*4.3. Effect of Inlet Gas Flow Rate*

The influence of the inlet gas flow rate on *K*G*a* in the RZB is given in Figure 7, which shows that *<sup>K</sup>*G*<sup>a</sup>* in the NaOH solution rose from 6.13 × <sup>10</sup>−<sup>5</sup> to 8.26 × <sup>10</sup>−<sup>5</sup> kmol/kPa m<sup>3</sup> <sup>s</sup> and from 6.67 × <sup>10</sup>−<sup>5</sup> to 9.65 × <sup>10</sup>−<sup>5</sup> kmol/kPa m<sup>3</sup> s, with the inlet gas flow rate increasing from 200 to 1200 L/h at the rotational speed of 600 rpm and 1200 rpm, respectively.

 ˉˉ**Figure 7.** Effect of inlet gas flow rate on *K*G*a* in the RZB (*L* = 25 L/h, *T* = 298.15 K, *T*gas = 298.15 K, *y*CO2-in = 4%, *C*NaOH = 0.15 kmol/m3).

Because *K*G*a* in the NaOH solution is affected by *k*G*a*, a rising inlet gas flow rate in the RZB increases the tangential gas velocity in the annular space between the rotating and static baffles, which leads to the increase of gas turbulence and a decrease of gas film thickness [16]. Therefore, the mass transfer resistance in the gas side reduces and consequently *k*G*a* increases, thereby enhancing *K*G*a* in the RZB. Hence, an increasing inlet gas flow rate brought about a rise in *K*G*a* in the experimental range.

#### *4.4. Effect of Rotational Speed*

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The variation of *K*G*a* with the rotational speed is shown in Figure 8. *K*G*a* augmented with a rise in the rotational speed from 400 to 1200 rpm.

**Figure 8.** Effect of rotational speed on *KGa* in the RZB (*L* = 25 L/h, *T* = 298.15 K, *T*gas = 298.15 K, *y*CO2-in = 4%, *C*NaOH = 0.15 kmol/m3).

When the rotational speed rises, a larger centrifugal force is created by the rotating baffles, leading to an enhanced liquid turbulence and higher tangential velocity of droplets departing from the rotating baffles according to Equation (7), which reduces the size of droplets in the space between the rotating and static baffles based on the expression of droplet diameter in Table 2. Therefore, *a* in zone I increase.

At the same time, rising rotational speed causes an increase in the number of droplets impinging on the turbulent filmy liquid as a result of the reduction in droplet size and a larger circumferential velocity of the turbulent filmy liquid in zone II, which is equal to the tangential velocity of the flying liquid sheet leaving the static baffles in zone III [11], resulting in a rise in the surface renewal frequency of the liquid film in the turbulent filmy liquid on the static baffles in terms of Equation (40) and a decrease in the lifetime of the flying liquid sheet in zone III according to Equation (11). The former factor brought about an increase in *k*L−II in zone II, and the latter factor was conducive to *k*L-III in zone III according to Equation (44).

The above analysis indicates that a higher rotational speed led to higher *a* and *k*L, which markedly an enhanced *K*G*a* of the CO2-NaOH system in the RZB.

#### *4.5. Effect of Absorbent Temperature*

The effect of the absorbent temperature on *K*G*a* is presented in Figure 9. The figure indicates that a higher temperature of NaOH solution is favorable for *K*G*a*, which increased from 7.95 × <sup>10</sup>−<sup>5</sup> to 8.80 × <sup>10</sup>−<sup>5</sup> kmol/kPa m<sup>3</sup> s and from 9.35 × <sup>10</sup>−<sup>5</sup> to 1.02 × <sup>10</sup>−<sup>4</sup> kmol/kPa m3 s with an increase in temperature from 293.15 to 313.15 K at the liquid flow rate of 25 L/h and 35 L/h, respectively.

In accordance with the Arrhenius equation for the reaction rate constant in Table 2, a higher temperature of NaOH solution increases the second-order rate constant *k*2, thereby leading to a larger pseudo-first-order reaction rate constant *k*app, which is favorable for the liquid-side mass transfer performance. Moreover, the resistance in liquid-side mass transfer reduces and the diffusion of CO2 in the liquid phase is improved with increasing temperature [12]. These factors promoted mass transfer and caused a higher *k*L, thereby leading to an increasing *K*G*a*.

ˉ ˉˉ

**Figure 9.** Effect of absorbent temperature on *K*G*a* in the RZB (*G* = 1000 L/h, *N* = 800 rpm, *T*gas = 298.15 K, *y*CO2-in = 4%, *C*NaOH = 0.15 kmol/m3).

#### *4.6. Effect of Absorbent Concentration*

Figure 10 illustrates the effect of NaOH absorbent concentration on *K*G*a* in the RZB. It is noted that *<sup>K</sup>*G*<sup>a</sup>* increased from 7.43 × <sup>10</sup>−<sup>5</sup> to 9.25 × <sup>10</sup>−<sup>5</sup> kmol/kPa m3 s with an increase in the absorbent concentration from 0.1 to 0.2 mol/L at the liquid flow rate of 25 L/h, while *<sup>K</sup>*G*<sup>a</sup>* increased from 8.62 × <sup>10</sup>−<sup>5</sup> to 1.07 × <sup>10</sup>−<sup>4</sup> kmol/kPa m3 s as the absorbent concentration rose from 0.1 to 0.2 kmol/m3 at the liquid flow rate of 35 L/h.

**Figure 10.** Effect of absorbent concentration on *K*G*a* in the RZB (*G* = 1000 L/h, *N* = 800 rpm, *T* = 298.15 K, *T*gas = 298.15 K, *y*CO2-in = 4%).

When the concentration of NaOH solution increases, the second-order reaction rate constant between CO2 and the absorbent rises according to the expression of *k*<sup>2</sup> shown in Table 2. Meanwhile, a higher *k*<sup>2</sup> and *C*NaOH can concurrently enhance the pseudo-first-order reaction rate constant *k*app, causing a higher *k*<sup>L</sup> in every mass transfer zone of the RZB. Hence, *K*G*a* increased with an increasing NaOH concentration.

#### *4.7. Comparison between Spray Column and RZB*

Table 3 reveals comparative results of mass transfer efficiency between a spray column and the RZB. It was found that the experimental *K*G*a* in the spray column was less than that in the RZB on the basis of a similar gas–liquid volume ratio. Additionally, the RZB possessed a greater mass transfer efficiency accompanied by a much lower NaOH solution concentration compared to the spray column, suggesting that an obvious enhancement of mass transfer in CO2 absorption can be realized by the RZB.


**Table 3.** Comparison between spray column and RZB.

Considering an enhanced dispersion and coalescence of the liquid phase in the annular regions between the static and rotating baffles, a shorter lifetime of the liquid element in the RZB is gained compared to the spray column, and the intensification of mass transfer is thus expected in the RZB, conducing to the CO2 absorption process.

#### **5. Conclusions**

In this study, by obtaining the analytical expressions of the gas–liquid effective interfacial area, liquid-side and gas-side mass-transfer coefficients in an RZB, a mathematic model of CO2 absorption into NaOH solution with irreversible pseudo-first-order reaction in the RZB was established to quantitatively describe the gas–liquid mass transfer process and predict *K*G*a*.

The *K*G*a* calculated by the model was consistent with the experimental data under different operating conditions. The calculated *K*G*a* exhibited deviations generally less than 10% in comparison with the experimental data, which demonstrated the excellent predictability of this model for CO2 absorption in an RZB. Meanwhile, the influences of various operating conditions on *K*G*a* in the RZB were predicted reasonably by this model. Experimental results indicate that higher liquid flow rate, inlet gas flow rate, rotational speed, absorbent temperature, and absorbent concentration favored gas–liquid mass transfer in the RZB. It was found that the rotational speed had the largest impact on *K*G*a* in the RZB. This study provides the theoretical basis for potential application of RZBs in CO2 absorption.

**Supplementary Materials:** The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/pr10030614/s1, Table S1: Comparison of mass transfer performance between RZB in this work and that in Reference 10; Table S2: Values of individual and overall mass transfer factors in RZB.

**Author Contributions:** Conceptualization, L.S.; methodology, Z.L.; validation, A.E.; formal analysis, H.Z.; investigation, D.W.; resources, Y.L.; data curation, Z.L.; writing—original draft preparation, Z.L.; writing—review and editing, Z.L.; supervision, L.S.; project administration, L.S.; funding acquisition, L.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China, grant number 22178021.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors gratefully acknowledge financial support from the National Natural Science Foundation of China (No. 22178021).

**Conflicts of Interest:** The authors declare no conflict of interest.

## **Nomenclature**


