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 thirdorder differential equation is used as the governing equation in this paper, rather than the traditional secondorder 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 Pitheorem and mathematical fitting.
Bad weather is frequent during laying offshore pipelines, so the pipeline abandonment and recovery operation is unavoidable. In offshore oil and gas engineering the pipeline laying engineers need to do detailed mechanical analysis to determine the operation parameters and then make sure that the pipeline will not overstress during the operation. To do the mechanical analysis the mathematical model is a very important problem. In the abandonment operation the A&R cable lowers a pipeline down to the seabed by a pull head and in the recovery operation lifts it up to the sea level. During the process the pipeline’s axial forces, bending moments must be controlled in a reasonable scope to prevent its strength damage. The calculation of these quantities is very useful to guide the operation. So the mathematical model of pipeline abandonment and recovery should be established.
The sketch of the pipeline abandonment and recovery operation is shown in Figure
Pipeline abandonment and recovery operation.
In this paper a mathematical model and a new strategy to tackle the moving boundary without contact analysis are presented. On the other hand the length of the suspended pipeline segment is very important because it can quicken the calculation. So finally a length approximate formula is presented based on Buckingham’s Pitheorem and mathematical fitting.
On the problem the following simplifications are made based on offshore engineering experience [
Mechanical parameters of the pipeline single point lifting and lowering model.
The pipeline is regarded as a tensioned beam. There are usually two kinds of differential equations which are used to analyze this problem, a secondorder one and a thirdorder one, and the thirdorder one is more suitable for the beginning stage of pipeline lifting and the ending stage of pipeline lowing [
Force analysis of a short pipeline segment.
Resolving forces normal to the segment axis leads to
According to the similar problems [
at the origin:
at the joint:
To sum up, the whole mathematical model for the pipeline abandonment and recovery is the following boundary value problem:
It is hard to get the analytical solutions of the mathematical model presented above. So in this research the traditional numerical method, fourthorder accurate finite difference has been used to get the numerical solutions.
Notice that the boundary conditions of the model are moving; in another word, the parameter
suppose
solve the boundary value problem (
get axial force
decrease the value of
For engineering application, the pipeline’s physical quantities during abandonment or recovery, such as pipeline’s configuration, bending moments, must be calculated. After numerical calculation of (
Using MATLAB, (
Basic values of the pipeline in the example.
Size (inch) 



12  31399320  350 
Consider the first case. Suppose that the angle
Different loads on the pipeline in the first case.

100  300  500  700  900  1100  1300  1500 
Configurations of the suspended pipeline in the first case.
Bending moments of the suspended pipeline in the first case.
Consider the second case. Keeping the tension
Different angles of the loads in the second case.

70  72  74  76  78  80  82  84  86  88  90 
Configurations of the suspended pipeline in the second case.
Bending moments of the suspended pipelines in the second case.
From Figures
It is necessary to compare the results calculated by the presented model and method with the traditional finite element analysis results. The software called DRICAS is developed by the model and method presented above. Meanwhile Orcaflex is also used, which is a world's leading package for pipeline finite element analysis and it tackles the moving boundary condition by the contact analysis formula [
Configuration result comparison between DRICAS and Orcaflex.
Bending moment result comparison between DRICAS and Orcaflex.
Sometimes it is necessary to simulate the pipeline recovery and abandonment by model experiments. According to dimensional analysis theory [
From the numerical calculation procedures it is known that the length of the suspended pipeline is a key parameter of this problem. A simple approximate formula will be very useful to quicken the solving of this boundary value problem. It is known that the length of suspended pipeline is related to
In offshore engineering the pipeline Slaying, Jlaying, abandonment and recovery operations can be all governed by (
Reasonable boundary conditions for the problem of pipeline abandonment and recovery are that at the TDP the angle and the bending moment are equal to zero and the tension loading is equal to the loading force horizontal component, and at the joint the bending moment is equal to zero. The whole mathematical model for this problem is (
The new direct tackling method for the moving boundary of this problem is effective and can get as accurate results as the traditional finite element method coupled with contact analysis.
The similarity criterions for model experiments of pipeline abandonment and recovery are
The suspended pipeline length can be calculated first by approximate formula (
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors have been supported by the National Basic Research Program of China (no. 2011CB013702) and the National Natural Science Foundation of China (no. 51379214).