Formulas for rope in tension will apply. The sag f = f(s) is an analytical curve called "catenary". There do exist formulas for catenaries "broken" locally by the presence of a load. The bending of the pipe is described by the classical formulas of beam-under-load. You would have to apply three ranges of equations "in series", with appropriate mutual boundary conditions.
Nothing you can't do analytically.
Of course, it MAY be faster with FEM, BUT... you have to have a software with an appropriate element formulation (tension-only link). Don't even try to model the rope in 3D with solid FE elements...