Surface Thermodynamics, Viscosity, Activation Energy of N-Methyldiethanolamine Aqueous Solutions Promoted by Tetramethylammonium Arginate

The surface tension and viscosity values of N-methyldiethanolamine (MDEA) aqueous solutions promoted by tetramethylammonium arginate ([N1111][Arg]) were measured and modeled. The experimental temperatures were 303.2 to 323.2 K. The mass fractions of MDEA (wMDEA) and [N1111][Arg] (w[N1111][Arg]) were 0.300 to 0.500 and 0.025 to 0.075, respectively. The measured surface tension and viscosity values were satisfactorily fitted to thermodynamic models. With the aid of experimentally viscosity data, the activation energy (Ea) and H2S diffusion coefficient (DH2S) of MDEA-[N1111][Arg] aqueous solution were deduced. The surface entropy and surface enthalpy of the solutions were calculated using the fitted model of the surface tension. The quantitative relationship between the calculated values (surface tension, surface entropy, surface enthalpy, viscosity, activation energy, and H2S diffusion coefficient) and the operation conditions (mass fraction and temperature) was demonstrated.


Introduction
China is a large coke producer, and coke oven gas (COG) is the second most abundant coking product after coke in the coking industry, with generation of 300-360 m 3 of COG as a by-product for every 1 t of coke produced [1]. The main components of COG are hydrogen and methane, which have high calorific values and application value. COG can be used as an urban or industrial fuel gas, in gas-fired power stations to generate electricity, or as a raw material to synthesize ammonia, methanol, and other chemicals [2]. However, COG contains impurities that must be removed before use, such as hydrogen sulfide (H 2 S). As an odorous, toxic, and corrosive gas, H 2 S can cause severe corrosion of equipment and transportation pipelines, and its combustion products, SO 2 , can also cause environmental problems, such as acid rain [3]. Therefore, COG must be desulfurized to improve the gas quality and protect the environment.
Chemical absorption using alkanolamines as absorbents is a mature desulfurization method [4,5]. The alkanolamine method has the distinguishing feature of large absorption capacity, high removal efficiency, and good stability and reliability. The most widely used alkanolamine is monoethanolamine (MEA), which can remove more than 98% of H 2 S from COG [6]. However, the MEA method has certain disadvantages. For example, because of its corrosiveness, the MEA content is generally not allowed to exceed 30% in a solution, its regeneration process is highly energy-consuming, and it is volatile and prone to degradation, which results in large consumption during operation [7]. N-methyldiethanolamine (MDEA), a tertiary alkanolamine, is significantly less corrosive than MEA, exhibits strong resistance to degradation and oxidation, has low reaction heat, and its concentration in the solution can be high, which reduces the energy consumption of the solvent regeneration process. Studies have shown that MDEA has excellent selectivity and efficiency for the removal of H 2 S [8,9].
In addition to containing a single alkanolamine, an absorbent solution often contains two or three alkanolamines to combine the advantages of each while avoiding their drawbacks. Many studies have shown that a mixed alkanolamine solution has better desulfurization performance than a single alkanolamine solution [9][10][11]. Our previous study indicated that adding small quantities of MEA to MDEA aqueous solutions can obviously improve the H 2 S absorption capacity and absorption rate [12].
Ionic liquids (ILs) are considered a green solvent with many excellent properties and are attracting increased attention in the field of acid gas absorption [13][14][15][16][17][18][19][20][21]. However, ILs are highly viscous and their current prices are relatively high, which hinders their use as a pure solvent in large-scale commercial applications. Therefore, it is desirable to use ILs jointly with alkanolamines. Amino acid ionic liquids (AAILs), which are synthesized from amino acids, have advantages over ILs. Furthermore, they can be synthesized from widely available raw materials and, thus, their costs are much lower. As a result, they are often used in H 2 S removal studies [22][23][24] [12,25].
Viscosity and surface tension are the two main physical parameters of a solution, and significantly affect the mass transfer, heat transfer, and gas-liquid flow process [26][27][28][29]. They play a vital role in process simulations and the development of desulfurization equipment. Zuiderweg [30] reported that the surface tension has a greater effect on mass transfer processes than other physical properties, such as the density, viscosity, and diffusion coefficient. The smaller the surface tension, the smaller the mean diameter of the bubbles, which increases the interfacial mass transfer area [31]. If the desulfurization equipment is a tray column, the surface tension impacts the bubble size by affecting the bubble stability, which has an effect on the mass transfer area. A high solution viscosity promotes bubble accumulation, which leads to a decrease in the mass transfer efficiency [32]. Therefore, the determination of these thermodynamic properties is vital for practical applications of a solution.  [Arg] ) in the solutions were changed from 0.300 to 0.500 and from 0.025 to 0.075, respectively, and the solution temperature was changed from 303.2 to 323.2 K.

Reagents
The reagents used in the experiments are shown in Table 1. Each component in the absorbent was accurately weighed using an analytical balance (FA1604A, uncertainty = ±0.1 mg) based on the required mass percentages, and the components were well mixed.

Instrumentation and Process
Surface tension was determined by the BZY-1 surface tension meter (which employs the Wilhemy plate method, uncertainty = ±0.1 mN·m −1 ). The viscosity was determined by the NDJ-5S digital viscometer (uncertainty = ±0.1 mPa·s). The operational procedures and the reliability of the instruments were documented in our previous studies and are not repeated here [33][34][35]. Table 2 presents the surface tension values of the aqueous MDEA-[N 1111 ][Arg] solutions at different mass fractions and temperatures. In addition to obtaining data experimentally, it is also important to develop an accurate model to fit and predict the surface tension values. The surface tension of a mixed solution depends on the composition and temperature of the solution. The model used in a previous study was adopted here because of its simplicity and prediction accuracy [36]:

Surface Tension and Model
where γ 0 and γ can be expressed as follows: where the subscripts 1, 2, and 3 in the formulas represent MDEA, [N 1111 ][Arg], and water, respectively; x i represents the mole fraction of component i; and γ i represents the surface tension of pure component i, which is linear with temperature. G ij represents the mutual influence between components i and j.
To adapt to the new solution system in this study, the calculation equation is obtained by modifying the equation used in the previous research [36]: By combining Equations (1)- (6), the surface tension can be formulated as: where γ i = (a i T + b i ) represents the surface tension of pure component i, which varies linearly with temperature. For a ternary solution, six adjustable model parameters should be optimized using experimental data so that the established thermodynamic model can provide accurate predictions. In the process of optimizing parameters, the average relative deviation (ARD) can be defined as follows: The superscripts cal and exp represent the experimental and calculated results, respectively, and n is the number of experimental data. The optimized parameters were determined to be the following: a 13 = −1.31, b 13 = 1.59, a 23 = −1.73, b 23 = −0.866, a 12 = 8.72, b 12 = 11.5, and ARD = 1.23%. The small ARD value indicates that the predicted results fit well with the experimental results. [Arg] and temperature. The surface tension gradually decreased as the temperature increased. This phenomenon may be because the molecular motion intensified as the temperature increased, which increased the kinetic energy and decreased the intermolecular cohesion, thereby reducing the surface tension [37]. In addition, as the w [N1111][Arg] and w MDEA increased, the surface tension showed a gradual decrease. This might be caused by the presence of alkyl groups in the solvent component, which makes them easier to distribute at the gas-liquid interface.
Gliński et al. [39] and Maham et al. [40] fit the surface tension values of alkanolamine solutions to a linear function of temperature, γ aq = K1 + K2T. Therefore, for a given mass fraction of alkanolamine, the S S and H S values of the solution are −K2 and K1, respectively. However, in this study, the absorption solution is a ternary mixture and may not be appropriate using the above equation. Given that Equation (7) can be used to fit the surface tension, it can be used in conjunction with Equations (9) and (10)   Moreover, the established model parameters can be used to calculate other surface thermodynamic properties of the solution, such as the surface entropy (S S ) and surface enthalpy (H S ) [35,38]: Gliński et al. [39] and Maham et al. [40] fit the surface tension values of alkanolamine solutions to a linear function of temperature, γ aq = K 1 + K 2 T. Therefore, for a given mass fraction of alkanolamine, the S S and H S values of the solution are −K 2 and K 1 , respectively. However, in this study, the absorption solution is a ternary mixture and may not be appropriate using the above equation. Given that Equation (7) can be used to fit the surface tension, it can be used in conjunction with Equations (9)         [Arg] may be because its molecules are more likely to be distributed on the surface; after the molecules migrate to the surface, the intermolecular forces decrease, which leads to the decrease in the order degree of molecular arrangement.

Viscosity and the Model
The viscosity data of MDEA-[N 1111 ][Arg] solutions were measured and results are shown in Table 3. Measuring all viscosity data is a highly expensive, time-consuming, and difficult process. An alternative means is to use an equation that can correlate the viscosities correctly. Numerous different equations have been proposed to correlate and predict the viscosity data of solutions [41][42][43][44]. Of these, the Weiland equation [44], which is a semi-empirical equation, can describe the dependence of solute composition and temperature on viscosity simultaneously. Thus, it is used for the correlation of viscosity data in this study [33,45]. For MDEA-[N 1111 ][Arg] aqueous solutions, it can be expressed as: where η mix represents the viscosity of MDEA-[N 1111 ][Arg] solution, and η 1 and η 2 are expressed as: where η water represents the viscosity of pure water, w = w MDEA + w    [Arg] is low, it has a significant impact on viscosity. Figure 5 presents the influence of temperature on the viscosity of MDEA-[N 1111 ][Arg] aqueous solutions, and shows that the viscosity decreases with increasing temperature at given w MDEA and w [N1111] [Arg] . This phenomenon may be explained by the expansion of the liquid with increasing temperature, which causes an increase in the molecular distance and a decrease in viscosity.    The viscosity activation energies (Ea) indicate the difficulty of material flow and can also reflect the sensitivity of viscosity to temperature changes. In this work, it was calculated by fitting the viscosity data using the following equation [46,47]: where is the viscosity at infinite temperature, R is the gas constant. Equation (14) was used to linearly fit the viscosity data shown in Table 3. Then the Ea values can be obtained by the slope of the fitted line: The Ea value shown in Table 4   The viscosity activation energies (Ea) indicate the difficulty of material flow and can also reflect the sensitivity of viscosity to temperature changes. In this work, it was calculated by fitting the viscosity data using the following equation [46,47]: where η ∞ is the viscosity at infinite temperature, R is the gas constant. Equation (14) was used to linearly fit the viscosity data shown in Table 3. Then the Ea values can be obtained by the slope of the fitted line: The Ea value shown in Table 4 increased from 20.6 to 32.0 kJ·mol −1 with the increasing w MDEA and w [N1111] [Arg] . This implies that the higher the viscosity of the solution, the higher the viscosity activation energy. Although higher w [N1111] [Arg] can improve the absorption capacity of H 2 S, it also weakens the mass transfer. The calculated Ea value in this study is larger than that of water (Ea water = 17.0 kJ·mol −1 ), but smaller than those of some common imidazolium-based ILs (e.g., Ea  In the process of absorbing H 2 S, the diffusion coefficient is also a significant parameter, and is highly important for the study of the gas-liquid mass transfer process. The Stokes-Einstein equation can express the relationship between diffusion coefficient and temperature and viscosity. It is generally accepted that the diffusion coefficient of a gas is inversely proportional to the viscosity of the solution [49].
Geert et al. [50] proposed a modified Stokes-Einstein relationship when studying the diffusion coefficient of N 2 O: Portugal et al. [49] proposed that the ratio of the diffusivity of a gas in an electrolyte solution to the diffusivity of the same gas in water does not vary significantly with the nature of the diffusant. Therefore, it is reasonable to use the so-called N 2 O analogy to estimate the diffusion coefficient of H 2 S in solutions: Combined with the above two equations, it can be obtained that [49,51]: where η solu is the viscosity of MDEA-[N 1111 ][Arg] solution. D H2S,w is the diffusivity of H 2 S in water. It can be fitted as a function of temperature according to the method of Versteeg et al. [51] using data from published studies by Haimour et al. [52] and Tamimi et al. [53]: The results are shown in Table 5. It can be seen that D H2S decreases with the increase in w MDEA and w [N1111][Arg] at a given temperature, and at a given mass fraction, it increases with the increase in temperature. This indicates that lower mass fraction and higher temperature are favorable for the diffusion of H 2 S in MDEA-[N 1111 ][Arg] solution.

Conclusions
In the present study, the viscosity and surface tension values of MDEA-[N 1111 ][Arg] aqueous solutions were measured, and thermodynamic models were used to fit the experimental data. The experimental results and models were used to explore the effects of the solution mass fraction and temperature on the viscosity and surface tension. Furthermore, the S S and H S values of the solutions were obtained using the fitted model of the surface tension. The viscosity activation energy and the diffusion coefficient of H 2 S were calculated based on the measurement of viscosity. The main findings were as follows: 1.
The surface tension decreased with the increase in solution mass fraction and temperature. The viscosity increased with the increase in solution mass fraction and decreased with the increase in temperature.

2.
The thermodynamic models accurately reflected the effects of the solution mass fraction and temperature on the surface tension and viscosity.

3.
With the increase in w MDEA , both the S S and H S decreased, whereas the S S increased and the H S decreased with the increase in w [N1111][Arg] . 4.
The increase in solution mass fraction can result in the increase in Ea and decrease in D H2S,solu .