ss5.1 environmental description of subsea system

7/26/2019 SS5.1 Environmental Description of Subsea System

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PgDip/MSc Energy Programme/Subsea Systems Environmental Description

Environmental Description

Review

Before engineers can design systems or define operations at sea they mustfirst gain an understanding of the environment in which they are working.This requires an understanding of the principal environmental factors whichwill influence their work. This topic covers how to describe wave and windconditions in statistical terms and what those descriptions mean to theengineer.

Content

Environmental Conditions

Weather Windows

Numerous offshore operations require relatively calm weather for a sufficient length oftime to complete the job of work. A window of opportunity is therefore required in theweather and this is commonly known as a weather window. Accuracy of weatherprediction is often an issue and experience of a particular location can play a key role indetermining whether a predicted weather window will in reality be calm enough and ofsufficient duration to carry out and complete work safely.

Operational Limitations

Operational limitations apply to weather window requirements for jobs like running andlanding a subsea tree from a rig for example, but also to the conditions in which the rigcan operate. The latter will be part of the rig design specifications. Typically theoperational limitations of a drilling rig will be largely dependent upon the environmentaldesign specifications more commonly referred to as the operating envelope (seebelow) of the marine riser.

Hurricanes and Other Regional Phenomena

Every region has particular weather characteristics. In the Gulf of Mexico,meteorological watches and surveys are carried out to determine the development and

routing of hurricanes, which can devastate the region. It is common practice to evacuaterigs and production platforms when they are on or near the predicted path of ahurricane. Remote control rooms are located within the downtown offices of a number ofoil companies so that in the event that GoM production stations are abandoned, theproducing facilities can be shutdown from town. It is of interest to note here that thehistorical reason why we have SCSSVs in wells was to shut off flow in the event that ahurricane or fire/explosion wiped out a GoM platform. The SCSSV is a development ofthe Storm Choke. Their inclusion in subsea wells is somewhat of an enigma. Anotherphenomenon, which is peculiar to the GoM, is that of Loop Currents. These are strongswirling currents, which can cause real problems during subsea operations. As withhurricane developments, they are monitored.

The Robert Gordon University 2001 1


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Vessel and Equipment Operating Envelopes

The limiting operational factor with a completion/workover riser will typically be theheave (as the drill floor approaches the proximity of the surface tree). In the event thatthe heave issue is not the limiting factor, the completion/workover riser analysis willdetermine at what point in deteriorating weather the operations must cease due to

imparted stresses and dynamic loading (fatigue loading) acting on the riser. Since thecompletion/workover riser does not have a flex joint, the operating envelope of acompletion or workover riser is somewhat limited compared to a marine riser. As aconsequence, a drilling rig has a much reduced operating envelope when carrying outcompletion and well intervention work.

Hostile v Benign Environments

The winter months in the North Sea can offer a very hostile environment, particularly thefurther north it is. Job planning should be scheduled to take maximum advantage ofbenign weather in order to reduce vessel downtime to a minimum. Some contractualagreements (particularly with monohull vessels) may be negotiated so that weather

downtime is taken by the contractor, however this will probably be restricted to workduring the summer months when weather risk is statistically low.

Seabed Soil Conditions

As far as remote intervention is concerned and diver and ROV work in particular, the soilconditions can cause poor visibility if the seabed mud is loose and silty. In suchconditions, even slight disturbance to the seabed can cause work to be halted for sometime in order to let the seabed settle and provide visibility close to the bottom.

In any subsea construction engineering work, the seabed soil conditions will determinewhat sort of foundation methods might be required. Understanding and predictinglaterally loaded pile and conductor behaviour embedded in soils is generally done with

the aid of p-y Curves. These form a graphical representation of soil resistance per unitlength, p and lateral deflection, y. Structural analysis can be conducted by using springrelationships to model the p-y behaviour of the soil and analytically the followingdifferential equation can be used to relate p and y:

Equation 14

4

dx

ydEIp =

where:

y = casing, conductor or pile deflection

x = length along casing, conductor or pile

EI = equivalent bending stiffness of casing, conductor or pile system

If the system geometry and boundary conditions are known, and if a family of p-y curvescan be developed, this equation can be solved using numerical integration techniques.Development of analytical and finite element analysis models are possible provided thep-y curves can be determined, however the p-y relationship is influenced by numerousfactors, including:

non-linear variation of soil properties with depth;

the general form of the casing/pile deflection;

the corresponding state of stress and strain through-out the affected soil zone;

the nature of environmental loadings.



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Soil strength data pertaining to the subsea wellhead locality is required for coupled riseranalysis and wellhead load path analysis (see topic Wave and Current Loading,Methods of Calculation).

Regional Differences: West Africa, West of Shetland, Gulf of Mexico

Regional variations can have an impact on the type of equipment used and thetechniques and methods of equipment deployment and operation. The loop currents andhurricanes of the Gulf of Mexico require weather tracking and specialised evacuationsystems. Fishing activities may not be a concern in deeper waters, however governmentrequirements on the likes of national content (in terms of contract award to a specifiedminimum percentage of local vendors) and abandonment legislation and can affect theoverall and longer term economics of a field development. The type of fluids producedalso affects the economic and safety aspects of an operation and the oil companies arealways more likely to put their developmental capital into an area where the greatestreturn on investment is likely.

Description of the Wind

Figure 1. Descript ion of Wind

You cant really describe the wind as illustrated in figure 1, but it is possible to describethe wind using standard statistical forms such as:

Mean wind speed;

Mean square wind speed.

Mean wind speed this is a broad description, usually qualified with additionalinformation such as:

the time of year the readings were taken, i.e. February 1998, or June 2000.

the direction in which the wind was blowing, i.e. North, East.

Even if a mean wind speed is available, when you are designing a structure for themarine environment you should be aware that average values arent everything. Whatabout the maximum values?



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There are three important areas of maximum:

statistics of maximum;

statistics of direction;

statistics of mean wind speed.

However, the terms mean wind speed and mean square wind speed are not generallytoo helpful when describing the wind unless you qualify the terms with additionalinformation such as the direction the wind was coming from, the time of yearmeasurement was recorded, or if you are stating an average.

The Wind Rose

One of the commonest conventions for the description of marine wind environments iscalled the Wind Rose. It is a presentational convention which gives a summary ofstatistical and directional information which is useful. As well as being a mathematicalrepresentation of information, it also provides a graphical representation of data. Inparticular, it can give an answer to questions such as:

What proportion of the time does the wind blow from direction and with a speedbetween A m/s and B m/s?

The wind rose is only useful however if you are given information about the time period itrepresents. For example a rose may represent the wind conditions experienced in eachyear from 1980 to 1990or it can give month by month information such as the windconditions for every January between 1980 and 1990.

The wind rose shown in Figure 2 is for the months of February between 1990 and1995 (Manticora Field an imaginary field).

Figure 2: Wind Rose for the Months of February 1990 1995.

Affectionatelytermed atelescope

Directionalpointer

NORTH

15m/s and over

10 to 15m/s

A

5 to 10m/s

0 to 5 m/s

20%

15%

10%

5%

Contour lines



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Telescopes represent the direction of the wind and the structure represents thestatistical distribution of speed:

1ststage wind speed 05 m/s;

2ndstage wind speed 510 m/s;

3rdstage wind speed 1015 m/s;

4thstage wind speed 15 m/s and over.

For example, telescope Ain figure 1 represents the winds from the west of the sectorduring February 1990 to 1995. It tells us:

Wind was from the west of sector


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Pis the proportion of time the wind blows for each direction and for each speed range

Mis the mid point of the particular speed range.

Sis the calculated mean wind speed.

D is the direction of the wind.

R is the speed range of the wind.

For example, Table 1 tells us that:

for 6% of the time, wind was from the west, with a speed between 05 m/s (readoff table);

for 23% of the time, wind was from the west (just add the values);

for 11% of the time, wind was from the east.

Influence of Height Above Sea level on Wind Speed

Wind speed is not constant; it varies. Wind speeds at sea are generally expressed at aheight of 10 metres above sea level. This recognises that the speed is, in most

circumstances, dependent upon proximity to the air/water boundary. SI units are alwaysused for unit description in marine systems. Be aware!

Figure 3. Variation in Wind Speed and its Effects upon Wave Height.

0

2

4

6

8

10

12

0 2 4 6 8 10 12

Height(m)

S

peed(m/s)

As you can see from Figure 3, at the sea surface wind speed tends to be relatively lowbecause of the sheltering effects of waves and drag effects.

In modelling this variation for design purposes it is usual to use a power law of the

form shown in Equation 3:

Equation 3

n

V

V

=

O0 H

H

V0is the observed wind speed at H0metres above sea level.Ho= 10 metres as this isthe reference level. The wind speed at anylevel should be related to the reference level.

Vis the wind speed at height H.

n is the terrain type see Table 2.



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Table 2. Terrain Type and Wind Speed

Terrain Type (n) Wind Speed

Sea 0.10 to 0.13

Grass 0.13 to 0.2

Woods/ suburbs 0.2 to 0.27

Urban areas 0.27 to 0.4

The Generation of Waves by the Wind

The interactions between the wind and ocean waves have been studied for at least 3000years, yet our understanding of the physics of wave generation is quite limited,considering the time period of study. The Greek philosophers are recorded to haveproposed their own theories as have Newton and other more contemporary

mathematicians, physicists and engineers. Unfortunately there are still no readilyaccessible mathematical models for accurate and consistent engineering predictionsregarding the growth of waves and their winds.

There is, however, one model widely accepted as being the physical system of wavegeneration. It has only been possible in the last few years to get some genuinemathematical analyses linking wind to wave generation using this model. It is termedJeffreys Theory and is illustrated in figure 4.

Figure 4. Illustration o f Jeffreys Theory.

Wind

water movementfrom high to low pressure

+

+

_

_

Crest of wave

The flow of air over the uneven water surface generates high and low pressure areaswhich result in the movement of water within what will become the waves. Eventually theprocess becomes self limiting as the water surface becomes unstable and energy is lostat the same rate at which it is transferred from the air to the water.

A wave flows from the high-pressure region to the low-pressure region, allowing thetransfer of energy between the kinetic energy of the wind and the wave energy content.This energy transfer tends to increase the structure of the wave. Hence it is reasonableto assume that the movement from high pressure to low pressure would contain andenhance the structure of the wave.



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The trouble with Jeffreys theory is that it is too simple and requires a number ofassumptions;

an infinitely flat surface;

no change in water density;

constant wind.

This theory is therefore too simplistic for engineers to use.In addition, Jeffreys theory does not state what causes the initial disturbance but there

are many possible mechanisms:

fish;

sea birds;

seismic disturbances;

other physical causes.

In the absence of wind the sea surface is in a state of stable equilibrium (flat andundisturbed). If anything disturbs the surface, friction will return the surface to its

original flat state. This is a bit like a ball-bearing in a bowl! As illustrated in Figure 5.

Figure 5. A Flat Calm Sea Surface.

In a wind, however, a flat sea surface represents an unstable situation. This is more like

a ball-bearing on top of a hill. Theoretically the ball can stay put but even the smallestfluctuation will set it moving as illustrated in Figure 6.

Figure 6. An Unstable Sea Situation.

Waves and Wave Fields

The definition of a wave is a moving transient fluctuation of the interface between thesea and the air. It can be described both physically and mathematically as somethingwith height, strength and direction. Waves travel in three dimensions unless they areconstrained.

However, in order to interpret how waves affect marine systems, an abstract conceptneeds to be introduced - the two-dimensional wave.



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Two-dimensional Wave

This two-dimensional wave is used to engender an engineers understanding of thewave. These waves travel in one direction only unlike those in the real sea, so they donot exist in nature. They do however exist in the laboratory, as Figures 7 and 8 confirm.

Although this is an abstract concept, it is very useful in engineering terms.Figure 7. Wave Machine at RGU

The wave machine at RGU is shown in Figure 7. The red block on the left-hand side ofthe picture is a large hydraulic flap that stimulates the water and forms a wave. In thispicture you can see a wave of approximately 0.5 metres in length being generated.Figure 8 gives a better understanding of the length of this wave machine, and the heightof the generated wave.

Figure 8. Illustrating Height of Generated Wave



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The Space Domain

If a two-dimensional wave is considered, it is possible to imagine a side-on snap-shottaken at an instant in time. This is the space domain representation and is shown inFigure 9.

Figure 9. Space Domain Representation.

(x)

xmean water

level

wave 1 wave 2 wave 3 wave 4

h

peak

trough

is the wavelength

his the wave height

Interface

between

water and

air

Note that the start and finish of an individual wave is determined according to the zero-upcrossing convention.

The Time Domain

An alternative is to use the time domain representation. In this case the descriptionrepresents the position of the water surface as might be recorded by an instrument fixedin space (such as a wave rider buoy, which is a fixed point device giving a verticaldisplacement of the sea surface, and giving a timed series of measurements).Traditionally the time domain has been more important than the space domain in theoffshore marine industry. This is also a conceptual domain and is illustrated in Figure 10.

Figure 10. The Time Domain Representation.

(t)

tmean water

level

wave 1 wave 2 wave 3 wave 4

h

TZ

peak

trough

TZis the zero-upcrossing period, not wav elength.

his the wave height



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Storm Waves and Wave Swell

During a "storm" waves will be generated locally due to the known interactions betweenthe air flow and the dynamics of the water in the vicinity of the ocean surface. Thesewaves are known, not surprisingly, as storm waves (In Orkney, they are known as "land

waves"). However, even in the absence of any local wind conditions we generallyobserve long wavelength waves with very low amplitudes. They may be travelling atconsiderable angles to any locally generated storm waves, which can produce veryunusual dynamics in vessels. These long waves are known as swell. They are the resultof distant storms (Figure 11).

Figure 11. Formation of Swell.

LittleDispersion

MuchDispersion

Energy spreads out

along wave fronts

Wind Direction

Storm

Area

-30 to 45 deg

+30 to 45 deg

We will find later in the course that the speed of a wave is a function of wave period.Short period waves travel slower than long period waves. So, at a distance from astorm, we will observer the arrival of long period waves before we start to observe theshorter period waves. The frequency of the incident swell, therefore, will vary with time.In addition the attenuation of short period waves is greater than for long period waves.Swell does, therefore, generally appear to a long period phenomenon.

Wave Measurement Systems

Two basic types of wave measuring device have been developed; those floating on self-contained buoys, and those requiring a platform on which they can be mounted. Thelatter type mostly measure the instantaneous water elevation directly (by a variety ofdifferent principles) whilst the former measure the motions (usually the accelerations) ofthe floating buoy and deduce the wave height from these. Closely allied with the buoysystems are ship-bome wave recorders, which measure the motions of a ship, togetherwith hull submergence from pressure transducers, and deduce the wave height. Inaddition, radar altimeters mounted on satellites, are also in use for the collection of waveheight data. The rapid passage of the satellite footprint across the ocean surface meansthat the data collected is not directly comparable with point measurements of waveelevation time history made by 'in situ ' instruments at a fixed location.

Wave measurements can be of point elevation only, in which case significant waveheight and the 'point' wave spectrum can be deduced. If information on wave direction



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and the directional spread of the energy is required, then either additional point elevationmeasurements are required close by, or alternatively the wave slope must be measured.Data from a wave measuring device must either be collected and processed in theinstrument or transmitted to some remote data logger for storage and analysis.

Point elevation measurements attached to fixed or floating platforms can operate on anumber of different principles. One of the first in common use was the so-called wave-

staff, which works by detecting the changes in electrical properties as the water levelmoves up and down it (Figure 12). This needs to be rigidly attached to a platform legcovering the full wave height and tidal rise and fall. They are therefore not particularlyeasy to install and maintain, and are vulnerable to damage. More recently systemsbased on laser light or microwaves reflected off the surface of the sea have found favourbecause of their greater ease of installation and maintenance (they just need a rigidattachment at platform deck level). They can however be affected by spray, especially ifthey are on the downwind side of a platform. Some now incorporate motion measuringsystems so that they can automatically correct for wave motions when attached to afloating platform or vessel.

Figure 12. Classical Conductivity Wave Staff.

Conductivity between aluminium legs isrelated to the depth of submergence

Water

Air

Some microwave and radar systems (e.g. MIROS and CODAR) have been developed toscan a larger area of sea and return signals that can be analysed to yield directionalwave spectra.

In addition to the platform-mounted sensors there are also seabed mounted, or sub-surface buoy mounted systems. Some of these work on the principle of an invertedecho-sounder, whilst others measure pressure. The latter only measure the longer wavecomponents, as the pressures associated with the shorter higher frequency componentsdecay quickly with depth.

The most common wave measuring device has been the Datawell Waverider Buoywhich has been in use for many years (Figure 14). The buoy is attached to a mooring

system designed to minimise influence on the buoy motions, and the buoy contains adevice detecting vertical acceleration, the signal from which is filtered and integrated toderive a wave elevation signal. It is therefore a point elevation measuring device. Thesignal is usually transmitted by VHF radio to a receiving and recording device installedat a convenient location in the vicinity.

More recently the wave buoy concept has been developed by an number oforganisations to measure wave directional properties, normally by detecting the waveslope (or the buoy's response to the wave slope) as well as the vertical acceleration.The size and ease of deployment of these buoys can vary widely.

Wave buoys suffer from difficulties in detecting low frequency components (sayperiods greater than 15 seconds ) because their elevation measurements are based onthe integration of accelerations, which must be high-pass filtered in order to prevent drift.

The arrangement of the buoy' s mooring system is also critical to its performance inlarge waves, as the buoy can be dragged through the crest of large waves as the



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mooring pulls tight, or can be subject to resonant rolling and pitching motions largeenough to submerge the transmitter aerial.

Figure 13. Wave Measuring Techniques.

Pressure

Transducers

Accelerometer

Pressure

Sensor

Radar Altimeter or Laser

Inverted Echo Sounder

Wave Rider

Buoy

Marker

BuoySubsurface Float

Radar

Downward Pointing

Radar or Infra-red

device

Satellite

Wave Staff

Figure 14. Datawell Waverider Buoy.



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Statistical Description of Wave Fields (Time Domain)

Not all waves have the same height or wavelength. Waves are non-deterministic and wetherefore cannot predict the occurrence of a wave. We have to use statistics to guide usin interpreting the environments in which we are working.

Wave statistics can be considered in two forms. Namely "short term" in which thestatistical parameters are constant throughout the duration of the duration of the studyand "long term" in which we should expect large scale variation in the underlyingstatistical descriptors such as mean wave height etc. A long-term analysis can beconsidered as a consecutive series of short-term analyses.

If HAV(t,T) = Average height of waves in the time from t to t+T, then T must be sufficientlylong to ensure that true and representative statistical values are obtained. (The problemis much simpler to consider if one uses the concept of stationary time series inconjunction with the concept of an ensemble of data sets this is however outside thescope of this course!). In terms of wave spectra (which will be covered in later Topics),this means that T must equal a multiple of the period of the longest component of the

sea.If we assume the time domain initially, using, for example, a rider buoy which is a fixed

point device giving a vertical displacement of the sea surface, then the device will give atimed series of measurements (Figure 15).

Figure 15. Timed Series of Wave Height Measurements.

t+Tt

metres

Time(seconds)

200 2501500 50 100

T

0.4

0.2

0

-0.2

0.4

Surface Elevation

If an experiment of duration T is performed, and T is considered sufficiently long, a timeseries obtained:

(t): 0 < t < T = vertical displacement of water

then it will be possible to divide the measurements collected into a series of individualwaves. Each of these will have a wave height and a zero upcrossing period.

Hiand Tzi Hi= wave number



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Mean Value Statistics

It is relatively easy to calculate the average value for the period and height of a wave. Itshould therefore be possible to determine:

mean wave height$H ;

mean zero upcrossing period)T

zby using Equations 4 and 5.

Equation 4 =

=N

1i

iHN

1H

)

{} indicates mean value.{^} indicates experimentally determined.

Equation 5 =

=N

1i

ziZ TN

1T

)

The space domain parameters can be described in exactly the same way to determine

the mean wavelength

)z .

However, mean values are not used heavily in marine design. We do use significantstatistics though. For largely historical reasons the significant statistics are the mostcommon. These are a collection of tables used to estimate storm values collated byseamen up crows nests!

Significant Wave Height (Hsig)

The significant wave height is defined as the mean value of the biggest 1/3rd

of wavesmeasured, see Notation 1.

1. Collect the individual wave height measurements Hi

2. Sort by size (big at top, and small at bottom).

3. Discard all but the biggest third of the measurements.

4. Determine the average value of the biggest third of the waves.

Notation 1 1/3sig HH =

We still however have to define certain parameters, specifically the month of the yearstudied and the direction of the wind.

Significant Period and Wavelength

The waves are still sorted by height:

1. Collect the individual wave height measurements Hi.

2. Sort by size (big at top, and small at bottom).

3. Discard all but the biggest third of the measurements.

4. Determine the average value of the periods of the remaining waves is calculated to

yield T .sigz

AND/OR

The average value of the wavelengths is determined to yield sigz



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Presentation of Wave Data

For some purposes quoting Hsig, Tsigand sigmay be enough. Sometimes, however, ascatter diagram is used, like the one shown in Table 3.

Table 3. Number of Waves Encountered per Thousand Versus Duration in Seconds.

Tz (seconds)

H (m) 4-5 5-6 6-7 7-8 9-10 10-11

5-6 10 15 20 15 8 3

4-5 20 30 50 20 10 5

3-4 50 95 150 80 40 10

2-3 40 80 100 70 20 5

1-2 30 40 60 30 10 5

0-1 10 20 50 20 8 4

Usually a table like this might be used for, say, The average January over the last tenyears, or some other well defined period and location. It is important to realise thatscatter diagrams are only meaningful, like wind roses, if they are properly qualified.These diagrams do allow you to predict the number of waves of a certain height for anarea. However predictions are only as good as the data they are derived from.

For example, in Table 3, out of 1000 waves, 40 waves had a height of 12 metres,and a period of 56 seconds.

If you have a time dimension measurement, you will need a 3D scatter diagram. It isimportant that you recognise the need to qualify your data, ie. the location charted andthe time period (June/January).

Specific Issues Relating to Long Term Wave Data

Statistics such as the significant wave height, mean wave period and significant waveperiod will vary in any "long term" description of a sea state. It is possible, however, touse a variation of the "scatter diagram". To generate an alternative format, in which Hsigand mean wave period (or spectral period) are presented (Table 4).



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Table 4. Long Term Wave Data (Representative of the northern North Sea).

Wave Predictions

Although we cannot truly predict waves, we can make storm-related wave statisticalpredictions as long as we know:

the Wind Speed (ten metres above the sea surface);

the Fetch.

Both must be accurate. We use the term prediction for when our data quality is nothigh.

The definition of a fetch is the length of water over which the wind is blowing togenerate waves in the location of interest, these are illustrated in Figures 16 to 18. Weknow that as a storm starts, wave height increases until the wave finally breaks. Basedupon observation over the last 100 years or so, enough information has been collected

about how storms start, how long they last, the wind speeds and the wave heights.

Figure 16. Fetch Length Defined Over Enclosed Waters

wi nddirect ion fe tch =L

poin t of

interest coast l ine



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Figure 17. Fetch Length Defined Over Semi-enclosed Waters

N

S

EW

coast l ine

Figure 18. Fetch Length Defined Over Open Ocean.

Winds around a lowpressure zone

The fetch can be readily defined for all but North Winds in Figure 16 and 17. But howcan we define the fetch length in Figure 18? Surely here we are dealing with swell!



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Prediction Methodology

If we know the wind speed (e.g. from the met office websitewww.meto.govt.uk/home.html), the fetch (and the water depth), we can use one of avariety of wave prediction charts. One of the most useful is Figure 6 in BS6349 Design

of Offshore Structures: Part 1, shown overleaf (reproduced here as Chart 1).This chart can be used to determine Hsig, Tsigand the minimum time the wind must

blow for the sea state to be fully developed. This means that the waves will get nobigger no matter how much longer the wind blows! Figure 19 gives an overview or keyof Chart 1.

Figure 19. Key to Prediction Chart BS6349.

Hsig

Tsig

Fetch length (km)

Wind Speed

m/s

Minimum storm duration line

(mdl)

20m/s

200km

Extract reproduced from BS 6349 Part 1 with the permission of BSI under licence number2001/SK0164. Complete British Standards are available from BSI Customer Services (Tel+44 (0) 208 996 9001.

For example: determine Hsig, Tsigand minimum time for full storm development, for afetch of 100km and a wind speed of 20m/s: Ans, 6 hours with Hsig=3.8m and Tsig=7.5s

With caution, these charts can also be used to make more sophisticated predictions inwhich the wind speed changes or when the storm is not fully developed(ie. shorterthan the duration suggested by the mdl). However, these are based on poorly verifieddata, so measurements are taken under fairly uncontrolled conditions. The significant

statistics, in this case, can be determined by locating the intersection between the windspeed on the y-axis and the appropriate storm duration as specified by the mdl.

For example: For the same 100km / 20m/s storm, with only 2 hours to develop:

1. Identify the 100km, 20m/s intersection point and find the nearest minimum durationline (mdl).

2. Move leftwards along the wind speed line until you cross the minimum duration linecorresponding to the duration of the storm.

3. Read off the new values for Hsigand Tsig.

Ans: Hsig=2m and Tsig=5.5s.

It can be seen quite clearly that waves do not grow indefinitely with time, but follow adevelopment similar to Figure 20.



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Chart 1. Figure 6 in BS6349 Design of Offshore Structures.



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Figure 20. Wave Height Growth with Time.

ttime given

by chart

Hsig

Wave Theories

Before you can apply wave statistics to real problems, you need some kind ofmathematical description of waves.

Question: How do we move from descriptions of waves (both measured andpredicted) to a quantitative assessment of, for example, cable mooringtensions?

Answer: Mathematical modelling.

The first stage of modelling involves developing equations that define how a wave

behaves. In other words in order that we can gain any kind of quantitative descriptions offorces and responses, it is necessary for us to develop a mathematical model for waves.The simplest useful model is that developed by George B Airy in 1845.

This will be examined in the next Topic.

ss5.1 environmental description of subsea system

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