	$c$	−1.4932	0.0215	1.6908
$A_1$	$a$	−29,279,977.3999	−6903.8084	−212,891.0602
	$b$	170,793.9954	−12.0764	1087.3001
	$c$	−281.5476	0.6502	−0.8913
$A_2$	$a$	1,130,127,942.1759	7134.8943	241,892.0192
	$b$	−7,848,704.4368	20.9358	−1233.8639
	$c$	13,825.2946	0.4399	2.0013

. The reported AARD and AMD for the correlated viscosities of MDEA + MEA + H₂O, DMEA + MEA + H₂O, and DEEA + MEA + H₂O mixtures are listed in

Table 17. Average absolute relative (AARD) and absolute maximum (AMD) deviations calculated based on correlations proposed using Equations (12)–(14).

Mixture	AARD (%)	AMD (mPa⸳s)
MDEA + MEA + H2O	0.14	0.013
DMEA + MEA + H2O	0.10	0.013
DEEA + MEA + H2O	0.07	0.010

and show that the proposed correlations fit viscosity data with acceptable accuracy.

The Supplementary Materials provide the information of the used MATLAB program for the calculation of parameters involve in viscosity correlation.

According to Meyer et al. [54], molecular interactions in liquid mixtures can be studied by adopting $\Delta G^{E\ast }$, similar to the ${\eta }^E$. Studies performed in References [41,55,56,57] suggested that a positive deviation of $\Delta G^{E\ast }$ indicates strong intermolecular interactions, such as H-bonds among unlike molecules, while a negative deviation of $\Delta G^{E\ast }$ signifies weak molecular interactions, such as dispersive forces.

The mixtures examined in this study demonstrated positive deviations for $\Delta G^{E\ast }$ for the considered amine concentrations and temperatures, indicating the presence of strong intermolecular interactions like H-bonds between the molecules in the mixtures. The presence of (–OH) and (–NH₂) groups in amines contributes to the formation of H-bonds between unlike molecules. For the MDEA + MEA + H₂O mixtures, the highest $\Delta G^{E\ast }$ was reported for the mixture of 30 mass% MDEA + 0 mass% MEA + 70 mass% H₂O. The highest $\Delta G^{E\ast }$ for DEEA + MEA + H₂O was reported for the mixture of 30 mass% DEEA + 0 mass% MEA + 70 mass% H₂O, while for DMEA + MEA + H₂O, the highest $\Delta G^{E\ast }$ was reported for the mixture of 30 mass% DMEA + 0 mass% MEA + 70 mass% H₂O. The increases of MEA concentration gradually decreased the $\Delta G^{E\ast }$ for all mixtures, as shown in the Figure 4.

The slope of the excess free energy of activation $\Delta G^{E\ast }$ against temperature $T$ at certain mole fractions gives the excess entropy of activation $\Delta S^{E\ast }$ for the viscous flow:

$$\Delta S^{E\ast }=-\left[\frac{\partial \Delta G^{E\ast }}{\partial T}\right].$$

(15)

Figure 5 shows the excess entropy of activation $\Delta S^{E\ast }$ for the viscous flow of MDEA + MEA + H₂O, DMEA + MEA + H₂O, and DEEA + MEA + H₂O in the temperature range of 293.15 K–343.15 K over the whole range of concentrations. The values for $\Delta S^{E\ast }$ were determined using Equation (15). Figure 5 reveals that the excess entropy $\Delta S^{E\ast }$ followed the same trend as $\Delta G^{E\ast }$, that is, $\Delta S^{E\ast }$ decreased with the increase of MEA concentration in the mixture. A maximum value for $\Delta S^{E\ast }$ was observed at solutions with 0 mass% MEA.

4. Conclusions

This paper discusses the densities and viscosities of MDEA + MEA + H₂O, DMEA + MEA + H₂O, and DEEA + MEA + H₂O mixtures at different concentrations of 15/15, 20/10, 25/5, and 30/0 for mass% (tertiary amine; MDEA, DMEA and DEEA)/mass% (primary amine; MEA) and temperatures.

The density of the mixtures was measured in the temperature range from 293.15 K to 343.15 K. The density of the mixtures increased with the increase of MDEA concentration and the density decreased with the increase of temperature for MDEA + MEA + H₂O mixtures. For the mixtures of DMEA + MEA + H₂O and DEEA + MEA + H₂O, the density decreased with the increase of DMEA and DEEA concentrations and the density decreased with the increase of temperature. The excess volume $V^E$ of the mixtures was determined and were correlated according to a Redlich–Kister-type polynomial to represent the measured densities. A negative sign of the excess volume $V^E$ indicates effective packing of the molecules and the presence of H-bonding among the unlike molecules. The proposed correlation was able to fit the density data with the acceptable accuracies of 0.013%, 0.004%, and 0.005% for AARD and 0.4 kg⸳m⁻³, 0.3 kg⸳m⁻³, and 0.3 kg⸳m⁻³ for AMD for the MDEA + MEA + H₂O, DMEA + MEA + H₂O, and DEEA + MEA + H₂O mixtures, respectively.

The viscosity of the mixtures was measured in the temperature range from 293.15 K to 363.15 K. The viscosity of the mixture increased with the increase of MDEA, DMEA, and DEEA concentration in the mixtures and the viscosity decreased with the increase of temperature. The viscosity deviation ${\eta }^E$ was negative for the MDEA + MEA + H₂O at low temperatures, indicating weak intermolecular interactions in the mixture compared to the pure liquids. A positive ${\eta }^E$ was reported for the DMEA + MEA + H₂O and DEEA + MEA + H₂O mixtures for the considered temperature range, signifying the presence of strong intermolecular interactions, such as H-bonds, in the mixtures. The excess free energy of activation $\Delta G^{E\ast }$ for viscous flow, as described by Eyring, showed positive values for all mixtures for the temperature range. This highlights the existence of strong intermolecular interactions, such as H-bonds, between the molecules in the mixtures. The correlation proposed for the calculated $\Delta G^{E\ast }$ from measured densities and viscosities was able to fit the $\Delta G^{E\ast }$ with 0.15%, 0.09%, and 0.07% for AARD for the MDEA + MEA + H₂O, DMEA + MEA + H₂O, and DEEA + MEA + H₂O mixtures, respectively.