The effect of slope of the seafloor on the significant variables for multiline spread moorings with composite mooring lines containing both wire rope and chain has been investigated mathematically. A field test of the mooring calculations was conducted using an actual drilling vessel in the Santa Barbara Channel moored over a sloping ocean floor in water 1300 ft deep at the vessel and with anchors in depths of from 1056 to 1494 ft. The tests demonstrated the ability of the calculations to accurately describe the tensions in the tested lines.
Floating drilling vessels use spread mooring systems to limit the horizontal offset from the wellhead that results from environmental forces acting on the vessel. In deep water, a spread mooring pattern may have anchors that are as far as two miles apart. In some areas, the ocean floor slopes sufficiently that the water depth can vary by several hundred feet from one side of a mooring pattern to the other. One such area is the Santa Barbara Channel, where the slope of the ocean floor sometimes exceeds 1200 ft/mile. Conventional mooring calculations for a flat bottom were considered inappropriate for these sloping bottom conditions. A numerical method accounting for a sloping bottom was developed and computer programmed. It accounts for all of the significant variables, such as mooring line tension, suspended line length, horizontal restoring force, and horizontal vessel offset; and it can handle composite mooring lines that contain wire rope and chain.
The equations used to relate the mooringline variables were derived from basic catenary equations. As the tension in a composite line consisting of both wire rope and chain increases, the equations describing the line change when the junction between the wire rope and chain is picked up from the sea floor or when the line becomes completely suspended. The equations were set up in a way that, with proper definition of variables, allows a single equation which is continuous and has continuous derivatives to apply for all ranges of tensions.
Given an initial configuration of the mooring system, the computer finds the restoring force in pounds that will be produced by a prescribed horizontal offset of the vessel. This restoring force is equal to and opposite in direction to the steady environmental force acting on the vessel. The number of mooring lines, the mooring pattern, the initial tensions in the lines, a description of each line, the slope of the ocean bottom or the water depth of each anchor, and the depth at the initial vessel position must be given as input to the program along with the magnitude and direction of specified vessel offsets. As output, the program gives (at each offset) the tension in the most heavily loaded line, the suspended length of that line, the maximum anchor load, and the total restoring force exerted by the mooring system in response to the offsetting environmental force.
