Modelling of Formation Pore Pressure Inversion during Tight Reservoir Drilling

Identifying and controlling a kicking well hinge on quickly obtaining reliable and accurate formation pore pressure. In this study, we derive an analytical model for estimating formation pore pressure when a gas kick occurs during tight reservoir drilling. The model considers the variations in gas volume and pressures in the annulus affected by mutual coupling between the wellbore and formation, as well as bubble migration and expansion in the annulus. Additionally, a numerical computation method that reduces the effect of measurement noise using the Hooke-Jeeves algorithm is proposed. The method is capable of estimating pore pressure during the early stage of a kick in real time, is robust to the inherit noise of the measurements, and can be applied in scenarios when a well shut-in process cannot be performed. The simulation results demonstrate that both kick simulation and formation pore pressure inversion can be conducted via the proposed methodology. The errors of the pore pressure estimating results are less than 2.03% compared to the field data of seven wells. The method is tested and validated to be robust to noise and maintain good convergence performance, thereby providing drilling engineers with a simple and quick way to estimate pore pressure during a kick.