Bubble Migration Velocity Model for Ultra-Deep Highly Deviated and Horizontal Wells

Deep and ultra-deep reservoirs are increasingly important, while gas kicks remain a major well-control risk. Accurate prediction of gas migration velocity across different wellbore inclinations is essential for locating the influx front, enabling timely kick detection, and optimizing well-killing procedures. Owing to pressure and temperature variations along the wellbore, the same influx gas may change from a highly compressed, relatively high-density state near the bottomhole to a lower-density, conventional gas-like state as it migrates upward. Accordingly, air bubbles and kerosene droplets were used to represent conventional and highly compressed gas, respectively. Adjustable-inclination annular experiments investigated CMC-controlled viscosity in bubble tests and HCOOK-induced coupled changes in density and viscosity in droplet tests. With increasing inclination, both dispersed phases became increasingly deformed. Bubble migration velocity decreased monotonically with viscosity and inclination, whereas droplet velocity first increased and then decreased, peaking at 15–30°. Along the tested HCOOK formulation path, droplet velocity varied non-monotonically. Based on 155 bubble observations and 75 droplet observations, separate correlations were integrated into a combined gas-migration model. Validation against three field wells yielded absolute relative errors of 8.75–11.20%, demonstrating its practical value for estimating field gas migration velocities.