Analytical solution for wave propagation due to pop-out phenomenon in solid expandable tubular technology

Solid expandable tubular technology has gained wide acceptance in the petroleum industry due to its operationally simplified and cost-effective solution in well drilling. The down-hole hydraulic expansion results in forward motion of a mandrel until it pops out of the tubular. The pop-out phenomenon, which occurs at the end of the tubular expansion process, leads to a sudden release of stored energy within a fluid-tubular system, causing unnecessary vibration. These vibrations can become severe and may cause permanent damage to the tubular. Hence, a complete understanding of the dynamics of the fluid-tubular system is essential to avoid premature failure. This paper focuses on the development of a mathematical model describing the dynamics of a fluid-tubular system due to pop-out phenomenon. The coupling between tubular, fluids, and formation is incorporated. An analytical solution for the propagation of displacement, stress, and pressure waves, originating due to the excitation caused by pop-out, is obtained. The model also identifies the potential failure locations along the tubular. The coupling effect is more prominent if the tubular material is elastic as compared to elastic-perfectly plastic material. A sensitivity analysis showed that the coupling effects vanish with increase in tubular stiffness and reach an asymptotic value with an increase in formation stiffness. The quantification of coupling effects is important in order to see the effects of pressure waves on the other subsystems present down hole.