## 4 Results and Discussion  
### Experiment Results  
In this study, different flow patterns in a porous bed are recorded by changing the gas flow rate while the liquid flow rate is fixed. During this process, bubbly flow, slug flow, annular flow, and the transition flow patterns among them are observed. The photos and diagrams of typical flow patterns are shown in Figure 4. At first, the gas flow rate is lower. At this time, the gas phase is scattered between the pores of the porous media bed in the form of small bubbles. With the continuous increase in gas flow rate, the number and volume of bubbles increase, and the flow pattern begins to transition to slug flow. When the flow pattern is completely transformed into slug flow, it can be seen that the bubbles between adjacent pores are connected to form irregular gas slugs, as shown in Figure 4b. In the whole experimental section, such gas slugs can be seen everywhere. As the gas flow  
Figure 3: Schematic diagram of BP neural network. rate further increases, the gas slugs are connected to form larger gas slugs, and the flow pattern transitions to annular flow. For a typical annular flow, the liquid is attached to the surface of particles and pipe walls in the form of a liquid film, and the gas flows rapidly through the gap between these liquid films, as shown in Figure 4c. It is worth mentioning that in porous beds with particle diameters of 1.5 mm and 6 mm, three typical flow patterns cannot be completely observed within the current working conditions due to the limitation of pore size. Bubbly flow cannot be observed in a porous bed with a particle diameter of 1.5 mm. For a porous bed with a particle diameter of 6 mm, annular flow cannot be observed. Only in the porous bed with a particle diameter of 3 mm are bubbly flow, slug flow, and annular flow are observed at the same time. Figure 4: Photos and diagrams of typical flow patterns. (**a**). Photo and diagram of bubbly flow. (**b**). Photo and diagram of slug flow. (**c**). Photo and diagram of annular flow. Figure 5 shows the diagram of differential pressure signals of typical flow patterns in porous beds with different particle diameters. As shown in Figure 5a,b, the differential pressure signals of bubbly flow in two porous beds fluctuate around 4.5 kPa, and the fluctuation ranges are about 1 kPa. The difference in particle diameter does not lead to an obvious difference between differential pressure signals. For slug flow, it can be seen from Figure 5c-e that there is a great difference between the differential pressure signals of bubbly flow and that of slug flow. The differential pressure signals of slug flow in porous beds with particle diameters of 3 mm and 1.5 mm fluctuate up and down around 5 kPa, and the fluctuation ranges can reach about 2 kPa, which is larger than that of bubbly flow. As for the differential pressure signal of slug flow in a porous bed with a particle diameter of 6 mm, although its fluctuation range is small, which is about 1.5 kPa. The average of the signal is around 3.5 kpa at this time, which is significantly smaller than 4.5 kPa of bubbly flow and 5 kPa of slug flow in the other two porous beds. By observing differential pressure signals of annular flow in Figure 5f,g, it can be found that the average value of the differential pressure signals is increased, both greater than 5 kPa. For the porous bed with a particle diameter of 3 mm, the fluctuation range of the differential pressure signal of annular flow is smaller than that of the slug flow. Figure 5: Diagram of differential pressure signals of typical flow patterns in different porous beds. (**a**). \(d=6\) mm, bubbly flow. (**b**). \(d=3\) mm, bubbly flow. (**c**). \(d=6\) mm, slug flow. (**d**). \(d=3\) mm, slug flow. (**e**). \(d=1.5\) mm, slug flow. (**f**). \(d=3\) mm, annular flow. (**g**). \(d=1.5\) mm, annular flow. In general, it can be found that there are certain differences in the features of differential pressure signals of different flow patterns, such as the mean value, dispersion degree, and so on.