Real-Time Estimation of CO₂ Absorption Capacity Using Ionic Conductivity of Protonated Di-Methyl-Ethanolamine (DMEA) and Electrical Conductivity in Low-Concentration DMEA Aqueous Solutions

Abstract

The present study investigates the real-time estimation of CO₂ absorption capacity (CAC) based on the electrical conductivity (EC) of low-concentration di-methyl-ethanolamine (DMEA) solutions (0.1–0.5 M). CO₂ absorption experiments are conducted to measure the variation in CAC and EC during CO₂ absorption, revealing a strong correlation between the two properties. The ionic conductivity of DMEAH⁺ formed during absorption is calculated to be 53.1 S·cm²/(mol·z), which is found to be larger than that of TEAH⁺ and MDEAH⁺. This can be attributed to the smaller molar mass and higher ionic mobility of DMEAH⁺. A significant finding is that the measured EC (EC_M) of the DMEA solutions consistently demonstrates a lower value than the theoretically predicted value. This discrepancy is due to the larger ionic size of DMEAH⁺, which results in a reduction in the real mean ionic activity coefficient. This effect becomes more pronounced with increasing DMEA concentration. Consequently, a higher CAC is required to produce the same change in EC at higher amine concentrations. Based on these findings, an empirical equation is devised to estimate CAC from EC_M in solutions of constant DMEA concentration. This equation will be employed as a practical approach for the in situ monitoring of CO₂ absorption using DMEA aqueous solution.

1. Introduction

Carbon dioxide (CO₂)—which is emitted from a variety of industrial processes, including fossil fuel combustion, cement production, and steel and chemical plants—constitutes a significant contributor to global warming. CO₂ constitutes approximately 76% of global greenhouse gas emissions, with annual emissions reaching 37.15 billion metric tons [1,2]. In July 2023, the UN Secretary-General underscored the urgency of the current climate change crisis, asserting that the era of global warming has concluded and that we have entered the period of “global boiling” [3]. To address climate change, ongoing research over the past 30 years has focused on the development of carbon dioxide capture and storage (CCS) technologies, which are characterized by high economic viability and performance. Various CCS methods, including bioconversion [4,5,6,7] and adsorption using novel materials [8,9,10,11,12], have been investigated; however, these approaches frequently fail to achieve the desired impact at a large scale. Among the various CCS technologies, chemical absorption using alkanolamine has been extensively studied over an extended period, and it is currently the only technology that has been successfully commercialized with the objective of addressing the urgent climate crisis [13,14,15,16,17].

Alkanolamines are a class of substances that contain both amino (-NH₂, -NHR, and -NR₂) and hydroxyl (-OH) functional groups. They are highly and selectively reactive with CO₂, and they can be classified as primary, secondary, and tertiary amines based on the number of R groups they contain. An absorption process using mono-ethanolamine (MEA), a member of the primary amine group, has been commercialized due to its rapid reaction rate and low cost [18,19,20,21,22]. However, the reaction of MEA with CO₂ limits the theoretical maximum amine utilization to 0.5 mol CO₂/mol amine in high amine-concentrated solutions. Moreover, MEA is highly corrosive to equipment, requiring a significant amount of energy to strip the CO₂ from the absorbent (or to regenerate the solutions). An alternative approach is being investigated in which tertiary amines are utilized as absorbents. Although these amines, such as tri-ethanolamine (TEA), methyl-di-ethanolamine (MDEA), and di-methyl-ethanolamine (DMEA), have been reported to have relatively low reaction rates, they achieve a maximum amine utilization of 1.0 mol CO₂/mol amine, are relatively less corrosive, and require minimal energy for CO₂ stripping. Most studies using tertiary amines as the absorbent have concentrated on their blending effect with primary or secondary amines to enhance the performance of the absorbents [23,24,25,26,27]. However, there has been a relative lack of research into the specific absorption performance and properties of tertiary amine solutions, which would be expected to furnish crucial insights for the continued advancement of absorbents.

Recent advances in sensor technology have demonstrated the potential of low-cost, real-time monitoring systems to enhance data collection for environmental and industrial processes. For example, low-cost sensors have been employed to monitor spatial and temporal pollution in urban areas, providing a practical solution for large-scale exposure assessments [28]. One study highlighted that the use of a dispersion model enabled the testing of dust pollution distribution in a seaside town, thereby significantly enhancing pollution monitoring [29]. In water quality monitoring, electrochemical sensors have emerged as a crucial tool due to their capacity to transduce chemical interactions into electrical signals, thereby enabling real-time, multi-parameter monitoring, which is feasible even in resource-limited settings [30,31]. Similarly, electrolytic conductivity sensors, which are widely used in diverse industries, offer reliable and precise monitoring of electrolytes in various applications [32,33]. Given these advantages, we opted to employ electrical conductivity (EC) measurements as an effective and economical method for the real-time estimation of CO₂ absorption capacity in aqueous DMEA solutions. In this way, we utilize the advantages of EC sensors to provide a practical solution for the continuous monitoring of CO₂ absorption processes in industrial settings.

In this context, the present study investigated the CO₂ absorption performance and electrical characteristics of the CO₂ absorption system using DMEA aqueous solution with a relatively low concentration of DMEA (0.1–0.5 M). First, the ionic conductivity (IC) value of protonated DMEA (DMEAH⁺) generated from the chemical absorption reaction between CO₂ and DMEA—which was achieved through a series of absorption experiments—was presented. The relationship between the CO₂ absorption capacity (CAC) (or the amount of CO₂ absorbed) and the EC of the solution at the arbitrary absorption time was also established for each solution, which finally resulted in the derivation of a general empirical equation for predicting the amount of CO₂ absorbed based on EC measurements of the solutions.

2. CO₂ Absorption Mechanism Using DMEA Aqueous Solutions

In the DMEA solutions prepared for the CO₂ absorption, a small amount of the DMEA molecule first receives H⁺ from the water to become DMEAH⁺ and OH⁻ in the solution, as expressed in Equation (1) [34,35].

$$\mathrm{D}\mathrm{M}\mathrm{E}\mathrm{A}+{\mathrm{H}}_2\mathrm{O}\leftrightarrow {\mathrm{D}\mathrm{M}\mathrm{E}\mathrm{A}\mathrm{H}}^{+}+{\mathrm{O}\mathrm{H}}^{-}$$

(1)

The two ionic concentrations are determined from DMEA’s base dissociation constant (pK_b) of 4.78 [36]. If CO₂ is then added to the DMEA solution to be absorbed, two reactions occur, as summarized in Equations (2) and (3) [34,35,37].

$${\mathrm{O}\mathrm{H}}^{-}+{\mathrm{C}\mathrm{O}}_2\to {{\mathrm{H}\mathrm{C}\mathrm{O}}_3}^{-}$$

(2)

$$\mathrm{D}\mathrm{M}\mathrm{E}\mathrm{A}+{\mathrm{H}}_2\mathrm{O}+{\mathrm{C}\mathrm{O}}_2\to {\mathrm{D}\mathrm{M}\mathrm{E}\mathrm{A}\mathrm{H}}^{+}+{{\mathrm{H}\mathrm{C}\mathrm{O}}_3}^{-}$$

(3)

When CO₂ is injected into the DMEA solution, OH⁻, which is generated via Equation (1), reacts with CO₂ according to Equation (2), thereby resulting in the formation of HCO₃⁻. Subsequently, CO₂ is absorbed by reacting with OH⁻ in the H₂O activated by DMEA molecules to produce DMEAH⁺ and HCO₃⁻, as expressed in Equation (3). The CO₂ absorption mechanism in tertiary amine aqueous solution is designated as the “base-catalyzed reaction” for CO₂ hydration [38]. This is illustrated in Figure 1.

In the absorption process, the DMEA molecule does not directly react with CO₂; instead, a lone pair of electrons on the nitrogen atom of DMEA forms hydrogen bonds with water molecules (illustrated by the dotted line in Figure 1), which activates the hydroxide ion (OH⁻) on the opposite side of the water molecule. This enhances its reactivity with the injected CO₂ molecule. Consequently, the formation of DMEAH⁺ and HCO₃⁻, as well as their zwitterion (DMEAH⁺·HCO₃⁻), occurs in the solution during CO₂ absorption. Additionally, CO₂ can be physically absorbed into the water component, as described in Equation (4), which is referred to as the amount of physical absorption of CO₂; this is also included in the total CAC of the solutions [39,40].

$${\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)+{\mathrm{C}\mathrm{O}}_2\left(\mathrm{g}\right)\to {{\mathrm{H}}_2\mathrm{C}\mathrm{O}}_3\left(\mathrm{a}\mathrm{q}\right)$$

(4)

The amount of CO₂ physical absorption under experimental conditions (25 °C, 1 atm, and a CO₂ partial pressure of 0.33 atm) is 0.023 mol CO₂/L of pure distilled water [41]. The H₂CO₃ produced by physical absorption increases the concentration of either HCO₃⁻ or CO₃²⁻ according to the pH of the solution. However, both concentrations are very small compared to those of the ions produced by the chemical absorption reaction (Equations (2) and (3)), so they are not included in the calculation of the EC of the solutions.

3. Experimental Methodology and Calculations

3.1. Experimental Setup for CO₂ Absorption

Figure 2 shows a schematic diagram of the absorption experiment with DMEA solution.

The experimental setup, including the equipment and methods used in this study, was established identically to that used in our previous work on other amine-based solutions [41,42,43]. The details of the setup are described below.

A cylindrical semi-batch reactor (D: 110 mm; h: 80 mm; total volume: 0.76 L) maintained at 25 °C by a jacket connected to a water circulator was filled with 0.5 L of 0.1–0.5 M DMEA (99.5%, Sigma-Aldrich, St. Louis, MO, USA) aqueous solution. Next, the empty space in the reactor was filled with N₂ gas (99.9%) and completely sealed to confirm tightness. For CO₂ absorption, N₂ and CO₂ gasses (99.99%) were passed through a gas mixture (D: 90 mm; h: 400 mm; total volume: 2.55 L) at respective flow rates of 2.0 and 1.0 L/min using a mass flow controller (MFC; TSC-200, MKPrecision, Siheung-si, Republic of Korea). This resulted in a gas mixture with a CO₂ concentration of 33.3 vol%. Prior to absorption, this gas mixture was bypassed from the reactor through a three-way valve installed at the top of the reactor, after which its CO₂ concentration was checked using a CO₂ analyzer (maMos-200, Madur Electronics, madur Polska Sp. z o. o., Zgierz, Poland). The gas mixture was then used as the absorption gas.

When the gas mixture was injected into the reactor, a glass fiber bubbler with a pore size of 1 um was fixed at the end of the inlet gas line. This was carried out to ensure uniform contact between the solution and the gas. The solution was stirred at 380 rpm using a magnetic stirrer while absorbing. A pH/EC meter (Orion 4 Star, Thermo Scientific, Waltham, MA, USA) was also used to measure the variations in the pH and the EC of the solution caused by CO₂ absorption in real time at 5 s intervals. The CO₂ concentration in the outlet gas from the reactor was measured using a CO₂ analyzer. The absorption completion point was determined as the point at which the CO₂ concentration in the outlet gas was equal to the initial CO₂ concentration of the inlet gas.

3.2. Calculation of Electrical Conductivity (EC) of the CO₂-Absorbed DMEA Solutions

The EC of a CO₂-absorbed solution was calculated using Equations (5)–(10) below [44,45,46,47,48].

$$\mathrm{E}\mathrm{C}(\mathrm{S}/\mathrm{m})=k_o{\gamma }^2,$$

(5)

$$k_o=\sum z_i{\lambda }_i{c}_i,$$

(6)

$$IS=500\sum c_i{z_i}^2,$$

(7)

$$\log \gamma =-A{z}_{+}{z}_{-}\sqrt{IS} (\mathrm{I}\mathrm{S}<0.01),$$

(8)

$$\log \gamma =-A{z}_{+}{z}_{-}{\displaystyle \frac{\sqrt{IS}}{1+\sqrt{IS}}} (0.01\le \mathrm{I}\mathrm{S}\le 0.1),$$

(9)

$$\log \gamma =-A{z}_{+}{z}_{-}\left({\displaystyle \frac{\sqrt{IS}}{1+\sqrt{IS}}}-0.2IS\right) (0.1<\mathrm{I}\mathrm{S}\le 0.5),$$

(10)

The EC of a CO₂-absorbed solution is the product of the EC of an infinitely diluted solution (k_o: (S/m)) and the square of the mean ionic activity coefficient (γ), as described in Equation (5) [44,45]. First, the value of k_o is calculated via Equation (6), using the absolute charge (z), ionic conductivity (λ: S∙m²/mol·z), and concentration (c: mol/m³) of ion i in solution. Secondly, the value of γ can be calculated selecting one of Equations (8)–(10) depending on the ionic strength (IS: mol/L) value of the solution, which can be calculated from Equation (7) [46,47,48]. Here, A is a Debye–Huckel constant—0.509 (kg/mol)^0.5 at 25 °C. Therefore, three factors are required to calculate the EC of a CO₂-absorbed solution—the concentration, charge value, and IC of the ions in the solution.

3.3. Calculation of Ionic Conductivity of DMEAH⁺

As CO₂ is absorbed into the DMEA solution, the ions produced or consumed are OH⁻, HCO₃⁻, and DMEAH⁺, and the charge value of these ions is 1. Of these, the ICs of OH⁻ and HCO₃⁻ have previously been reported in the literature as 198.6 and 44.50 S∙cm²/(mol·z), respectively [49,50]. However, the IC value of DMEAH⁺ is not yet known; therefore, it is essential to know in order to calculate the EC value of the solution in accordance with the absorption reaction. The variation in the concentration of ions present in the solution is also necessary to calculate the EC value of the solution during the absorption reaction. Since the concentration of ions in the solution can be estimated based on the amount of CO₂ chemical absorption measured in real time using Equations (2) and (3), the EC variation in the solution during the absorption can be calculated after determining the IC of DMEAH⁺. To find the IC of DMEAH⁺, the initial guess value was assumed to be 1, and it was increased by increments of 0.01 until reaching the IC of H⁺, which is the largest value (349.8 S∙cm²/(mol·z)) among all the ions [51]. Then, the EC was repeatedly calculated via Equation (5) (referred to as EC_C). Finally, the EC_C value was determined as the value entered at the time when the mean absolute percentage error (MAPE) between the EC_C value and the measured EC (EC_M) was minimized. The MAPE between the EC_M and the EC_C value during the absorption in 0.1–0.5 M DMEA solution was calculated using Equation (11) [52].

$$\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}\left(\%\right)={\displaystyle \frac{100}{n}}{\sum }_{i=1}^n{\displaystyle \frac{\left|{\mathrm{E}\mathrm{C}}_{\mathrm{M}}-{\mathrm{E}\mathrm{C}}_{\mathrm{C}}\right|}{{\mathrm{E}\mathrm{C}}_{\mathrm{M}}}},$$

(11)

The calculation was performed using MATLAB 2024a.

4. Results and Discussion

4.1. CO₂ Absorption Performance of 0.1–0.5 M DMEA Aqueous Solutions

The CAC and EC_M of the 0.1–0.5 M DMEA solutions according to time are shown in Figure 3a and Figure 3b, respectively.

The CAC of the solution varied with the shape of the square root function; the slope here refers to the CO₂ absorption rate. The initial absorption rates of all solutions were steep. However, as time progressed, the slope gradually decreased until absorption was completed. This is because the amine concentration in the solution is high at the beginning of absorption, but as the absorption progresses, the concentration decreases as the amine is consumed, as expressed in Equation (4). The trend of EC_M variation according to time, shown in Figure 3b, is also similar to that of CAC, which indicates that the EC_M value of the solution is directly affected by the concentration of ions generated by the CO₂ absorption reaction.

Table 1. Total, chemical, and physical CO₂ absorption capacities (CACs), total absorption time, and overall CO₂ absorption rate in 0.1–0.5 M DMEA solutions.

	Initial Amine Concentration of DMEA Solution (mol/L)
	0.1	0.2	0.3	0.4	0.5
Total CAC (mol CO2/L)	0.135	0.238	0.345	0.448	0.550
Chemical CAC (mol CO2/L)	0.100	0.200	0.300	0.400	0.500
Physical CAC (mol CO2/L)	0.035	0.038	0.045	0.048	0.050
CO2 absorption time (min)	15.0	23.8	35.0	44.9	52.8
Overall CO2 absorption rate (mmol CO2/(L·min))	9.0	10.0	9.9	10.0	10.4

The average standard deviation of CAC and CO₂ absorption time is ±0.012 and ±0.5, respectively.

summarizes the total CAC of 0.1–0.5 M DMEA solutions at the absorption completion point, the amount of chemical and physical absorption, the total absorption time, and the average slope of Figure 3a, i.e., the overall CO₂ absorption rate of the solutions.

Here, the total CAC is the sum of the CO₂ chemical absorption, which is stoichiometrically calculated based on the DMEA concentration using Equations (2) and (3), and the CO₂ physical absorption given in Equation (4), which is calculated by subtracting the amount of chemical absorption from the total CAC. The amount of CO₂ physical absorption was at its lowest at 0.032 mol CO₂/L in a 0.1 M solution, whereas it was at its highest at 0.050 mol CO₂/L at 0.5 M. This amount is slightly higher than that of pure distilled water (0.023 mol/L), as referenced in Section 2, and it increases proportionally to the amine concentration. This is because the HCO₃⁻ produced by the chemical absorption of CO₂ with DMEA in the solution shifts the equilibrium point of the carbonate ions in the solution, which can produce more H₂CO₃ or CO₃²⁻ in the solution than in pure distilled water; consequently, additional trace amounts of CO₂ are absorbed.

Although the overall CO₂ absorption rate was slightly lower at 9.0 mmol CO₂/(L·min) in the 0.1 M solution, the overall absorption rate converged to about 10.0 mmol CO₂/(L·min), regardless of the initial amine concentration in the solution. This is consistent with previous studies on the kinetics of tertiary amines, which have shown similar behavior [53,54,55,56]. For example, W. Jiang et al. reported a pseudo-first-order rate constant of 1.5–3.0 s⁻¹ in 0.075–0.175 M DMEA solutions, corresponding to a second-order rate constant of 22.19 m³/(kmol·s) [53]. This indicates that the reaction is more dependent on CO₂ concentration than on DMEA concentration. This is attributed to the fact that DMEA, as a tertiary amine, follows a base-catalyzed reaction mechanism that facilitates the reaction of H₂O with CO₂. Therefore, the absorption rate is more dominated by the CO₂ concentration than the DMEA concentration in the solution. Thus, at relatively low concentrations of 0.5 M or less, the absorption rate was not found to be insensitive to the concentration of DMEA.

4.2. Ionic Conductivity of Protonated DMEA (DMEAH⁺)

The IC and charge values of the ions produced from the CO₂ absorption reaction (Equations (2) and (3)), including the dissociation reaction (Equation (1)) of the DMEA solution, are presented in

Table 2. Ionic conductivity, absolute value of electric charge, and molar mass of ions generated from chemical CO₂ absorption in DMEA solutions with other tertiary amine solutions.

Ions	Ionic Conductivity (S∙cm2/(mol∙z))	Absolute Value of Electric Charge (z)	Molar Mass (g/mol)	Reference
OH−	198.6	1	17.0	[49]
HCO3−	44.5	1	61.0	[50]
DMEAH+	53.1	1	90.1	This work
MDEAH+	46.5	1	120.1	[41]
TEAH+	37.6	1	150.1	[41]

.

As mentioned in Section 3.3, the IC of the OH⁻ and HCO₃⁻ ions have previously been shown to be 198.6 and 44.5 S·cm²/(mol·z), respectively [49,50]. However, the IC of DMEAH⁺ was not identified in the published literature. Consequently, in this study, the IC of DMEAH⁺ was calculated using the trial-and-error method described in Section 3.3. This calculation was based on the ionic concentrations calculated from the amount of CO₂ chemical absorption (as determined using Equations (2) and (3)), as well as the EC_M. The calculated IC of DMEAH⁺, as determined in this study, is 53.1 S∙cm²/(mol∙z) with an MAPE of 13.06%. The IC of DMEAH⁺, as determined by the present study, is larger than the values that have been reported for the other two of the three kinds of tertiary amines, namely TEAH⁺ (37.6 S·cm²/mol·z) and MDEAH⁺ (46.5 S·cm²/mol·z), in prior studies [41]. These values are inversely proportional to the molar masses of the three ions, which is likely attributable to the observation that the smaller and lighter ion with the same charge generally exhibits increased mobility in solution. This is consistent with the results of previous research, which has indicated that an increase in ionic mobility leads to an increase in ionic conductivity [57]. Moreover, as the range of absolute values obtained for IC in the case of DMEAH⁺ is similar to that of the other two tertiary protonated amines, the result of the IC of DMEAH⁺ obtained herein may be considered to be reliable.

4.3. EC_C and EC_M Variation According to CO₂ Absorption in 0.1–0.5 M DMEA Solutions

When using the IC of DMEAH⁺ (53.1 S·cm²/mol·z), the theoretical EC values of 0.1–0.5 M DMEA solutions, as calculated using Equation (5), are shown in Figure 4, along with the variation in EC_M (Figure 3b).

As can be seen in Figure 4, the variations in EC_M and EC_C were similar for all solutions. However, as CO₂ absorption neared completion, the discrepancy between the two EC values increased with the initial amine concentration. For example, at the absorption completion point of 0.1 M solution, the EC_M and EC_C values were 6.00 and 5.88 mS/cm, respectively, with an MAPE of 2.1%. In contrast, for a 0.5 M solution, the EC_M and EC_C values were 22.07 and 24.70 mS/cm, respectively, with an associated MAPE of 11.9%. These results are attributed to the tertiary amine nature of the DMEAH⁺, the molecular structure of which is large and complex, resulting in a reduced mean ionic activity coefficient in the solution compared to that predicted using Equation (10). Sami-ullah et al. investigated the relationship between molecular weight and the activity coefficient in ionic liquid systems, revealing an inverse proportionality between the two [58]. H.-N Jeon et al. developed an artificial neural network-based model to predict the infinite dilution activity coefficients of organic molecules, utilizing parameters such as molecular structure, polarizability, and hydrogen bonding [59]. The results of our research also exhibited a similar trend to those of previous studies. Thus, as the concentration of amines increased, the mean ionic activity coefficient decreased, and this was accompanied by an increase in the difference between the EC_M and EC_C values, with the EC_M being measured at a lower value than the EC_C. However, in contrast to the other solutions, the EC_M was slightly higher than the EC_C in the 0.1 M solution, and it also had the smallest MAPE. This is due to the relatively very low concentration, as well as the fact that EC_M is augmented by the EC derived from the trace amount of CO₃²⁻ or HCO₃⁻ generated through the physical absorption process.

4.4. Correlation Between CO₂ Absorption Capacity and Electrical Conductivity

The trend in variations in CAC and EC_M according to absorption time was highly similar for the 0.1–0.5 M DMEA solutions, as illustrated in Figure 3a,b. The correlation between the CAC and the EC_M of the solution measured at the same time is depicted in Figure 5a, while the results of their regression analysis are presented in Figure 5b.

The correlation between CAC and EC_M in all solutions was linear, which indicates that EC_M was linearly proportional to CAC, and that both were directly related to the ionic (or molecular) concentration in the solution. This is valid for all CO₂-absorbed DMEA solutions with concentrations of 0.1–0.5 M, which showed linearity in the CAC and EC_M of the solution. As a result, the correlation equation between the two variables was derived through regression analysis (Figure 5b), and can be expressed as shown in Equation (12) below.

$${\mathrm{C}\mathrm{O}}_2\mathrm{a}\mathrm{b}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{c}\mathrm{a}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}\left(\mathrm{C}\mathrm{A}\mathrm{C};\mathrm{m}\mathrm{o}\mathrm{l}{\mathrm{C}\mathrm{O}}_2/\mathrm{L}\right)=a·{\mathrm{E}\mathrm{C}}_{\mathrm{M}}+b,$$

(12)

The slope (a) and y-intercept (b) of Equation (12) were calculated for all solutions and summarized according to the initial amine concentration (C_DMEA) of the solution; these values are presented in Figure 6a,b.

The slope (a) and y-intercept (b) exhibited linear proportionality to the initial amine concentration in solution. Here, the slope represents the requisite CO₂ absorption capacity (mol CO₂/L) in solution to achieve a 1 mS/cm increase in the EC of the solution, which exhibits a proportionality to the initial amine concentration of solutions (Figure 6a), as evidenced by the relation expressed in Equation (13).

$$\mathrm{s}\mathrm{l}\mathrm{o}\mathrm{p}\mathrm{e}(a;\left(\mathrm{m}\mathrm{o}\mathrm{l}{\mathrm{C}\mathrm{O}}_2/\mathrm{L}\right)/(\mathrm{m}\mathrm{S}/\mathrm{c}\mathrm{m}\left)\right)=0.0181·{\mathrm{C}}_{\mathrm{D}\mathrm{M}\mathrm{E}\mathrm{A}}+0.0155,$$

(13)

The y-intercept (b) value of Equation (12) shown in Figure 6b decreased proportionally to the initial amine concentration, and the correlation coefficient was found to be 0.998 as a result of a linear regression, thus indicating a highly linear relationship with respect to the initial amine concentration. The correlation between the two variables was expressed as shown in Equation (14).

$$\mathrm{y}-\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{p}\mathrm{t}(b;\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{C}{\mathrm{O}}_2/\mathrm{L})=-0.1193·{\mathrm{C}}_{\mathrm{D}\mathrm{M}\mathrm{E}\mathrm{A}}+6.0·{10}^{-3},$$

(14)

The y-intercept value represents the amount of CO₂ absorbed when the EC of the solution is zero. However, even before CO₂ absorption, a constant EC value for the DMEA solutions could be observed due to the presence of DMEAH⁺ and OH⁻ ions in the solution, with a certain concentration, as described in Equation (1). Consequently, the y-intercept value is merely a mathematical representation of the correlation between EC and CAC.

Therefore, the slope and y-intercept of Equation (12) could, respectively, be generalized from Equations (13) and (14) for 0.1–0.5 M DMEA solutions to derive an empirical equation that estimates the CAC of each solution as a function of the EC_M and initial amine concentration, as shown in Equation (15).

$${\mathrm{C}\mathrm{O}}_2 \mathrm{a}\mathrm{b}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{c}\mathrm{a}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}\left(\mathrm{m}\mathrm{o}\mathrm{l} {\mathrm{C}\mathrm{O}}_2/\mathrm{L}\right)=0.0181·{\mathrm{C}}_{\mathrm{D}\mathrm{M}\mathrm{E}\mathrm{A}}·{\mathrm{E}\mathrm{C}}_{\mathrm{M}}+0.0155·{\mathrm{E}\mathrm{C}}_{\mathrm{M}}-0.1193·{\mathrm{C}}_{\mathrm{D}\mathrm{M}\mathrm{E}\mathrm{A}}+6.0·{10}^{-3},$$

(15)

Shown above, Equation (15) may be used for the estimation of CAC in real time based on the variations in the EC of DMEA solutions of the given initial amine concentration. Finally, Figure 7 illustrates the relative behavior of the CAC (y-axis) of DMEA solutions in terms of the C_DMEA ranging from 0.1 to 0.5 M (z-axis), as well as the EC_M value of the solution (x-axis). Moreover, this Figure presents variations in the amount of saturated CO₂ absorbed and the maximum EC_M value of each solution (parameters), and the data presented in Figure 7 provide information in relation to the relative behavior and interactions of the three variables in this system.

The correlation equation among CAC, EC_M, and DMEA concentration demonstrates that EC_M can serve as a reliable indicator for estimating CAC in real systems in real time, providing practical insights for CCS technologies. Recent studies emphasize the significance of such empirical models in enhancing the efficiency of CO₂ capture systems through real-time monitoring and control capabilities [13,60,61]. This approach has been confirmed to be applicable to other amine systems, including MEA, AMP, and TEA [41,42]. Consequently, this research offers a methodology for optimizing CCS processes by utilizing the variation in EC_M of DMEA solutions, establishing a reliable empirical model, and investigating their electrical properties.

However, the results are limited in two main respects. First, the research focused on low-concentration (0.1–0.5 M) DMEA solutions, which are considerably lower than those typically employed in industrial contexts. Second, the research was conducted under a restricted range of conditions, considering a single pressure and temperature to determine the ionic conductivity of DMEAH⁺, which limits the scope for providing more detailed data on CO₂ absorption. Therefore, future research focuses on extending the experimental conditions to cover a broader range of amine concentrations, temperatures, and pressures. Furthermore, it is essential to incorporate a numerical model based on vapor–liquid equilibrium (VLE) simulations for the amine–CO₂–H₂O system to enhance the predictive capabilities of the electrical conductivity in the electrolyte model. Additionally, future research should focus on the application of more comprehensive models, such as the extended Non-Random Two-Liquid (NRTL) or Universal Quasi-Chemical (UNIQUAC) models that consider both long- and short-range interactions, and the traditional Debye–Huckel model that mainly considers long-range interactions.

5. Conclusions

The present study investigated the CO₂ absorption characteristics of low-concentration (0.1–0.5 M) DMEA solutions, aiming to develop an empirical equation for the real-time estimation of CO₂ absorption capacity (CAC) based on the electrical conductivity (EC) of these solutions. A laboratory-scale semi-batch reactor was employed to evaluate the CO₂ absorption performance and the variation in EC of DMEA solutions during CO₂ absorption.

As CO₂ was absorbed into the DMEA solution, the measured electrical conductivity (EC_M) of the solution and CAC varied similarly over time, providing a basis for predicting CAC through changes in the EC_M. The overall CO₂ absorption rate for 0.1–0.5 M DMEA solutions was approximately 10.0 mmol CO₂/(L·min), independent of DMEA concentration. This consistency arises because the amine concentration is very low, while the absorption reaction follows a base-catalyzed mechanism predominantly influenced by CO₂ concentration. Moreover, the ionic conductivity (IC) of protonated DMEA (DMEAH⁺) was determined to be 53.1 S·cm²/(mol·z), which was larger than that of other tertiary amines such as TEAH⁺ (37.6) and MDEAH⁺ (46.5). This outcome can be attributed to DMEAH⁺ having the smallest molar mass among them. In the case of the 0.1 M DMEA solution saturated with CO₂, the EC_M was greater than the theoretically calculated EC (EC_C). This discrepancy is due to the low amine concentration and the presence of trace amount of HCO₃⁻ and CO₃²⁻ ions formed from physically absorbed CO₂. However, for 0.2–0.5 M DMEA solutions, the EC_M is lower than the EC_C. This discrepancy increased with higher DMEA concentrations. This can be explained by the larger ionic size of DMEAH⁺, resulting in the actual mean ionic activity coefficient being smaller than the theoretical value as the concentration increases. Furthermore, the CAC required to increase the EC_M of the DMEA solution by 1 mS/cm increases proportionally with the initial amine concentration. This is due to the decreased activity of ions at higher concentrations, necessitating the production of a larger amount (concentration) of ions through absorption for a given change in EC.

Finally, the empirical equation derived from this study offers a practical approach for estimating CAC from EC measurements in DMEA solutions, enhancing the efficiency of CO₂ absorption processes through the real-time monitoring of CAC. However, limitations include the low concentrations of DMEA used in experiments and a restricted range of operational conditions such as temperatures and pressures. Further research is required to extend the study to higher DMEA concentrations and varied conditions to enhance the model’s applicability and consider a more advanced activity coefficient model.