A physical model for liquid leakage flow rate during plunger lifting process in gas wells

Plunger lift is an economical method to solve the liquid loading problem in industry and has been paid more and more attentions in recent years. Because of the inevitable annular gap between plunger and tube wall, the liquid above the plunger may leak downward during lifting process. How to model and reduce the liquid leakage flow rate is still challenging to optimize the plunger lift method. In this paper, the geometric and operating parameters affecting the liquid leakage in plunger lifting process were determined and discussed. Seven different diameter ratios between plungers and tube of 0.90-0.98 were investigated experimentally, and the optimal diameter ratio (0.96) was obtained. Based on the force balance over plunger and liquid column, a physical model for the liquid leakage during plunger lifting process was proposed. Combining the experimental data of pressure loss in tube, a dimensionless correlation of liquid leakage flow rate for the optimal diameter ratio (0.96) was developed. The results showed that the relative deviation of the correlation is less than ±10.0%. The influencing parameters including the Euler number of liquid, the gas-to-liquid density ratio, the gas and liquid Froude number, the liquid Reynolds number, and the ratio of lifting distance and loading liquid height were studied. The decrease of the initial differential pressure of liquid column and the increase of the gas production mass flow rate make positive contributions to reduce the liquid leakage flow rate during lifting process.