Mooring Line Dynamics: Comparison of Time Domain, Frequency Domain, and Quasi-Static Analyses
Authors: Kwan C.T. , Bruen F.J. 
Published: October 2008

ABSTRACT
This paper discusses the modeling and verification of frequency and time domain dynamic mooring analysis procedures, their applications and limitations, and compares them with conventional quasi-static mooring analysis. It presents a number of examples in which the maximum line tensions, anchor loads, and suspended line lengths, as derived by various procedures, are compared for generic Mobile Offshore Drilling Units (MODU) and Floating Production Systems (FPS) operating in various environments.
The discussion in this paper provides the basis for many recommendations on mooring analysis procedure incorporated into the API RP-2FPl "API Recommended Practice for Design, Analysis, and Maintenance of Mooring for Floating Production Systems".

INTRODUCTION
Exxon Production Research Company (EPR) has conducted significant research in mooring line dynamics in the last two decades. The research activities include:Developing a time domain dynamic mooring analysis computer program.Verifying the time domain program through model test and field measurement programs.Conducting a parametric study to compare quasi-static and dynamic analysis methods.Participating in the MIT JIP (Joint Industry Project) to develop a computer program for frequency domain dynamic analysis (References 5, 7, 8).Participating in the Noble Denton JIP on deepwater FPS mooring systems (Reference 6).Modifying the MIT frequency domain program to incorporate a linearized bottom friction model.Developing procedures and criteria for dynamic mooring analysis (Reference 3).Leading the API Mooring Design Work Group in the development of the API RP-2FPl for FPS mooring design, which emphasizes dynamic analysis (Reference 1).
The recently completed API RP-2FP1, which has been approved by API for publication in early 1991, incorporates many recommendations derived from the above research activities. Some of the research results have been published in Reference 3 in support of the API document. This paper, which further supports the API document, discusses the following topics:The differences between quasi-static and dynamic analysis.EPR's time domain dynamic model, and its verification through model test and field measurement programs.Linearizations required in frequency domain dynamic analysis, development of a linearized bottom friction model, and its verification through comparison with time domain analysis.Application of the various techniques to a range of typical mooring designs with particular reference to the computation of maximum line tensions, anchor loads, and suspended line lengths.
The emphasis in this paper is on the application of the various procedures to mooring designs, rather than a detailed explanation of the underlying theory.

MOORING ANALYSIS METHODS

Dynamic Versus Quasi-Static Analysis
In general, environmentally induced responses of a floating vessel can be divided into three frequency ranges:Steady state, including responses to current force, mean wind and mean wave drift forces.Low frequency (normally below 0.02 hertz) vessel motions due to wind and waves.Wave frequency vessel motions. The response of a mooring system to steady state forces is predicted by a static approach.