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RESEARCH PAPERS

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

[+] Author and Article Information
A. C. Seibi

Mechanical Engineering Department, Petroleum Institute, P.O. Box 2533, Abu Dhabi, UAEaseibi@pi.ac.ae

T. Pervez, S. Al-Hiddabi

Mechanical and Industrial Engineering Department, College of Engineering, Sultan Qaboos University, P.O. Box 33, Al-Khod 123, Oman

A. Karrech

Ecole Nationale des Ponts et Chaussées, 77455 Marne La Vallée, Cedex 2, Paris, France

J. Energy Resour. Technol 128(4), 247-256 (Mar 17, 2006) (10 pages) doi:10.1115/1.2358139 History: Received November 23, 2004; Revised March 17, 2006

## Abstract

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.

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## Figures

Figure 1

Tubular fluids–formation system under study

Figure 2

Internal pressure variation in terms of time and space: (a) internal pressure, pi(z,t) at z=0, 10, 15, and 20m, (b) internal pressure, pi(z,t) at t=0, 0.10, 0.15, and 0.20s, (c) 3D pressure variation

Figure 3

Variation of the axial stress in the tubular in terms of time and space: (a) axial stress, sz(z,t) at z=0, 10, 15, and 20m, (b) axial stress, sz(z,t) at t=0, 0.10, 0.15, and 0.20s

Figure 4

Outer pressure variation in terms of time and space: (a) outer pressure, po(z,t) at z=0, 10, 15, and 20m, (b) outer pressure, po(z,t) at t=0, 0.10, 0.15, and 0.20s

Figure 5

Tubular radial displacement variation in terms of time and space: (a) radial displacement, u(z,t) at z=0, 10, 15, and 20m, (b) radial displacement, u(z,t) at t=0, 0.10, 0.15, and 0.20s

Figure 6

The first four modes of propagation of inner pressure

Figure 7

The first four modes of propagation of outer pressure

Figure 8

Wave propagation in the three mediums

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