When dealing with kicks or evacuating from drilling platform during drilling,well shut-in procedure is needed.If the formation pressure is greater than the wellbore pressure after well shut-in,the formation fluid will invade the wellbore.Because the law of multiphase flow in shut-in wellbore is different from that in normal drilling process,the wellbore pressure after gas kick during well shut-in is also different,so it is necessary to carry out relevant research on calculation of wellbore pressure after well shut-in.Firstly,based on the theory of multiphase-seepage in reservoir and multiphase flow in wellbore,the dynamic growth model of invasive bubbles and the calculation model of gas kick rate considering the properties of formation porosity,permeability,pressure difference between formation and bottom hole rheological property of drilling fluid and surface tension are established.Through indoor simulation experiments of gas kick mechanism under shut-in conditions,the experimental results verified the reliability of the prediction model of initial bubble size and the calculation method of gas kick rate.After that,the single bubble migration velocity in drilling fluid and the bubble group migration velocity in shut-in condition were studied experimentally.The empirical formulas of drag force coefficient and Reynolds number for single bubble and bubble group migration were established.The gas migration velocities of single bubble with different equivalent radius and average bubble group equivalent radius could be calculated by the formula.At the same time,the calculation method of rising velocity of bubbles in water is obtained according to the experimental results.The experimental results show that the bubble size in the bubble group is significantly smaller than that of the single bubble generated by the orifice.When the viscosity of drilling fluid is low,the velocity of the bubble group increases with the increase of the average diameter of the bubbles.When the average diameter of the bubbles exceeds 1 mm,the velocity of bubbles does not change with the bubble diameter.Finally,the wellbore pressure control equations after gas kick are established through the continuity equation and gas mass conservation equation in the drilling wellbore after gas kick under shut-in condition.Considering the initial bubble shape after gas kick,the velocity of the gas when the gas bubble group rises and the distribution of the void fraction of the gas migration in the wellbore,the auxiliary equations of gas-liquid two-phase flow in the wellbore after gas kick after shut-in are established,and the auxiliary equations of gas-liquid two-phase flow after shut-in are constructed.The multiphase flow model in wellbore during gas kick is solved by finite difference method.A numerical example is used to simulate the variation of bottom hole pressure during gas kick under well shut-in condition.The simulation results showed that with the increase of formation porosity,pressure difference between formation and bottom hole and the decrease of drilling fluid density,the balance time between wellbore pressure and formation pressure is shorter after gas invasion.The results also showed that with the increase of drilling fluid viscosity,the initial size of the invasive gas bubble increased.With the increase of drilling fluid viscosity,the larger bubble volume contributes more to the gas migration velocity than the resistance caused by viscosity.Thus,the time for the wellbore pressure to reach equilibrium is shorter. |