Automated Optimization and Design of Mooring Systems for Deep Water

Abstract

This master thesis focuses on automated optimization of mooring systems at deep water. The optimization work is based on the mooring system of the deep draft semisubmersible DEMO2000 developed by Statoil. This is a semisubmersible with mooring system designed for 1500 m water depth. The automated optimization algorithm implemented in the simulation software SIMA, developed by Marintek, is used for the optimization. This automated optimization algorithm is not yet commercialized, and the work performed in this thesis can be seen as part of a pilot study.

Mathematically, optimization of a mooring system is the minimization of a cost function subjected to constraints on its variables. Hence, automated optimization algorithms refer to the application ofmathematical search algorithms in this optimization process. A collection of optimization algorithms is available. SIMA however, uses a subsequential quadratic programming method algorithm called NLPQLP.

The optimization is carried out for amaximumdesign condition based on metocean data formthe Heidrun field. The environment is applied in-line propagating from Northeast with a combination of wind, waves and current in accordance with the requirements for the Norwegian continental shelf.

The optimization problem for this thesis is defined based on a cost function, variables and constraints. The mooring line is constructed of three segments, for each of these segments the diameter and length is defined as variables. In addition, the pretension of the mooring line is set as a variable. This allows the anchor positions to change during the optimization. The cost function is based on the price of each mooring line segment, which again depends on length and diameter. Two constraints are included in the optimization. The first constraint concerns the safety factor of the most loaded mooring line, while the second restricts the maximum offset of the semisubmersible in the direction of the environmental loading. The optimization problem is formulated in terms of workflows in SIMA workbench, and the optimization is carried out in the time domain using SIMO.

Three optimization cases are defined. The first case is the base case that requires a safety factor of 2.2 and a maximum offset of 150 m. The second case requires a safety factor of 1.8 and a maximum offset of 150 m, while the third case requires a safety factor of 2.2 and a maximum offset of 75m.

Two different mooring systems, based on the mooring system provided by Statoil, are optimized separately for all three cases. One mooring system is constructed of polyester rope and chain, while the other is constructed of steel wire rope and chain. The results of the optimization cases and relevant sensitivity studies show that the cost may be reduced significantly by use of the automated optimization algorithm.

For the polyester rope and chain mooring system, the constraint concerning safety factor is observed to dominate the optimization. The difference in cost for the first and third case is therefore small, while the cost for the second case is significantly lower. The second case does also provide the lowest cost for the steel wire rope and chain mooring system. However, both constraints influence the optimization of this system. The third case is therefore observed to result in much higher cost compared to the two other cases. Compared to the initial system the cost of the polyester rope and chain mooring system for the base case is reduced by 29.4 %, while the cost of the steel wire rope and chain mooring system for the base case is reduced by 19.3 % compared to the initial mooring system of this type. However, the polyester rope and chain mooring system is observed to provide the lowest cost.

As the optimization algorithm only consider the cost of the mooring system, the maximum and minimum values of the variables need to be chosen carefully. Both optimized mooring system tend to have unrealistic lowpretension, which indicates that the minimumvalue for the pretensionwas too low. The chain segments are also very short for the optimized systems, as chain is the most expensivemooring line material included. Polyester rope and steel wire rope is therefore close to having contact with seafloor for the optimized mooring systems at maximum offset.

Dynamic analyzes of the tension in the most loaded line for both mooring systems are performed using RIFLEX. The top end motions calculated in SIMO are for these analyzes imported to RIFLEX. Analyzes of the mooring system in the frequency domain using MIMOSA is also performed. For the polyester rope and chain mooring system only small differences are observed for the quasi-static and dynamic analysis results. The dynamic effects are neglectable for this system as the elongation of the mooring line dominates the stiffness. The differences in the results of the analysis performed in time domain and in frequency domain is also very small, indicating that the linearization performed in the frequency domain analysis have close to no impact on the top end tension. For the steel wire rope and chain mooring system, large dynamic effects are observed. This is as expected as mooring lines in a catenary system will have a lot of lateral movement. The large water span will also influence these effects. Differences are also observed in the results from the calculation in the frequency domain and the time domain. Hence, the linearization in the frequency domain will affect the top tension remarkably.