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

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 VE 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 ∆GE* and excess entropy of activation ∆SE* 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 VE and ∆GE* 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.


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 postcombustion 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). Table 1 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).

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.

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).

Experimental Uncertainty
Several uncertainty sources of material purity , temperature measurement , weight measurement , and repeatability 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 = ±0.003, = ±0.012 K, = ±2 × 10 −4 kg, and = ±0.13 kg⸳m −3 . The maximum gradient of density against temperature, ⁄ , was found to be 0.88 kg⸳m −3 ⸳K −1 and the corresponding uncertainty in , ⁄ ⸳ , 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 = ±2.97 kg⸳m −3 . Then, the combined expanded uncertainty of the density measurement 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 = ±0.003, = ±0.012 K, = ±2 × 10 −4 kg, and = ±0.008 mPa⸳s. The combined standard uncertainty for the viscosity measurement was calculated to be = ±0.008 mPa⸳s. Then, the combined expanded uncertainty of the viscosity measurement was found to be ±0.016 mPa⸳s (level of confidence = 0.95).

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 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 Tables 3-5, 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 of the mixtures were determined using the molar volume of the mixture and pure components as follows: where , , , and 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, = 3 to represent the ternary mixture and subscripts are as follows: = 1 for the tertiary amine, = 2 for the primary amine (MEA), and = 3 for H2O.
The calculated from Equation (1) for MDEA + MEA + H2O, DMEA + MEA + H2O, and DEEA + MEA + H2O mixtures are given in Tables 3-5, 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: where , , , , and 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: = 1 for tertiary amine, = 2 for primary amine (MEA), and = 3 for H2O.
where 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: and the absolute maximum deviation: where , , and 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 correlation are given in Tables 6-8. 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. 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.

AARD (%) AMD (kg⸳m
The excess molar volume of the ternary mixtures showed a negative sign for the considered amine concentrations and temperatures. The negative sign of 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 . The highest negative values were reported in the mixtures with a 0 mass% MEA concentration. The increased with the increasing of MEA concentration in the mixtures. Further, 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]. Table 10 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 Tables 11-13, 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.  [43]; "◇"-Li and Lie [24]; "x"-Kummamuru et al. [44]. Viscosity of DMEA: "---"-this work; "◻"-Bernal-García et al. [33]; "◇"-Chowdhury et al. [45]; "x"-DiGuilio et al. [46]. Viscosity of DEEA: "---"-this work; "◻"-Maham et al. [32]; "◇"-Chen et al. [47]; "x"-Ma et al. [48].    The viscosity deviation of the mixtures was calculated as follows:

Viscosity and Excess Free Energy of Activation for Viscous Flow
where , , , and refer to the viscosity of the mixture, viscosity of the pure component, viscosity deviation of the mixture, and mole fraction, respectively. Here, = 3 represents the ternary mixture and the subscripts are as follows: = 1 for the tertiary amine, = 2 for the primary amine (MEA), and = 3 for H2O.
The viscosity deviation is a property that provides a qualitative measure of intermolecular interactions between component molecules in a liquid mixture. A negative deviation ( < 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 at temperatures <343.15 K, and gradually increased with increasing temperature. As described by Domínguez et al. [50], the can become negative when intermolecular interactions between the molecules are stronger for the pure compounds than for their mixtures. The gradual increase of 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 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 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 Δ * ⁄ represents the cage in which Δ * and 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: where , , ℎ , , , , and Δ * 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 Δ * in terms of the viscosity and molar volume of the pure components: where , , , , , , , and Δ * 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: = 1 for the tertiary amine, = 2 for the primary amine (MEA), and = 3 for H2O.
According to Meyer et al. [54], molecular interactions in liquid mixtures can be studied by adopting Δ * , similar to the . Studies performed in References [41,[55][56][57] suggested that a positive deviation of Δ * indicates strong intermolecular interactions, such as H-bonds among unlike molecules, while a negative deviation of Δ * signifies weak molecular interactions, such as dispersive forces.
The mixtures examined in this study demonstrated positive deviations for ∆ * 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 ∆ * was reported for the mixture of 30 mass% MDEA + 0 mass% MEA + 70 mass% H2O. The highest ∆ * 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 ∆ * was reported for the mixture of 30 mass% DMEA + 0 mass% MEA + 70 mass% H2O. The increases of MEA concentration gradually decreased the ∆ * for all mixtures, as shown in the Figure 4. The slope of the excess free energy of activation ∆ * against temperature at certain mole fractions gives the excess entropy of activation ∆ * for the viscous flow: Figure 5 shows the excess entropy of activation ∆ * 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 ∆ * were determined using Equation (15). Figure 5 reveals that the excess entropy ∆ * followed the same trend as ∆ * , that is, ∆ * decreased with the increase of MEA concentration in the mixture. A maximum value for ∆ * was observed at solutions with 0 mass% MEA.
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 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 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 was negative for the MDEA + MEA + H2O at low temperatures, indicating weak intermolecular interactions in the mixture compared to the pure liquids. A positive 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 Δ * 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 Δ * from measured densities and viscosities was able to fit the Δ * with 0.15%, 0.09%, and 0.07% for AARD for the MDEA + MEA + H2O, DMEA + MEA + H2O, and DEEA + MEA + H2O mixtures, respectively.