In gas drilling, hole-cleaning problem is serious due to formation water production when water layer drilled. Drill pipe sticking will affect seriously and drilling work cannot carry out. Therefore, formation water production is the most serious case. In this paper, we research that if formation water production is small, there are two migration model in annulus considering water absorption characteristics of cuttings when formation water production is greater than water absorption. One situation is the migration occurs under the condition that cuttings completely absorb the formation water. Another is cuttings and pure liquid migrate in the form of liquid droplet at the same time when cuttings do not completely absorb formation water. By using the minimum kinetic energy method, we consider the effects of gas influx under the two conditions and find that in most cases liquid carrying need more minimal gas influx than cuttings carrying. When formation water production is small in drilling work, increasing the amount of gas injection should used in order to ensure gas drilling safely and smoothly.