How to do a pipeline laying study without software

It is essential to do a pipelay analysis in starting any offshore rigid pipeline project to verify the potential barges' capabilities. The typical software packages are OFFPIPE, Orcaflex, and the like, but what if, for some reason, there is no software available?

No problem. We only need to know the tension and the bending moment at the sage bend (and perhaps the hoop stress.), and the rest is a bit of mathematics. But how to get these values?

There is very important research done by Brando, P. et al., that uses dimensionless analysis to correlate water depth, pipe weight, stiffness, tension, and bending moment. The idea is based on choosing one ‘dimensionless axial tension’, predetermined by the research. Then plotting other parameters on a series of dimensionless graphs until reaching the tension and bending moment. The following is a step-by-step procedure so that it is easy to grasp:

1. Calculate the characteristic (dimensionless) length of the pipe as follows:

 where Q is the submerged weight per until length.

2. As mentioned above, choose an initial dimensionless axial tension

among the following values: 0, 0.313, 1.311, 2.81, and 8.819.

 Note: the initial tension is the tension at the touchdown point.

Let us assume that we have chosen in the above step the value 0.313, which is the second value.

3. Now we know, Q, and L0, we can get N0

4. From N0, we get Nm (maximum tension or tensioner tension) from this formula:

Nm= N0 + Q.Hm

where Hm is the water depth (or the maximum height)

At this point, you will continue the calculations to ensure that the above tensioner tension (Nm) is adequate.

5. So in the below graph, we go to the second curve and plot from the tip of it (which is the maximum bending moment) the value on the y-axis (ML0/EI), and the value on the x-axis, the lay angle (which, in this case, is approximately at 30 degrees)

6.     From the graph, ML0/EI is approximately 0.62. Now, we can obtain M because we know L0, E, and I. We chose the tip of the curve because we are concerned here by the maximum bending value that is likely (but not necessarily) to generate the maximum Von Mises stress.

7.     As we obtained the lay angle as 30 degrees previously, likewise, we go to the following tension graph to obtain the corresponding characteristic tension (N/Nm).

8. Now, I know N/Nm, and Nm, so I can get N (the tension at the point under consideration.) Consequently, I now have the tension and the bending moment at a point on the pipeline near the sag bend that I think has the maximum stress.

9.     Calculate the tension, and bending stresses from the basics of the mechanics of material, and subsequently, obtain the equivalent stress (Von Mises.)

10. Try to repeat steps from 5 to 9 at different locations of the bending graph (near the sag bend) to reach the maximum possible Von Mises stress.

11. Compare the Von Mises stress with the maximum allowable stress.

12. If the stress is acceptable, you can adopt the tension value you obtained in step 4; otherwise, you will have to go back to step no. 2, selecting another dimensionless initial tension and reiterating the procedure.

References:

1. Offshore Structures, D. V. Reddy, M. Arockiasamy
2. Brando, P. & G. Sebastiani, Courtesy OTC.