Propagation characteristics and transient response of pressure disturbances in deep wellbores

Abstract:

To address the significant propagation time lag of pressure disturbances in long wellbores during deep drilling and the inadequacy of steady-state hydraulic models in accurately characterizing bottomhole transient fluctuations under narrow density windows—which may readily induce well control risks—a one-dimensional transient hydraulic model for the wellbore was established. Taking absolute pressure and volumetric flow rate as primary variables， the model couples the Tait high-pressure equation of state， the Korteweg system wave speed correction， and non-Newtonian fluid rheology with pressure-viscosity enhancement， thereby constructing a state-dependent closure system for frictional dissipation along the wellbore. The governing equations are solved in the time domain using the method of characteristics that satisfies the CFL stability condition. Steady-state benchmarking and propagation time lag verification show that the maximum deviation of the steady-state equivalent circulating density is 0.64%， and the relative error of the dynamic time lag is less than 0.01%. On this basis， continuous field validation was conducted by utilizing dynamic mud logging pump rate sequences from a deep well with a static pressure up to 20 MPa. The predicted standpipe pressure was controlled within ±1.5 MPa of field measurements， confirming the model''s physical accuracy under strongly time-varying boundary conditions. Further analysis indicates that bottomhole pressure fluctuations share the same dominant frequency as the wellhead input， yet exhibit a distinct time lag and amplitude attenuation. The propagation time lag increases approximately linearly with well depth， whereas the peak-to-peak amplitude of bottomhole pressure fluctuations exhibits non-monotonic variation. The amplitude-frequency characteristics of the transfer function reveal that this phenomenon originates from the combined modulation of standing wave interference and frequency-domain resonance in the long wellbore； at specific depths， the in-phase superposition of incident and reflected waves leads to anomalous pressure amplification. The proposed model effectively reveals the propagation process of pressure disturbances and the dynamic response characteristics at the bottomhole in long wellbores， providing a theoretical basis and computational tool for hazardous frequency avoidance and dynamic pressure early warning in managed pressure drilling under narrow density windows.