# Experimental Study on Geysers Induced by the Release of Trapped Air in Storage Tunnel Systems
## 3 Results and Discussion
### Free Surface and Interface  
Firstly, we defined the following parameters: \(H_{1}\) is the level of the free surface, \(H_{2}\) is the level of the water-air interface head, \(h_{0}\) is the length of the water column at the initial moment when the air pocket head reaches the shaft position, and \(H_{net}\) is the net motion of the water-air interface relative to \(h_{0}\) which can be understood as the reduced length of the water column due to the rise of the air column. The relationships among these four variables can be defined as follows: \(H_{net}=h_{0}-(H_{1}-H_{2})\). Correspondingly, we establish that \(v_{1}\) and \(v_{2}\) are the velocity of the free surface and water-air interface, respectively, and \(v_{net}\) is the net velocity of the water-air interface. Consequently, \(v_{1}=dH_{1}/d_{t}\), \(v_{2}=dH_{2}/d_{t}\), and \(v_{net}=v_{2}-v_{1}\).  
Figure 5 shows the level variation of the free surface and water-air interface in the process of gas-flow geyser. In operation mode A, there is no external pressure, the air column rises only depending on its own buoyancy, the free surface and interface are still affected by the system pressure oscillation, the free surface has a level oscillation phenomenon, and the lift height of the free surface level is small. The value of \(H_{net}\) increases roughly linearly along with time, and the corresponding velocity is \(v_{net}\) = 0.25 m/s which is approximated with the Taylor bubble velocity provided originally by [PERSON] and [PERSON] [22] as \(v_{taylor}=0.35\sqrt{gD}\) = 0.245 m/s. For a Taylor bubble, the free surface level remains constant when the rising bubble is subject only to buoyancy action. Likewise, in geyser flow, when the air pocket is dominated by buoyancy, the variation of the free surface level is mainly caused by air compression and expansion. Thus, the maximum level of the free surface is equivalent to the maximum height of level oscillation.  
As shown in Figure 5b, in operation mode B, the free surface level and interface level both exhibit accelerating rise. The \(H_{net}\) value increases roughly linearly along with time, but the \(v_{net}\) value is significantly greater than the Taylor bubble velocity. This shows that external pressure has an obvious role in causing high-speed gas flow; this may be the major reason for the development of gas-flow geysers.  
Figure 6 shows the variation of the free surface level and pressure head in the process of surge-type geyser, where \(H_{3}\) is the free surface level relative to the PT1, and \(H_{p}\) is the pressure head of the measuring point PT1. In the process of a surge-type geyser, firstly, the pressure rises rapidly and reaches the highest value within a short period of time, and the rise of the free surface level significantly delays the increase of pressure which also proves that the surge-type geyser is caused by the instantaneous high pressure of the system. Because a large amount of air is carried into the water during the surge process, the water-air mixture in the shaft is subject to pressure and buoyancy. The rising height of the free surface level is significantly higher than the extreme value of instantaneous pressure, and the difference value depends on the air content of the mixture in the shaft.