Numerical study of gas-liquid flow in wellbores during coexistence of kick and loss in different formations

The coexistence of influx and loss in different formations represents the most complex scenario in well control. Accurate prediction of the gas–liquid two-phase flow behavior and pressure distribution within the wellbore is essential for effectively dealing with such high-risk incidents. In this study, a one-dimensional coupled gas–liquid two-phase flow model of the wellbore and the formation is developed under conditions of simultaneous influx and loss. By adjusting the distributions of pore pressure and fracture pressure to alter the relative positions of the influx and loss zones, the upper-influx/lower-loss and lower-influx/upper-loss scenarios are simulated. Additionally, by specifying different fracture pressures for the loss zone, the varying resistance of the formation to drilling fluid loss is simulated. The model is solved using a finite-difference numerical method, yielding the transient distributions of gas holdup, pressure, and velocity along the well depth under different operating conditions. The simulation results indicate that the fracture pressure of the loss zone is a key factor governing the flow regimes within the wellbore. When the fracture pressure is sufficiently high, the influx does not evolve into more complex conditions. At lower fracture pressures, a transition from influx to loss occurs within the wellbore. If a weak section with extremely low fracture pressure exists, a subsurface blowout characterized by the coexistence of influx and loss may develop. Under the upper-influx/lower-loss scenario, if the loss zone at the bottomhole has a relatively high fracture pressure, the influx within the wellbore ceases and the system evolves into a no-influx/no-loss state, with the shut-in casing pressure continuing to increase. When the fracture pressure of the loss zone is lower, a transition from influx to loss occurs, and the shut-in casing pressure first increases and then stabilizes. When the fracture pressure is further reduced, a subsurface blowout characterized by simultaneous influx and loss develops. The shut-in casing pressure initially increases and then rises slightly, and the inflection-point pressure is lower than the stabilized value in the influx-to-loss transition scenario. Under the lower-influx/upper-loss scenario, as the fracture pressure of the loss zone decreases, the flow regimes within the wellbore successively evolve from no-influx/no-loss, to influx-to-loss transition, and finally to simultaneous influx and loss. The variation of shut-in casing pressure is closely related to the fracture pressure. A lower fracture pressure corresponds to a lower inflection-point value of the casing pressure. In the no-influx/no-loss and influx-to-loss transition cases, a finite-length contaminated drilling fluid section detaches from the bottom and migrates upward. In contrast, under simultaneous influx and loss, a continuous contaminated section forms above the influx zone, while a high gas-fraction section with nearly constant gas holdup exists below it.