Abstract: Aiming at the complex problems of drilling with high temperature and high pressure and narrow density safety window in drilling, based on the principles of managed pressure drilling technology and the two-phase flow model of annular air and liquid, considering the fracture pressure of weak formations and the bearing capacity of wellhead pressure control equipment, a pressure-controlled drilling circulating / shut-in overflow risk matrix with back pressure and overflow flow rate as indicators and a calculation model of wellhead back pressure threshold are established. The partial differential equations of two-phase flow were solved using finite difference iteration. Based on the pressure curve of overflow control, the threshold of overflow flow is determined, and the corresponding control measures are formulated based on the results of the quantization of the matrix intervals. By combining examples to validate the back-pressure calculation model, the results show that constructing a wellhead back-pressure threshold calculation model and a pressure control drilling overflow risk matrix can significantly reduce the frequency and degree of downhole complexities, ensuring the safety of pressure control drilling construction.