Transactions on the Built Environment vol 68, © 2003 WIT Press, www.witpress.com, ISSN 1743-3509
Safety assessment of offshore pipelines anchor damage by means of simulation method L. Gucma & P. Zalewski Maritime University of Szczecin, Poland
Abstract This paper presents the simulation method of underwater pipeline safety evaluation in the aspect of emergency anchoring vessels. The simulation model is a probabilistic one based on the Monte Carlo simulation principle including a simplified human decision algorithm and mechanics of ship anchoring. The results achieved with the use of the presented model can be applied for determination of underwater pipelines safety and as guidelines for pipeline protection. The paper also presents an example case study of safety determination of sub-sea gas pipeline located on the Baltic Sea.
1 Introduction The evaluation of the safety of complex marine systems demands creation of various models which include such parameters like: ship's traffic, meteorological conditions, human reliability and other relevant navigational features. Most of these parameters have random nature and analytical models are not fully suitable to describe it. Evaluation of safety of such systems can be performed by simulation methods using particularly Monte Carlo method. The paper presents the methodology of simulation models applied for safety of offshore pipelines determination in consideration of possible damage caused by anchoring ships. The basic advantage of applied models is the fact that it is possible to obtain more quickly the large amount of simulated data from a wide space of time and any further changes in the input parameters are very simple [6]. It should also be noticed that presented model takes into account the human factor related with any errors and decisions to be made (for example: dropping the anchor decision). The presented method take also account of physics and
Transactions on the Built Environment vol 68, © 2003 WIT Press, www.witpress.com, ISSN 1743-3509
hydrodynamics of modelling processes like ships behaviour in different conditions and under anchor.
2 Estimation of anchor damage probability by means of traffic simulation model There are several important parameters which affect the input parameters. The most significant of them are concerned with modelling of ships traffic, meteorological conditions, technical failures and human reliability. 2.1 Ship's traffic The traffic of ships along a definite route is considered as a process affected by numerous factors changing with time, as well as the route length. These factors make the traffic a random process, and probabilistic methods are used for its description. The flow of the stream of ships in the water area can be presented on a time axis, where the moments of ships passing through a given point are random occurrences. The random stream of ships can be analysed by examining the distribution of: the number of ships passing through a given point in time At, time intervals between ships, local ship speeds; and the scatter of ship positions from the assumed (mean) trajectory. The number of ships passing through a given route point in the case of free movement, that is such movement where the ships are free to choose the speed and manoeuvres, can be considered as a random process described by Poisson distribution (Fig. 1).
l Figure 1:
0
1
2 3 ship [ship/bw]
4
5
Sample of ship's entering and leaving ~winouj~cie Port fitted to Poisson distribution.
Transactions on the Built Environment vol 68, © 2003 WIT Press, www.witpress.com, ISSN 1743-3509
The ship's speed in free traffic can be described by normal or lognormal distribution [3]. Ships parameters such as length, breadth, drought, and type can be easily calculated with use of distribution function usually obtained from statistical data. 2.2 Course and position of ships The scatter (offset) of ship positions from the chosen trajectory (route course) can be described by normal distribution, and in the case of navigational obstruction by asymmetric distributions (e.g. Rayleigh's). Usually for modelling the ships traffic in open waters the combination of normal and uniform distributions is applied. It is often assumed that 1% of traffic is uniformly distributed and normal distribution is therefore modifying accordingly [l, 51.
2.3 Weather conditions modelling Effect of wind and current are usually crucial in presented models. The wind and current affecting behaviour of disabled ships (drift speed and direction) and can be very useful for modelling the consequences of an accident. The wind vector is usually modelled with use of available long term statistical data. It should be noted however that wind speed is correlated with its direction and thus distribution of conditional probability of wind from given direction should be applied.
2.4 Technical failures Technical reliability (influence of possible breakdown of some navigation devices) can be taken into account for the devices such as main engines, steering gears, auxiliary engines, generators, radars etc. It can be estimated by the technical reliability functions. In order to calculate the reliable operation of the above appliances, there is used an intensity function of damage at time, which is a density function of damage occurrence on the condition that no damage has taken place so far. After multiplication of probabilities with assumption of its independence the overall failure technical probability can be estimated. For commercial vessels it's approximately on level 10.~failure per hour of operation. In presented models the technical failures are calculated with use of exponential distribution taking into account the time of sailing near examined structure.
3 Effect of external conditions on the movement of disabled and anchored ships The technical failure of main engine and lack of propulsion can be dangerous for ships especially during unfavourable external conditions (waves, wind). The extensive rolling could lead to cargo shifting and lost of stability. In bad conditions after main engine damage navigator usually tries to drop an anchor and thus stop drifting of ship. The anchor drop should be performed with minimal
Transactions on the Built Environment vol 68, © 2003 WIT Press, www.witpress.com, ISSN 1743-3509
as possible speed - the chance of anchor chain break increases with ship's speed and size. After dropping anchor it can be dragged due to insufficient holding force. In this case the ship under anchor will be moving with determined speed. In order to determine the movement parameters of the ship's hull in conditions of wind and wave effect, analytical-experimental equations were made use of [7,8,9]. 1) To assess the velocity of the wind drift of the stopped vessel there were determined [S]: a) pressure of wind causing drift of the hull:
where: v,, - relative speed of the wind [ d s ] , for a stopped ship equal to the real speed of the wind; F, - windage area [m2], maximally the surface of the longitudinal cross section of the above-water part of the ship occurring when the ship drifts; a, - course angle of the wind ["l, with lateral thrust sins,= l ; b) resistance of the underwater body of the drifting vessel:
where: - resistance coefficient amounting to 0.1 for drift speed close 1 .l5 for common drift speeds (empirically v20.5mis); y to 0, to specific gravity of the water [N/m3], for the southern Baltic equal to 10150 N/m3 on the average; v& -drift speed [mis], F, = LT - surface of the longitudinal cross section of the underwater part of the ship; comparing the equations (1) and (2) the maximal speed of the wind drift can be determined:
while the drift direction corresponds to the direction of the wind; 2) To determine the movement parameters of the proceeding ship, affected by the wind and the drift, [7,9] established: a) loss of speed due to the drift:
where: v - ship's speed with wind wave [ d s ] ; v, - ship's speed in calm waters [mls]; H - mean height of waves [m]; a - course angle of the wind or waves ["l; D - ship's displacement[t]; b) value of the drift angle: - for the ship's larger than the speed of wind:
Transactions on the Built Environment vol 68, © 2003 WIT Press, www.witpress.com, ISSN 1743-3509
where: p - wind drift angle, k - drift coefficient, determined experimentally for a given ship, for ships in the range from 2,000 to 20,000 t displacement equal to 1.3; v, - wind velocity [&S]; - for a ship speed smaller than the wind speed the direction of their resultant vector was assumed, c) speed of the drift current:
where: v,, - speed of the drift current [&S]; t, - time length of the wind [h]; - geographic latitude ["l; d) to determine the direction of the wind current on the surface of the open sea it was assumed that it is deviated from the wind direction due to the effect Coriolis force in the northern hemisphere by about 40" to the right. 3) The holding force of the anchor was determined by establishing the multiple coefficient of its weight depending on the kind of anchor and bottom 181.
+
In the area researched the value of the anchor force coefficient equals kkOt13.3 for the Hall anchor. The anchor holding force for particular ship size groups was determined on the basis of the graph (Fig. 2) showing average changes in the anchor weights along with the deadweight, according to the following dependence: Rko, = kko, Pko,
[NI
(7)
where: Pkot- anchor weight. 4) speed of the ship, at which the anchor chain will be broken [8]:
where: vb - speed breaking the anchor chain; - force moment breaking the anchor chain according to the test certificate [Nm]; p - density of overboard water (1028 kg/m3 for salt water); L - ship's length between perpendiculars; T - average draft of the ship; 6 - hull block coefficient; B - breadth of the ship [m]. It is practically assumed, on the whole, that for a new chain for ships of over 3000 t dislocation speed v,, is contained in the range of 1 to 2 knots [8]. This is why it was assumed in the model that for a ship speed over the bottom of 2 knots
Transactions on the Built Environment vol 68, © 2003 WIT Press, www.witpress.com, ISSN 1743-3509
the chain will be broken, and for the speed in the range 1-2 knots in 50% of cases the anchor will be broken or dragged, and the holding power of the anchor falls 30% of its maximum value (for a corresponding chain length) 181. Anchor welght [XIOOO
0
5 0
NI
100
150
200
Shlp's deadweight
250
300 [xlOOO
l1
Figure 2: Average anchor weight depending on the ship's deadweight [g]. The variables occurring in the formulae mentioned, dependent on the size and type of vessel, were averaged for particular ship groups occurring in the researched area. For this purpose, for groups systematised according to length (45m, 75m, 105m, 135m, 165m, 195m) average coefficient values were accepted and multiplied by length, in order to obtain deadweight, draft, anchor weight, windage area, breadth, wetted surface and inertial braking parameters.
4 Example results (case study) The example application is presented for one class of models designed for accident probability determination of offshore gas pipeline due to emergency anchoring ships. Presented example model is based on Monte Carlo simulation methodology with an implemented human decision algorithm of anchor dropping and a physical model of anchor working with the effect of wind acting on the vessel. In the model, possible pipeline damages was divided into three groups varying with their consequences. The damage can occur due to: 1. anchor dragging during emergency anchoring, 2. dropping an anchor in the close vicinity of the pipeline, 3. the ship's running aground in the pipeline landing area. The most common type of damage is type 1, where the ship, due to extremely unfavourable conditions, will not be able to hold on to the anchor and will move towards the gas pipeline while dragging an anchor. Fig. 3 presents simulated examples of places where technical failures occur (e.g. breakdown of the main engine) during 100 years of the system operation. An analysis of the results presented in the picture confirms the self-evident thesis that technical failures occur mostly in places of the highest traffic intensity. On
Transactions on the Built Environment vol 68, © 2003 WIT Press, www.witpress.com, ISSN 1743-3509
Fig. 3 presents also gas pipeline accidents during 30000 years of simulation. Most fi-equent breakdowns are caused by dragging anchor in bad meteorological conditions. The distance of anchor dragging is different for various accidents, but it does exceed 10 km as a rule, and the direction is in agreement with the wind direction.
Figure 3: Simulation results for one of examined pipeline alternative. The most important results obtained with use of presented model are concerned with investigated accident probability. In case of systems with relatively long time between accidents the time of model working should be sufficient to get stable results (30000 years in presented model). After main simulation sensitivity analysis should be performed with consequently change in the main model parameters. Other important safety factor is time distribution between successive simulated pipeline accidents. The obtained in simulations times between pipeline accidents were fitted to the known distributions of random variables. It was found out in accordance with previous supposition that the best fit is provided by the exponential distribution. Mean time between failures estimated as h=391 years (Fig. 4). By means of this distribution it can be estimated that an accident will occur in shorter time than the expected lifetime of the gas pipeline (40 years). This probability amounts to 11.0% for the whole section of the examined pipeline.
5 Conclusions Presented methodology of safety modelling of can be applied for determination of ship collision with offshore structures accident probability. Furthermore the marine risk assessment could be performed with application of consequence modelling. The further steps on this field should be concerned with verification of basic model parameters and creating more sophisticated models of human
Transactions on the Built Environment vol 68, © 2003 WIT Press, www.witpress.com, ISSN 1743-3509
300 Marine Trchnologv V decision in different conditions and models of physical ships behaviour before and after accident.
Figure 4: Time distribution between simulated successive gas pipeline accidents.
References [l] Fancourt, R. 1991. Fixed and Floating Structures - Maritime Risk Assessment and Desiderata for Safe Navigation, The Journal of Navigation Vol. 44. [2] Gucma, L. & Materac M. 2002. Risk of collision of ships with maritime offshore wind farms in aspect of its localization (in polish). Influence of Ofshore Wind Power Plants Location on Navigation Safety, Wind Power Planning and Realization; Proc. Intern. Con$, Sopot 2002. [3] Gucma, L. 2002. Distributions of ship's on ~zczecin-~winouj~cie waterway. The Role of Navigation in Support of Human Activity on the Sea; Proc. Intern. Con$, Gdynia 2002. [4] Hansen, P.F. & Simonsen, B.C. 2000. GRACAT: Software for Grounding and Collision Risk Analysis. Collision and Grounding of Ships; Proc. Intern. Con$, 2000 Copenhagen. [S] Karlsson, M. & Rasmussen, F. & Frisk, L. 1998. Verification of Ship Collision Frequency Model, In H. Gluver & D.Olsen (eds), Ship Collision Analysis. Rotterdam: Balkema. [6] Merrick, J.R.W. et al. 2001. Modelling Risk in Dynamic Environment of Maritime Transportation. 2001 Winter Simulation Conference; Proc. Intern. Con$, Washington 2001. [7] Nogid L. M.: Theory of Ship Designing (in polish). Wydawnictwo Morskie, Gdynia 1962. [S] Nowicki A.: Science of Seagoing Vessels - Basics of Theory and Practice (in polish). Wyd. Trademar, Gdynia 1999. [9] Walczak A., at al.: Effect of Hydrometeorological Conditions on the Size of Drift and Changes in the Vessel S Speed (in polish). Scientific Bulletin of Maritime University no. 3, Szczecin 1973. [l01 Wennink, J. 1988. Offshore Platform Collision Exposure to Passing Ships, The Journal of Navigation Vol. 4 1.
