# An Experimental Analysis of Gas Reduction in Multiphase Flow with a KMS Helical Static Mixer
## 5 Multiphase Numerical Analysis  
From the previous CFD configuration for the free-falling conditions, some additional simulations were tested including a mixture of water and oil (density \(\rho_{0}=997\) Kg/cm\({}^{3}\) and viscosity \(\mu_{0}=31.5(cps)\)), as well as added gas with the proportions as described in Table 2 for different incoming velocities and volumes. The pressure at the output was set according to the one in the horizontal separator for the real process as 10.54 Kg/cm\({}^{2}\). The only refinement of the numerical code consisted of a new sensitivity mesh analysis, resulting in a configuration of 3.5 million elements and a skewness of 0.81 for the same configuration parameters in Table 1. Case 1 in Table 2 corresponds to the configuration for water without gas, but only the accumulated air in the pipe before the liquid flows through the KMS. The velocity is defined as free-falling along 250 mm after the KMS. For Cases 2-4, the dynamics through the KMS is depicted in a transversal XY plane in Figure 6 from the perspective of the oil phase at 10 seconds once the stationary regimen has been achieved. Notice that, since the configuration does not consider additional gas and the velocity is higher than the preliminary simulations, the KMS behaves as a pure mixer with a low dispersion for \(n=4\) regarding Equation (2), and the mixture totally fills the pipe independently of the volume of phases in the liquid mixture. Though the KMS induces the centrifugal effect, the absence of a gas phase does not produce an evident adhesion of liquid on the pipe wall; however, the device produces a bubble of air at the bottom end of the KMS (\(d_{l}=0\) mm), from the air at the beginning of the simulation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case** & **\% Water** & **\% Oil** & **\% Gas** & **Velocity** \\ \hline
1 & 100 & 0 & a\({}_{i}\) & Free falling \\
2 & 40 & 60 & 0 + a\({}_{i}\) & 3 m/s \\
3 & 30 & 70 & 0 + a\({}_{i}\) & 3 m/s \\
4 & 20 & 80 & 0 + a\({}_{i}\) & 3 m/s \\
5 & 37 & 60 & 3 + a\({}_{i}\) & 3 m/s \\
6 & 32 & 60 & 8 + a\({}_{i}\) & 3 m/s \\
7 & 32 & 60 & 8 + a\({}_{i}\) & 0.3 m/s \\
8 & 32 & 60 & 8 + a\({}_{i}\) & 1 m/s \\
9 & 32 & 60 & 8 + a\({}_{i}\) & 2 m/s \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Cases of study for multiphase analysis. \(a_{i}\) is the initial air in the tube before the experiment. Figure 5: Numerical performance of liquid thickness \(\delta\), compared with the experimental fitting curve. The cases with gas in the mixture are quite different, as expected, and proportions are motivated by data provided by Nuvoil from samples of the extracted mixture in a typical oil well where the jet-pump ALS is applied. Cases 5 and 6 are depicted in Figure 7, where the gas becomes the lightest phase and becomes distributed at the center of the pipe. In the figure, three instances of the dynamics are depicted at \(t=1\), 2, and 3 s after the entrance, and it can be observed that Case 6 has a more visible gas concentration since the gas phase in the mixture is higher. It can be noticed that at \(t=2\) s and \(t=3\) s, no significant changes are perceived, and an irregular gas concentration is obtained. In addition, according to Figure 5, a preliminary stable concentration could be identified at \(d_{l}=200\) mm. Figure 6: Oil performance in the lateral plane at 10 s of simulation. Figure 7: Gas distribution in the multiphase mixture. The concentration at the center of the pipe can be noticed. However, to verify the effect of velocity on the phenomenon, Cases 7-9 were analyzed with different conditions at \(t=3(s)\) after the fluid entrance. In Figure 8, the dynamics of air as the initial component in the pipe is shown, which, for the low velocity in Case 7, remains at the center while the liquid is in the wall, a similar result as Case 1.