*3.5. Phase Distribution*

Figure 8 showed the phase distribution of gas–water–oil at different viscosities and gas flow rates. With an increased gas flow rate, the frequency with which bubbles impacted the interface also increased. When the gas flow rate was increased to 500 mL/min, the bubble size increased, bubble breakage and aggregation increased, and a stable cylindrical interface formed between these two phases. When the gas flow rate was increased to 1500 mL/min, the cylindrical interface became unstable. When it was increased to 4000 mL/min, the interface disappeared, and the two phases were completely mixed. At the same gas flow rate, with an increased oil viscosity, the interface was more stable and fluctuated less; similarly, less water entrainment occurred (50–100 mL/min), the bubble column became more narrow and stable (500–1500 mL/min), and the two phases mixed less thoroughly (4000 mL/min).

**Figure 8.** Gas–liquid–liquid distribution with different gas flow rates and different silicone oil viscosities.

The height of the water–oil interface changed as the bubble crossed the water–oil interface and was defined as the difference between the height of static water–oil interface and the interface height when bubbles had just separated from the water–oil interface. The jet height, *h*, could be measured from the high-speed images shown in Figure 9.

**Figure 9.** Measuring method of water–oil interface jet height.

Figure 10 shows the jet height of the water–oil interface caused by rising bubbles. The interface was impinged with continuous single bubbles when the gas flow rate was less than *Q*1, *Q*2, and *Q*<sup>3</sup> for different oils. When the gas flow rate was increased beyond *Qi*, the aggregation between bubbles was improved, thus, the impingement was changed by multiple bubbles and the jet height was also substantially increased. The stability of the water–oil interface was enhanced, and the *Qi* was also increased with increasing viscosity of the oil phase.

**Figure 10.** Jet height with different gas flow rates.

When the gas flow rate was less than *Qi*, the jet height and gas flow rate showed a certain linear relationship and the slope approximated to 0.01. The intercept, b, was related to viscosity and decreased with an increase in oil phase viscosity. When the gas flow rate was greater than *Qi*, the jet height increased exponentially with an increase in gas flow rate. The exponential factor approximated to 0.01 and the coefficient *K* changed slightly with the increase in oil phase viscosity. The relationship between *h* and *Q* could be approximately expressed as follows:

$$\begin{cases} \begin{array}{c} h \approx 0.01Q + b \\ h \approx K(Q - Q\_i) \end{array} \begin{array}{c} (Q < Q\_i) \\ (Q > Q\_i) \end{array} \end{cases}$$
