## Journal of Applied Mathematics

• J. Appl. Math.
• Volume 2014, Special Issue (2013), Article ID 298281, 7 pages.

### Mathematical Model of Pipeline Abandonment and Recovery in Deepwater

#### Abstract

In offshore oil and gas engineering the pipeline abandonment and recovery is unavoidable and its mechanical analysis is necessary and important. For this problem a third-order differential equation is used as the governing equation in this paper, rather than the traditional second-order one. The mathematical model of pipeline abandonment and recovery is a moving boundary value problem, which means that it is hard to determine the length of the suspended pipeline segment. A novel technique for the handling of the moving boundary condition is proposed, which can tackle the moving boundary condition without contact analysis. Based on a traditional numerical method, the problem is solved directly by the proposed technique. The results of the presented method are in good agreement with the results of the traditional finite element method coupled with contact analysis. Finally, an approximate formula for quick calculation of the suspended pipeline length is proposed based on Buckingham’s Pi-theorem and mathematical fitting.

#### Article information

Source
J. Appl. Math., Volume 2014, Special Issue (2013), Article ID 298281, 7 pages.

Dates
First available in Project Euclid: 26 March 2014

https://projecteuclid.org/euclid.jam/1395854704

Digital Object Identifier
doi:10.1155/2014/298281

#### Citation

Zeng, Xia-Guang; Duan, Meng-Lan; An, Chen. Mathematical Model of Pipeline Abandonment and Recovery in Deepwater. J. Appl. Math. 2014, Special Issue (2013), Article ID 298281, 7 pages. doi:10.1155/2014/298281. https://projecteuclid.org/euclid.jam/1395854704

#### References

• A. C. Palmer, G. Hutchinson, and J. W. Ells, “Configuration of submarine pipelines during laying operations,” ASME Journal of Engineering for Industry, vol. 96, no. 4, pp. 1112–1118, 1974.
• R. M. M. Mattheij and S. W. Rienstra, “On an off-shore pipe laying problem,” in Proceedings of the 2nd European Symposium on Mathematics in Industry (ESMI '88), H. Neunzert, Ed., pp. 37–55, Springer, 1988.
• D. S. Zhu and Y. K. Cheung, “Optimization of buoyancy of an articulated stinger on submerged pipelines laid with a barge,” The Ocean Engineering, vol. 24, no. 4, pp. 301–311, 1997.
• F. Guarracino and V. Mallardo, “A refined analytical analysis of submerged pipelines in seabed laying,” Applied Ocean Research, vol. 21, no. 6, pp. 281–293, 1999.
• S. Timoshenko, S. Woinowsky-Krieger, and S. Woinowsky, Theory of Plates and Shells, McGraw-Hill, New York, NY, USA, 1959.
• S. Lenci and M. Callegari, “Simple analytical models for the J-lay problem,” Acta Mechanica, vol. 178, no. 1-2, pp. 23–39, 2005.
• M. Kashani and R. Young, “Installation load consideration in ultra-deepwater pipeline sizing,” Journal of Transportation Engineering, vol. 131, no. 8, pp. 632–639, 2005.
• S. F. Gong, Y. He, J. Zhou et al., “Parameter sensitivity analysis of S-lay technique for deepwater submarine pipeline,” The Ocean Engineering, vol. 4, p. 014, 2009.
• S.-F. Gong, K. Chen, Y. Chen, W.-L. Jin, Z.-G. Li, and D.-Y. Zhao, “Configuration analysis of deepwater S-lay pipeline,” China Ocean Engineering, vol. 25, no. 3, pp. 519–530, 2011.
• L.-Z. Wang, F. Yuan, and Z. Guo, “Numerical analysis for pipe-line installation by S-lay method,” in Proceedings of the 29th ASME International Conference on Ocean, Offshore and Arctic Engineering (OMAE '10), pp. 591–599, ASME, Shanghai, China, June 2010.
• L.-Z. Wang, F. Yuan, Z. Guo, and L.-L. Li, “Numerical analysis of pipeline in J-lay problem,” Journal of Zhejiang University A, vol. 11, no. 11, pp. 908–920, 2010.
• L.-Z. Wang, F. Yuan, Z. Guo, and L.-L. Li, “Analytical prediction of pipeline behaviors in J-lay on plastic seabed,” Journal of Waterway, Port, Coastal and Ocean Engineering, vol. 138, no. 2, pp. 77–85, 2012.
• M.-L. Duan, Y. Wang, S. Estefen, N. He, L.-N. Li, and B.-M. Chen, “An installation system of deepwater risers by an S-lay vessel,” China Ocean Engineering, vol. 25, no. 1, pp. 139–148, 2011.
• M. Szczotka, “A modification of the rigid finite element method and its application to the J-lay problem,” Acta Mechanica, vol. 220, no. 1–4, pp. 183–198, 2011.
• F. Yuan, Z. Guo, L. Li, and L. Wang, “Numerical model for pipeline laying during S-lay,” Journal of Offshore Mechanics and Arctic Engineering, vol. 134, no. 2, Article ID 021703, 2011.
• F. Andreuzzi and G. Maier, “Simplified analysis and design of abandonment and recovery of offshore pipelines,” Ocean Management, vol. 7, no. 1–4, pp. 211–230, 1981.
• T. K. Datta, “Abandonment and recovery solution of submarine pipelines,” Applied Ocean Research, vol. 4, no. 4, pp. 247–252, 1982.
• Y. J. Dai, J. Z. Song, and G. Feng, “A study on abandonment and recovery operation of submarine pipelines,” The Ocean Engineering, vol. 18, pp. 75–78, 2000 (Chinese).
• J. Z. Xing, C. T. Liu, and X. H. Zeng, “Nonlinear analysis of submarine pipelines during single point lifting,” The Ocean Engi-neering, vol. 20, pp. 29–33, 2002 (Chinese).
• X. G. Zeng, M. L. Duan, and J. H. Chen, “Research on several mathematical models of offshore pipe lifting or lowering by one point,” The Ocean Engineering, vol. 31, pp. 32–37, 2013 (Chinese).
• H. M. Irvine, Cable Structures, MIT Press, Cambridge, Mass, USA, 1981.
• D. Dixon and D. Rutledge, “Stiffened catenary calculations in pipeline laying problem,” ASME Journal of Engineering for Industry, vol. 90, no. 1, pp. 153–160, 1968.
• C. P. Sparks, Fundamentals of Marine Riser Mechanics–-Basic Principles and Simplified Analysis, PennWell, 2007.
• G. A. Jensen, N. Säfström, T. D. Nguyen, and T. I. Fossen, “A nonlinear PDE formulation for offshore vessel pipeline installa-tion,” The Ocean Engineering, vol. 37, no. 4, pp. 365–377, 2010.
• L. F. Shampine, I. Gladwell, and S. Thompson, Solving ODEs with MATLAB, 2003.
• O. Manual, 2009, http://www.orcina.com/SoftwareProducts/ OrcaFlex/Documentation.
• A. A. Sonin, The Physical Basis of Dimensional Analysis, Department of Mechanical Engineering, MIT, Cambridge, Mass, USA, 2001. \endinput