A dynamic model of drillstring under internal and external countercurrent-axial flows is presented, and the stability of drillstring under different drilling parameters is analyzed. Results are compared to previously published simplified models (e.g., fluid-free models, influx models, outflow models). The dynamic governing partial differential equation (PDE) of drillstring is established under internal and external countercurrent-axial flows by means of the differential element method. The equation taking into account the mechanical force, the fluid pressure, the buoyancy force, the inertial force, the gyroscopic force, and the Coriolis force. PDE equation can be converted into the ODE equations by using the Differential quadrature method (DQM) and combining the boundary conditions under different working situation of drillstring. The vibration response to submerged drillstring under different parameter αc, which represents the annular clearance, is studied by plotting the stability diagram. The results were compared with the reference model established by the former researcher. Two cases, cantilever beam model and hinged-hinged boundary conditions, were discussed and found that increases the value of αc that means the annular gap increases, the outflow velocity should be decreasing, thus the effect of fluid induced vibration would be decreasing. As for cantilever case, the stability region will change obviously with the change of parameter αc, but for Hinged-Hinged case, parameter αc has little influence on the stability region. The novelty of the new dynamic model of drillstring is lying in considering the internal and external countercurrent-axial flows effect for the first time. The numerical results can be implemented in drilling engineering to predict drillstring vibration and guide drillstring design.

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