Wellbore Pressure Inversion Model Based on Wavelet Analysis During Gas Kick

Summary Wellbore flow calculation is critical for managed pressure drilling during the kick. However, the wellbore pressure inversion calculation faces challenges due to undefined invasion boundary conditions. This paper establishes a forward model of wellbore pressure based on the wellbore flow and heat transfer model, which is solved by the finite difference method. Then, a method for calculating pressure wave propagation and attenuation is developed through the flow governing equations and small disturbance theory. Furthermore, the kick pressure fluctuation is quantitatively extracted by wavelet analysis and frequency spectrum analysis, which is considered as the inversion model boundary. Finally, a fast kick inversion method integrating forward and inverse models is proposed by combining the flow model, heat transfer model, wave propagation method, and pressure wave boundary. The results demonstrate that the gas kick will cause the spectrum of pressure signals processed by wavelet analysis to transition from a single peak to dual peaks. Using these abrupt signals as inversion boundaries, the wellbore pressure inversion combined with the forward model successfully achieves efficient computation. The results show that the mean relative errors of the standpipe pressure, bottomhole pressure and gas holdup of the inversion results are approximately 0.032, 0.004, and 8%, respectively. The inversion model maintains effective for formation pressure changes within 4 MPa. The inversion model is expected to provide a new auxiliary method for real-time monitoring and wellbore pressure management.