Elsevier

Structural Safety

Volume 26, Issue 1, January 2004, Pages 1-28
Structural Safety

A reliability-based control algorithm for dynamic positioning of floating vessels

https://doi.org/10.1016/S0167-4730(03)00018-3Get rights and content

Abstract

The present paper is concerned with utilization of reliability methods in relation to on-line control of dynamic systems. The particular application is to dynamic positioning of marine vehicles in connection with reliability of mechanical subsystems. The present focus is on top and bottom angles of marine risers which are suspended between the seabed and the floating vessel. These angles are of crucial importance during, e.g. drilling and workover operations. The relationship between surface floater motion and angle responses is first considered. The possibility of reducing the maximum angular response levels by dynamic positioning of the floater is then investigated.

Typically, and somewhat dependent of variation of current with depth, minimization of one of the riser top and bottom angles by adjusting the vessel position will take place at the cost of increasing the other angle. Hence, an optimum position should be defined by considering both angles but with different weight functions. An attractive approach is to determine these weights as functions of the respective reliability indices for each of the two angles. A further possibility is to apply an object function (loss function) which is purely expressed in terms of reliability indices. The viability of different schemes of this type is explored by numerical simulation for a specific riser configuration.

Introduction

Several problems have been experienced during drilling operations due to excessive top and bottom risers angle response levels. For the upper part of the riser, contact between the riser pipe and the surface vessel (e.g. the moonpool) may easily lead to serious damage. For the lower part, even moderate angles (2–4°) may imply that the drill-pipe within the riser gets into contact with the ball-joint or well-head. Wear due to metal-to-metal contact implies that damage of the well-head may occur over time, and in some cases a blow-out at the seabed can be the final result. For large riser angles (>4 to 6°) at the seabed, the operation has to be interrupted and for increasingly larger angles (>6 to 7°) a controlled disconnect of the lower part of the riser must be performed. The actual riser angle limits depend on type of riser and BOP which is applied, in addition to the type of subsea installation. If the bottom angle increases too quickly, an emergency disconnect is activated automatically on many installations. If these safety components do not work properly, the subsea components will generally have to be replaced due to serious damage.

It is accordingly of interest to minimize the response levels for the riser angles. One way of achieving this is by moving the surface floater to a given position. If mooring lines are applied, this can only be performed at certain time intervals. If a dynamic positioning (DP) system is applied, the attractive option arises to implement riser response criteria within the control loop. See e.g. Balchen et al. [1], Sørensen et al. [8], [10] for a description of presently implemented DP-algorithms. Extended algorithms accounting for criteria based on riser response have been investigated, e.g. in Imakita et al. [5] and Sørensen et al. [9], [13]. At present, it seems that no such systems have been implemented on an offshore drilling unit. Typically, control of the wave-frequency motions of the vessel is both unrealistic and frequently unnecessary. Instead, it is aimed at controlling the slowly varying low-frequency (LF) motions from wind loads, second order and mean wave loads and current loads.

A basic problem is that minimizing the response level for one of the angles will typically imply that the response level for the other angle increases (somewhat depending on the current profile as a function of depth). Accordingly, relative weights must be put on the criteria for the top versus the bottom angle. An attractive approach is to express these weights as functions of the respective reliability indices for each of the two angles. A further possibility is to apply an object function which is purely expressed in terms of reliability indices. The viability of different schemes of this type is explored by numerical simulation for a specific riser which operates at a waterdepth of 1000 m.

The methods considered here should also be of more general interest. Other applications would comprise cases where the process to be controlled is a random process with slowly developing “global characteristics” such as mean value and variance. The short-term behaviour of such processes is then characterized by a constant mean value with random dynamic fluctuations around this value.

In Section 2, the general framework for DP control of floating vessels is reviewed, and the numerical model applied for the riser is described in Section 3. The possibility of significant dynamic amplification of the riser response due to low-frequency and wave-frequency excitation is discussed in Section 4. Alternative methods for reliability-based control are outlined in Section 5. Different categories of such methods are considered, and subsequently control actions based directly on reliability indices are focused upon. Application of the corresponding algorithm is investigated in relation to a particular example Case study in Section 6.

Section snippets

Background

A general view of a vessel-riser system is shown in Fig. 1 (from Chen [2]). In order to implement riser response criteria within a dynamic positioning control loop, a description of the presently operating control schemes is first given. Such control schemes are typically based on a fixed setpoint which is the target position of the surface vessel. Typically, this setpoint is taken to be the position right above the well-head. If criteria related to riser response are to be included, this

Background

As discussed earlier, the ‘influence coefficients’ for the riser angle components play a key role in the dynamic positioning based on optimal setpoint chasing. These coefficients are studied in the following, and the possibility of establishing simplified relations for these coefficients is also explored.

Riser model based on the finite element method (FEM)

The differential equations governing the static and dynamic behaviour of the riser can in general not be solved exactly for arbitrary riser properties and arbitrary load patterns. Hence,

Inclusion of dynamic riser response

There is a possibility of significant dynamic amplification of the riser response due to LF motion of the surface floater. Even when control of the LF motion is performed, there will still be a remaining small component of LF motion which is not compensated. If the control scheme is based on the measured (or estimated) mean value of the riser response, such dynamic riser response components are not taken into account. If the additional dynamic response is significant, control schemes utilizing

Alternative reliability-based control methods

As already discussed, a basic dynamic positioning scheme corresponds to application of a fixed reference setpoint. A second step is provided by the scheme outlined earlier which introduces a setpoint that is continuously updated, and that also accounts for riser response criteria. The instantaneous values of the angles which enter the expression for the incremental offset should not include dynamic response components. This is due to the relatively rapid change of the angles corresponding to

General

A simulation study of a dynamically positioned semi-submersible conducting offshore drilling is carried out to demonstrate the effect of introducing criteria related to the riser response. The floater is a semi-submersible which is equipped with 4 azimuthing thrusters each able to produce 1000 kN. These are located at the four corners at the two pontoons.

The operational draught is equal to 24 m, the vessel mass at operational draught is 45 000 tons, the length is 110 m, and the breadth is 75 m.

Fixed weighting and reliability-index control with symmetric object function

As seen from the earlier formulas, some of the options for control of riser angles coincide if only a single angle is relevant. This applies to the procedure based on fixed weights (also including weights based on reliability indices) and to the reliability-based approach with symmetric object function. For this case the optimal position increment is given by Eq. (26).

The mean values resulting from this option are shown in Fig. 17 as a function of time. As should be expected, the mean value

Summary and conclusions

Based on the earlier parametric studies and numerical simulation of different control algorithms, the following observations are made:

  • Positioning schemes based solely on mean values are not able to capture dynamic effects (as represented by e.g. the variance of the response process) properly.

  • The applied reliability indices are able to reflect the dynamic response. The simplest approach for incorporation of these effects corresponds to reliability index monitoring.

  • Control actions derived from

Acknowledgements

ABB AS is gratefully acknowledged for fruitful cooperation. Furthermore, the contributions from Quiaofeng Chen and Jann-P Strand are gratefully acknowledged.

References (13)

There are more references available in the full text version of this article.

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