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NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET Institutt for marin teknikk Faggruppe Marine konstruksjoner Page 1 of 16 Contact during the exam: Institutt for marin teknikk, Tyholt Professor Jørgen Amdahl, 95 74 56 63 Professor 2: Sverre Haver 480 72 026 EXAM IN SUBJECT TMR4195 DESIGN OF OFFSHORE STRUCTURES Tuesady 20. May 2008 Time: hrs 09.00 – 13.00 Approved help (D): Results available: Neither printed nor handwritten notes are permitted. Approved, simple calculator is permitted. 11. June 2008 The problem text is on 16 pages and includes 4 problems. NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET Institutt for marin teknikk Faggruppe Marine konstruksjoner Page 2 of 16 PROBLEM 1 An oil company, Student Oil, is to develop the small oil field, Polar Bear, on the Norwegian Continental Shelf. A project team is mobilized for an early phase consideration and you are a member of this team. At the first project meeting, the project manager presents what is the initial company vision for the development of this field. As a part of this he discusses the various phases of the field development chain. During this presentation he is frequently referring to CAPEX, OPEX and Net Present Value. a) At the coffee break you are approached by one of the team members. He has his first day in company today and is rather confused by all standard notations used by the project manager. Can you briefly explain to him what is meant by OPEX, CAPEX and Net Present Value? After the coffee break, the selection of possible structural concepts is discussed. The planned production profile suggests that production will at least go on for 10 years. Water depth in the area is 90m. In view of Student Oil previous experience with a similar field development, the base case platform selection is a jacket as the production rig, while a jack-up will be used for the drilling of wells. At the closing of this session, the project manager requests that the team establish the most important regulations, standards and recommended practises regarding the design of the structures to be used at the field. After an enthusiastic discussion around the table, the structural design group concludes on the following documents; i) “Student Oil Company Standard – Best practise for structural design”, ii) “Petroleum Safety Authority Norway: The Framework Regulations”, iii) “NORSOK N-001 Structural Design”, iv) “Det Norske Veritas: Recommended Practise DNV-RP- C205 Environmental Conditions and Environmental Loads” and v)”Petroleum Safety Authority Norway: The Facilities Regulations”. b) The group did not rank the documents in order of governing power regarding health, safety and environmental issues. Can you perform this ranking? Do you miss any document on their list? c) The meeting is closed with a quiz where the winner will be the owner of Student Oils Polar Bear mug in lead crystal. For the members of the structural design group the quiz includes the following questions: What is the primary difference between Torsethaugen - and JONSWAP spectrum? What do we mean by super-harmonic loading. Can it be a problem for the selected base case concepts – jacket and jack-up? Explain your answer. You are going to calculate the total horizontal load on a vertical bottom-fixed surface piercing vertical column (representing a platform leg). The column has a diameter of 2m.The incoming wave has a wave length of 200m and a wave height of 20m. How would you in principle calculate the load on the column? Assume that the wave is a sinusoidal wave, and show by drawing the wave profile relative to the column when the horizontal load on it attains its maximum. For fatigue, loads of lower waves are of concern. Show the wave profile relative to the column NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET Institutt for marin teknikk Faggruppe Marine konstruksjoner Page 3 of 16 when the horizontal load is at its maximum when the wave height is 2m and the wave length is the same. PROBLEM 2 The jacket to be used will be designed particularly for the Polar Bear Field. You are member of the follow-up team of the early phase design of the jacket. A four legged jacked structure with a deck weight of 8000 tons is found to fulfil the production requirements for the field. The jacket with some characteristic length measures are shown in Fig. 2.1. The diameter of the platform legs varies from 4m at the bottom to 2m at the deck level. MSL denotes the mean sea level. 20m 23m MSL 90m 40m Fig. 2.1 An eigenvalue analysis shows that the largest natural period is 1.4s. A summary of the metocean design conditions for the Polar Bear Oil Field is given at the end of the text. a) Select the method you will recommend to use for calculating the 10-2 – annual probability wave induced response for the jacket. Give the reasons for your recommendation. Specify the wave height and the wave period characteristics you will use in combination with your selected method. Which wind speed and current speed will you use for design? Current induced speed is much smaller than the wave induced speed. In spite of this it is important to include it for calculation of design loads – why? An available Student Oil jacket design will when used for 90m water depth have an airgap (distance form mean sea level (MSL) to underside deck of 23m. An important part of the jacket design is to ensure that the platform shall have a sufficient airgap to avoid a wave-deck impact in combination with a 10-4 annual probability crest height. The required airgap level can be found from the Metocean Design Report, Table 6. It is seen NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET Institutt for marin teknikk Faggruppe Marine konstruksjoner Page 4 of 16 that the 10-4 – annual probability required airgap is 23.5m, i.e. slightly higher than the airgap of the available jacket design. The project manager decides that the team shall predict their own estimate for the 10-4 – annual probability crest height in order to verify whether or not the standard jacket can be used unchanged. From the metocean consultant used by Student Oil a verified long term distribution of the 3-hour maximum crest height at Polar Bear Field is received: c1.235 1.7935 FC3 h (c) exp exp 2.6015 (2.1) b) Explain to the rest of the team what is meant by a long term distribution of 3-hour maximum crest height by defining the short term variability and the long term variability and showing how they can be combined. You can assume that a short term sea state is characterized by the significant wave height, Hs, and the spectral peak period, Tp. c) Use the long term distribution given in (2.1) and estimate the crest height corresponding to an annual exceedance probability of 10-4. Use the storm surge given in Table 6 of the Metocean Report, add an extra meter to account for uncertainties related to water depth measurements, reservoir subsidence and possible climate change and recommend if the platform airgap of 23m needs to be raised. NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET Institutt for marin teknikk Faggruppe Marine konstruksjoner Page 5 of 16 PROBLEM 3 The jack-up to be used for drilling at the Polar Bear Field will be hired for a period of 3 years. As a member of the design team you are asked to be involved in specifying how Student Oil can ensure that the hired jack-up fulfils standard rules and regulations for the Norwegian Continental Shelf. The philosophy of Student Oil is to use standard Norsok design schemes and not the Maritime Legislation that possibly could have been an alternative here. In his bid for the job, the rig owner has specified that the largest natural period for the jack-up at this water depth is 5.5s. In his documents you find that he has used a design wave method for calculating the characteristic design responses in the platform when it is operating at the Polar Bear Field. He has used a Stoke 5th order profile for 10-2 – annual wave height (from the Metocean Design Data report for Polar Bear Field) and has determined a dynamic amplification factor in an approximate way by modelling the jack-up as a single degree of freedom system. He finds that the 10-2 – annual probability responses in the platform are typically 5-10% lower than the characteristic values against which the platform is originally designed. Therefore he concludes that the jack-up can be used for the present operation at the Polar Bear Field. No assessment of 10-4 conditions is made. a) You do not agree with the rig owners recommendations – at least not without further verifications? Why not? b) You recommend that the environmental contour method together with time domain analyses of the structural behaviour should be used for estimating 10-2 – annual probability responses. You refer the rig owner to Fig. 1 in the Metocean Design Data report. The rig owner is not familiar with this method. Can you briefly explain the steps he has to perform when using this method for estimating 10-2 – annual probability response? c) When you get the results of the analysis, the estimated extremes are lower than you would have expected in view of his results obtained when using the design wave method. You ask him to explain in detail how the time domain simulations are performed. His answer is: “We start by simulating a 3-hour sea surface elevation using deterministic amplitudes and random phases. Our frequency resolution when writing the sea surface process as a sum of sinuoidals is 0.001Hz . Thereafter the load vector on the structure is determined for each time step of 0.25s and, finally, the equation of motion is solved using a standard step by step integration method. We are identifying the largest value of this 3-hour simulation and we repeat the simulation 10 times with different random seeds. A Gumbel distribution is fitted to the 10 observed 3-hour maxima. Regarding the proper short term characteristic we follow the Student Oil recommendation.” Can you from his answer see possible reasons for the surprisingly low extremes? In your response to his bid, you did also ask him to check the platform against the 10-4 crest height. It turns out that the platform will experience a modest wave-deck impact at the accidental probability level. At 90m depth the rig is at its limit and it is not possible to NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET Institutt for marin teknikk Faggruppe Marine konstruksjoner Page 6 of 16 increase the height of the deck. A careful structural analysis has shown that the rig with acceptable margins can resist the estimated impact load when the impact load is considered as a static load. However, you ask them to estimate the dynamic response. The rig-owner declines against doing this. Arguments being that this will be a very complicated dynamic analysis and there will be very larges uncertainties for example related to the load history and the damping coefficient. d) Knowing that the static deck displacement is 2.5m, can you estimate the maximum dynamic displacement using simple methods? Do you own assumptions when necessary, but explain why you make those assumptions. What is in your view the largest uncertainty? e) After discussing with you subject under c), the rig-owner comes back with updated results. Due to available time schedule, he is still using ten (10) 3-hour simulations for the critical sea state. The Gumbel model used for estimating characteristic loads is fitted to the 10 observed 3-hour extremes. Show how you in principle can estimate the uncertainties in the characteristic load/response value when it is estimated from a Gumbel distribution based on 10 observations. You can assume that the Gumbel model is the true model. NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET Institutt for marin teknikk Faggruppe Marine konstruksjoner Page 7 of 16 PROBLEM 4 60 m Flare tower 40 m CG 60 m Figure 4.1 Semisubmersible platform You shall consider a semisubmersible platform for use in the North Sea, see Figure 4.1. The platform has a displacement of 20,000 tons. It consists of two pontoons, each with two columns at each end supporting the topside structures. The diameter of the columns is 15 m. The distance between the platform pontoons is 60 m. The roll radius of gyration for the platform floating in water is 40 m. The platform has a flare tower of length 60m. The mass of the flare tower can be assumed to have an intensity of 4000 kg/m at the bottom, linearly decreasing to zero at the top. The rig owner has supplied you with the transfer functions shown in Figure 4.2 for the platform in roll and heave. Density of sea water: 1000 kg/m3. Acceleration of gravity: 10 m/s2. NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET Institutt for marin teknikk Faggruppe Marine konstruksjoner Page 8 of 16 Normalized response amplitude Roll Heave 1.0 0.01 1 roll heave roll 0.01 5 10 15 20 25 30 Wave periods [seconds] Figure 4.2. Transfer functions a) Explain what you understand by transfer function. Explain the various crests and troughs of the transfer functions shown in Figure 4.2 and, to the extent possible, perform simple calculations to check that the transfer functions are credible. (This concerns especially the crests and troughs). Introduce any necessary assumptions for these calculations. b) The wave spectrum for the ULS design storm is given in Figure 4.3. Do you consider the platform being fit for use in the area? Explain why. How will you go about to calculate the response spectrum for the platform for the design storm? (Note: no calculations required) NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET Institutt for marin teknikk Faggruppe Marine konstruksjoner Page 9 of 16 S() 0.25 0.5 0.75 1.0 Wave circular frequency [rad/s] Figure 4.3 Wave spectrum for ULS design storm c) The rig owner says that he is going to order a new platform and that he wants to have a design which is more optimized with respect to use in the North Sea with the environmental conditions given above. What kind of design changes would you recommend to be made to the rig? Discuss the implications of the design changes with respect to important design parameters like size, stability etc. Are there any conflicts between the requirements? It is presupposed that the payload capacity of the original platform meets your requirements. d) Extreme simultaneous values of heave and roll accelerations of the platform about the centre of gravity are estimated to be 2 m/s2 and 0.05 rad/s2, respectively, with = 600. (The effect of the accelerations shall be assumed to add). For this case you shall perform a quasi-dynamic analysis of the tower (wind forces are not considered). Calculate and sketch the resultant acceleration field which is relevant for determination of global shear force and bending moment of the tower. e) Calculate and sketch the load distribution corresponding to the acceleration field. Calculate the shear force and bending moment at the tower bottom. f) Use the results from pt.e) and propose a reasonable structural layout and dimensions of the tower at the bottom based on simple calculation models. The flare tower is basically a truss-work system, consisting of circular pipes, both for the chord and NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET Institutt for marin teknikk Faggruppe Marine konstruksjoner Page 10 of 16 brace members. (If you have not arrived at results in pt e) you may assume that the shear force and bending moment are 1.08 MN and 22.8 MNm, respectively g) Describe very briefly some basic structural strength design checks you will have to undertake for the tower bottom. Provided text book information Waves: Wave propagating in positive x-direction: ( x, t ) 0 sin( t kx) Corresponding velocity potential, deep water: ( x, z, t ) Dynamic pressure, deep water: p d ( x, z, t ) g 0 e kz sin( t kx) Horizontal particle velocity: u ( x, z , t ) Circular frequency: Wave number: k Dispersion equation, deep water: 2 gk g 0 e kz cos(t kx) x 2 , T = wave period T 2 , = wave length Dynamics: Equation of motion: mx cx kx f (t ) I c k m(t ) Steady state solution for harmonic load, f(t) = f0 sint: x p (t ) f0 DAF sin( t ) k where DAF 1 2 2 1 2 0 0 2 1/ 2 NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET Institutt for marin teknikk Faggruppe Marine konstruksjoner Page 11 of 16 2 0 arctan 2 1 0 Natural circular frequency: k m 0 Roll radius of gyration of platform floating in water(definition) r4 I 4 A4 M A3 Unit impulse response: h(t ) exp 0 t sin ( d t ) d M t Convolution integral: x(t ) F ( ) h(t ) d 0 Dynamic amplification for impulse type loading: Wave loads: NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET Institutt for marin teknikk Faggruppe Marine konstruksjoner Page 12 of 16 f ( z) cD Morison load: 1 D2 D u | u | c M u 2 4 Wave loading regimes: Drag term dominates Linearizing Drag term ? Mass term dominates Difraction analysis Velocity potential: 6 i d k k 1 Morisons equation Force per unit length 1 f c D d u | u | c M d 2 u 2 4 Response statistics: Response spectrum: s XX ( f ) | H ( f ) | 2 s ( f ) Variance: X2 s XX ( f ) df f Rayleigh distribution: 1 x FX ( x) 1 exp 2 X 1 xn ) Most probable largest maximum out of n maxima: 1 FX ( ~ n 2 NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET Institutt for marin teknikk Faggruppe Marine konstruksjoner Page 13 of 16 Gumbel distribution: x FX ( x) exp exp Weibull distribution: x FX ( x) 1 exp Selected tables from NORSOK N-001 and N-003 N-001 From N-003 NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET Institutt for marin teknikk Faggruppe Marine konstruksjoner Page 14 of 16 Summary from Metocean Design Basis for Polar Bear Oil Field Table 1 Extreme wind speeds (m/s) with 1, 10, 100 and 10000 year return period for different averaging time intervals 10 m above MSL. Return period [years] All year 1 10 100 10000 Table 2 Table 3 10min 1min 32.0 36.0 40.0 46.0 35.4 40.0 44.8 52.0 39.7 45.2 51.0 59.8 The normalized logarithmic design wind profile, u(z,t)/U0 for Uo = 40 m/s. Height (m) 10 20 40 80 150 1h 1h 10min Averaging time 1min 15s 3s 1.00 1.11 1.21 1.32 1.41 1.12 1.22 1.32 1.42 1.50 1.27 1.37 1.45 1.55 1.62 1.37 1.45 1.54 1.63 1.70 1.47 1.56 1.63 1.72 1.78 Marginal omni directional extremes for the significant wave height, H s, and corresponding values for the spectral peak period, T p. Sea state duration: 3 hours. Annual probability of exceedance 0.63 10-1 10-2 10-4 Hs (m) 11.0 13.0 14.9 18.2 Tp (s) 14.2 15.1 16.0 17.5 Extreme sea states 90% range of Tp (s) 12.1 - 16.5 13.1 - 17.3 14.0 - 18.2 15.5 - 19.7 NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET Institutt for marin teknikk Faggruppe Marine konstruksjoner Page 15 of 16 Table 4 Design waves, Stokes' 5th order profile. Annual probability of exceedance) 0.63 10-1 10-2 10-4 Table 5 Height above MSL (m) 12.3 14.6 16.5 21.1 Mean value 12.7 13.6 14.4 15.8 Wave period (s) 90% interval 10.9 11.8 12.6 13.9 14.8 15.6 16.3 17.7 Omni-directional extremes for the 10 minutes mean current speed (cm/s) versus depth for 1-, 10- and 100-years return period. Depth (m) Surface 30 75 3 m above seabed Table 6 Wave height (m) 22.0 25.5 29.0 36.5 1-year return period 106 92 85 66 10-year return period 117 102 98 39 100-year return period 126 110 110 85 Water levels with return periods of 100 and 10000 years. Tidal amplitude (m) Storm surge (m) Height of wave crest (m) Extreme water level above MSL (m) Return period (year) 100 1.0 0.9 17.6 19.5 10 000 0.0 1.1 22.4 23.5 NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET Institutt for marin teknikk Faggruppe Marine konstruksjoner Page 16 of 16 Figure 1 Contour lines in the Hs – Tp plane for annual probabilities of 0.63, 10 -1, 10-2 and 10-4 (Return periods of 1, 10, 100 and 10 000 years). Duration of sea state is 3 hours.