4.6 Results and discussion
4.6.3 Determination of second order reaction rate constants
In Eqs. (4.20) and (4.24), kapp or kov is function of k2. Using the data presented in Tables 4.2 – 4.4, the kinetic parameters for (2-PE + H2O), (AHPD + H2O) and (PZEA + H2O) systems were determined by a nonlinear regression method using MATLAB® (The MathWorks, Natick, MA) and are summarized in Tables 4.2 – 4.4 (typical M-file with computational outputs are shown in Section V.1.1 of Appendix V). The average deviation from the regression is found to be about ±9%, ±6.4% and ±2.0% (2-PE + H2O), (AHPD + H2O) and (PZEA + H2O) systems, respectively. The second order rate constants were correlated as a function of temperature using Arrhenius equation over the experimental range with the following results:
10 2,2-PE
45171 4.103 10 exp
k RT
⎛ ⎞
= × ⎜⎝− ⎟⎠ (4.29)
13 2,AHPD
65155 8.667 10 exp
k RT
⎛ ⎞
= × ⎜⎝− ⎟⎠ (4.30)
12 2,PZEA
47308 4.5 10 exp
k RT
⎛ ⎞
= × ⎜− ⎟
⎝ ⎠ (4.31)
The average deviation from the correlation is about ±3.0%, ±3.4% and ±1.1% for (2-PE + H2O), (AHPD + H2O) and (PZEA + H2O) systems, respectively.
Using the values of kov presented in Table 4.5 for the blends of (PZEA + MDEA), the kinetic parameters, k2, PZEA and k2,MDEA, were also determined and are summarized in Table 4.5. The average deviation from the regression is found to be about ±6.0% for 24 data points.
The second order rate constants, k2,PZEA and k2,MDEA, were correlated as a function of temperature over the experimental range with the following results:
12 2, PZEA
46943 4.16 10 exp
k RT
⎛ ⎞
= × ⎜⎝− ⎟⎠ (4.32)
10 2, MDEA
56767 4.04 10 exp
k RT
⎛ ⎞
= × ⎜− ⎟
⎝ ⎠ (4.33)
The average deviation for the values of the rate constants calculated from the correlations is about ±6.8%. The activation energy for k2, PZEA is calculated to be 46.9 kJ mol-1 which can be compared with the value obtained (47.3 kJ mol-1) in this study of the absorption of CO2 in (PZEA + H2O) systems. The second order rate constant of PZEA for any particular temperature obtained for the absorption of CO2 into (PZEA + H2O) and (PZEA + MDEA +H2O)systems are very close to each other (average deviation is 5.6%).
The calculated and experimental Arrhenius plot for (2-PE + H2O) and (AHPD + H2O) systems are shown in Figure 4.10 (typical M-file with computational outputs for evaluation of Arrhenius parameters are shown in Section V.1.2 of Appendix V). For AHPD solutions, a strong temperature dependency is exhibited, indicating that it may require relatively high regeneration energy for reclamation process. In addition it is likely that, at temperature higher than 315 K, the reaction rate of CO2 with AHPD is faster than 2-PE. The same phenomenon can also be observed (shown in Figure 4.10) between AEPD (Yoon et al. [19]) and AMPD (Yoon et al. [20]) and between 2-PE (Xu et al. [24]) and AMP (Xu et al. [57]). According to Figure 4.10, there is a deviation between the values of k2,2-PE for 2-PE obtained in the present study with the results of Xu et al. [24] at 303 and 313 K. The deviation, that exists, may be due to the use of different reaction mechanisms. Xu et al. [24] did not consider the hydrolysis of the carbamate ion in their kinetic analysis although they mentioned the possibility of the hydrolysis of the carbamate ion in their paper. In our analysis if we neglect the hydrolysis of the carbamate ion in the mechanism, the value of k2,2-PE obtained as 835 and 1365 m3 kmol-1s-1 at 303 and 313 K, respectively, which are very much close to the results reported by Xu et al.
[24] However, Shen et al. [23] reported a much lower value of k2,2-PE. They assumed that the
zwitterion formation reaction was rate limiting and the reaction was first order in both CO2 and 2-PE. They neither corrected for the reaction of hydroxyl ions with CO2 nor did they report the CO2 loading of amine at the experimental conditions. So, the results of Shen et al.
[23] were not possible to compare in Figure 4.10. The activation energy for k2,2-PE is calculated to be 45.2 kJ mol-1 which is comparable with the value (44.6 kJ mol-1) obtained by Xu et al. [24]. The value of activation energy obtained by neglecting the hydrolysis of carbamate ion in the present case is 44.7 kJ mol-1, which is very close to the value obtained by Xu et al. [24].
Figure 4.11 shows the comparison of the calculated and experimental Arrhenius plot of k2 for PZEA and PZ obtained in the present study and other literature [21] over a wide range of temperatures. In Figure 4.11, the solid line for absorption in PZEA is obtained by calculating k2,PZEA using Eq. (4.31). The observed second order reaction rate constant in case of PZEA is slightly higher than that of PZ [21].
Figure 4.12 shows the comparison of the Arrhenius plot of k2,MDEA for MDEA aqueous solution obtained in this study with the literature values [53, 56, 58, 59]. The solid line is calculated by Eq. (4.33). The activation energy obtained from Eq. (4.33) is 56.8 kJ mol−1 which can be compared with the values of the literature (42.4 kJ mol−1 of Versteeg and van Swaaij [53]; 48.0 kJ mol−1 of Littel et al. [58]; 38.07 kJ mol−1 of Rinker et al. [59];
42.4 kJ mol−1 of Ko and Li, [56]). The value of activation energy obtained in this study exhibits quite higher value than the values reported by other investigators. The values of k2,MDEA obtained in this study are for the absorption into (PZEA+MDEA+H2O) systems while the literature values are for (MDEA+H2O) systems. So, the reaction between CO2 and MDEA is influenced by the systems of which the reaction actually occurs.
The measured and calculated rates of absorption using Eqs. (4.29) – (4.33) are compared in the parity plot shown in Figures 4.13 – 4.16. There is excellent agreement between the model calculated and experimental results, the average absolute deviation (AAD%) being about 6.6%, 4.0%, 1.1% and 3.2% for (2-PE + H2O), (AHPD + H2O) and (PZEA + H2O) systems, respectively.