Numerical Simulation of Gas–Liquid Gravity Displacement in Vertical Fractures during Drilling of Carbonate Formations

[Image: see text] In petroleum drilling, carbonate formations characterized by natural fractures can result in troublesome gas–liquid gravity displacement, which refers to the phenomenon that the drilling mud leakage and gas kick are simultaneously triggered. This work focuses on clarifying the mechanism of gas–liquid displacement in vertical fractures during the drilling of carbonate formations and investigating the characteristics of gas–liquid displacement under various conditions. First, the bottom hole pressure allowing for gas–liquid gravity displacement is analyzed, which determines the coexistence condition of leakage and kick in vertical fractures. Then, a theoretical model of gas–liquid displacement flow in a vertical fracture is established. To verify the reliability and accuracy of the model, the results of numerical simulation are compared with those of a visualization experiment. The development process and flow characteristics of gas–liquid displacement in the fracture under different conditions are numerically simulated. The effects of pressure difference, drilling mud property, and fracture geometry on the gas–liquid displacement rate are analyzed. It is found that the drilling mud leakage rate increases with the increase of fracture width, fracture height, and drilling mud density, while it decreases with the increase of pressure difference and fracture length. The gas invasion rate increases with the increase of fracture width, fracture height, and pressure difference, while it decreases with the increase of drilling mud density and fracture length. The equations for leakage rate and gas invasion rate are derived by the response surface method, and the methods for mitigating gas–liquid gravity displacement are discussed. It is expected that the present work provides a better understanding of the gas–liquid gravity displacement in carbonate formations.