This paper presents a comprehensive study based on multiphase seepage and wellbore multiphase flow theories. It establishes a gas intrusion rate calculation model that considers various factors including formation pore permeability, bottomhole pressure difference, drilling fluid rheology, and surface tension. Experiments were conducted to investigate the gas intrusion mechanism under shut-in conditions, and the experimental results were employed to validate the reliability of the proposed gas intrusion rate calculation method. Furthermore, the research explores the transportation rates of single bubbles and bubble clusters in drilling fluid under shut-in conditions. Meanwhile, 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. Additionally, a method was developed for calculating 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 the single bubble generated from the orifice. When the viscosity of the drilling fluid is low, the bubble cluster transportation velocity exhibits a positive correlation with the average bubble diameter. When the average bubble diameter exceeds 1 mm, the bubble velocity no longer varies with the change in the bubble cluster diameter. The initial bubble size of intrusive gas, the transportation speed of intrusive gas in the wellbore, the gas intrusion rate, and variations of the wellbore pressure after gas intrusion were analyzed. The research results provide theoretical support for wellbore pressure prediction and pressure control under shutdown conditions.