## 1 Introduction
The reaction of CO\({}_{2}\) with H\({}_{2}\)O is usually neglected in the overall reaction rate equation resulting the terms of \(r_{\text{CO}_{2}\text{,H}_{2}\text{O}}\) in Equation (11) and \(k_{\text{H}_{2}\text{O}}[\text{H}_{2}\text{O}]\) in Equation (13) can be neglected. The reaction of CO\({}_{2}\) with amines found that the reaction rate constant with CO\({}_{2}\) are 3630 [39], 2585 [39], and 2202 m\({}^{3}\)/s-kmol [37] for MEA, DIPA, and TEA, respectively. However, the reaction constant is affected by pKa and temperature [40; 45]. At a given temperature, in \(k_{2}\) is proportional to \(pK_{a}\). In addition, the activation energy in Table 1 shows that reactions with high E\({}_{a}\) is very temperature-sensitive and reactions low E\({}_{a}\) is very temperature-insensitive [46]. However, the reaction rate constants for AMP and PZ were 810.4 and 48,533, respectively. The reaction rate constant for PZ is much higher than the other amines. Therefore, the addition of PZ into amines has a powerful potential to promote the absorption rate. For mixed amines, the overall rate can be expressed as:  
\[r_{o,Mixed}=\sum_{i}r_{\text{CO}_{2}i}+r_{\text{CO}_{2}\text{OH}^{-}}=k_{ obs,mixed}[\text{CO}_{2}], \tag{14}\]  
where \(r_{\text{CO}_{2}i}\) is the reaction rate of \(i\)th amine and \(k_{obs,\ Mixed}\) is overall rate constant of mixed amines. Equation (14) states that the reaction rate is affected by concentration of various amine, [OH\({}^{-}\)] and [CO\({}_{2}\)]. In addition, the gas-liquid contact method and temperature are also affecting the reaction rate [46]. Here, the means of CO\({}_{2}\) capture was explored to search for the best-mixed amine using a combination of amines including MEA, MEA + DIPA, MEA + TEA, MEA + AMP, and MEA + piperazine (PZ). In the capture process, however, several important factors need to be considered, such as the ratio of mixed amines, the liquid-flow rate, the gas-flow rate, the concentration of total amines, and the liquid temperature. In this study, the CO\({}_{2}\) absorption experiment was performed by using a continuous bubble-column scrubber because bubble columns have higher mass-transfer coefficients in the range of 0.04-1.54 s\({}^{-1}\) and higher specific surface area in the range of 100-1500 m\({}^{2}\)/m\({}^{3}\) compared with packed bed, whose mass-transfer coefficient and specific surface area are in the range of 0.02-0.38 s\({}^{-1}\) and 100-600 m\({}^{2}\)/m\({}^{3}\), respectively. The larger the mass-transfer coefficient, the smaller the column size [47; 48]. In addition, the bubble column is comparable with packed bed although the pressure drop for a bubble column was higher than a packed bed. The scrubbing factor for the former is higher than the latter [20]. Due to this, the bubble-column has been found that it shows a superior performance, such as a high absorption, high mass-transfer coefficient, simple structure, higher scrubbing factor, and easy operation, compared with other scrubbers. In order to evaluate the performance of solvents, the indexes of solvents include the removal efficiency (\(E_{F}\)), the absorption rate (\(R_{A}\)), the overall mass-transfer coefficients (\(K_{G}a\)), and the scrubbing factor (\(\phi\)). To achieve this purpose, the Taguchi method was used in the experimental design to reduce the cost and save time. From the experimental data, the optimum conditions and sequence of parameters could be obtained through the S/N (signal/noise) ratio analysis. Verification of optimum conditions was required. Accompanying various indexes, the best-mixed amines for the CO\({}_{2}\) capture process could be obtained. Finally, solvent regeneration for the best amine was also explored. A schematic of the research framework is shown in Figure 2.