Study on Variation Law of Volume Flow of Residual Gas Absorbed by Circulating Exhaust in Pressure Controlled Drilling

We developed a mathematical model of the gas-liquid two-phase flow in pressure-controlled cyclic exhausts by considering parameters such as gas solubility, gas slip, and oil-based drilling fluid volume coefficient, and presented a method to calculate the residual gas volume flow in pressure-controlled cyclic exhausts. The multiphase flow is solved by explicit differential calculus. It has been shown that gas may be dissolved in the drilling fluid at the bottom of the well during pressure-controlled cyclic venting, with a 0-gas flow at the bottom of the well and a gas-liquid multiphase flow at the wellhead. The length of the toroidal 0 gas flow increases with increasing backward pressure, decreasing gas intrusion rate, and decreasing oil-to-base ratio. To control the back pressure by adjusting the throttle, the back pressure was increased from 0.1MPa to 4.0 MPa and the length of the toroidal 0 gas flow was increased from 1000 m to 2700 m. The error in the maximum gas content of the bore cross-sectional area in the circulating exhaust is 21.22% compared to neglecting the 0 gas flow. The oil-to-gas ratio increases from 0.1 to 5 during the pressure-controlled cyclic exhaust, and the length of the Annular 0 gas flow increases from 1,500 m to 2,250 m. The error on the maximum gas content of the ring is 26.57% compared to the case without gas flow. The accuracy of the trap pressure calculation can be improved by considering the solubility of the gas in the multi-phase flow of the trap.