Sea Bed Sand Waves Studied To Help Pipeline Planners

Pipeline & Gas Journal s

International/Offshore Report

Sea Bed Sand Waves

Studied--To Help Pipe ¡ne Planners

By C.F. van der Mark, M.F. de Koning, A. Bfom, S.J.M.H. Hulscher, and A. Stolk, The Netherian

F

(ir pipeline laying and operations on the bed of llie North Sea. the industry needs information OÊI the average geo-metric properties of sand waves and their variability. Németh et al. (2003) outlined how Important il is lo have more insight into sand wave behavior. Illustrated here is the importanee of sand wave variability using two cif their examples.

1. Pipelines sometimes have to cross a sand wave field. Migrating sand u-aves can form a threat i f they expose a pipeline. Free spans may develop, causing stresses in the pipeline due !o gravity and water flow. The pipeline may start vibrating due to turbuienee generated under the free span. This may cause the pipeline to bend or break. Onee exposed a pipeline can be damaged by a ship anehor or fishing gear. Knowledge on the deepest troughs thai may occur in a sand wave field helps us in determining how deep a pipeline should bo buried.

2. Navigational chuméis often need to be dredged so as to be wide and deep enough for ships to pass safely Naiitieal charts pro-vide, among other things, infomiaiion on the areas with the shallowest water depths. Infonnation on tbe highest sand waves or highest crest elevations which can oectir in a sand wave field may result in a more efñcient monitoring and dredging strategy. The objective of the study was to get more insight into Ihe variability of sand wave charae-tenstics in the North Sea. We performed a data analysis to investigate probability density func-tions, eoefficients of variation and extreme val-ues of the following geometric properties; sand wave length, sand wave height, erest elevation, trough elevatioti. and sand wave asymmetry.

Data Processing

We used multi-beam measurements o f three tlelds in the North Sea in which sand waves occur (Figure 1 ). We considered six areas in the Noordhinder sand wave field (Figure 2), two areas in the Twin field, and the area Hcomorfi (Figure 3). Figure 2 shows a three-dimensional sand wa\'e pattern, whereas Figure 3 shows a two-dimen-sional sand wave pattern in which the crest unes are more or less parallel. We classified the sand waves of the Noordhinder area and alsii the Twin area as short-crested sand waves mid ihe ones in the EcomorO area as long-crested sand waves.

In order to draw longitudinal bed elevation profiles from these measurements, we first

Figure 1: Ecomorf3

Noordhinder

determined the orientation of the sand wave field using a part of the digipol method (RliCZ. 1997, chapter 4). For each orientation (from 0-Í80 degrees) we deter-mined the gradient in bed eleva-tion. The angle at which the high-est gradient is found is assumed to correspond best with the direction perpendicular to the crest lines and is assumed to be the orientation of the sand wave field.

Given the orientation of the sand wave field, longitudinal bed eleva-tion profiles are processed using the bedfonn tracking tool (BTT) of Van der Mark & Biom (2007). The BTT detennines geo-metric properties of sand waves from the measured bed elevation profiles as ^ objectively as possible. We analyzed sand wave length X. sand wave height A, erest elevation tlj.. trough elevation Ti(. and sand wave asymmetry A in the detrended bed eievation profiles (Figure

42 44 489 Figure 3: 25 27 490 491 X co-ordinate (km) 492 S831 5832 5833 5834 Y co-ordinate (km) 5835 5836

1650 1700 1750 X co-ordinate (m) 1800 Normal Gamma RayWgh Exponential Lognormal Gumbel Weibull Figure 4: _{Figure 5:} 0 1 2 3 4

Dimensionless trough elevation (-)

4). Sand wave asymmetry is computed as A = IXI -XI)IX.

Probability Density Functions

We determined the probability density func-tion (PDF) of measured trough elevafunc-tions in one area. We then fit Normal. Ganinui, Rayleigh. Weibuil, Hxponcntial. Log-normal, and Gtimbel distributions to the data using a maximum like-lihood estimation. Figure 5 shows an example

of fitted distributions for trough elevations occurring in one of the Noordhinder areas. The appropriateness of the fitted distribulions was determined for the probability density function of trough elevations. We plotted probability density ñjnctions for all nine sand wave fields, and for each geometric property. For sand wave length, sand wave height, erest elevation, and trough elevation we found that the Weibull and Ciamma distributions provide the besl fit. For

sand wave asymmetry the Normal distribution provided the best fit.

Coefficients Of Variation

For each geometric sand wave property the coefficient of variation was determined. The coefTicient of variation C is defined as C = a/(i, in which a denotes the standard devia-tion, and \x the mean value of the geometric sand wave property. Figure 6 shows the

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Pipeline & Gas Journal s

International/Offshore Report

•a ISO S ' EcomorO NoordhMw Twn 0 BO 100 150 !O0 250 300 350 4 « Mean sand wave length (m)

Figure 6:

tionship between standard deviation of sand wave length and the mean sand wave length. It appears that the long-crested sand waves of Ecomorß have more regular sand wave lengths than the short-crested sand waves of the other areas. This is also the case for sand wave height, crest elevation, trough elevation, and sand wave asymmetry.

Furthermore, if we only consider the short-crested areas, we find that the coefficients of vari-ation of sand wave length, sand wave height, crest elevation, and trough elevation are more or less constant values, while the coefficient of variation of sand wave asymmetry is not. The coefTicienl of v-ariation of sand wave length C^ equals more or

less 0.55 (Figtire 6), The coefficients of variation of sand wave height crest elevation, and trough elevation are C ¿ = 0.49, Cr|c = 0.59. and Cr|c = 0.64. respectively. The slandard deviation of sand wave asymmetry appears to he more or less con-stant (CA = 0.35). independent of the mean .sand wave asymmetry.

A constant coefficient of variation of sand wave length means tiiat tlie standard deviation in sand wave length aui be estimated if the mean sand wme length and the coefficient of variation for sand wave length C;^ are known. The same holds for sand wave heigiit, cn;st elevation. ;md trougli ele\'ation.

Extreme Values

We analyzed the 5"/í) highest and 5% longest sand waves, the 5"/i. deepest troughs and 5% highest crests. For shon-crested sand waves we found that, for sand wave length, sand wave height, crest elevation, and trough elevation. the 95% values are linearly related to the mean value. For instance, for sand wa\'e length we found that the 95"/íi coefficient for sand wave length C)^.95 = (?w)5 - pX) / |A = 1.1. Likewise, we found that the 95% coefficients for sand wave height, cresi elevation, and trough elevation are C^c.95 = 0-9- CT^^.95 = 1.0. and C^c,95 = '-2-respectively. This means that we can estimate the extreme geometric sand wave properties, given the 95% coefficient and the mean value.

Note that the given coefficients of varia-tions and 95% coefficients are only valid for short-crested sand waves.

Planning Pipelines

Knowledge on the variability of sand waves may help us. for instance, in determining the optima! depth of a pipeline trench. The optimal depth depends on factors such as dredging costs, pipeline construction costs, monitoring costs, and risk {Németh et al.. 2003). Consider, for instance, a sand wave field through which a pipeline has to be constructed. Assume that it is known from previous monitoring surveys that the sand waves are short-crested, and that the sand waves migrate, but do not grow or decay, as there are no dredging activities and net currents are more or less constant.

We also know from a previous survey that the mean sand wave heiglit is more or less four meters. Our data analysis shows that mean crest elevation is smaller than the corresi.x)nding mean trough elevation such thai a sand wave height of four meters corresponds to a mean trough eleva-tion of 2.5 meters and a mean crest elevaeleva-tion of 1.5 meter. From our analysis we may conclude that the standard deviation in trough elevations is: G( = C«j |i™ = 1.6 m. The 95% trough eleva-tion is: ^^ 95 = (Cr^t_95 + I ) n,^t = 5.5 m.

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sand waves, five of llicse siind waves will have a trough elevation that is equal to or laiïier than 5.5 meters. Taking into accotmt the risk one is willing to accept (which may depend on the type of liquid that is transported), one may decide to place the pipeline at a depth of more or less 5.5 meters below the mean bed elevation. If the pipeline is exposed by one of these five deep migrating traiighs, this trough will probably noi be much deeper than 5.5 meters, and the free span length wiîl be small. As this example illustrates, our simple relationships may help in yetting a first estimate for the optimal deptli of a pipeline. ACKNOWLEDGEMENT

This research projec! is part of VICl project Rough Waler (STW TCB.6231) and is supported by ihe Technology Fouiidalioii STW. the applied science division (if NOW and the tedinology program of ihe Minislry nf Economie Affairs. Tlie work by ihc second author served the patiiyl fulfillnient of the requirements for tlie M.S. degree in civil etigineoring ai University of Twentc. the Netlicrlands. We acknowledge tlie North Sea llii-eetorate of the Ministry of Tran.'iporl. Public Works, and Water Miuiiigemtnt for providing us with the bathyniclric data.

.iuthors: C, F. van der .Mark i.s im-olwii in Water Engineering df Mami^'ment at the Vnive¡s¡t\' of Twcntt: PO. Bax 217. 75(K) AE. hischeik. the Nctheiiiintb. Entail: C.Evumh'rMaiiúi'iituvnte.nl. MJ'\ de Koningis imnhed inWater Euffiieeiing & Management at the Unhvrsity ofTwente. PO.

Ba\2¡7. 75mAE. Emchede. Ihe Netherlands. A. Blom is associated with the Envimnmental Fluid Mechanics Section. Delft University of Technology. Delft, the Netherlands.

S.J.M.H. Huhcher is involved in Water Engineering & Management at the University ofTwente. PO. Box 217. 7500 AE. Enschede. the Netherlands.

.4. Stolk is in the North Sea Directorate. Ministry of Transport. Public ii'orks. and Water Management. The Hague, the Netherlands.

REFERENCES

Huischer. S. J. M. H. {1996). Tidal induced targe-scale reg-ular bed fonn patterns in a three-dimensional shallow water model. J. üeophys. Res., 101 (C9), pp. 20,727-20,744. Némeih, A. A.. Hulsclier. S. J. M. H,. and De Vriend. H. J. (2002). Modelling sand wave migration in shallow shelf seas. Com. Shelf Res., 22 (18-19), pp. 2795-2806. Németh, A. A., Hulsghcr, S. J. M. H., and De Vrirad, H. J. (2003 ). Offshore sand wave dynamics, engineering problems and fliture solutions. Pipeline Ga.s J.. 230 (4), pp. 67-69. RIKZ (1997). User ttianual, Digipol Vl.O. Tech. rep., National Institute for Coastal and Marine Management (RIKZ), The Hague, the Netherlands.

Van der Mark. C. F and Blom, A. (2007). A new and widely applicable tool for determining the geometric properties of bcdforms. CE&M research report 2OO7R-003/WFM-0()2 ISSN l5hS-4i>52. t'niversity ofTweme, Enschede, the Nethcrljiuts.

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