## 2 Description of the Experiment
### Mass Transfer through the Interfacial Area  
The rate-based model is based on the two-film theory that describes the mass transfer between gas and liquid [26]. The film theory is based on the assumption that when two fluid phases are coming in contact with each other, a thin layer of stagnant fluid exists on each side of the interface [32]. From Figure 5, the partial pressure of component \(i\) drops from \(P_{i}\) at gas bulk to \(P_{i}^{I}\) at the interface [32; 33]. This pressure difference creates a driving force \(\left(P_{i}-P_{i}^{I}\right)\) for component \(i\) to transfer it from the gas bulk to gas film and then from the gas film to liquid film [33]. The accumulation of the component \(i\) at the liquid film creates a concentration difference between the liquid film and the liquid bulk. Similarly, this concentration difference creates a driving force \(\left(C_{i}^{I}-C_{i}\right)\) for component \(i\) to transfer from the liquid film to the liquid bulk [32; 33]. The molar flux \(N\) of component A from the bulk of one phase to the interface is written as below [33]:  
\[N=k\Delta c \tag{20}\]  
where \(N\) is the molar flux of the component (moles per unit area per unit time) and \(\Delta c\) is the driving force for mass transfer between the bulk and the interface. Consequently, Equation (11) can be written for phase and liquid phase [33] as:  
\[N_{A,G}=K_{G}\left(P_{i}-P_{i}^{I}\right) \tag{21}\]  
\[N_{A,L}=K_{L}\left(C_{i}^{I}-C_{i}\right) \tag{22}\]At steady state, the flux of \(i\) from bulk gas to the interface must be equal to the flux of \(i\) from the interface to the bulk liquid [33]:  
\[N=N_{L,i}=N_{G,i} \tag{23}\]  
\[N=K_{G}\Big{(}P_{i}-P_{i}^{I}\Big{)}=K_{L}\Big{(}C_{i}^{I}-C_{i}\Big{)} \tag{24}\]  
\(K_{G}\) and \(K_{L}\) are two different overall mass transfer coefficients (with different units). If equilibrium conditions exist at the interface, the overall mass transfer coefficient can be calculated as follows [35]:  
\[\frac{1}{K_{G}}=\frac{1}{k_{G}}+\frac{H}{Ek_{L}} \tag{25}\]  
where \(H\) is [PERSON]'s law constant, \(E\) is the enhancement factor. \(k_{G}\) and \(k_{L}\) are the mass transfer coefficients without reaction in the gas and liquid phase. The mass transfer coefficients and the wetted interfacial area for mass and heat transfer were calculated according to the correlations proposed by several studies [30; 35; 36] as following:  
\[k_{L,i}a_{eff}=C_{L}\Big{(}\frac{g}{v_{L}}\Big{)}^{1/6}\Bigg{(}\frac{D_{L,i}}{ d_{h}}\Bigg{)}^{1/2}a^{2/3}U_{L}^{1/3}\Big{(}\frac{a_{eff}}{a}\Big{)} \tag{26}\]  
\[k_{G,i}a_{eff}=C_{G}(\varepsilon-h_{L})^{-1/2}\Bigg{(}\frac{a^{3}}{d_{h}} \Bigg{)}^{1/2}D_{G,i}\Bigg{(}\frac{U_{G}}{av_{G}}\Bigg{)}^{3/4}\Bigg{(}\frac{v _{G}}{D_{G,i}}\Bigg{)}^{1/3}\Bigg{(}\frac{a_{eff}}{a}\Big{)} \tag{27}\]  
\[\frac{a_{eff}}{a}=1.5\ (ad_{h})^{-0.5}\ \Bigg{(}\frac{U_{L}d_{h}}{v_{L}} \Bigg{)}^{-0.2}\Bigg{(}\frac{U_{L}^{2}p_{L}d_{h}}{\sigma}\Bigg{)}^{0.75}\Bigg{(} \frac{U_{L}^{2}}{g^{d_{h}}}\Bigg{)}^{-0.45} \tag{28}\]  
\[d_{h}=4\frac{\varepsilon}{a} \tag{29}\]  
where \(k_{L,i}\) and \(k_{G,i}\) and are the mass transfer coefficients of component \(i\) in the liquid and gas phase respectively, \(a_{eff}\) is the effective interfacial area per unit packed volume, \(a\) is the total surface area per unit packed volume, \(C_{G}\) and \(C_{L}\) are the gas and liquid and transfer coefficient parameter respectively; characteristic of the shape and structure of the packing, \(g\) is gravitational constant, \(v_{L}\) and \(v_{G}\) are  
\[N_{A,G}=K_{G}\left(P_{i}-P_{i}^{I}\right) \tag{21}\]0 Concentration profiles based on the two-film model [34], * refers to the conditions at the equilibrium state.