## 3 Results and Discussion
### Effect of the Inlet Gas Flow Rate Hydrodynamic Characteristics of Sieve Tray
#### 3.2.2 Effect of the Inlet Gas Flow Rate on Clear Liquid Height  
Since wet pressure drop is equivalent to the clear liquid high on the tray, one can calculate clear liquid height as  
\[h_{cl}=\Delta P_{wet,tray}\times 1.01972\times 10^{-2} \tag{3}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Inlet Gas Flow Rate,** & \multicolumn{3}{c}{**The Standard Errors of the Measurements**} \\ \cline{2-4}
**Nm\({}^{3}\)/h** & **P = 0.22 MPa** & **P = 0.24 MPa** & **P = 0.26 MPa** \\ \hline
12 & 0.00043 & 0.00003 & 0.00011 \\
14 & 0.00025 & 0.00027 & 0.00007 \\
16 & 0.00023 & 0.00014 & 0.00024 \\
18 & 0.00017 & 0.00017 & 0.00022 \\
20 & 0.00011 & 0.00015 & 0.00029 \\
22 & 0.00014 & 0.00015 &Figure 5: Effect of the inlet gas flow rate on (**a**) total tray pressure drop, (**b**) dry tray pressure drop, (**c**) wet tray pressure drop.  
There are several correlations in the literature for estimating the clear liquid head. [PERSON] (1883) [10] proposed an equation to calculate the liquid flow rate across the exit weir with rectangular cross section. The [PERSON] equation is  
\[Q=3.33{h_{1}}^{3/2}(L-0.2{h_{1}}) \tag{4}\]  
where \(Q=\) discharge in \(f^{3}/s\) neglecting velocity of approach, \(L=\) the length of weir in ft, \(h_{1}=\) head on the weir in ft.  
From this equation, we can conclude that the height of the clear liquid and the liquid accumulation are only affected by the change in liquid flow. The gas flow has no influence. [PERSON] et al. (1983) [11] developed a correlation for clear liquid height as  
\[h_{cl}=\alpha_{e}\left[h_{W}+C\left(\frac{Q_{L}/W}{\alpha_{e}}\right)^{0.67}\right] \tag{5}\]  
\[\alpha_{e}=exp\left[-12.55\left(u_{b}\left(\frac{\rho_{G}}{\rho_{L}-\rho_{G}} \right)^{0.5}\right)^{0.91}\right] \tag{6}\]  
\[C=0.5+0.438 exp(-137.8{h_{W}}) \tag{7}\]  
where \(h_{cl}\) is the clear liquid height, \(h_{W}\) is the outlet weir height, \(C\) empirical constant, \(Q_{L}\) is the liquid flow rate, \(W\) is the weir length, \(u_{b}\) is the bubbling velocity, \(\rho_{G}\) is the density of gas m\({}^{3}\)/kg, \(\rho_{L}\) is the density of liquid m\({}^{3}\)/kg, and \(\alpha_{e}\) is the effective liquid volume fraction. It can be noted that the liquid clear high is a function of the bubbling velocity and the liquid/gas density.  
[PERSON] et al. (1979) [12] have developed an Empirical correlation as  
\[h_{cl}=0.6\Psi^{0.25}{h_{W}}^{0.5}A^{0.25} \tag{8}\]  
\[\Psi=\frac{Q_{L}/W}{u_{s}}\sqrt{\frac{\rho_{L}}{\rho_{G}}} \tag{9}\]  
where \(A\) is the hole pitch, m; and \(u_{s}\) is superficial velocity.  
It can be see that Hofhuis equation is a function of flow ratio group \(\Psi\), weir height, and hole pitch. [PERSON] model can be applied to both froths and spray regimes ([PERSON], [PERSON], et al., 2018) [13].  
Taking into account these studies, the Hofhuis correction can be modified to accommodate the height of the clear liquid on the sieve tray studied as  
\[h_{cl}=1.75\Psi^{-0.1}{h_{W}}^{0.5}P^{0.25} \tag{10}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Inlet Gas Flow Rate,**} & \multicolumn{3}{c}{**The Standard Errors of the Measurements**} \\ \cline{2-4}  & **P = 0.22 MPa** & **P = 0.24 MPa** & **P = 0.26 MPa** \\ \hline
12 & 0.00555 & 0.00535 & 0.00525 \\ \hline
14 & 0.01886 & 0.01299 & 0.03397 \\ \hline
16 & 0.01482 & 0.00982 & 0.01135 \\ \hline
18 & 0.02145 & 0.01216 & 0.01368 \\ \hline
20 & 0.02208 & 0.01817 & 0.01705 \\ \hline
22 & 0.03704 & 0 Figure 6 shows the comparison between the experimental data and the results from Equation (10). It appears that there is agreement within the relative error \(\pm\)5.5%.  
Figure 6: Effect of inlet gas flow rates on clear liquid height compared with Equation (10), at pressure 0.22 MPa (**a**), 0.24 MPa (**b**), and 0.26 MPa (**c**).