深部井筒压力扰动传播特征与瞬态响应分析

Propagation characteristics and transient response of pressure disturbances in deep wellbores

摘要:

针对深部钻井长井筒内压力扰动传播时滞显著，以及窄密度窗口下稳态水力模型难以准确刻画井底瞬态波动、易诱发井控风险的问题，建立了一维井筒瞬态水力学模型。模型以绝对压力和体积流量为主变量，通过耦合Tait高压状态方程、Korteweg系统波速修正以及非牛顿流体流变与压黏增强机制，建立了状态依赖型的沿程耗散闭合体系，并采用满足CFL稳定性条件的特征线法开展时域数值求解。稳态基准对比与传播时滞校核结果显示，稳态当量循环密度最大偏差为0.64%，动态时滞相对误差小于0.01%。在此基础上，引入静压达20 MPa的深井真实动态录井排量序列开展现场连续验证，立管压力预测误差控制在±1.5 MPa以内，验证了模型在强时变边界下的物理准确性。进一步分析表明，井底压力脉动与井口输入同频，但存在明确时滞与幅值衰减。传播时滞随井深增加而近似线性增长，而井底压力脉动峰峰值则呈非单调波动。传递函数幅频特性揭示该现象源于长井筒驻波干涉与频域谐振的共同调制，特定深度下入射波与反射波同相叠加会引发压力异常放大。所建模型有效揭示了长井筒内压力扰动的传播过程及井底动态响应特征，为窄密度窗口控压钻井的危险频率规避与动态压力预警提供了理论依据与计算工具。

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.