An Extended Tension Leg Platform Design for Post-Katrina Gulf of Mexico. John Murray, Chan K. Yang and Wooseuk Yang FloaTEC, LLC Houston, Texas

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1 A Exteded Tesio Leg Platform Desig for Post-Katria Gulf of Mexico Joh Murray, Cha K. Yag ad Wooseuk Yag loatec, LLC Housto, Texas Partha Krishaswamy, J. Ray McDermott, Housto, Texas Ju Zou Housto Offshore Egieerig, Housto, Texas ABSTRACT The ew metocea criteria for the Gulf of Mexico (GoM) affect chages to existig desig procedures for future ad existig offshore platform desigs i that regio. loatec, LLC is completig the pre- EED desig o a versio of its exteded tesio leg platform (ETLP) for deploymet i this ew eviromet at a water depth of 5, ft. This ew GoM desig was tested at a model scale of 1:92 uder the ew metocea criteria ad istrumeted to measure extreme resposes, icludig wave ruup, airgap tedo tesios, ad six-degree-offreedom motios. The paper presets ad discusses the results of the predictios from a ucoupled ad fully coupled model i compariso to the measured test data. KEY WORDS: Exteded Draft Tesio Leg Platform; ucoupled ad coupled model; Scaled model tests; Post-Katria Gulf of Mexico coditios. NOMENCLATURE M : system mass matrix, M : equivalet costat mass matrix modelig tedo effect, UC K : system stiffess matrix (hydrostatic), K : equivalet costat stiffess matrix for tedo ad riser effect, UC C : equivalet liear dampig matrix to model the viscous dampig, a M ( ) : equivalet added mass of the body at ifiite frequecy, () 1 ( 2) () t = () t + () t :first ad secod-order wave excitatio, I I I R (, ) ( ) xt & = R t τ xd & τ : radiatio dampig force, 2 siωt : retardatio fuctio dampig coefficiet, R() t = C( ω) dω π ω t : wid force, wid ( ) 1 x t CD A u x u x 2 (, ) = ρ ( & ) & : force o the Moriso members, m A : projected area of the Moriso member, u : particle velocity ormal to the member (wave + curret) u& : particle acceleratio ormal to the member (wave + curret) x& : velocity of the model elemet, K : time- ad motio- depedet coupled stiffess matrix, C C ( x, x&, & x, t) : couplig tedo ad riser force vector. w : weight of the model elemet per uit legth, s : hydrostatic force o the model elemet per uit legth, d : hydrodyamic force o the model elemet per uit legth. INTRODUCTION The ew metocea criteria [API, 27] for the Gulf of Mexico (GoM), brought o by the aftermath of recet hurricaes will affect chages to recommeded desig procedures for future ad existig offshore platform desigs i that regio. The accuracy of the sizig tools ad procedures used to predict the resposes of floatig systems become more striget as a better uderstadig ad quatificatio of the margis of coservatism take a critical role. I more practical terms, more accurate desigs tools ca idetify the level of coservatism used i the origial. This is useful i establishig whether the existig desig is suitable for the ewly defied criteria. Sizig tools for floatig offshore structures are geerally based o coupled [Kim et al, 1994] [Ra et al, 1997] or ucoupled [Ora, 1983] techiques. I some cases the ucoupled methods produce coservative quatities; however the coverse ca also be true. loatec, LLC is completig the pre-eed desig o a versio of its Exteded Tesio Leg Platform (ETLP) for deploymet i this ew eviromet at a water depth of 5, ft. The mai feature of the ETLP desig discussed later i this paper is extesios o the potoo from which the structure derives its ame. Paper No. ISOPE Murray Total umber of pages 7

2 The desig tool used to size this hull ad tedos ivolves a fullycoupled time domai solutio icorporatig top tesioed risers (TTRs), tedos, ad the ETLP hull. This ew ETLP desig has udergoe a model test program at a scale of 1:92 uder the ew GoM metocea criteria [API, 27]. The test program icluded wid tuel ad wave tests. Data geerated from the model tests are used to evaluate the desig tool ad to compare ad discuss the predictios geerated from a ucoupled model. The Exteded Tesio Leg Platform (ETLP), illustrated i ig. 1, cosists of four colums coected uderwater by four potoos. The potoo extesios move the tedo coectio poit outboard of the colums. The extesios effectively icrease the restorig effect of the tedos while reducig the colum spacig. This reduces the deck spa betwee colums ad thereby captures a savig i deck steel weight. The colums are circular for structural efficiecy ad to miimize evirometal loadig. ig. 2 ETLP Cofiguratio Table 1 ETLP Specificatios The structure is moored usig 12 tedos; three tedos per corer, coected 18 ft above the keel. Pricipal prototype dimesios of the hull are give i ig. 2 ad listed i Table 1. UNCOUPLED AND ULLY COUPLED - EQUATIONS O MOTION The three typical methods of solutio for the equatios of motio of the TLP are frequecy domai, ucoupled time domai, ad coupled time domai. The equatios of motio are the same i all methods, but their solutio formulatio reflects the limitatios of the method selected. The frequecy domai aalysis is the closed form solutio of equatios to estimate resposes to radom waves, icludig platform motios ad acceleratios, tedo loads ad agles, ad hydrodyamic loads. The most sigificat limitatio of frequecy domai techiques is that all oliearities i the equatios of motio must be igored or replaced by liear approximatios. I cases where both time ad frequecy domai techiques are applicable, the frequecy domai ofte has the advatage of simplifyig the computatios; so it is typically used for prelimiary desig sice it ca be used to estimate the short-term statistics of the variable of iterest. However, the liearizatio required for frequecy domai aalysis might lead to iaccurate results for extreme loads. Time domai aalysis is the direct umerical itegratio of the equatios of motio, allowig the iclusio of all system oliearities. Equatio (1) describes the equatio of motio for ucoupled aalysis. All terms are defied i the omeclature. a M + M ( ) + M C && x+ [ C] x & + [ K+ KC] x= I ( t) + R( x &, t) + m( x, t) + wid( t) (1) ig. 1 Exteded Tesio Leg Platform (ETLP) The mass matrix term i Equatio (1) shows a term M C, which is a equivalet mass matrix term for the tedos ad risers [Ora, 1983]. This represets a diagoal matrix for mass ad added mass compoets i the horizotal ad vertical directios. The stiffess matrix of the equatio also shows a matrix of liearized stiffess costats, K C [Garrett, 1982], to accout for the riser ad tedo reactio forces with the hull. This fully populated coefficiet matrix is geerated as a fuctio of the ETLP offset from its still-water equilibrium positio. Aalyses with tedos ad risers modeled i this method have o iertia or bedig respose. The forcig fuctios o the right had side of the equatio do ot cosider ay evirometal loads o the tedos or risers directly.

3 Equatio (2) describes the equatio of motio for the fully-coupled oliear model. All terms are defied i the omeclature. ( ) ( ) () ( ) ( ) () a M+ M && x+ K + KC xt, x = I t + R xt &, + m xt, + wid t + C( xxxt, &, &&,) (2) The M C term i the mass matrix is ow part of the right had side cotaiig the forcig terms, expressed as C. The respose of the tedos is calculated simultaeously with the platform respose. Dyamic force iteractio betwee the tedos ad risers ad platform at the poits of attachmet is icluded. The model icludes dyamic tesio ad bedig accoutig for the oliearities i each riser ad tedo as well as couplig effects. These effects are accouted for i the matrix K C (x,t) which resolves the coefficiets for each positio usig the fiite-elemet model of the tedos ad risers [Patel, 1983]. Thus, this matrix chages as a fuctio of positio ad accouts for oliearities i the global restorig forces [Kim et al, 1994] [Ra et al, 1997]. computed from equatio (4). d A I M I D D ( u x& ) = C ρ A & x + C ρa u& + C ρa u x& (4) The total force o the member at time, t, is foud by itegratig alog total legth, S, as give i equatio (5). ( x, x, & x t) C, & (5) = q ds M x 3 r ds r + dr s r r r r M q m + d M + dm x 2 ig. 4 Sample of Computer Model NUMERICAL MODEL x 1 ig. 3 Illustratio of Sleder Rod Model Tedo loads cosist of both static ad dyamic compoets. Static loads arise from tedo pretesio, tide, platform offset due to steady evirometal forces ad foudatio istallatio positio errors. These loads ca be determied from the equilibrium coditios of the platform, tedos, ad risers. Dyamic tedo loads arise from platform possible seismic iduced motios, ad direct hydrodyamic forces. The ucoupled ad fully coupled umerical model used compute the resposes of the ETLP are based o the equatios of motio described i Equatios (1) ad (2), respectively. A time domai solutio is used to predict the six-degree-of-freedom rigid body motios, tedo ad riser tesios ad airgap. The potetial flow hydrodyamic coefficiets are foud from the boudary itegral techique described i [Lee, 1995]. The model icludes Morriso members to accout for viscous effect i the hull, tedos, ad risers. Waves, wid, ad curret forces are geerated for three hour simulatios i both the u-coupled ad fully coupled models. ig. 4 shows a computer idealizatio of the model illustratig the paelized hull ad the Morriso members. The forces o the tedos iteractig with the hull are foud usig the techique illustrated i ig. 3. The figure shows the cofiguratio of a sleder rod model ad the free body diagram of forces ad momets. The positio vector rst (,) is a fuctio of the arc legth s of the rod at time t. ad M are the total resultat force ad momet, respectively, actig o the rod cross sectio. The distributed load q is divided per equatio (3). s d q w = + + (3) Whe a tedo or riser is free to move i wave ad curret, the idepedet flow field model is obtaied by liear superpositio of two idepedet flow fields; a far field due to the wave ad curret ad a ear field reactig to the structure motio. The hydrodyamic force compoet o a tedo or riser is the ig. 5 Photos of Model Tests

4 The free surface paels also used to itegrate the sum ad differece frequecy QTs are ot show i ig. 4. MODEL TESTS The model tests were carried out at the Offshore Techology Research Ceter (OTRC) i College, Statio, Texas. The model was istrumeted to measure six-degree-of-freedom global motio, airgap, ad ruup o the colums, tedo ad riser tesios, ad riser stroke. The prototype desig cotais 12 Top Tesioed Risers (TTRs) which were modeled as a group of four risers as illustrated i ig. 2. Photographs of the model uder test coditios are provided i ig. 5. The model was subjected to a extesive test program i various combiatios of wid, waves, ad currets. ACILITY CALIBRATION Details of the evirometal post-katria evirometal coditios used i the aalysis are provided i Table 2. Table 2 Post-Katria 1-Year Hurricae Coditio wave crest (ft) umerical simulatio wave basi crest = height/ wave height (ft) ig. 7 Wave Crest vs Wave Height performig a zero-crossig aalysis o the waves idetifyig the crest heights ad the wave heights. The respective data sets are raked i ascedig order ad plotted agaist each other. This method assumes that the largest crest height occurs i the largest wave. The igure also compares the crest heights of the waves geerated i the wave basi to the crest heights simulated from a liear summatio. The results show that the heights of the crests from the wave basi are higher tha the simulated crests, particularly i the higher waves. Also, the maximum crest height is ot attaied i the umerical simulatio. This is a limitatio of the umerical wave simulatio. Dyamic Wid orce Waves were calibrated without the model i the basi. Measuremets were made at six locatios usig three calibratio probes ad three referece probes. The referece probes remai i positio after the model was istalled. The calibratio probes were positioed at iteded model locatio. A sample of the wave spectrum measured at oe of the calibratio probes is provided i ig. 6. The dyamic wid force was applied usig a lie attached to a feedback cotrolled servo-wich. The lie was fixed to the ETLP at the elevatio of the ceter of pressure. The dyamic wid force drive sigals were calibrated based o the wid force spectra ad target RMS values measured i the wid tuel tests. A compariso of the target ad modeled spectrum for the 1-Year coditio is show i ig x Wave Spectrum (m 2 S/rad) Model Test JONSWAP Wid orce Spectrum (KN 2 /Hz) requecy (Hz) Period (sec) ig. 6 Sample of Target ad Modeled Wave Spectrum ig. 7 is a raked plot comparig the wave heights ad wave crests from the sequece of waves i the time series correspodig to the spectrum measure i the wave basi. The raked plot is geerated by ig. 8 Sample of Target ad Modeled Wid Spectrum Curret ad SCR orces The mea curret force was applied usig a weight over a pulley. The curret force was combied with the steel cateary riser (SCR) force ad applied at the same elevatio.

5 COMPARISON O NUMERICAL SIMULATIONS AND MODEL TESTS 9, 8, -Coupled -Ucoupled Static Offset Tests The model test setup is first evaluated by static offset tests to compare the predicted ad measures restorig forces ad hull setdow as a fuctio of offset. Results of these tests are compared to the umerical predictios from the fully coupled ad ucoupled models i ig. 9~1. Applied Horizotal orce (KN) Setdow (m) 45, 4, 35, 3, 25, 2, 15, 1, 5, -Coupled -Ucoupled Offset(m) ig. 9 ad Offset vs Restorig orce Coupled -Ucoupled Offset (m) ig. 1 ad Offset vs Setdow These results show very good agreemet betwee the fully-coupled predictios ad the measure model results for both the setdow ad the offset restorig forces. The ucoupled predictios are liear for the full rage of offsets. Reasoable agreemet betwee the ucoupled predictios ad the measured restorig results is show for offset up to approximately 35 ft. Ucoupled predictios of the setdow are geerally over-predicted at offsets less tha approximately 3 ft ad uder-predicted at offsets greater tha 3 ft. ig. 11~12 show typical resposes of the tedo ad riser tesios, respectively, as a fuctio of offset. Agai, there is very good agreemet betwee predictios from the fully coupled ad measures tesios. The predicted tesios o both the tedos ad the risers are highly oliear with respect to the offset. The tesios are uder- Tedo Top Tesio (KN) 7, 6, 5, 4, 3, 2, 1, Offset (m) ig. 11 ad Offset vs Riser Tesio TTR Top Tesio (KN) 3, 25, 2, 15, 1, 5, -Coupled -Ucoupled Offset (m) ig. 12 ad Offset vs Tedo Tesio estimated for offsets less tha 3 ft ad over estimated for offsets greater tha 3 ft. Compariso of Respose Amplitude Operators ollowig the static offset tests, the model setup was subjected to white ose spectra to measure the Respose Amplitude Operators (RAOs). The measured RAOs are compared to the predicted frequecy domai resposes for surge, heave ad pitch i ig. 13~15, respectively. The white oise wave spectra were geerated at a sigificat wave height of 2 ft as idicated i the figure. I geeral, good agreemet was foud at the lower periods for all three RAOs. The computed surge RAO teds to over-predict the surge respose at the higher periods. This is due to viscous effects that are ot accouted for i the frequecy domai model. A similar tred appears i compariso of the heave RAO. Also, the cacellatio poit i the predicted RAO approaches zero at approximately 15.4 sec. This is the poit where the forces o the colum cacel the forces o the potoos but i the umerical model, does ot accout for the viscous effects. Whe the oliear dampig is icluded, a o-zero respose occurs at the cacellatio periods. These occur because a drag force exists at all periods eve whe the iertia forces o the colums ad potoos cacel. Compariso of ully-coupled ad U-Coupled Resposes Time domai solutios from the coupled ad ucoupled models are,

6 Predict-Coupled Predict-Ucoupled Surge Motio RAO (m/m) (m) or (%) Wave Period (sec) ig. 13 Compariso of Surge RAOs -6. Max Offset Mea Offset Mi Heave ig. 16 ETLP Motio Statistics Heave Motio RAO (m/m) Tedo Top Tesio (KN) 6, 5, 4, 3, 2, Predict-Coupled Predict-Ucoupled.1 1, Wave Period (sec) ig. 14 Compariso of Heave RAOs Mea Max ig. 17 Compariso of Tedo Tesio Pitch Motio RAO (deg/m) Wave Period (sec) ig. 15 Compariso of Pitch RAOs compared to model test data for hull motios, tedo ad riser tesios ad airgap measuremets. All comparisos are made for the 135-deg icidece headig. ig. 16 compares the maximum offset (as a percetage of water depth), miimum heave, ad miimum airgap. The maximum offsets at approximately 35 ft (approximately 7% of water depth) show good agreemet amog the coupled, ucoupled, ad model test data. There is also very good agreemet amog all three data sets for the mea offset at 3 ft (approximately 6 % of the water depth). This is expected sice the horizotal resorig force, as illustrated i ig. 9, is approximately equal at these offset rages. There is good agreemet betwee the model test measuremets ad the fully couple model for miimum heave ad miimum airgap. The heave is related maily to setdow. Sice the ucoupled model uder predicts the setdow at this offset, as show i ig. 1, it is expected that the miimum heave is also uder-predicted. Air Gap ad Ruup Aalysis Usig Raked Plots The raked plots are used to examie the airgap. ig. 19 shows a raked plot of the airgaps for the ETLP. The airgaps ad crest heights are raked i ascedig order ad plotted agaist each other. These plots show a high correlatio betwee the airgaps ad the crest heights eve with the oliear crests i the measured waves. Although the maximum crest height is ot achieved i the umerical simulatios, the plot ca be used to extrapolate to the maximum wave crest height ad estimate the air gap. ig. 2 shows a raked plot of the ruup o two colums idicated i the figure. The plot compares the waves calibrated i the wave basi to the measuremets. These plot exhibit more oliear effects of the colum o the wave.

7 Predict-Coupled Predict-Ucoupled deg 25, 2. ru up 1 TTR Top Tesio (KN) 2, 15, 1, 5, ruup (m) ruup 1 ruup 2 air gap ru up Mea Max crest height (m) ig. 2 Raked Plot of Ruup airgap (m) ig. 18 Top Tesioed Riser Tesio simulatio model test crest height (m) ig. 19 Raked Plot of Airgap SUMMARY AND CONCLUSIONS 135-deg air gap ru up 2 ru up 1 This paper compares the results of umerical simulatios to the measuremets from a 1:92 scale model of a ETLP desiged for the Gulf of Mexico i the post-katria eviromet. The umerical simulatios iclude predictios from both ucoupled ad fully coupled models. The followig coclusios are based o the compariso: The ETLP desig meets all criteria for the itact coditio i the 1-Year Hurricae post-katria coditio. I geeral, there is good agreemet betwee the frequecy domai predictios of the RAOs ad the measured resposes. I surge, viscous drag effects are apparet i loger wave periods, ad the frequecy domai teds to over predict the respose. Viscous effects are also apparet i the model test heave data, which shows a ozero respose at the cacellatio poit ad lower respose at the loger periods. There is geerally poor agreemet betwee predictios of the ucoupled model ad the model test measuremets for extreme resposes. This is attributed maily to the tedo ad riser restorig forces at the extreme offsets. Very good agreemet was foud betwee the fully coupled simulatios ad the model test measuremets. Setdow ad cosequetly heave ad airgap i the extreme offsets show poor agreemet i the ucoupled model but very good agreemet betwee the model tests ad predictios from the fullycoupled model. The riser ad tedo tesio predictios by the ucoupled model show poor agreemet with the model test data. Agai is because couplig effects of the offset restorig force are ot icluded i the model. Very good agreemet is foud betwee the fully coupled ad model test measuremets. Raked plots showed a high correlatio betwee wave crest heights ad the airgap measures i the ceter of the model. Wave ruup ad airgap measured at or ear the colums exhibited more o-liear relatioship with the crest heights due to the presece of the colums. ACKNOWLEDGEMENTS The authors wish to thak loatec, LLC for the model test data used i this paper. REERENCES API, 27, Iterim Guidace o Hurricae Coditios i the Gulf of Mexico, Bulleti 2INT-MET. Garrett, D.L., 1982, Dyamic Aalysis of Sleder Rods, Joural Eergy Resources Techology 14, pp Kim, C.H., Kim, M.H., Liu, Y.H., Zhao, C.T., 1994, Time Domai Simulatio of Noliear Respose of a Coupled TLP System, Iteratioal Joural of Offshore ad Polar Egieerig 4, Lee, C.H., 1995, 1995, WAMIT Theory Maual, Departmet of Ocea Egieerig, MIT, MA. Ora, Ceap, 1983, Overall Dyamic Characteristics of Tesio Leg Platforms, Proceedigs of OTC 83, OTC 464, pp Patel, M.H., 1983, "Dyamics of Offshore Structure", Butterworths, pp Ra, Z., Kim, M.H., 1997, Noliear Coupled Resposes of a tethered Spar Platform i Waves, Iteratioal Joural of Offshore ad Polar Egieerig 7, pp