Analysis of coupling axial vibrations between drilling fluids and drillstring

Considering the Possion coupling mechanism between them, the equations of motion for the drillstring and drilling fluids inside and outside the drillstring are developed. The eigenvector method is used to study the effects of shear modulus of formation and Possion ratio of drillstring on stress wave and pressure wave propagations. The frequency equation of drillstring axial vibration is deduced. The theoretical results show that the strong coupling occurs between the inner and outer fluids because of approximately the same wave speed, while the coupling effect between the fluid modes and the pipes mode is much weaker. Thus the coupling has more effect on mud pulse telemetry than drillstring acoustic telemetry. Furthermore, since the inner and outer drilling fluid pressure adds the inertial mass of drillstring, the natural frequency of drillstring axial vibration drops compared with inexistence of drilling fluids. The coupling equation of axial motion for the drillstring is expressed in terms of viscous inertial mass, viscous damping coefficient, drilling fluid pressure and inertial force.