Coupled Stress and Pressure Waves Propagation in an Elastic Solid Tube Submerged in Fluids

The present paper studies the effect of mandrel pop out on the dynamics of a solid tubular submerged in fluids of a typical vertical wellbore. A mathematical model describing the stress and pressure waves within the tubular-fluid system (inner and outer fluids as well as solid tube) has been developed. The model takes into account the coupling effect of the three mediums. A specific case of a $127mm$ solid tubular, placed inside a $340mm$ borehole with different inner and outer fluids was considered. An analytical solution of the developed model was obtained. It was found that the excitation of the system splits into several components and propagates within the three mediums. In addition, the coupling effect revealed modification in the normal waves’ speeds and frequencies as compared to the uncoupled solution and identifies associated natural frequencies. Moreover, it was noticed that the maximum vibration occurs at the free end of the tubular and that the tube may experience local buckling in the neighborhood of the fixed end.