Drag chains

The drag chain is modeled as a concentrated weight on the seabed, with a chain between it and an attachment point on the pipe (see Figure 1).

Figure 1. Drag chain model.

Given a uniform drag chain of total length ${\mathrm{\ell }}_c$, weight per unit length w, and friction coefficient $\mu$ between it and the seabed, attached to the pipeline at height h above the seabed, the length of chain on the seabed at slip, ${\mathrm{\ell }}_0$, is given by

and the horizontal projection of the suspended length, ${\mathrm{\ell }}_1$, is

Thus, the equivalent model should have a friction limit of $\mu w{\mathrm{\ell }}_0.$ The horizontal length at slip, $\mathrm{\ell }$, can be taken as any value from ${\mathrm{\ell }}_1$ to ${\mathrm{\ell }}_1+{\mathrm{\ell }}_0$. Comparison with experiment has shown that taking this length as $\mathrm{\ell }={\mathrm{\ell }}_1+{\mathrm{\ell }}_0/2$ is a reasonable choice.

When the pipeline attachment point is directly above the weight, there will be no horizontal force or horizontal stiffness offered by a drag chain element; this position is assumed as the initial condition. As the pipe moves relative to the seabed, the horizontal force on the pipeline caused by the drag chain opposes the relative motion and gradually increases (an approximation to the catenary equation is used to relate the force to the offset $\mathrm{\ell }$) until the drag chain slips when the force reaches the friction limit. The height, h, is assumed to be small compared to $\mu {\mathrm{\ell }}_0$.