Investigations on the Mechanical Behavior of an Innovative Subsurface Tension Leg Platform in Ultra-Deep Water(Part I)

ZHEN Xing-wei,HUANG Yi,ZHANG Qi

(School of Naval Architecture,Faculty of Vehicle Engineering and Mechanics,Dalian University of Technology,Dalian 116024,China)

0 Introduction

In the present days,petroleum exploration of offshore fields proceeds into water depths close to 3 000 meters.Thus,innovative concepts of offshore production systems are needed to overcome the demanding challenges presented by huge water depth and harsh environment in ultra-deep water.In this scenario,hybrid riser concept[1-5]seems to be an attractive alternative.Normally,hybrid riser consists of a vertical bundle of steel pipes upwardly tensioned by external buoyancy,and flexible jumpers connecting the top of vertical riser to a Floating Production Unit(FPU)at the sea surface are used to decouple the riser bundle from FPU motions.

Thus far,the present hybrid riser concepts are all subsea field development solutions,which have their focus on the important issues of riser system and provide a degree of vessel and field expansion flexibility with simplified riser interface,but at the expense of high drilling and workover costs as well as high flow assurance requirement of long flow lines on cold seabed.In this case,Atlantis concept[6]for deep-water drilling seems to be a promising solution.It is composed of three parts:Atlantis unit(200 to 400 meters below the sea surface),a tieback casing connecting the subsea wellhead with the upper wellhead of Atlantis unit and a drilling riser connecting the upper wellhead to the drilling unit.This means that conventional Blow-Out Preventer(BOP)can be installed on the Atlantis unit directly and subsea equipment is not necessarily subjected to very low temperatures with associated flow assurance problems.Since June 2004,China Oilfield Services Ltd(COSL)[7-9]has carried out a series of tests to prove the feasibility of this new concept to deepwater drilling and large trial operations had been gone in the South China Sea.However,the safety of Atlantis concept is still in dispute.Many of the drilling man argue that it is unsafe for the sake of a catastrophic failure of the tieback casing,which is used as an anchoring system.What is more,the stability of Atlantis unit as well as field layout problems of large offshore developments as stated before are also not satisfying under extreme current condition.

Aiming to overcome the drawbacks of existing offshore production systems in ultra-deep water as well as combine the benefits of the current dry tree and subsea tree systems,an innovative STLP system concept[10-14]is proposed for offshore petroleum production.This paper investigates in detail the mechanical behavior of the STLP at a depth of 3 000 meters.Part I of this topic here addresses the mechanical behavior of the rigid riser.Firstly,the design philosophy of STLP is introduced.Then,the mathematical models and numerical modeling approach are presented.After that,the related design process and theory are presented.On this basis,the calculation results of rigid riser’s strength,buckling as well as VIV fatigue performance are presented and discussed in detail to ensure the technical feasibility of the STLP.Finally,conclusions and discussions are made.

1 Design philosophy of STLP

1.1 STLP configuration

STLP primarily consists of three parts:a tethered subsurface Sea-star Platform(SSP),rigid risers and well completion equipment,as shown in Fig.1.

全碳纤维复合材料车体为薄壁筒形整体承载结构，主要尺寸如下：车体基本长度为19 000 mm，车体宽度为2 800 mm，车体顶面距轨面高度为3 478 mm。

The steel components of the rigid riser include standard riser joint,tapered stress joint,and keel joint.These components are strength designed per API RP 2RD[21].As the rigid riser comprises an external casing and inner production tubing,an equivalent modeling method is adopted for better computational efficiency.The basic process of the rigid riser global strength analysis is shown in Fig.7.The loading conditions selected for the strength assessment are presented in Tab.4.

Fig.1 Sketch of STLP

Fig.2 SSP dimension and overall layout

In the present study,hydrodynamic loads on tethers,risers and SSP are calculated by using an extended form of Morison’s equation,as shown in follows:

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Fig.3 STLP riser plan layout

Tab.1 Properties of rigid riser

Tab.2 Properties of stress joints and keel joint

The STLP mooring system consists of three vertically loaded sheathed spiral strand tethers,which are secured to the seabed using suction piles.The mooring system provides the stability of the SSP from which the installation of rigid risers and subsurface well completion equipment will benefit,and constrains rigid risers to move collectively and ensures positive separation as well.Tab.3 presents the detailed tether properties.

Tab.3 Tether properties

1.2 Working principle of STLP

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(4)The stress differences in the operating condition and extreme condition are small.This result indicates that the severe environment conditions do not dominate the riser stress of STLP in the present study.

Fig.4 Sketch of STLP with flexible jumpers

Fig.5 Sketch of manifold assembly

As noted preciously,specific advantages of STLP concept are offered as follows:

(1)Riser loads on the FPU are substantially reduced.

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(2)Field layout is optimized and allows large offshore developments and unforeseen future field expansion,as a large number of risers can be supported.

该指标体系主要从外在能力和潜在能力两个领域进行设计，共由5个一级指标、13个二级指标和40个三级指标。其中外在能力包含知识和技能2个一级指标，5个二级指标和15个三级指标；潜在能力则涵盖动机、特质、意识等3个一级指标，8个二级指标以及25个三级指标，见表1。

(3)Direct access to local subsea wells is provided,and demanding flow assurance requirements can be met.

(4)In place riser fatigue is low,as the FPU motions are directly transferred to the flexible jumpers and not to the STLP,which will not be subjected to direct wave loading either due to the SSP depth.

(5)New technology of the SWC offers improved technical and commercial performance.

(6)Flexibility of the installation schedule is improved,as FPU arrival at the field site is not necessary.

2 Mathematical and numerical models

2.1 Hydrodynamic loads

Five rigid risers are supposed to connect to the wellhead located at SSP directly with‘fixed’ tensioners[17],and all these risers are composed by an external casing and inner production tubing,which conducts the oil.The space between these two structures is filled by nitrogen.The detailed properties of rigid risers are presented in Tab.1.It should be noted that the connections between the risers and subsea wellhead and between risers and SSP are made by steel tapered stress joints.Besides,a steel keel joint between the riser and the keel opening of SSP is used to locally stiffen the fatigue critical region of the outer casing.The steel material of API X-80 is preferred,whose σy(yield stress)is 80 ksi.More details regarding the stress joints and keel joint are presented in Tab.2.A projection of rigid risers spread from SSP to the seabed is shown in Fig.3.Note that the spacing between neighboring risers at SSP is primarily driven to provide enough space for the shallow-water rated X-mas trees,whereas the well spacing at the seabed is chosen to avoid clashing.

where Fwis the fluid force,Δ is the mass of fluid displaced by the body,awis the fluid acceleration relative to earth,Cais the added mass coefficient,aris the fluid acceleration relative to the body,ρ is the fluid density,Vris the fluid velocity relative to the body,Cdis the drag coefficient,S is the drag area.The term in parentheses is the inertia force and the other term is the drag force.

2.2 Riser mechanical behavior

2.2.1 Riser governing equation

The rigid riser can be analyzed as a tensioned beam under axial tension,lateral loads and the effect of hydrostatic pressures due to internal and external fluids.The governing differential equation[18]for the riser static behavior undergoing small deflections can be obtained from the balance of forces and moments,as follows:

where EI is the bending stiffness,Ttwis the true wall tension,piis the internal pressure,Aiis the internal cross-sectional area of the riser,peis the external pressure around the riser,Aeis the cross-sectional area of the riseris the lateral load per unit length;wt,wiand weare the weights per unit length of the riser,the internal fluid,and the displaced fluid,respectively;x is the in-line axis,and z is the vertical axis.

2.2.2 Dynamic behavior equation

The riser motions for the in-line and transverse directions in matrix can be represented as follows:

2.3 Numerical modeling approach

Details about the physical model of STLP have already been introduced before.However,under the riser’s design point of view,it is important to further point out that the final top tension is un-adjustable as the position is fixed relative to the wellhead of SSP.Besides,the final top tension will be almost constant since STLP primarily suffers from the steady current induced load while the influence of direct wave loading is minimized.

Marine dynamics program Orcaflex[19]is used to model STLP configuration.The SSP is modeled as a 6 degrees of freedom lumped buoy,whose geometric and hydrodynamic properties are accurately derived and imported into Orcaflex.All rigid risers and tethers are simulated by a line unit,and line contact model is used to simulate the interaction between the keel joint and the SSP.The finite element model of the rigid riser is translated into a single beam element with properties which represent the equivalent composite structure.Note that the contribution from the production tubing is considered to influence the bending and torsional stiffness simply but the axial stiffness[20].

按照仿真好的单腔,双腔及抽头结构的参数初始值搭建带通模块,在驱动模式(Driven modal)下的每个谐振杆上设置集总端口(Lumped Port)激励,输入输出端口设置为Wave Port激励并进行仿真。把HFSS的仿真数据导入到Designer电路中,对全腔进行协同仿真调试[7-8]。

A great amount of time was dedicated in the present study to develop a proper way of modeling required constant top tension on the rigid risers.As risers are tied to the SSP directly without stroke,the conventional tensioning model of Winch provided by the Orcaflex is not suitable.The final solution to this problem is to adjust the risers’length to meet the top tension requirement when the total net buoyancy provided by SSP is determined.Fig.6 is an illustration of the STLP global modeling consideration.

Fig.6 STLP global finite element model

3 Design process and theory

3.1 Steel component strength

The SSP provides a stable subsurface working platform and supports rigid risers as well as subsurface well completion(SWC)equipment.The STLP configuration evaluated in the present study places the top of the SSP,200 meters below Mean Water Level(M.W.L)to minimize direct wave loading and mitigate current effects.The Sea-star hull design features a single column with three cantilevering trusses to which the tethers are attached radiating outwards at the base.The three cantilevering trusses are the important feature of the Sea-star structure that is designed to eliminate clashing risks between the tether and the adjacent riser while minimizing the current induced load it suffers[15].What is more,with respect to the unique design feature of SSP,no obvious phenomenon of vortex-induced motion(VIM)is demonstrated by preliminary computational fluid dynamics(CFD)[16].The main dimension and construction details of SSP are given in Fig.2.

2.1 患者一般情况 1 053例先天性上睑下垂患者中，男性752例、女性301例，年龄3～18岁，平均(6.43±4.40)岁；就诊时体质量12～42 kg，平均体质量为(23.8±7.91)kg。其中，轻度眼睑下垂174例(16.5%)，中度416例(39.5%，)，重度463例(44.0%)；单侧上睑下垂占664例(63.1%)，双侧眼睑下垂389例(36.9%)。

Fig.7 The basic process of the rigid riser global strength analysis

Tab.4 Loading cases for strength assessment

3.2 Buckling analysis

The most significant design innovation on the STLP is the first implementation of a tethered SSP,which supports all the rigid risers.As the rigid riser is fixed relative to the top of SSP,the effective length of the riser is constant and riser tension varies with the SSP offset.Especially,the top tension of downstream risers will be reduced to some extent.Thus,the downstream risers may be subjected to negative tension and consequently cause the risers to buckle under the combine action of current load and the SSP offset.Global and local buckling analyses are carried out according to DNV-OS-F101[22]for the safe design of STLP.

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3.3 Fatigue analysis

With the unique feature of STLP concept as stated before,riser cumulative fatigue damage is primarily induced by vortex induced vibration(VIV).Both long term and short term VIV fatigue analysis are considered for the rigid risers of STLP by using the mode superposition program SHEAR7 in conjunction with OrcaFlex software.It should be noted that the in-line VIV damage was also accounted for by assuming the in-line RMS stress amplitude as a percentage of the cross-flow RMS stress amplitude(0.4 in this analysis)at double the cross-flow frequency[23].Besides,fatigue damage due to long term VIV is calculated at 16 points on each cross section of the rigid riser with a 22.5°interval.The section point locations are shown in Fig.8.Finally,according to the guidance note of DNV-RP-F204[24],the design fatigue factor of 10 is selected for both long term and short term VIV analysis.

Fig.8 Section point locations

Fig.9 Current profiles

4 Results and discussions

4.1 Design environment

The effective tension and axial strain variations along the downstream riser for all the cases are presented in Fig.14 and Fig.15,respectively.It can be observed from Fig.14 that no negative tension exists in the downstream riser and can also be found from Fig.15 that the maximum compression strain is 0.042%in the extreme condition,which is far below the design compressive strain of 2.16%with respect to the DNV code.To sum up,both global and local buckling will not happen to STLP risers.Nonetheless,when flexible jumpers are connected,the SSP offset will be increased due to jumpers’drag loads and consequently the top tension of downstream risers will be reduced ulteriorly.Thus,the buckling analysis on the downstream risers of STLP with flexible jumpers needs special concern and should be further studied.

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4.2 Strength analysis

When the global strength analysis for the equivalent riser is accomplished as stated in section 3.1,the maximum radical stress,hoop stress,and axial stress in the equivalent riser can be distributed into the external casing by certain methods.Figs.10-13 illustrate the main results of external casing obtained for all loading cases described in Tab.4.The following observations can be made:

(1)Stresses at the ends of the riser and the keel opening of SSP are low in all cases due to the presence of tapered stress joints.

(2)Higher stresses are observed near the top stress joint and the keel joint.

(3)In all cases,the stresses in the risers are lower than the allowable for the X80 steel,and X65 steel can be used for most part of the riser’s length.Thus,riser joints with various steel grades can be selected in response of the need of the cost reduction.

In the present study,STLP is aimed to act as the aided subsurface petroleum production and exporting system together with any FPU,including FPSOs,semi-submersibles,TLPs and Spars.It is assumed that the subsea wells required are pre-drilled.Then,STLP including SSP,rigid risers and SWC equipment is installed and in service at the field site.Finally,the petroleum from the reservoir is transmitted from STLP to the FPU by means of flexible jumpers,which are in a slack catenary shape to isolate the STLP from FPU motions.The overall view of the STLP with flexible jumpers is shown in Fig.4.

With respect to the new technology of SWC,shallow-water rated X-mas trees are mounted atop SSP directly,and there will be three strings of production tubing contained in one rigid riser typically.In order to reduce the number of flexible jumpers to optimize the interface with the FPU and eliminate the risk of twisting,a functional manifold[11]is designed to make strings connection,as shown in Fig.5.The top of the manifold supports gooseneck assembly connection for the flexible jumper.

(5)Compared to other cases,higher stress utilization occurs in the operating condition,as a consequence of the lower allowable stress associated.

Fig.10 Riser’s max stress in LC01

Fig.11 Riser’s max stress in LC02

Fig.12 Riser’s max stress in LC03

Fig.13 Max stress of riser’s top section in LC03

4.3 Buckling analysis

The buckling problem of downstream riser is checked under the combined load of tension and bending moment,and the loading conditions selected are the same as strength assessment.

The governing environment condition used to investigate on the global behavior of STLP and short term VIV analysis in particular is 100-year return period typhoon current profile v100without combination of wave load case,unless specified.The 10-year return monsoon current profile is used to evaluate the strength and buckling analysis in the operating condition.Besides,a total of 104 current profiles are used for the riser long term VIV analysis,which is benchmarked against 1-year return monsoon current profile.Three types of current profiles mentioned above are comparatively given in Fig.9.

Fig.14 Effective tension variations of the downstream riser under different loading conditions

Fig.15 Axial strain variations of the downstream riser under different loading conditions

4.4 VIV fatigue analysis

Long term and short term VIV analysis results for the riser are summarized in Tab.5,and detailed results are illustrated in Figs.16 and 17.It can be found that both long term and short term VIV fatigue lives meet the practical engineering requirements well,and the minimum fatigue life of 169 years is obtained at the keel joint,where the currents influence is supposed to be stronger.Besides,the fatigue life of the major part of the riser is basically the same and far above the design requirement,so no VIV suppression devices are needed.

Tab.5 VIV fatigue analysis results

Fig.16 Short term fatigue damage of VIV analysis

Fig.17 Long term fatigue damage of VIV analysis

Fig.18 Probability of occurrence versus participation in damage

The participation in response of the main current profiles for long term VIV analysis is shown in Fig.18.It can be observed that the top 10 current profiles accounts for 92.30%in total fatigue damage,while the probability of these current is just 6.63%.

5 Conclusions

This paper investigates in detail the global behavior of the STLP at a depth of 3 000 meters.Part I of this topic here addresses the global behavior of the rigid riser.The main conclusions are as follows:

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(1)The severe environment conditions do not dominate the riser stress of STLP.Nonetheless,great concern should be taken to the adjacent part of the riser’s stress joint and keel joint where high stresses are observed.The material of low steel grade,such as X65,can be used for the most part of the riser’s length in response of the need of the cost reduction.

(2)Great concern should be taken to the downstream riser which is more susceptible to undergo the compression.

(3)The fatigue life of the major part of the riser is basically the same and far above the design requirement,so no VIV suppression devices are needed.

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(4)The global analysis including strength analysis,buckling analysis,and VIV fatigue analysis,demonstrates that the STLP design complies with relevant specifications and industrial codes well.

(5)The obtained conclusions and techniques in the study have wide ranging applicability in reference to the engineering design and design analysis aspects of deepwater free standing hybrid riser system.

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In summary,the investigations on the global behavior of the riser have confirmed the technical feasibility and economic advantage of this system as the alternative for well and riser solution in ultra-deep water.The STLP behaves almost quasi-statically and can eliminate nearly all wave induced challenges for the conventional offshore production systems,using proven components and technologies.Part II of this topic will follow for the mooring pattern as well as unique design criteria establishment on the STLP stability.

Acknowledgment

This research is financially supported by the National Natural Science Foundation of China(No.51709041)and China Postdoctoral Science Foundation(2017M610178).Particularly the kind suggestions and comments by anonymous reviewers are appreciated.

数字化施工图审查系统在具备施工图审查业务模块之外，增加对勘察设计行业信息采集和监督管理板块，有利于建设行政主管部门全面了解勘察设计产业状况和从业单位人员信用情况，进一步提升对勘察设计行业的有效监管，规范勘察设计市场秩序。

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