SNAME Transactions, Vol. 91, 1983, pp. 275-305

Conceptual Design Process of a Tension Leg Platform Frank S. F. Chou,1 visitor, Susobhan Ghosh, 2 Member, and Edward W. Huang, 2 Associate Member This paper presents an outline for a conceptual design process of a tension leg platform (TLP). Although a TLP hull is very similar to that of a semisubmersible platform, the two designs differ considerably. Some characteristics of a TLP make it resemble a fixed platform but in other ways it is like a floating structure. For example, the TLP has a very high natural frequency in its vertical plane, which makes it resemble a fixed structure. However, its compliance in the horizontal plane is similar to a moored floating vessel. Furthermore, the TLP concept has many unique design activities and considerations such as tether design, fabrication, mating, and installation methods. The major design considerations at various design stages are also presented in this paper. Basic vessel design requirements together with state-of-the-art analytical methodologies are detailed. An optimization process as the core of evaluating vessel performance is elaborated with a flow chart. Guidelines for the preliminary estimation of a TLP's principal dimensions, weight and other important parameters are also given. With the increasing knowledge of TLP behavior, these guidelines are expected to be modified, but the design philosophy and optimal process should remain valid:

Introduction DURING the late seventies, the concept of a tension leg platform (TLP) began attracting attention as a possible candidate for use in deepwater production. Today, it is considered to be one of the most promising deepwater structures of the offshore industry. For water depths beyond 1500 ft, this concept is especially desirable because of its economical feasibility. The TLP concept is relatively new and possesses many complex and challenging deepwater design features. To design an economically viable and safe TLP requires extensive preengineering work to study various tasks specific to the structure. Once the relative importance of those tasks is established, a detailed conceptual design to optimize the hull configuration is necessary before attempting the final design. This paper will identify the major requirements and stages of a TLP design process and discuss their influence on the design criteria of a conceptual design. They include the owner's specifications, design criteria, deck arrangement, geometry selection, and preliminary structural and fatigue analysis. The geometry selection is carried out first by evaliaating the performance of the vessel on the basis of estimated weight, statical stability, motion responses, tether fatigue life, and preliminary structural and transportation analyses. A parametric study of related parameters, such as displacement, column and pontoon sizes, ballast requirement, payload, tether stiffness, and tether pre-tension, is used to perform the geometric selection. Appropriate constraints required by other tasks (fabrication, installation, towing) have to be incorporated in the parametric study. This paper will describe each of these in detail to convey an understanding of their influence in the design process as a whole. Basic flow charts illustrating various inherent logics will also be discussed. ] President, Frank Chou & Associates, Houston, Tex. z Research project engineers, Brown & Root Inc., Houston, Tex. Presented at the Annual Meeting, New York, N.Y., November9-12, 1988, of THE SOCIETYOF NAVALARCHITECTSAND MARINEENGINEERS. 275

The analytical work required to evaluate the performance of the TLP in the conceptual design stage will be detailed. Related analytical methods for stability calculation, motion analysis, computation of hydrodynamic loading, structural analysis, and tether fatigue life estimation will also be explained. The paper will discuss how the fabrication facilities, transportation method, installation procedures, etc,, influence the geometry selection in .the conceptual design process. It is the authors' opinion that a well-organized TLP conceptual design in the early design stages can save millions in the final design and installation of a TLP. T L P description As shown in Fig. 1, a tension leg platform resembles a semisubmersible platform except in its mooring system and foundation structure. A semisubmersible is usually moored by the conventional catenary system which offers restoring forces in the horizontal plane, but the stiffness of this system in the vertical plane is negligible. The mooring lines for a TLP are usually vertical and are often referred to as "tethers" (or tendons). These tethers are pretensioned by the excess buoyancy provided in the vessel and have such high stiffness in the vertical plane that the natural periods of heave, roll and pitch are limited to 2 to 4 sec. The restoring forces in the horizontal plane for a TLP are provided by the horizontal component of pretension in tethers in the offset position. These components are small, and thus the natural periods for sway, surge and yaw are in the order of 100 sec. Figure 2compares the natural periods of a TLP with those of a semisubmersible. It may be noticed here that a catenary-moored semisubmersible responds at periods longer than the dominant wave period of a typical design sea state, whereas the pitch, roll and heave natural periods of a TLP are much less than the dominant wave period. Thus, a good semisubmersible design attempts to keep heave and pitch periods as long as possible, whereas a good TLP design endeavors to keep them on the shorter side. A TLP consists bas!cally of the following components:

• Deck s t r u c t u r e - - T h e deck structure for a drilling and production TLP is similar to that of a conventional drilling and production platform. Most of the production platforms are fixed and their decks do not have to support the production riser load. But in the case of a TLP, its deck has to support all the riser tensioners and load. The deck area mainly provides the space for accommodations and functional requirements, including a working area, control room, processing facilities, drilling derrick, heating/ventilation/air-conditioning (HVAC), mud pump, pipe rack, cranes, flare boom, and helideck. The deck can be laid out in configurations such as rectangular, square, triangular, pentagonal, or hexagonal. Structurally and

functionally, a TLP deck structure is similar to that of any conventional floating platform. • Hull s t r u c t u r e - - T h e term "hull structure" is used in this paper to refer to the structure supporting the deck structure and subjecting the tether to tension by its excess buoyancy. The two most publicized hull configurations are structures consisting of (i) columns and pontoons and (ii) bottle and truss. The column and pontoon type of hull structures may also require some bracings to provide adequate structural strength. The cross section of the pontoons and columns may be circular, rectangular or square. The space within the column is used for elevators, stairwells, the tether holding system, and inspection and

,Nomenclature A = total tether cross-seciional area A - = reflected wave a m p l i t u d e Ac = projected area against current At = area of the i-th w i n d a g e Atk = c o m p o n e n t of a d d e d mass coefficient Awp = w a t e r p l a n e area Axx(w) = added mass coefficient for surge (sway) A=z = a d d e d mass c o e f f i c i e n t for heave a = wave a m p l i t u d e Btk = c o m p o n e n t of d a m p i n g force coefficient Co = d r a g coefficient Ct = frictional d r a g coefficient Cki = matrix of restoring force coefficient C, = shape factor C,h = shield factor dlw = w i d t h of the leeward m e m b e r dww = w i d t h of the windward member D = water depth /9 = d i s p l a c e m e n t vector Dki = total viscous d a m p i n g matrix E = modulus of elasticity of tether material f(~0~) = spreading function F1/a = significant tether tension F1/m = average l/m highest tension Fa.,g = average a m p l i t u d e tension Fc = current force Fj = c o m p o n e n t of complex amplitude of wave exciting force F ~ = slow varying drift force F m a r g i n = m a r g i n of uncertainty in tether tension Fmax = m a x i m u m tether tension F m i n = m i n i m u m tether tension F v i b r a t i o n = tether axial d y n a m i c load F~ = wind force Fy = m e a n drift force of a regular wave train g = acceleration of gravity hw = wave height H = reference height for wind velocity m e a s u r e m e n t Htt~ = c o m p o n e n t of hydrostatic restoring coefficient Kki = compohent of retarded d a m p i n g coefficient

276

Kzz = AE/L, axial stiffness of tether system as a whole L = length of t e t h e r / c a b l e m e m bers L~k = c o m p o n e n t tensions in i t h tether mkj = c o m p o n e n t of impulsive a d d e d mass Mlk = c o m p o n e n t of inertia matrix M . = n t h m o m e n t of wave or response spectral density functions M]/a = significant value f o r ' w a v e or motion fi = normal vector of a s u b m e r g e d surface 1In = an exponent for wind profile assumed to be between 1/13 and 1/7 n(~q) = n u m b e r of stress cycles at a stress range ~rt N(a~) = a v e r a g e n u m b e r of stress cycles to failure at a stress range ai P = pretension at m i d d l e of tether /3 = fluid pressure Po = position of/5 on body surface Pq in phase part Of second-order force transfer function Pr = riser tension 5 Pt = pretension at tether bottom P(o) = probability density function of stress range Qq = out-of-phase part of secondorder force transfer function = position vector of tether top /~ = position vector of tether anchoring point Sc = s u b m e r g e d body surface SM (w) = spectral density function of wave or motion Ss (w) = one-dimensional sea spectrum Ss(w, #,~) = two-dimensional sea spectrum Sz(w) = spectral density function of linear motion So(w) = spectral density function of angular motion T = t i m e duration of r a n d o m stress process or wave period Tavg = a v e r a g e period for stress variation in a r a n d o m process ATe = tether elongation Tlt~ = c o m p o n e n t of tether m e m b e r stiffness

Tx~ = surge natural period Tyy = sway natural period Tzz = heave natural period VI = pontoon d i s p l a c e m e n t (volumetric) V2 = c o l u m n d i s p l a c e m e n t (volumetric) V = current velocity VH = wind velocity at some reference height above m e a n w a t e r level V~ = wind velocity at centrod of A~ V~ = wind velocity at height z above m e a n water level Wtether = tether weight in air Xh = allowable horizontal excursion xk = wave force or m o m e n t in kth mode XG, YG, ZG = coordinate of center of gravity XT, YT, ZT = coordinate of tether top X.o = stress response a m p l i t u d e ratio Za = linear motion a m p l i t u d e . cr = stress range o"a = stress a m p l i t u d e for nonzero stress O'o = s t r e s s a m p l i t u d e for zero m e a n stress O'm = m e a n stress level o"n = ultimate stress ay = yield stress p = mass density w = circular f r e q u e n c y A = displacement, in salt water, long tons 0 = angular displacement amplitude or vector 01/3 = significant angular motion r / = wave elevation = vertical motion of a point on body E = a spectral b a n d w i d t h p a r a m eter v = wave n u m b e r # = wave h e a d i n g

Conceptual Design Process of a Tension Leg Platform

Metric Conversion Table

1 ft = 0.3048 m 1 lb/ft a 1 ksi 1 short ton 1 nautical mile

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16.018 k g / m a 6.90 M P a 0.9 m e t r i c ton 1.852 k m

ballast, if necessary. The compartments within the pontoon may be used for ballasting and some machinery, pumps and fittings, as required. The bottle-and-truss type of hull uses a footing type of column and truss to provide the required buoyancy. These )ECK footing-type columns are usually of circular cross section and are connected to each other by small-sized bracings to provide needed structural strength. " • Tether and riser s y s t e m - - T h e tether system consists of tether members, tether connectors, and tether handling machinery. The tether members may be made of wire rope, and solid or hollow regular shape tubes. The system may require high-strength steel or other high-strength material. A wire rope makes it possible to have a single unbroken member from surface to sea bed with a multitude of paths and reduced risk of sudden failure. The tubular members, when used as tether, are required to be connected at approximate intervals of 40 ft for the entire tether length. In this case, the tether members are required to be rigidly connected. A few of the various ways of connecting are welding, threading, bolting flanges, and clamping flanges. Tubular tether members are easier to handle ILE and probably lighter than wire rope. The riser system can be described as the umbilical cord or" extension of the well bore to the floating platform during drilling or production. The principal components Of a marine riser system are the riser pipe, bottom ball joint and slip joint. The riser pipe extends from the ball joint at the top of the blowout preventer (BOP stack) to the slip joint barrel beneath the platform. The slip joint allows the pipe to extend during the vessel excursion in the horizontal and vertical plane. The Fig. 1 TLP production platform additional components of a riser system are guidelines, choke-and-kill lines, joints, connectors, separators, buoyancy devices, and tensioner system and the emergency disconnect arrangement for the weather deck and the main deck of a TLP system. The choke-and-kill lines allow the circulation of is shown in Fig. 4. drilling mud if and when the BOP is closed. An illustrative The primary consideration for laying out a deck arrangement sketch of a drilling riser is shown in Fig. 8. is functional efficiency. A TLP is quite weight-sensitive by • Foundation structure--The foundation structure is nature and, thus, it is desirable to keep the required ballast to needed to keep the platform in place. The structure will act a minimum in order to provide a lower-cost vessel. Due conas an anchorage for the tether system and may also include the sideration is given in laying out various items on the deck to drilling template. A foundation structure for a TLP will ex, keep the center of gravity of the deck as close as possible to the perience cyclic tens!on loads from the tethers. The structure geometric center. may be constructed as a single piece or multipiece, which may depend on the installation method. The structure can be anPrincipal dimensions and p l a t f o r m chored to the sea bed by either tension piles or gravity ancharacteristics chors. The principal dimensions of a TLp are given by the physical size of the deck structure, the hull structure consisting of colGeneral arrangement The space allocation and access for a layout and general ar- umns and pontoons, and the tether sizes or cross-sectional area. rangement of any platform are influenced by particular construction goals such as operational objective, desired level of performance, necessary equipment and individual preference. A TLP deck structure will usually consist of two functional decks to accommodate the operational equipment and provide spaces for crew members and utilities. The upper deck, which is exposed to the weather, is often referred to as the weather deck. This deck usually provides space for the following: drilling derrick, drilling generator package, water and fuel tank, mud pump package, riser pipe rack, drill pipe rack, dry storage package, surge tank, waste-heat recovery, control room, cranes, flare boom, heliport and perhaps some living quarters. The other deck is called the main deck--sometimes called the second or quarters deck. This deck accommodates the various pieces of processing equipment, utilities, drilling equipment and numerous miscellaneous mechanical and electrical systems. Often a mezzanine deck is provided for additional living quarters and storage. This deck may not extend over the active main deck area. A typical deck

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Conceptual Design Process of a Tension Leg Platform

277

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Fig. 3 Drillingriser The dimensions of the members of thehull structure, the de- floating vessel [1].3 A well-planned parametric study should sired draft, and the displacement of the vessel are all interre- deliver sets of principal dimensions which should form the basis lated. The column should be high enough to avoid wave for selecting the final vessel geometries. slamming of the deck in a storm condition. For a semisubAn optimal design requires logical steps to select geometries mersible, the American Bureau of Shipping (ABS) recommends to meet the basic functional requirement for safety and cost a n air gap of (0.60 hw + 5.00) ft. For a TLP, it is appropriate effectiveness. This is accomplished by developing a suitable to add the highest astronomical tide and set down of the plat- iteration scheme of major tasks which include specifying basic form at its extreme horizontal excursion in a design storm requirements or design criteria, general arrangement, esticondition. The value of setdown depends mainly on the water mating displacement, selecting principal dimensions, and an depth, tether characteristics and pretension in tethers, and this evaluation method for screening candidates. A schematic flow value may be estimated as 0.2 percent of water depth. • chart of the conceptual design process is presented in Fig. 5. Major platform characteristics such as column spacing, disIn the design of ships, barges or other conventional floating placement, draft, tether characteristics, center of gravity, mass vessels, the displacement, principal dimensions, propulsion moment of inertia, and tether pretension have a direct influence system, etc., are estimated on the basis of parent vessels. In the on the vessel's performance and its ability to satisfy the design case of a TLP design, there is no such data base. Consequently, criteria. For example, the tether size depends on the preten- a wider range of candidates has to be used in the evaluation and sion, wind and current forces, and the allowable maximum screening process. The evaluation of a particular TLP is done horizontal excursion. The tether stiffness, together with hy- on the basis of its performance which, in turn, is measured by drodynamic characteristics of the underwater hull geometry, how well it satisfies the design requirements. displacement, center of gravity and radii of gyration, directly To determine the vessel's performance, advanced analytical influences the motion response of the platform. technology is needed. The needed analyses in a conceptual Thus, for proper accounting of platform characteristics, an design will include the stability evaluation, vessel motion reelaborate system is necessary to maintain a detailed record of sponse determination, preliminary structural analysis, the exweight, location of center of gravity and the shape of each item treme tether loads estimation and tether fatigue life analysis. of the TLP. This record-keeping provides an accurate calcu- In addition, considerations of fabrication ease, transportation lation of the center of gravity, mass moment of inertia and radii method and installation schemes have to be taken into account of gyration of the platform for any specified loading condition. as necessary criteria in evaluating a vessel's performance. These mass properties are necessary for analyses related to stability, motion responses of the vessel, tether cyclic loading, Parametric study stresses on tethers, and tether fatigue life. It is a common practice for naval architects to carry out a parametric study during the design process of a floating vessel. Conceptual design approach This will provide an economic and safe structural configuration. The approach for a TLP conceptual design outlined in this The importance of a parametric study for a new concept like paper recommends an elaborate parametric study as the core the TLP is even more significant than that of other conventional of the design process. This approach does not deviate very types of vessels. The design of an economic and safe TLP demuch from the standard procedures followed by naval archi- mands a thorough understanding of the effect of various patects in selecting an optimal geometric configuration for a 3 Numbers in brackets designate References at end of paper. 278

Conceptual Design Process of a Tension Leg Platform

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rameters on the performance of that structure. Combinations of parameters may satisfy one or more of these requisites; however, as these requisites are affected by a large number of variables, it is essential that the sensitivities of the various parameters and their interaction be well understood before any optimal design is attempted. The important physical parameters which have direct and indirect effects on the performance of a TLP are the vessel displacement, underwater configurations or shapes, tether characteristics and pretensions, etc. Other items which have influence on these physical parameters will be introduced later in the related discussion. Since the performance of the vessel will be measured by the degree to which it satisfies the design requirement, a parametric study to select an optimal geometrical configuration for a TLP should be planned by incorporating consideration of each important physical parameter, design criterion, performance evaluation procedure and screening method. The success of this method will, however, depend partly on the selected logical sequence of various related activities. The flow chart shown in Fig. 6 presents a recommended procedure for all the important activities. The parametric study starts with the determination of processing equipment, laying it out, and preparing a weight summary. Other major activities to follow are • establishing the design requirements and criteria, • estimating displacements, • selecting the range of principal dimensions, and • evaluating the process and the screening method. The remainder of this section is devoted to a step-by-step explanation of each of the aforementioned activities. Design r e q u i r e m e n t s and criteria The main objective in designing a TLP is to satisfy the design requirements for its function, performance, and necessary accommodations and, at the same time, to meet other constraints imposed by safety considerations. Thus, the design requirement of a production platform usually includes the production rate of oil and/or gas, water depth, environmental data and other constraints imposed by factors such as fabrication facilities, transportation route, and installation method. Based on the production rate, the various types of processing equipment should be determined and laid out on the basis of functional efficiency. The other equipment and utilities, as required by the accommodation and safety considerations of the vessel and the crew members, should be arranged to obtain an optimal deck size. To achieve the performance requirements, the design process usually specifies design criteria which are based on judgment, experience, results of the analytical study and experimental work. For instance, the important considerations for a TLP design are the allowable maximum horizontal excursion, natural periods of pitch, roll and heave, required static stability, the effect of tether dynamic loading, and the fatigue life of tether 280

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and structural joints. The horizontal excursion is limited somewhat by the consideration of production and the practical difficulty of designing the bottom flexible joint. The natural period of the vessel in the vertical plane needs to be low so that these natural periods can be away from the dominant wave energy of the sea state. Lower natural periods help-in minimizing stress amplitude but increase the number of vibration cycles. The fatigue life of structural members and tethers, particularly for a TLP, depends on the static stress level, and the dynamic stress amplitude with its associated number of cycles. Another important consideration is the assurance that tethers will not slacken under any circumstances. This consideration is vital to the buckling of the tether and the incapability of tether connectors to withstand compressive loading. The stability requirements ensure adequate stability of the vessel during transportation, installation and offshore mating, if necessary. Since the stability criteria related specifically for a TLP are still insufficient, it may be a good exercise to check the redundancy of tethers. This will ensure that the breaking of one or more tethers does not jeopardize the safety and integrity of the vessel. Another important consideration is the safety of a TLP in the event of an oil well blowout. In such a case the oil and water rises, causing the formation of plumes which may result in the loss of TLP buoyancy and cause the tethers to go slack. Other criteria imposed by physical limitations of the fabrication facilities, transportation route and sometimes by the proposed installation scheme are also important. Since the TLP structure is huge, factors such as the available fabrication facilities, scheduling, cost, and transportation routes may prove a single-piece fabrication unfeasible, and two-piece fabrications with offshore mating may be necessary. The shallowness of waterways in the transportation route may also necessitate fabricating the deck and hull in two pieces. Displacement estimation Before any attempt to select the geometry and size of the TLP, the displacement of the vessel has to be estimated. The vessel must have adequate displacement to support weights for the following items: (a) structural steel weight of deck and hull, (b) submerged tether weight, (c) pretension in the tether, (d) riser tension, (e) payload, and 0c) minimum ballast requirement. Since the TLP concept is relatively new, very few data for estimating displacement are presently available. To help start the estimation process, some guidelines for various major weight items will be discussed next with empirical formulas. (a) Structural weight estimation--The TLP structure consists of three major components--namely, deck, columns

Conceptual Design Process of a Tension Leg Platform

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and pontoons. Since the deck structure is very similar to that of a standard production platform, it may be estimated from past experience. On the basis of previous deck design experience, .it was found that a typical TLP deck weight for a production platform may be approximated as 8.00 lb/ft 3 of deck volume. The TLP hull structure consists of columns and pontoons which may be idealized as stiffened cylindrical shells subjected to an external pressure load. The external pressure load varies with wave height and draft, and it can be divided into two major components: (i) hydrostatic pressure varying with water depth, and (ii) hydrodynamic pressure due to the highly oscillatory water particles flowing around the member. Hydrostatic pressure in a wave flow can be computed by means of wave theory such as Stokes's fifth-order wave theory. Hydrodynamic pressure that accounts for fluid movement around a member can be computed by wave diffraction theory. However, limited comparison shows that the pressure due to

fluid movement is secondary to the hydrostatic pressure which is calculated based on the wave profile. For preliminary weight estimation in a TLP conceptual design, the columns and pontoons may be treated as a pressure vessel. With this assumption, cylindrical stiffened shells of various diameters (20 to 80 ft) at ambient pressures, due to drafts (ranging from 40 to 200 ft) and a design wave height of 100 ft, were analyzed to obtain the weight in short tons (ST) for each 40-ft-high segment of columns. Typical weights of these segments, obtained by using BS 5500 [30], are presented in Table 1, which also gives weight per unit length of column segments exposed in air. The external pressure head of a column increases as the water becomes deeper, as does its weight per unit length. Thus, for column weight, the submerged portion of the column should be divided into 40-ft-high segments as suggested in Table 1. (b) Tether weight--Tether weight is directly proportional to its cross-sectional area A, length L, and the specific weight

Conceptual Design Process of a Tension Leg Platform

281

Table 1

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of the tether material. Tether cross-sectional area is implicitly determined by the criteria for vessel natural periods, level of prestress, stress variation and the fatigue life. It can be estimated only through elaborate iteration procedures which require evaluation of motion responses and tether fatigue life. Tethers are initially pretensioned by the excess buoyancy provided in the column and pontoon. At the top, tether members are expected to support the additional buoyant tether weight. The initial or prestress of tethers should be high enough to avoid the tether being slack under any circumstances; at the same time, it must be low enough to provide adequate tether fatigue life. As a rule of thumb, the initial stress should be in the range of 20 ksi for steel tethers. (c) Tether pretension--When a TLP is subjected to environmental loading of wave, wind and current, it moves horizontally and oscillates about an offset position. The horizontal offset is contributed by the static wind, current and wave drift forces; and the restoring force in the system is provided by the tether pretension. The maximum offset includes the horizontal static offset plus the maximum dynamic response amplitude in the horizontal plane. The static offset is due mainly to wind; thus, the wind force estimation should be done carefully. Consideration should be given to minimize the wind force by proper arrangement of wind-exposed objects. The dynamic response amplitude is in the order of 20 to 30 percent of the horizontal static offset. The stiffness of the system in the horizontal plane is provided by the tether pretension. The tether pretension increases with water depth and can be reasonably estimated as Pt = 1.20 (Fw + Fc) * D/Xh

(1)

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Xh = allowable horizontal excursion (d) Riser tension--Risers are kept in constant tension by the tensioner system below the deck. The riser load Rr varies with water depth and may be estimated as Rr = 700 + 1.25 * D

(2)

where riser load is in short tons. (e) Payload--The word payload is frequently used to include certain items which vary from project to project. In this • paper the term payload will include weights of various pieces of equipment for processing, drilling, mechanical and electrical activities, utilities, accommodations, and other miscellaneous items. The payload is usually in the range of 6000 to 15 000 ST, and it is significant for the estimation of total displacement. The weight of utilities and accommodations may be estimated on the basis of existing conventional platforms. The processing equipment will depend on the rate of production, method of process and the associated equipment. It is preferable, if 282

332.4 383.2 475.6 564.8 602.4

425.2 535.6 657.6 740.8 845.2

70 10.1

80 12.9

578.4 701.4 851.4 1014.6 1114.4

731.6 867.2 1045.2 1288.4 1383.6

possible, to estimate the weight for each piece of equipment rather than estimating a total weight. (f) Ballast requirement--In the early stage of the design, it is difficult to estimate the ballast. A first estimate for ballast as 3 to 5 percent of displacement is a good start in a parametric study.

Selecting range of principal dimensions To perform a parametric study, the principal dimensions of the vessel must be selected to cover - - r a n g e of displacement, --various configurations of interest, --different geometrical shapes of hull structure, and - - a desired range of ratio of column displacement (V2) to pontoon displacement (V1). The vessel dimensions will be required to satisfy the stability criteria specified in the design requirement. Thus, while evaluating the principal dimensions, a crude check of stability is recommended. Since displacement of the vessel is estimated based on the weights of various items, it may be expected that the estimated displacement will have some error. To incorporate the sensitivity of displacement on the performance of the vessel, a range of displacement given by an estimated displacement of 4-10 percent should be considered in the selection of principal dimensions. A TLP may consist of various configurations--for instance, rectangular, triangular, pentagonal, hexagonal toroidal hull or rectangular twin hull. The other alternative configuration could be a bottle-truss type. In this configuration, the pontoons are eliminated by providing bottle-shaped columns which are connected to each other by a truss-type structure to provide adequate structural strength. The authors prefer the square twin-hull configuration for its simplicity and ease of fabrication; however, there is no convincing reason for not considering other configurations. Thus, preparation of sets of principal dimensions may include a broad range of configurations for sensitivity study. However, factors such as fabrication ease or redundancy of columns and tethers, may prove some of the configurations unfeasible in the very early stages of the study. Considering the background of recent accidents of the semisubmersibles Alexander Kielland and Ocean Ranger, Norway's Maritime Directorate is trying to introduce new safety standards. These, if enforced, will require every semisubmersible to remain afloat with whole or major parts of one column missing by providing reserve buoyancy in the deck structure. To cope with this requirement, vessels with a larger number of columns may have to be chosen and, thus, a triangular hull may not be suitable. The underwater geometry directly influences the hydrodynamic loading on the vessel. Therefore, to study the effect of different shapes on the performance of the vessel, the principal dimensions selected for the parametric study should include hull structures of different shapes, including at least the rectangular and circular cross section. • It may be pointed out

Conceptual Design Process of a Tension Leg Platform

that a hull structure with rectangular columns may have advantages as far as fabrication ease is concerned. The authors found that on a hydrodynamic basis the choice between a circular column with a circular pontoon and a circular column with a rectangular pontoon is a close one. Nevertheless, the hull with a Circular column and a rectangular pontoon may be preferred for other considerations such as mooring and towing. References [2] and [3] indicate that by proper choice of ratio column displacement (V2) to pontoon displacement (VI), the frequency of zero heave excitation force can be shifted somewhat and, consequently, the motion responses Of a semisubmersible can beoptimized. A similar phenomenon is expected for a tension leg platform, so, in selecting the sets of principal dimensi9ns, a range of (Vz/V1) ratios probably in the range of 2 to 4 should be included.

Evaluation and the screening process These two acti~,ities are not separable and are very much interrelated. It is preferable to do the screening of the set of principal dimensions in several stages. In Fig. 6, four rounds of the sereening process are suggested; screening is based on the evaluation of the performance. The evaluation methods gradually become more sophisticated as the screening process continues. -In the first round of screening, the evaluation is based on the estimated natural periods of heave, pitch and roll, the estimated horizigntal excursion, and a rough stability check. During this first round, simplified formulas for natural periods, related to motion analysis, may be applied using empirical hydrodynamic coeffi~ierits. The natural periods of heave and sway can be written in the simplified form as 27r { [ ( 1

HEAVE:

4- A=z) * A + 0.:33 Wtethe,]

SURGE: (SWAY)

Txx(vv) =

(3) 27r , / [ ( 1

+ Axx(y!/)) * A + 0.2(3 • Wtether]

Where Axx(v z) = = L = £ =

%

Awo = g = Wtether =

p = A=

surge (sway, heave) added mass coefficients tether stiffners in heave mode tether length pretension at middle of tether Pt + 0.5 * (submerged tether weight) waterplane area acceleration due to gravity tether weight in air density of water platform displacement

The vessel excursion in the horizontal plane is due to the pseudo-static forces of wind, current and the mean wave drifting forces; in the region of the Gulf 6f Mexico, wind forces contribute the most. The method for calculating wind and current forces is suggested later in the section on stability analysis. The horizontal excursion of the vessel is resisted mainly by the tether pretension. The excursion can be determined b~, solving the force equilibrium equation of the system consisting of wind force, current force and the component of pretension in the appropriate direction.. The excursion due to waves.must be determined by detailed analysis; however, (1/2 × design wave height) may be used as the first estimate. If the given set of principal dimensions passes the test of natural pe-

riods and maximum allowable horizontal excursion, a stability test is required for the free floating vessel during transportation and installation. At the end of first round of screening, 12 sets of principal dimensions should be selected to cover a range of displacement and V2/V1 ratios, that is, the upper, middle and lower displacements, together with four sets of V2/V1 ratios for each displacement. In the second round of screening, the evaluation is based on the results of the motion response amplitude operator (RAO) during transportation, tether RAO, and significant tether loads in a design sea state. During transportation, the ' heave natural period should be kept away from the wave period having dominant energy for the worst storm condition expected. It may be necessary to tow in the column to increase the heave period of the vessel itself. The transportation route and duration may affect the decision in the geometrical selection. Tether RAO gives a general indication of the tether load variations at different wave periods (see Fig. 7), while the significant tether loads indicate the maximum and minimum tether load for a design sea state. In general, the maximum tether load is the major decision factor in this round of screening and, for a given displacement, it is a function of the V2/Vt ratio as shown in Fig. 8. With a proper range of Vz/V1 ratio, the optimal ratio for the minimum tether load can be interpreted directly from the curve. At the end of round two, the optimal V2/VI ratio for the three given displacements should be established, and a minor adjustment of the geometrical configuration will be needed for the new optimal V2/V1 ratio. The third round of screening is based on the preliminary tether fatigue life estimate. The tether fatigue life is a function of mean stress level; stress variation and its corresponding number of cycles, statistical wave data, stress concentration factor and the material S-N curve. At the end of this stage of screening, three to four sets of geometry may be selected for the final round of screening. The time history of responses for the ve~el and the tether loading of these three to four candidate principal dimensions should then be determined by a nonlinear time-domain solution to check the maximum horizontal excursion and the maximum and minimum loading of tethers. The maximum loadihg on the tether indicates the maximum stresses to which the tethers will be subjected, while the minim u m stress, if negative, indicates that the tethers are in compression-that is, they are slack. The final geometrical configuration for preliminary design will be selected from among these candidates on the basis of minimum horizontal excursion, tethers not slackening, fabrication ease and cost estimate.

Analytical works The evaluation and the screening process in the conceptual design cycle will require identifying the evaluation basis. The evaluation basis is also dependent on the design criteria determined in the design premise. The evaluation process in a TLP conceptual design is carried out to check mainly the following items: • adequate stability during tow, • maximum tether stress, • minimum tether stress, check for tether slack (that is, compression), • tether fatigue life, • horizontal excursion in design storm condition, and • primary structural strength. To check these items, the required analyses are a stability analysis for intact and damaged conditions, motion response in frequency domain and time domain; a comprehensive tether fatigue life analysis; and a preliminary structural analysis. The analytical description of these analyses follow.

Conceptual Design Process of a Tension Leg Platform

283

J TETHER TRANSFER

M

X

FUNCTION

SURGE.TRANSFER

FUNCTION

COLUMN / PONTOON VOLUME RATIO = 1.0

0

COLUMN / P O N T O O N V O L U M E RATIO':" 1.0

COLUMN / PONTOON VOLUME RATIO = 2.5

A

COLUMN / P O N T O O N

VOLUME R A T I ( ~ = 2.5

COLUMN / P O N T O O N V O L U M E RATIO - - 4 . 0

X

COLUMN / P o N T o o N

VOLUME RATIO = 4 . 0

COLUMN / P O N T O O N VOLUME RATIO :

9

COLUMN / P O N T O O N VOLUME RAI"IO = E.6

5.6

1.50

150.00

1.20

120.00 u.

a. :E

f

90.00

0.00

:E


r~

4,000.

~ ~0

3.000.

v

Z w

l-

Z:

DECK HEIGHT FACILITy WEIGHT

2.000-

TLP DISPLACEMENT

DECK CLEARANCE STRUCTURE VOLUMETRIC WEIGHT

1-

DRAFT COLUMr~I/PONTOON VOLUME RATIO 1.000 25,000

i

I

30.000

35.000

TLP DISPLACEMENT

Fig. 8 ( a )

IN S H O R T

40.000

TONS

Tother load variation with displacement

5,000 z >. CI

£1- oI-v

Z

4.500-

0

4.000-

FIXED PARAMETER:

VARIED PARAMETER:

DECK HEIGHT FACILITY WEIGHT

COLUMN/PONTOON VO~ RATIO

DECK CLE;~,'~J~NCE S'~RIJC'P,J~E VOLUMETRIC WEIGHT DRAFT

w 1w 1-

TLP DISPLACEMENT 3,500

I

I

|

|

I

1.0

2.0

3.0

4~

5.0

COLUMN/PONTOON

Fig. 8 ( b )

284

20.

FULL SCALE WAVE PERIOD IN SECONDS,

VOLUME

RATIO

Tothor load variation with Ve/V1 ratio

Conceptual Design Process of a Tension Leg Platform

.6.0

25.

TEMPORARY BRACINGS

Stability analysis

A TLP can be considered as a semisubmersible until the tethers are hooked into place. Thus, the stability evaluation of a TLP for various conditions can be carried out as for a semisubmersible. The loading conditions critical to the stability evaluation may, however, depend on the methods selected for fabrication and towing. Figure 9 presents a conceptual scenari° °f a TLP installati°n" This sequence °f events assumes that the fabrication will be done in two pieces and mated offshore before the tethers are connected to the vessel. Since the mating is expected to be carried out in a sheltered location, criteria for stability evaluation during mating, with the prior consent of regulatory agencies, may be relaxed from those of a floating semisubmersible vessel. During tow-out the vessel is expected to be exposed to the environment for a considerably longer time than during any other operation. S0, as far as t0w-out' is concerned, the criteria for adequate stability, which are set by the regulatory agencies, should be used. The following analyses should be adequate for stability evaluation.

F ~

HULL TRANSPORT

l

=-_~

!

!

II

b. OFFSHORE MATING

I

M~

M

c. FOUNDATION TEMPLATE AND TETHER LOWERING

-_-.

'

=.7-

HI~

I

ILI d. TETHER IN PLACE

I N I

I n t a c t stability during t o w

Basically the determination of the righting moment and the wind heeling moment at various heeling angles will be required. The righting moment for a given condition of'a floating vessel depends on the hydrostatic characteristics and the location of the center of gravity for that particular condition. The hydrostatic characteristics depend on the geometry of the vessel and can be calculated either by hand or by any of the available computer programs. The wind fori~e depends on windage, wind velocity, shape and shielding coefficients of the windage. The wind force Fw may be written as

Fw = E K(Vi)2(Cs),(Csh),A, i=l

(4)

Fig. 9

Transportation

and installation sequence

where V~ = Cs = Csh = A~ = K=

wind velocity at centroid of Ai shape factor for ith width shielding factor for ith width area.of ith windage 0.00256 for English unit; 0.0473 for metric unit

The recomrriended shape coefficients for various geometries are available in references [4] and [5]. Shielding coefficients should be used when adjacent objects expos'ed to wind lie close enough behind the first one. The use of l~heshielding coefficient is generally left to the discretion of the designer. For units with columns, however, ABS [4] recommends not using any shielding allowance. If desired, the shielding factors may be determined [5] when two members are located behind each other in the wind direction and the center-to-center-distance x is less than seven times the width (or. diameter) dl of the windward member. The shielding factor may be estimated

as (Csh), = 1 _ dww dlw (1 - ~

x)

of such data, the wind profile may be approximated as [6]

Wz- [HI l/n where

Vz = wind velocity at height z above mean water ,

level

VH = wind velocity at some reference height H above mean water level

1/n = an exponent, usually l/is.for gusts and 1/8 for sustained wind speed For stability evaluation, the sustained wind velocities rather than the gust should be used for wind force calculation. Furthermore, if the reference wind speeds are not available, Table 2 may be used. Table 2

Recommended wind velocity [5]

for dw,v < dlw

x fordww > dlw 7dlw = 1.00 for x > 7dlww where dlw is the width (or diameter) of the leeward member. The wind velocity profile, to be used in the foregoing expression for wind force, should be determined by appropriate analytical means for collected wind data [5]. In the absence

(5)

V10

_

Type of Area Sheltered location Normal open sea Severe open sea (North Sea and NorwegianShelf) Extreme area

All Seasons m/s (ft/sec) 40 45

(131.2) (147.6)

50 55

(164.0) (100.4)

Conceptual Design Process of a Tension Leg Platform

Summer (May 15-Sept. 15) m/s (ft/sec)

45

(147.6) 285

RIGHTING OR WIND HEELING MOMENT

ANGLE OF HEEL AREA

Fig.

10

(A4-B) ~> 1.3 AREA ( B + C )

Dynamic stability curve

During tow, the vessel is expected to satisfy the following intact stability criteria [5]: • The static equilibrium heel angle due to wind should not exceed 15 deg. • The second intercept of the righting moment and the heeling moment curves should not occur at an angle smaller than 30 deg. • The metacentric height should be at least 1.0 m (--~&0 ft) in all operating and transit conditions, and should not be less than 0.:3 m (-~ 1.0 ft) in all temporary positions. • The area under the righting moment curve to the second intercept, or the downflooding angle, should not be less than 30 percent in excess of the area under the wind heeling moment curve to the same limiting angle (see Fig. 10). A stability analysis of a column-stabilized unit requires calculation of hydrostatic properties, wind force and wind heeling moment, dynamic stability curve for intact vessel, and also checking the adequacy of watertight compartmentation. The various steps of the calculations are basic naval architectural calculations and will not be elaborated upon. Reference [1] discusses the stability of a semisubmersible in detail; the wind force calculation steps shown there follow the ABS method. The wind heeling moment should be calculated about the axis. The various criteria related to stability of a semisubmersible are listed in Table 3 of reference [1].

Damaged stability during tow To check the adequacy of watertight compartmentation, the ,#ariotts regulatory agencies require a stability analysis with one compartment adjacent to the sea flooded. This analysis will confirm that the vessel will not capsize as a result of progressive flooding due to damage in one compartment. In assessing the damaged stability of column-stabilized units, the regulatory agencies require that the extent of damage [5] be assumed as follows: • Columns, pontoons and bracings are flooded when damage occurs at any level between 5.0 m (--~16.0 ft) above the maximum draft and 3.0 m (-~ 10.0 ft) below the minimum draft specified in the operating manual. • Only the columns, pontoons and bracings on the periphery of the unit are to be damaged and the damage is in the exposed portion. • Vertical damage extent to be 3.0 m (-~ 10.0 ft) occurring at any level between 5.0 m above and 3.0 m below the waterline in question. • Horizontal damage extent to be 3.0 m (~-10.0 ft), measured along the periphery of the column or pontoon. • Horizontal penetration to be 1.5 m (--~5.0 ft) measured radially from the shell. The vessel will be considered by ABS [4] to have adequate compartmentation if the unit possesses sufficient reverse stability, in the damaged condition, to withstand an additional 286

overturning moment due to a 50-knot wind. The waterline at the damaged equilibrium condition should be below the lower edge of any opening through which downflooding may take place. Due to recent accidents of Alexander Kielland and Ocean Ranger, the Norwegian Maritime Directorate has come with a new requirement of reserve buoyancy in the deck structure. This requires that the platforms be provided with a means of buoyancy in the deck structure sufficient to remain afloat after the loss of buoyancy equivalent to the volume of the whole or major part of any one column. This is assumed to occur when the platform is at the maximum Operating draft and with the maximum allowable vertical center of gravity. The authors believe, however, that this requirement may be too stringent in the case of a TLP, because it functions like a semisubmersible only for a very short time when compared with its lifetime.

Stability during protected operations The mating and installation operations are expected to be carried out in relatively calm weather. The mating operations are required only when fabrication is done in two pieces. So, generally speaking, efforts should be made to mate those sections in a sheltered area. For such protected operations, the criteria for adequate stability should be more relaxed than those of towing conditions. The vessel will be expected to be stable if it can be assured to have positive metacentric height or about a minimum of 3 ft at any conceivable loading condition during protected operations.

Considerations unique to TLP in place When a TLP operates in place, the wind and current forces move the platform in the horizontal plane, which is referred to here as the static offset because the wind and current forces are considered to be static. The vessel also undergoes dynamic excursion in the horizontal plane due to wind and wave forces (which will be discussed later in the motion analysis); the static part becomes more dominant with increasing water depth. The wind force calculation should be done as described earlier. To determine the corresponding static offset, an exponent of l/s should be used in equation (5) for wind force calculation. For the forces on submerged parts of the structure due to current alone, the following equation may be used for calculating the current force Fc per unit length Fc = (0.5 CopVZA¢)

(6)

All of the preceding values are to be taken in a consistent system of units, Co being dimensionless. Typical values of CD, for various shapes of submerged bodies, are listed in Table 3. When the platform is subjected to static forces, as shown in Fig. 11, the tethers at the equilibrium position are elongated and the platform attitude changes from that of the original condition. As the platform tends to move horizontally, the following forces come into play in the system: • Component of tether pretension in the horizontal plane tends to restore the platform back to its original location. • Tether elongates and tends to pull down the platform. • Platform gains some buoyancy and tends to elongate the cable. • Wind and current produce a static force and moment. • Platform heels and/or trims, resulting in (i) hydrostatic restoring moment and (ii) unequal elongation of the cable, causing some countermoment. At the static equilibrium position, the system of forces has •to be balanced; the balanced position is determined by the appropriate scheme of iteration. Finally, to assess the redundancy of the tether system and the adequacy of compartmentation, the effect of breaking one or

Conceptual Design Process of a Tension Leg Platform

Table 3

Drag coefficients [5]

Shape of Member

Current Direction

Right circular cylinders

v ~

d'

Flat bars~ rolled sections, other sharp-ended sections

~ ~ l

d

Rectangular parallelopiped with corner radius r(0 < r < d/2), as shown in sketch

~

"

~b

11

•

•

0.7 KL

2.0 KL

v

QuadratiCparalleltob°X'flow°nediagonal

Co

2.0KLKrKb

d

I~

k,..L

~

~d

1.5 KL

where 0.5 + 0.1 (L/d); = 1.0; kb = 1.0;

KL =

= Kr = = =

(8-b/d)/6;

0.5; 1.0; (4.3-13 r/d)/3 0.35

for L/d < 5 L/d > 5 for b/d < 2 2 < b/d < 5 b/d > 5 for rid < 0.10 0.10 < r/d < 0.25 rid > 0.25

-~_-----.-

W,~ J -

. . . .

~.-~ _ ~

DOWN WIND.~

CURRENT~

-~-

/,4

/

- ":

HEEL ANGLE (EXAGGERATED;, IT IS VERY SMALL)

- - 2

I

I

/

I

I I

I

I

I

I

I

I

I

/

I

/ I /

I

I

I

/ / /

Fig. 11

TLP equilibrium position

Conceptual Design Process of a Tension Leg Platform

287

more tethers and the flooding of one or more compartments should be investigated. In these cases, the system of forces is similar to that described in the preceding. When a particular tether breaks, it can easily be made nonexistent in the system. And when the compartment(s) are flooded, the hydrostatic characteristics and, thus, the associated stiffness need to be changed accordingly.

acting on the structure. A brief outline of these modeling techniques and methods to evaluate the motion response of a TLP is given in the following. The submerged geometry of a TLP is divided into three types of members. In general, these are a vertical member or column, a horizontal member or pontoon and an inclined member or brace. Summing up the hydrodynamic forces for each type of member gives the total forces on the submerged hull. For a vertical column, MacCamy and Fuchs's [7] method for Motion analysis calculating the wave force for a vertical circular cylinder in The purpose of motion analysis is to evaluate the motion finite water depths has been extended to include the calculation response of a given TLP configuration at various wave condi- of the added mass and damping coefficients with the correction tions. It also forms the basis for the dynamic stress analysis and to the forces in the vertical direction. In the case of a vertical the tether and the structural fatigue life estimations. Since the asymmetric body, the method used by Black [81 and subsesafety of the tether and the structure depends considerably on quently improved by Fenton [9], which uses the symmetric the TLP's motion response, a thorough investigation of the cylindrical three-dimensional Green function, has been exmotion behavior in a random sea is essential to the success of tended by Kim [10] to calculate the added mass and damping the conceptual design. coefficient by using radiation potential. This also satisfies the The TLP motion analysis can be separated generally into the dynamic boundary condition on the body. This method gives frequency and the time-domain solutions. In the frequency a better prediction of forces in the vertical direction for a verdomain, the in-place and the free-floating conditions are to be tical circular cylinder than MacCamy and Fuchs's method. studied. In the in-place condition, the vessel is permanently Nevertheless, its cost for computation is quite high. Unless moored on the sea floor by tensioned tether members. Because there is significant doubt about the prediction of vertical forces of the very high stiffness of tether in its axial direction, TLP 'using the MacCamy and Fuchs method, it will not be of much motion responses in the vertical plane are almost eliminated. advantage to use the 3-D Green function in the motion calcuConsequently, as far as TLP motion is concerned, the integrity lation. of tether, that is, the tether loads, is our major concern in the For a horizontal pontoon, the close-fit source distribution stage of conceptual design. method, pioneered by Frank [11] and subsequently extended Tether loads are induced mainly by the displacement of by Kim [121 to account for the interaction between two parallel tether tops which are fastened on the TLP hull, and by the ve- slender members, is used to compute the hydrodynamic forces locity and acceleration imposed on the tether top due to the via strip theory. For pontoons perpendicular to each other, a vibration of the TLP hull. In general, the effect of tether top proper adjustment for the wave heading and phase relationship displacement on the tether tension can be estimated based on to the vessel's center of gravity is necessary. the static analysis, while the effects of velocity and acceleration Hooft's [13] method of calculating the wave exciting forces give the dynamic tether stresses which are superimposed on the and moments on the inclined bracing member is a very constatic loads. The effects of dynamic stress are considered in two venient and efficient tool. The contribution of the bracing ways. They will either increase or decrease the static maxi- member to the overall TLP motion and tether load calculation mum and minimum tether loads and, at the same time, their is less significant. Therefore, in the conceptual design stage, oscillating nature contributes itself to the fatigue damage of the its hydrodynamic effects generally may be ignored. Since the tether member. TLP is very weight sensitive, the brace steel weight and For tether members consisting of tubular pipe, special con-' buoyancy need to be taken into account in the calculation of siderations need to be addressed in the conceptual design stage. TLP mass properties. Since the vessel is moored on site permanently, the tether Summing up all the member forces gives the total wave exmember not only needs to be strong enough to hold the vessel citing force, added mass and damping coefficients acting at the in place during a 100-year storm, but it must also have enough TLP center of gravity (CG). The six degrees of freedom of the pretension to prevent the tubular member from becoming slack. RAO at the center of gravity--namely, surge, sway, heave, roll, To provide enough pretension, more displacement is needed pitch and yaw--are calculated by solving the six linear coupled and, in turn, more displacement means higher costs and higher equations of motion written in the following condensed system natural periods. Consequently, in designing a TLP, it form: is desirable to minimize its displacement rather than increasing it, and, at the same time, to have its tether members strong and 6 ~_, [Mik + Aik)Xk + BikX + CikX] = Fje~,,,t, flexible. Since the tether top motions--this is, the displacement, ve- k = l i=1...6 (7) locity and acceleration--are determined from the responses of the TLP at its center of gravity, it becomes critical to estimate where Fi, I' = 1 . . . 6, represent the wave forces corresponding the motion responses of the TLP accurately enough to ensure to surge, sway, heave, roll, pitch, and yaw motions, respectively; the safety of its mooring leg. Mik is the component of the generalized mass matrix for the In the frequency-domain solution, the TLP is treated as a structure; Aik and Bik are the added mass and damping coefrigid body with six degree of freedom, and each tether is reficients; Cjk is the sum of the hydrostatic restoring coefficient, placed by an equivalent linear spring. The vessel is assumed Hik, and tether member stiffness, Tjk; and F i is the complex to vibrate in an equilibrium position with small-amplitude osamplitude of the exciting force.and moment. A detailed decillation. In evaluating its hydrodynamic forces and moments on the vessel, Airy's wave theory is adopted. Computations for scription of each item in equation (7) can be found in Appendix 1. the added mass, damping forces and wave exciting forces and Once the motion RAO's are obtained, tether RAO's are calmoments are performed based on the potential theory. Beculated in proportion to the maximum elongation during the cause of the complexity of the TLP geometry, various modeling motion cycle. Calculation of maximum tether elongation is techniques and methods have to be combined to provide an based on the transformation of motions at the CG to the tether accurate prediction on the hydrodynamic forces and moments 288

Conceptual Design Process of a Tension Leg Platform

PITCH

HEAVE

R.A.O. (0 DEG)

/~ PLATFORM INSTALLATION

4.00

4.00

3.00

3 . 0 0

2.00

2.00

1.00

1.00

o.oo,_,.,_,-~z.-o- - . ~ 5.

~-'~"'~-':~ ~

10.

15.

R,A.O. (0 DEG)

r'l HULL TOW

I'1 HULL T O W ~, PLATFORM INSTALLATION

20.

25.

O.OOt ~ 5.

.

r

10.

15.

20,

FULL SCALE WAVE PERIOD IN SECONDS

FULL SCALE WAVE PERIOD IN SECONDS

Fig. 12 Motionresponse during tow and installation

top ends, which are connected to the bottom of the TLP columns. Let DCG be the displacement vector for translatory motion at the vessel's center of gravity (Xc, YG, ZG) and 0 be the angular displacement vector; displacements at the location of the tether top (XT, YT, ZT) are given by

/SLOC = /5cc +/)x(; -- ;c)

(8)

where r and rc are the position vectors of the tether top end and vessel CG with respect to a global coordinate system. Let R be the position vector of the tether anchoring point with respect to the global axis; the elongation of tether ATe can be directly calculated using

ATe =

I/)LOC + ~ --

and tether loads are proportional

-

to

le

-

(9)

A T e as

AE TLOAD = ~ 0 ATe

(10)

Another important consideration in the TLP motion analysis is the response of a TLP in its free-floating conditions. Owing to the absence of the highly tensioned tethers, the amplitudes of the out-of-plane motion s, that is, heave, roll and pitch, are no longer negligible. In certain sea states, the natural periods of heave, roll and pitch can be very close to the wave period with dominant energy, and, consequently, the motion-induced dynamic loads on the TLP structure become critical to the safety of the vessel. • The important tasks in a free-floating analysis consist of TLP hull under tow, deck transportation, hull and deck mating and hull and deck under tow. In general, the motion responses of a free-floating TLP vary significantly with its loading and environmental conditions (see Fig. 12), and a thorough investigation of its motion behavior at each task becomes necessary. In the case of TLP hull tow, the natural periods of roll and pitch motions are more critical to that of a case for complete hull and deck under tow. For example, in the CONOCO Hutton TLP the natural periods of heave, roll and pitch are around 16 to 18 sec when only the hull is towed, while those natural periods increase to around 30 tO 35 seconds for the hull and deck under tow. Since the period of dominant wave energy seldom reaches 30 sec, the shifting of natural periods from 16 to 30 sec reduces significantly the roll- or pitch-induced

dynamic loads on the TLP structure. As far as heave motions are concerned, their natural periods remain almost the same and, consequently, there is less improvement in the heaveinduced dynamic loads. The ideal location for performing hull and deck mating requires a sheltered place with sufficient water depth for the large draft (130 to 150 ft) of the TLP hull. In general, the design wave height for a mating operation is in the order of 5 ft maximum. In a typical mating scenario, the hull is moored on location first with a spread mooring system. The TLP deck is then brought into position by a barge with special mounting devices to carry the deck. Special fendering shock-absorbing systems need to be designed to absorb the impact loads between the TLP hull and the barge, and between hull and deck. Once the hull and deck are locked into position, the deballasting of the hull begins and the deck load is gradually transfered from the barge to the TLP hull. At this stage, the impact load induced by the motions becomes critical and special real-time simulation becomes vital to the success of the mating operation. Another interesting problem in the TLP motion analysis is the hydrodynamic interaction between its adjacent members, especially between the large-diameter vertical columns. This is due to the fact that the presence of the multiple columns within close proximity to each other tends to either reinforce or diminish the hydrodynamic forces on the neighboring 'member. For example, when two large columns are in line with the wave direction, the forces on the first member which encounters the wave increase because the wave is reflected from the second member. On the other hand, the forces on the second member tend to decrease due to the incoming wave being partially blocked by the presence of the first column. There are two different methods of calculating the interaction force between two large cylinders. The first approach, adopted by Garrison and Chow [14], Hogben and Standing [15], and Wybro [16], is based on a wave diffraction computer program in which a body of arbitrary geometry is represented by a finite number of 3-D source distribution. This method is quite complicated. The second approach, proposed by Hwang and Tuck [17], Isaascson [18], and Ohkusu [19], is to model the vertical cylinder as a distribution of vertical line wave sources extended from the sea bed to the free surface. Analytical results versus model test are plotted in Fig. 13.

Conceptual Design Process of a Tension Leg Platform

289

F! R =m

M o t i o n s and t e t h e r loads in i r r e g u l a r seas

Fo

Fo H O R I Z O N T A L FORGE A C T I N G ON T H E F I R S T C O L U M N W I T H O U T T H E P R E S E N C E OF S E C O N D C O L U M N F! T O T A L HORI~EONTAL F O R C E A C T I N G ON T H E F I R S T C O L U M N W I T H T H E P R E S E N C E O F SECOND C O L U M N D OTC 3067,

1978 EXPERIMENTAL RESULTS

& THEORETICAL PREDICTION

2.0

.1~I DIA = 1 . 5 ~

WAVE

QQ DA

1.6

1.2

-1.2 o N

E -1.6

- 2.0

1.0 2.0 3.0 DIAMETER x WAVE NUMBER

ko

/ , I DIA=2.5 ~

WAVE Q o w.

_

4.0

G D,A

1.6

tt o

1.2

.J

-1.2

Results from the frequency domain solutions--that is, the tether RAO for the TLP in the in-place condition and the motion RAO for a free-floating case--can be used to estimate the tether and motion amplitude in irregular seas. This is achieved by applying the probabilistic theory to the description of a random sea state and the use of the principle of superposition to the motion and the load responses of a linear system. Before proceeding further, an introduction to the basic theories in describing a random sea state and the evaluation of the motion response spectra will be offered. There is no set pattern to wave height, length, or period in true irregular seas. However, irregular sea-wave behavior can be defined by its direction and its wave energy in a range of frequency bands. One of the concepts in the description of an irregular sea is a two-dimensional seaway, that is, a long-crested sea which can be simulated in a wave tank. Calculations for a vessel's significant motion responses in irz'egular seas are based on the spectral theory, which describes how regular wave elements combine into irregular sea patterns and how each wave component affects vessel behavior. The theoretical principle underlying the calculations of significant vessel responses is based on the theory of linear superposition (St. Denis and Pierson, 1955), which states that a ship's response to an irregular sea can be represented by a linear summation of its responses to harmonic (sinusoidal) component waves. A vesselresponse spectrum is derived by combining two elements: the harmonic or regular wave motion transfer functions, called response amplitude operators (RAO's), and wave energy spectra. Significant motions and significant wave heights are then determined by an integration process. The significant wave heights are calculated from wave spectra that represent sea states, and significant motion responses are derived from RAO's and wave spectra. To calculate significant wave heights, the significant value for wave height obtained from the integration of wave spectra is expressed as the product of a constant and the square root of the spectral area. The equation to calculate significant wave height is

Mt/a =

o:

4.0

SM(~o)dco

(11)

-1.6

where

M]/a = -2.0

2.0 3.0 DIAMETER x WAVE NUMBER

4.0

1.0

2.0

u.o

J~l OIA=4.0

I~

"~

value of significant wave or motion, ft SM = spectral density of wave or motion, ft2-sec/rad w = circular frequency, rad/sec

Six most commonly used theoretical spectra are the International Ship Structure Committee (ISSC), Pierson-Moskowitz (P-M), Scott, JONSWAP, Bretscheider, and the Neumann spectrum. The various formulas for these wave spectral density functions for an energy spectrum are described in Appendix 2. The response spectra used to calculate significant motion responses are derived by combining RAO's and wave spectra, and utilize the following formulas:

d

1.6

u..-

1.2

ANGULAR -1.2

MOTIONS:

So(w) =

(ROLL, PITCr~YAW)

o z

LINEAR MOTIONS: S~(CO) = (HEAVE, SURGE SWAY)

-1.6

~a X l,

l(z)l

where -2.0

• 1.0 2.0 3.0 DIAMETER x WAVE NUMBER

Fig. 13 Comparisons of column interaction 290

4.0

0 = angular motion amplitude co = circular frequency S(co) = wave spectrum density

Conceptual Design Process of a Tension Leg Platform

X S(w)

X S(~0)

(12)

(la)

linear motion amplitude v = wave number

Z a -~

and

01/3 = 4.0 W/ ~oo~ So(w)dw where

(14) ,-

1/3 = value of significant motion ffaotion response spectrum density w = circular frequency

So =

The wave spectrum describing long-crested areas is often called the point, or one-dimensional, spectrum, as it is obtained by measuring surface fluctuations at a single point. The process for long-crestedseas, however, does not detect the multidireetionality of wave direction, and a more complete representation of ocean waves is given by using short-crested (multidirectional) irregular waves. The true sea state consists of irregular Wave trains of different periods and heights traveling in a number of different directions Simultaneously. This condition is generally referred to as a short-crested or multidirectional sea. The term short-crested evolves from the length of the wave crests perpendicular to the direction of motion, which is short when compared with a unidirectional or long-crested sea state with its infinitely long wave crests. The directional spectrum for short-crested seas is generated from the unidirectional or point spectrum by the use of a spreading function. This direction spectrum is written as the product of two functions:

S(w, #o~) =

S(o~) • f(#~)

(15)

where f(#~) is the spreading function. The cosine-squared spreading function has been frequently used to calculate the directionality of short-crested seas. This spi'eading function is written as f(/.t~) = 2 cos2~t~

(16)

71"

The cosine formulation is convenient, since a value of unity is obtained when the calculation is integrated over +90 deg. The unity value reduces the direction spectrum back to the point spectrum from which it was derived. Thus 2

~)d~

= 1

(17)

The spreading function is applied to determine component point wave spectra (unidirectional spectra) for a series of wave directions up to 90 deg from the principal wave heading. Component point spectra are then applied to the corresponding vessel RAO's to produce the component response spectra. Component response spectra for each wave frequency and direction are integrated to determine the significant responses in short-crested seas.

T e t h e r f a t i g u e life p r e d i c t i o n Since one of the principal sources of tether damage is due to fatigue, it is important to estimate the fatigue life of a tether due to the effect of oscillatory TLP motions such as heave, pitch, and roll. There are still uncertainties in the practical way of predicting tether fatigue life based on probabilistic theory. Those uncertainties include the bandwidth of tether load response spectra, the representation of environmental condition by wave scatter diagram, the effect of tether "ringing" (that is, high-frequency resonance due to second-order wave force), etc. Consequently, the predicted result of tether fatigue life

based on the frequency-domain solution gives us only a quantitative base for comparison purposes. It is a common practice for offshore engineers to ignore the effect of mean stress in calculating fatigue damage of fixed offshore structures. However, it is not so for a tether made of tubular members. The mean stress level will affect the fatigue life considerably. Several formulas have been suggested to estimate the effect on the S-N curve due to the presence of nonzero mean stress. In general, the cyclic stress range aa for a nonzero mean stress ~r,~ is estimated from the S-N curve for zero mean stress. The

suggested empirical formulas are SOLDERBERG:

ff---£ + if0

°'~m = 1 0"y

GERBER: -0"a - -{- /O'm/2 = Oo

1

(19)

~ O'n /

GOODMAN: O'.___£a + O'__~_m = 1 O"0

(18)

(20)

O"n

where Crois the fatigue strength for a given number of cycles, N, for zero mean stress, ay is the yield stress, and o-n is the ultimate stress. The foregoing relations may be applied in an elaborate fatigue life analysis. In the computation of the cumulative fatigue damage ratio, it is assumed that the structures are subjected to stresses continuously varying.with time. A probabilistic approach, as described in the following, is recommended to calculate the cumulative damage ratio (CDR). According to Miner's rule, a discrete application of sinusoidal stress gives CDR as CDR = 7. n(6~) (21) N(cq) where n(ai) is, the number of stress cycles at a stress range cq, and N(ai) is the average number of stress cycles to failure at a stress range cq. Fatigue failure is expected to occur when CDR equals unity. For a continuous stationary random stress process, CDR is given by

CDR = ~vg ~O ~ P(~r)

(22)

where T = T(a~I = = N(a) =

time duration of random stress process avg. period for stress variation in a random process probability density function of stress range average number of cycles to failure at a stress range 0"

N(cr) is the equation of the curve of the stress range versus the number of cycles to failure (known as the S-N curve). A typical S-N curve may be represented by: NOr) = n / ~ T M

(28)

where A and xm are obtained from experimental data. For a narrow-hand response spectrum, the probability distribution function P(a) can be represented approximately by a Rayleigh distribution in the form

P(a) = ~

e-~2/8Mo

(24)

For unidirectional waves, the wave spectrum can be fully described by S(w). The nth moment of the wave spectrum about the origin is

M, =

Conceptual Design Process of a Tension Leg Platform

.2 °

wnS(w)d¢o

(25) 291

.

=_=

.

.

.

i

400

.

.

.

.

I

500

'

,

,

,

WIND D X

400 ¢0

3201

DUST

i

,

,

i

.

.

.

.

p

800

WIND [DERIVED

% "x 45.0

SPEED

GUST

FROM FOR

.

i

SPECTRUM

TIME

VARYING

WIND

PURPOSE)

u.

30.0 (

_z o 22.5

160

"5

t

15.0

i~, 7.5

80

.5

1.0

1.5

FREQUENCY

2.0

2,5

%._ .5

e = x / ( M o M 4 - M~)//(MoM4)

(26)

and O < E < 1. The term Tavg in the expression defining CDR can be computed from

]1,2

(l - E2)

(27)

Having P ( a ) and N(a) defined, the integration can be solved numerically: A = N ( o ) . a XM

(28)

X M = l°g(N(a])/N(~rz)

(29)

and log(a2/a~) Finally, equation (2) becomes ff e-,4/SMo

CDR = ~o ~ 4Mo A/aX M

1.5

2.0

2.5

(RADISEC)

Time history of wind speed and wind gust spectrum

Expressing P ( a ) as a Rayleigh distribution is exact for a stress spectral bandwidth parameter (E) of zero, where E is defined by

Tavg = 27r

1.0 FREQUENCY

(RADISEC)

Fig. 14

da

a(1 + ×M/e-~qsM0 d a

(30) (31)

4AMo

if the S - N curve is represented by a straight line in a log-log plot and P(r) c a n b e described closely by a ltayleigh distribution; under such conditions, the CDR is given by

CDR = (T!¢) (8M~---xM/eF (1 + -~-~) '

(32)

where/~ (1 + X M / 2 ) is the gamma function and T the duration of the application of the cyclic stress.

292

.

8 'L~ 3 7 . 5

A

WAVE

1

.

1000

VERIFYING

¢

_

.

900

SPECTRUM

FIRST ORDER SECOND ORDER TOTAL

240

uJ ¢3

,

IN SECONDS

E

==

,

700 TIME

DAVENPORT

i

600

¢

Nonlinear responses in time domain In reality, the ?esponses of a TLP are subjected to other e n vironmental forces such as wind, current and second-order wave forces in addition to the linear wave forces. Other factors such as the effect of tether mass, the dynamic wind forces, the effect of TLP setdown due to the restraint of tether members, the nonlinear restoring forces and moments for the TLP under large excursion, and the effect of finite wave height make the problem even more complicated. Consequently, it is necessary to apply the technique of time-domain simulation to investigate the importance of these major factors. Two of the most important factors are the effects of dynamic wind forces and the second-order wave forces, and a brief description of each will be given preceding the equation of motions in time domain. E f f e c t of dynamic wind forces The extensive superstructures of a TLP, necessary to meet the requirement of deck clearance for the survival storm condition, and the buoyancy needed for pretensioning the tethers increase significantly the structure's exposure to wind-induced loadings. In general, the method usedto calculate the quasistatic wind forces is based on one-minute average wind speed, and it assumes that the design wind force remains constant over a certain length of time. In reality, wind speed is unsteady and may produce slowly varying components whose natural periods may well be close enough to the natural periods of surge, sway or yaw motions of a TLP. Thus, significant amplification in tether tension can occur due to the resonant phenomenon of a dynamic system. Figure 14 shows the time history of wind speed and the wind gust spectrum. The method of generating the dynamic wind spectrum was derived by Davenport [20] and Kareem [21]. This method is partially based on the empirical equation and an outline of it is given in Appendix 3.

Conceptual Design Process of a Tension Leg Platform

Mean and slowly varying wave drift force

To simplify the calculation, Newman [33] assumes that

Although the magnitude of wave drift force is small compared to the highly oscillating first-order wave force, the frequency of the oscillating drift force may fall very closely to the natural frequency of the system. In this case, the horizontal motion of the TLP structure may be significantly pronounced due to the oscillating drift force. Especially during TLP tether installation when only a portion of all the-tethers is installed, the natural frequency of the partly moored system becomes very close to the natural frequency of a conventional catenary mooring system, and the dynamic effect of the slowly varying drift force becomes even more dominant. In regular waves, the wave drifting force is steady and its magnitude does not vary with time. In irregular waves, the wave drift force has two components--the mean component and a long period oscillation. There are two different approaches in evaluating the mean drift force in regular waves; one is based on momentum principles while the other integrates the pressure field on the surface ,of a floating structure. In the first approach, Mario's formula [22] has been generally accepted. The mean drift force of a regular wave train is thus expressed as Fv = -~ y

1A-21dx

(33)

where the integration is over the vessel length and 1A-1 is the amplitude of reflected wave. In the second approach, Pinkster and Van Oortmerssen [23] integrate the fluid pressure over the wetted surface of a floating body to calculate the mean force, Fy. It is expressed in vector notation as ,

?y -- ~

eq = Qq = Q. = 0

(37)

and the slowly varying drift force cfin be written in the following simplified form N

F~ = E

N

Y~ ~+SjPq m cos[(wi -- wi)t - (ei - ei) [

(38)

i = l 1=1

In the present study, a numerical method which utilizes the Inverse Discrete Fast Fourier Transformer is used to calculate the second-order wave forces. Its methodology for calculating the second-order wave forces is based on the linear superposition of reflected wave components due to the presence of the TLP. A detailed description can be found in [28]. A sample of a time-history digital simulation of the second-order slowly varying wave drift force is shown in Fig. 14. The inclusion of second-order wind and wave forces adds a refinement to the first-order wave force for analyzing a TLP in an irregular seaway and requires a suitable mathematical tool to simulate the TLP behavior in a time-domain solution. The equations of motion in the time domain formulated by Cummins [29] are 1=1

[(Mkj +

m,j)xj+ f_tK,j(t-r)xj(r)d+

CkjxJl

= XkCt) + i=1 ~'. L,k(t)

(39)

where Lik(t) is the component in the kth mode of the tension in the ith mooring line which depends on the instantaneous length of the line, the orientation of the line and the loadelongation characteristics. A relationship has been shown between these quantities and the frequency-dependent added mass and damping coefficients as

Kki(t) = 2 f = 71" J o

(a4) where Po is the position of P linked to body surface, ~ - ~ is the relative wave height including body vertical motion, 0 is the angular displacement; 4~ the velocity potential, Sc the submerged surface, T the period, and ti is normal vector. The most general form of the slowly varying wave drift force together with the second-order mean wave drift force, according to Faltinsen and Loken [24], Pinkster I25], and Kim et al [261, can be expressed as N

F~ = E

N

E wp 0.076(x) - 0.22

SF(--) = (CopAY)2So(n)

= 27r ~-~(X) -°.33]

The relationship between wind speed, fetch length, and significant wave height is U = 111,4 x -°615 (Hs/~.28) l°s

(75)

Co A V v

= = = =

drag coefficient projected area mean hourly velocity fluctuating velocity

From Morrison's formula, the mean hourly wind force is

where

Fo = 1/z C o p A V z

(82)

4F~ SF(n) = ~ san)

(83)

then

U = wind speed, knots = gx/U 2 (nondimensional parameter) X = fetch length, nautical miles Hs = significant wave height, ft

The fluctuating wind force is of the form:

Bretsehneider spectrum H2 004 S(00) = 0.8125 ~ e - 1.~(60/60)4 005

(81)

where

X fet!h length U = wind speed g = gravitational constant

300

(77)

In equations (70) through (76) the mean spectral wave period, that is, the characteristic wave period is

= real part of wave exciting force

a

006

e(t) = 7 V 2 (76)

where

Conceptual Design Process of a Tension Leg Platform

+

v2 l

1

~/ = 2 CD 7rA

Fo

where Sv(00) is the spectrum of velocity fluctuations. Substituting 3' = (Fo/V2):

The power spectral density of SF(60) is

4Pfi _

sF(o~) = -F~-sA )

SF(o~) 4~2Vzsv(:o) =

+ 2312 f ~oSv(~) . Sv(oO - f / ) d f ~ Jo

(85)

+ 2

f0

so(

-

(86)

Discussion Cuneyt C. Capanoglu, Member

The authors are to be commended for having presented a very thorough and timely paper. In addition to providing the reader with the overall approach to conceptual design, the paper presents up-to-date information on interaction of the variables and a thorough discussion of comprehensive, detailed analyses. The following comments are offered to further enhance a very good paper. The authors present tether load variations as a function of column-to-pontoon displacement ratio (V~/V1). Though it is possible to evaluate tether load variations of a TLP platform geometry given on Fig. 1 as a function of Vz/Vi, this approach cannot be implemented on a TLP platform consisting of bottle-type columns and interconnecting bracing system. A more general and correct parameter to study tether load variations in column waterplane area (variable buoyancy forces) to column tributary displacement ratio (hydrodynamic forces). It should be noted that tether loads at a column vary as a function

of • not vertical force on an individual column • moment due to varying net vertical forces on columns • moment due to lateral forces Since the authors so thoroughly discussed the generation of excitation forces on the platform and the response of the platform to these forces, discussion of the motions of the platform could have been expanded to further assist the reader in assessing the scope of conceptual and detailed design efforts. That is to say, the6-degree-of-freedom solution of the TLP superstructure motions needs to be supplemented by a coupled interactive solution of motions for the superstructure and the tethers. In relatively deep water, the mass of the tether will affect the motions and influence the platform surge and variation of tether loads. S. J. keveretle, 4 Visitor

Authors Chou, Ghosh, and Huang are to be commended for attempting to show some of the complexity of detail and the interactive nature of TLP design. The importance of an extensive preliminary design to .account for the interactive nature 4 Gulf Oil Exploration & Production Co., Houston, Texas.

Fig. 21

of the system cannol: be emphasized enough. The interaction between weight, loads, and payload is much more finely balanced than any structure the offshore industry has installed to date. In this sense, the TLP is closer to a vessel such as a submarine than to a typical civil engineering structure. As such, it represents a major change in design philosophy for the offshore industry. However, I believe the paper is somewhat misleading in providing very simple procedures for preliminary design without adequately stating the assumptions and limitations of the proposed methodologies. The proposed methods are generally presented as the only approach, without acknowledgment of acceptable and sometimes preferable alternatives. The reader is referred to papers from the 1982 offshore Technology Conference (OTC) on the Hutton TLP design, to J. A. Mercier (1982), to a paper to be presented at the 1984 OTC by D. T. Damery, and to an API Recommended Practice on Tension Leg Platform Design, which is now in first draft form. As an example of the level of effort which may be required in TLP preliminary design, I would like to discuss three topics which may be of interest to the potential TLP designer or analyst. They are areas which are somewhat unconventional and may require extra effort over what would normally be anticipated in a preliminary design effort. Tether ringing--The response described in the paper as "tether ringing" was first observed and recognized as a potential problem in model tests during design exercises. The effect is simply a response of the high-frequency modes of platform response (pitch, roll, and heave) to hydrodynamic excitation. The response is most easily observed in the measurement of tether tensions. Figure 21 shows an example of the'tension response of one leg of a TLP during model tests in a severe irregular sea state. The response has been high pass filtered to remove wave frequency tension variations, and is plotted along with the exciting wave trace. Possible mechanisms range from superharmonic wave forces to nonharmonic vortex shedding and wake effects. "Discoveries" of such phenomena during the final design process can be expensive. The net effect of accounting for this response can be as much as several thousand tons of displacement and a 10 to 15 percent increase in maximum loads on the tethers. A detailed preliminary design which

Tether ringing: wave trace and filiered tether tension trace

Conceptual Design Process of a Tension Leg Platform

301

:". \ 36 34"

" \

32" 30A v 28I-"lt.j 26~

Ix/ w ~

/

24

\

/

22

............ \;

20

18

16

1~0

Fig. 22

1'2

1'4 1'6 1,q WAVE PERIOD

20 (S)

22

24

Wave height/period design contour and design response curves

includes appropriate model tests can minimize any effects of such responses on the final design and ensure a more orderly design process. Damping--A second issue which is important in TLP analysis is the damping which controls resonant dynamic responses of the structure. This is important both in predicting extreme responses and in the fatigue analysis. The damping mechanisms for low- and high-frequency events differ, and both are difficult to predict with any certainty. High-frequency damping (pitch, roll, and heave) comes from wave radiation, from the foundation/soil interaction, and to some extent from local hydrodynamic drag effects around small members and sharp corners. The amplitudes of the motions are on the order of a few inches and hence the related hydrodynamic flows are very limited. Because of the changing geometry of a TLP moving in waves, a strong nonlinear coupling between the high-frequency modes is almost always ensured, and the total system damping rather than the damping in each mode needs to be considered. The damping in surge and sway includes both radiation and drag effects, and seems also to be dependent on the amplitude of the sea state, the wind field, and the current. Contributions come from the risers and tendons as well as from the structure itself. Care is required in assembling these damping numbers, and combinations of contributions from frequency domain, time domain, and model test calculations are recommended. Design criteria--The third area of interest is the one of specifying design conditions, and ultimately design risk. TLP's have been treated as civil engineering structures with a set of design events established at the beginning of the design. A number of design exercises have now demonstrated that the TLP is a dynamic interactive structure which depends on multiple boundary conditions and driving forces. Each of these inputs has its own distribution function, which is not necessarily identically correlated with the distributions of other inputs. In some responses, extremes are produced by minima in some of the exciting forces. Because of the TLP's sensitivity to frequency and to combinations of events, the conditions leading 302

to a maximum for any one response are not always obvious, and even if that discrete event is identified, traditional approaches still do not allow an accurate estimate of the risk associated with the event. The ideal solution would be to go to a fully probabalistic analysis and calculate responses to all possible combinations of events. However, the miJltiple parameters, the nonlinearity of the responses, and the lack of complete joint probability data preclude this approach with our current capabilitie s. The interim solution has been to allow the design cases to be modified as part of the preliminary design. The engineers are provided with a more complete environmental data set, and the criteria for design becomes not a specific event, but rather a given probability of exeeedirig the design response. Combinations of deterministic and probabilistic analysis are then employed to identify appropriate sets of conditions which provide the extreme responses and estimate their associated probability levels. Joint probability density functions have been used to define design contours, providing a continuum of extreme design conditions which can be investigated for each response (Leverette et al, 1982). Figure 22 shows an .example design contour in wave height/wave period space with various constant response lines plotted over it. In addition leo the responses prov!ded, the riser maximum stress condition is governed by the steepest waves at around 12 seconds and the deck clearance is governed by the highest Waves around 14 seconds. By considering all relevant responses, the overall reliability of the structure to waves can be estimated from the integrated wave height/period probability density function within the design boundary. A similar type of analysis could be performed in Hs/Tz space, or with the joint distributions of wind, wave, current, and tide. To summarize, the TLP requires a very extensive preliminary design stage to allow for the interactions and balances necessary in a good design. In addition to the broad range of activities described by th e authors, there are a number of areas which may require more detailed study and possibly model tests. Finally, TLP's are ~ufficiently complex in their responses to a multiparameter environment that the specification of de- ' sign conditions must be part of the iterative design procedure. Additional references

31 Leverette, S. J., Bradley, M. S., and Bliault, A., "An Integrated Approach to Setting Environmental Design Criteria for Floating Production Facilities," Proceedings, Third International Conference on Behavior of Off-Shore Structures, Massachusetts Institute of Technology, Cambridge, Mass., Aug. 2-5, 1983. 32 Mercier, J. A., "Evolution of Tension Leg Platform Technology," Proceedings, Third International Conference on Behavior of Off-Shore Structures, Massachusetts Institute of Technology, Cambridge, Mass., Aug. 2-5, 1983. P. Y. Chang, 5 Visitor

I would like to congratulate the authors for their excellent paper on an important subject. The parametric study logics is useful and its principles can be applied to the design Of m a n y other ocean systems. There is only one area which, I think, needs some improvement. That is the fatigue problem. As pointed out by the authors, there are still uncertainties in fatigue life prediction. But this should not be an excuse for treating the fatigue problem lightly. With reliable wave statistics for the site and accurate stress analysis, the fatigue life of ocean systems can be predict~l with reasonable accuracy with the following improvemenl~s. First, since the cumulative damage to the structure is much greater in high:energy waves associated with greater period 9 f 5 Designers & Planners, Inc., Arlington, Va.

Conceptual Design Process of a Tension Leg Platform

stress variation, the concept of using one average period for stress variation is not reliable. A more accurate approach is to use different periods associated with a series of wave spectra. The frequency of occurrence, P/, and the weighting factors of the wave spectrum and wave direction, Pj and Ph, should also be considered. The fatigue life of the Lth structural element, such as one tether, can be expressed as follows: A TL =

(87)

Y~ ~'. Y~. PiPiPhnLj/CL aLj,m i

j

k

where aLj,,~ = rms stress associated with jth wave spectrum 1

moj = area under short-term response spectrum mei = second moment of short-term response spectrum CL, a = fatigue strength constants determined by fatigue test data A = cumulative damage from fatigue tests; it may be greater or less than unity A brief description of this approach is given in reference [33] (additional references follow some discussions). Secondly, it is not enough to consider the fatigue life of the tether only. The disaster of the platform Alexander L. Keilland is due to the fatigue era secondary member, not the main column. For this reason, the fatigue life of other members should also be predicted. Thirdly, most fatigue data are obtained from specimens of structural material under unaxial loads. In applying these data for fatigue analyses, the effects of stress distribution, stress components, and the types of welds should also be considered. In summary, the conceptual design process proposed by the authors is a great contribution to the state of the art. A more careful treatment of the fatigue problem will make it even better. Additional reference

33 Chang, P. Y., "Fatigue Life and Reliability of Ocean Systems Subjected to Random Loads," Proceedings, ASME Winter Annual Meeting, 1981; published also in the Journal of Ocean Science and Engineering, 1982. G. E. Burns, 6 Visitor

The authors have done a commendable job condensing a complex iterative design process into a single paper. Their process is reasonably straightforward in most areas, but there are several places where a reader can be misled or left without a clear method of estimating the quantity in question. Displacement estimation--The proposed estimate for deck steel is 8 lb/ft 3 of "deck volume." When applied to the design considered by Standard Oil Company of California (SOCAL), it overpredicts deck steel by a factor of four. The SOCAL TLP deck system is open trussed with center and edges supported by structural bracing, and is based on single-piece construction of hull and deck. This alternative should be included in the parametric study. Table 1 shows weight estimates for columns and pontoons, but only after searching the text can one find that the weights shown are for 40-ft lengths. When applied to the SOCAL TLP, weight was underpredicted by 25 percent. Equation (1) could prove to be a useful first estimate of tendon pretension, but the wind force required must be calculated 6 Standard Oil Company of California, San Francisco.

from (4), and it is not consistent with the units (ft/sec) provided in Table 2. Also, one is left with the question of which wind to use. Is "sustained" the same as the one hour mean? Equation (2) attempts to define riser tension independently from the number of risers or the weight of each. Because the TLP is more dependent on the drilling program than vice versa, we suggest that drilling engineers specify deck space requirements and riser tensions before a parametric study is started. The message intended by this discussion is not to be critical, but rather to encourage the authors to be more complete in this very important area of estimating structural weights, tendon tension, and riser tension. Motion analysis--For the purpose of conceptual designs, the methods suggested for first- and second-order wave forces are too complicated to be explained completely, and out of context with the first part of the paper. Also, viscous effects, which can dominate second-order drift force and surge damping, have been omitted. Continued effort should be spent on separating and condensing the complex formulations for second-order effects so that each effect can be studied separately. Only then will a configuration change in the TLP produce a predictable change in response. Y. S. David Tein, Member

The authors should be thanked for preparing this paper, which clearly delineates in a systematic fashion the conceptual design process of a tension leg platform. The parametric study logics, the evaluation and screening process, and the empirical formulas should be very instrumental in the selection of a TLP geometry. The discusser would appreciate the authors' comments on the following: • Cost estimation--The most inspiring endeavors recently have been undoubtedly the Hutton TLP project and its competing concept, the Exxon Lena Guytower. It would be of interest if the authors could expand on the cost aspect in the parametric study logics in light of these recent experiences. • Design load--One of the difficulties in TLP design is the determination of design load for TLP structures. The procedure for determining design loads for the survival condition and the operating conditions may differ substantially and is not discussed in the paper. In the section entitled "Displacement Estimation," the authors suggest that the wave hydrodynamic pressure is small compared with hydrostatic pressure. There appears to be a certain confusion in the definition of hydrodynamic pressure. Strictly on pressure load itself, one would anticipate that the magnitude of the hydrodynamic pressure load would be the same as that of hydrostatic pressure. • Model test--In addition to the analytical studies outlined in the paper, it is emphasized that the evaluation process and screening process must be augmented by model tests. Currently analytical tools need further refinement in the following areas: (a) hydrodynamic interactions among major TLP components; (b) drag forces and vortex shedding; (c) wave slamming force around the wave splash zone; and (d) coupling between the tether and TLP responses in deepwater applications. A carefully designed model test program will ensure that no important facet of the design has been overlooked which might prove an unpleasant surprise. American Bureau of Shipping, New York

The authors are to be complimented for a most interesting and informative paper and for sharing the results of their work on TLP preliminary design with the industry. The paper's detailed description of a conceptual design cycle for TLP's and its numerous empirical relationships and estimating formula--which are so useful in the preliminary design pro-

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303

cess--should prove particularly valuable to anyone involved in TLP design work. The paper is also of great interest to those of us at ABS who are involved both in the analysis of TLP's and in Classification Rule development. Our comments on a few of the sections of this extensive paper are. as follows: • On tether fatigue life prediction--ABS certainly agrees with the authors' view that a fatigue assessment during conceptual design is needed for the types of tether joint connectors that are currently being designed. We would like to raise several issues on this topic: 1. The authors cite three suggested empirical formulas (namely, Solderberg, Gerber, Goodman) to account for the effects of tether mean stress on the S-N curve. The question as to which formulation is most appropriate arises. This can be answered by constructing the tether stress half-cycle count matrix.from a time domain simulation. A mean stress correction directly applicable to tether stress could then be derived f r o m the joint probability density function of the mean and alternating stress. Would the authors comment on this question of determining a mean stress correction? 2. The treatment that leads to the determination of the cumulative damage ratio (CDR) given in equation (32) of the paper,is well accepted. However, it should be pointed out that such treatment is applicable only to a single cell of the wave scatter diagram. The CDR for the life span of the specimen in question requires weighting of the contribution of all the cells of the wave scatter diagram. While this will certainly be obvious to the authors, a word of clarification on this might be of use to the readers. 3. On the effect of bandwidth, it is believed that Wirsching's rain-flow correction factor [34] offers a simple yet effective method to account for bandwidth effects. 4. An important topic which is not addressed in the paper is the acceptance criterion of fatigue failure, say, in terms of CDR. Certainly a CDR less than unity should be specified, but how much less than 1 is a difficult question to answer. Research supported by\ABC on probability-based fatigue design criteria for TLP's is addressing the tether string as a series system of components and attempting to derive a relationship between component and system reliabilities. While we have not arrived at a recommended allowable CDR as yet, we believe this "series system" aspect of the problem is important and should be taken into account. • On motions and tether loads in irregular seas--Referring to this particular section, it is not clear whether the authors advocate the use of a deterministic design wave approach or a probabilistic approach utilizing the entire wave scatter diagram for motion and load analysis during conceptual design. It appears that in final design the latter should be favored. The authors' thoughts on the appropriateness of those two approaches would be appreciated. • On time domain simulation--In the time domain simulation described in equations (39) through (42), in the paper, it is not clear how the draft-dependent added mass and damping forces are taken into account using the linear frequency dependent damping evaluated up to the mean waterline. Also, would the authors comment on how other nonlinearities such as nonlinear viscous damping and wave exciting forces up to the instantaneous waterline are considered in the computation of TLP rigid body motions. The acceleration time histories in Fig. 15 show a high-frequency component for roll and pitch but not for heave, while in the horizontal plans, only surge shows a high-frequency content. Do the authors have any observations on these results? It is interesting to see that the tether tension spectrum calculated from the time domain simulation in Fig. 18 shows nonlinear response while the frequency domain analysis, as 304

expected, does not predict the slowly varying drift force and ringing phenomena. However, the result does raise a question. It seems that the peak around 18 seconds is caused by the wave spectral peak energy, and the peak around 9 seconds is caused by the large wave force in the vertical direction. Would the author's comment on the cause of the spectral peaks at 7 and 5 seconds? • On stability during t o w - - O n the topic of stability criteria for a TLP during tow the authors cite criteria from both ABS and DnV Rules for Mobile Offshore Drilling Units. The stability criteria which will actually apply to a particular unit depend on the national authority having jurisdiction over the unit, and the requirements of the pertinent authorities should be ascertained on a case-by-case basis. • O n design guidance--As pointed out by the authorsl design guidelines for TLP's are not currently available, though a number of classification societies, standard-setting bodies and regulatory groups are working on guidance and rules. ABS has undertaken an extensive experimental test program on the buckling strength of stiffened cylinders applicable to TLP's as well as a comprehensive study on limit-state design of TLP's. The ultimate objective of this work is the development of Rules for Building and Classing TLP's which will include both a working stress design format and an alternative, reliabilitybased limit state format, which we trust will be of interest to the authors and of use to the industry. Additional reference: 34 Wirsching, P. H., "Digital Simulation of Fatigue Damage in Offshore Structures," Computational Methods for Offshore Structures, American Society of Mechanical Engineers, 1980.. Authors' Closure The authors are grateful for the comments submitted by all the discussers and for the several accounts of their up-to-date developments in TLP design. Since some of the questions are raised by more than one discusser, it is the intention of the authors to try not to repeat their answers to similar questions. To start with, we would like to point out to Mr. Capanoglu that the application of column-to-pontoon displacement ratio (V2/V1) to a TLP consisting of bottle-type columns is not apparent as in the case of a TLP consisting of circular columns with horizontal pontoons. Nevertheless; a similar application of (V2/V1) to TLP with bottle-type columns was done by authors. As far as the effect of (V2/V1) on TLP design is concerned (see references [1] and [3] of the paper), it determines the wave period at which the wave forces on the column cancel with those on the pontoon. Interactions between tethers and TLP hull structures increase as the water depth increases, and the effect of tether mass on TLP motion becomes increasingly important. The problem of fatigue was stressed by several discussers. " Mr. Chang gave valuable comments on the concept of utilizing a wave spectra family in estimating fatigue life. However, as far as the TLP is concerned, the uncertainty of fatigue failure is also caused by the difficulty of predicting TLP motion in high frequencies, by the uncertainty of viscous damping, by the effect of tether ringing, by the tether under variable high tensions, by the poor quality in the tether material itself, etc. Mr. Leverette's comment on the simplicity of the present approach reflects different points of view in one's approach in solving a practical problem. As far as TLP conceptual design is concerned, we feel the present approach provides an optimal path which is quite adequate. The separation of first- and second-order wave forces, as suggested by Mr. Burns, has frequently been used by most hydrodynamicists. However, we would point out that the

Conceptual Design Process of a Tension Leg Platform

second-order wave forces depend on TLP motions which are 1. ' The tether CDR certainly requires the weighting coninduced by the first-order wave forces. tribution of all the cells of the wave scatter diagram. Continuing our response to the discussion by Mr. Burns, we 2. The entire system reliability is important in the design agree that single-piece construction of a TLP hull and deck of a TLP, and yet a clear procedure to assess the combinations should be included as an alternative in the parametric study if of possibilities has not been clearly defined in the industry. one-piece construction is feasible. The authors agree that a 3. W e propose to use 100-year storm wave spectrum to deck designed as open trussed supported by bracings would be obtain the statistical maximum motion and tether load relighter, but it was never expected to be four times lighter. The sponses. overprediction of deck steel by a factor of four may have been 4. The linear su~erposition technique is used in predicting caused by the difference in payloads, in TLP span, or the the wave forces and moments on a TLP. The impulsive added number of decks, etc. The 25 percent difference in column mass ~ind the retardation ~unction o~ damping are evaluated weight is quite acceptable as a first guess to a special design. based on the mean waterline. The nonlinear components such The unit in equation (4) should be specified as mph (or km/hr) as viscous damping are linearized using equivalent linear and the wind force calculated in pounds (or Newtons). damping. Another alternative would be the use of an iteration Mr. Leverette's comments about the uncertainties in tether procedure at each time step. The effects of nonlinear wave ringing and viscous damping can partially be answered by the forces are omitted in the motion calculation. This is justifiable, results from model tests. Research efforts, as mentioned by Mr. since the method of linear superposition provides an upper Leverette, will be needed for a thorough understanding of these bound as far as wave forces on the TLP are concerned. 5. From Fig. 15 we expect to have a high-frequency phenomena. Design criteria based on the risk level will be a valid alternative in designing a TLP. However, the conceptual component in heave acceleration time histories too. Neverdesign process suggested by the authors does not exclude the •theless, the coupling effects caused by roll and pitch motions use of other design criteria such as suggested by Mr. Leverette, are almost negligible for a TLP with symmetric geometry. The and there was no intention whatsoever of presenting it as the reason it is not noticeable in Fig. 15 is due to its relatively small only approach rather than a logic approach. magnitude with respect to the amplitude of heave acceleration To answer Mr. Tein's comments, cost estimation was not the induced by sway motion and als0 the poor resolution of the intention of this paper. The hydrodynamic loads should be plot. regarded as inertia loads which are induced by TLP motions. 6. The cause of the spectral peaks at 7 and 5 seconds in Fig: Model tests results would be valuable in assisting the design of 18 is due to the effect of column spacing, which produces a net a TLP, especially in the preliminary design stage. vertical force on the tether. The authors certainly agree with most of the American BuIn summary, the conceptual design approach suggested by reau of Shipping's points of view and would like to suggest the the authors can easily be modified to adopt different design following points in response to ABS's discussion: criteria in order to provide a sound basis for TLP design.

Conceptual Design Process of a Tension Leg Platform

305