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This paper presents a comprehensive study based on multiphase-seepage and wellbore multiphase-flow theories. It establishes a model for calculating the rate of gas intrusion that considers various factors, including formation pore permeability, bottomhole pressure difference, rheology of the drilling fluid, and surface tension. Experiments were conducted to investigate the mechanism of gas intrusion under shut-in conditions, and the experimental results were employed to validate the reliability of the proposed method for calculating the gas intrusion rate. Furthermore, this research explores the transportation rates of single bubbles and bubble clusters in drilling fluid under shut-in conditions. Additionally, empirical expressions were derived for the drag coefficient for single bubbles and bubble clusters in the wellbore. These expressions can be used to calculate gas transportation rates for various equivalent radii of single bubbles and bubble clusters. The initial bubble size of intrusive gas, the transportation speed of intrusive gas in the wellbore, the rate of gas intrusion, and variations in the wellbore pressure after gas intrusion were analyzed. Additionally, a method was developed to calculate the rising velocity of bubble clusters in water based on experimental results. The study reveals that the average bubble size in the bubble cluster is significantly smaller than the size of single bubbles generated from the orifice. When the viscosity of the drilling fluid is low, the transportation velocity of the bubble cluster exhibits a positive correlation with the average bubble diameter. When the average bubble diameter exceeds 1 mm, the bubble velocity no longer varies with changes in the bubble-cluster diameter. The research results provide theoretical support for wellbore pressure prediction and pressure control under shutdown conditions. [ABSTRACT FROM AUTHOR]