Abstract: During tripping,improper operation might lead to kick or even blowout when wellhole conditions could not be described by U-tube theory if the bit was off-bottom.Based on the theory of two phase flow,a Y-tube model is built through analysis of wellbore fluid properties in overflow,shut-in and well killing when the bit is off-bottom.Three branches of Y-tube represent the drill string,annulus and wellbore below the bit,respectively.For the drill string and annulus,the wellbore pressure may be analyzed by the typical Y-tube theory.Fluid properties in interval below the bit(namely lower branch of Y-tube)should be considered,when the changes of killing parameters(e.g.bottomhole pressure)during shut-in and killing are investigated,Then,the characteristics of entire wellbore pressure with bit off bottom are described with Y-tube theory.Based on this theory,the moment at which the shut-in pressure is determined from shut-in pressure buildup curve is proposed,the density calculation formula of fluid in interval below the bit is derived,and the design method of killing fluid density is given.Actual calculation indicates that gas potential in the interval below bit is significant for acquiring the formation pressure and killing fluid density.So,the gas potential should be analyzed first in design of killing parameters.