A new model for predicting the critical liquid-carrying velocity in inclined gas wells

Based on the assumption of gas-liquid stratified flow pattern in inclined gas wells, considering the influence of wettability and surface tension on the circumferential distribution of liquid film along the wellbore wall, the influence of the change of the gas-liquid interface configuration on the potential energy, kinetic energy and surface free energy of the two-phase system per unit length of the tube is investigated, and a new model for calculating the gas-liquid distribution at critical conditions is developed by using the principle of minimum energy. Considering the influence of the inclination angle, the calculation model of interfacial friction factor is established, and finally closed the governing equations. The interface shape is more vulnerable to wettability and surface tension at a low liquid holdup, resulting in a curved interface configuration. The interface is more curved when the smaller is the pipe diameter, or the smaller the liquid holdup, or the smaller the deviation angle, or the greater gas velocity, or the greater the gas density. The critical liquid-carrying velocity increases nonlinearly and then decreases with the increase of inclination angle. The inclination corresponding to the maximum critical liquid-carrying velocity increases with the increase of the diameter of the wellbore, and it is also affected by the fluid properties of the gas phase and liquid phase. The mean relative errors for critical liquid-carrying velocity and critical pressure gradient are 1.19% and 3.02%, respectively, and the misclassification rate is 2.38% in the field trial, implying the new model can provide a valid judgement on the liquid loading in inclined gas wells.