## 2 Materials and Methods
### Analysis of Dynagraph Cards under Different Operating Conditions  
The analysis of dynagraph cards under different operating conditions can help us understand potential issues and faults in the pumping unit system [18]. Here is an analysis of dynagraph cards under several common operating conditions:  
* Normal Pump Operation: The dynagraph card shows a regular pattern without any anomalies, as depicted in Figure 3a.
* Fluid Pound [19]: Fluid pound refers to the impact force generated during the pumping process due to the interaction between the pump barrel and the gas-liquid drive system. Fluid pound is characterized by sudden spikes and steep drops in the dynagraph card. It is often caused by factors such as the excessive downward speed of the pump rod, seal failure between the pump rod and the fluid, and unstable motion of the fluid column (Figure 3b).
* Gas Interference: The presence of gas has a significant impact on pump operation [20]. In the dynagraph card, gas interference is indicated by compression areas during the upstroke and downstroke of the pump, resulting in relatively smooth curve shapes. Gas interference is typically caused by factors such as gas production in the well, gas  
Figure 2: Theoretical indicator diagram.  
accumulation between the pump rod and the fluid, and failure of the gas-liquid drive system (Figure 3c).  
* Gas Lock [21]: Gas lock refers to the accumulation of gas in the lower section of the pump rod or at the bottom of the well, creating an obstruction that prevents the fluid from entering the pump rod completely and hinders the downward motion of the pump rod. This condition is identifiable on the dynagraph card by an extended compression area during the downward stroke of the pump rod, represented by a relatively flat waveform. Gas lock is often caused by factors such as excessive gas production in the well, declining fluid level, and poor sealing of the pump rod (Figure 3d).
* Delayed Closure of the Traveling Valve [22]: Delayed closure of the traveling valve refers to the phenomenon where the traveling valve in the pump closes with a delay during the upstroke of the pump rod. In the dynagraph card, the delayed closure of the  
Figure 3: Different working conditions of the dynagraph card: (**a**) Normal Operation; (**b**) Fluid Pound; (**c**) Gas Interference; (**d**) Gas Locked Pump; (**e**) Delayed Closing of Traveling Valve; (**f**) Pump Barrel Split; (**g**) Fluid Pound and Delayed Closing of Traveling Valve.  
traveling valve results in an increase in the downward speed of the pump rod, leading to an accelerated descent and steeper slope during the downward stage (Figure 3e).
* Pump Barrel Slippage: Pump barrel slippage occurs when the pump barrel becomes dislodged and separates from the pump rod [23]. In the paragraph card, pump barrel slippage is indicated by a sudden decrease in the slope during the descent stage, resulting in a smoother curve waveform. Pump barrel slippage is typically caused by factors such as poor installation of the pump barrel and wear of the pump barrel (Figure 3f).
* Fluid Pound and Delayed Closure of the Traveling Valve: The occurrence of both fluid and delayed closure of the traveling valve has an impact on the normal operation of the pump. Fluid pound can lead to damage to the pump rod and other components, while the delayed closure of the traveling valve can increase the upward speed of the pump rod, resulting in increased friction between the pump rod and the wellbore and affecting the stability of the pump rod's operation (Figure 3g).