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Parametric study of multicomponent mooring lines at catenary form in terms of anchoring cost
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4th International Conference on Energy and Environment Research, ICEER 2017, 17-20 July 2017, Porto, Portugal 15thof International Symposium on District Heating Parametric The study multicomponent mooring linesand atCooling catenary form in terms of anchoring cost Assessing the feasibility of using the heat demand-outdoor Paulo A. Figueiredo, Francisco M. Brójo temperature function for a long-term district heat* demand forecast Universidade da Beira Interior, Departamento de Ciências Aeroespaciais, Covilhã 6200-001, Portugal
I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc a
IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France
Abstract
The process of anchoring FPSOs (floating production storage offloading) is one of the most important parameters in the preparation for exploitation of new oilfields in terms of capital expenditures [1] (CAPEX). Precise position and the motion control are indispensable factors for offshore platforms. Mooring passive systems are the most reliable and common devices to obtain the Abstract required position and control. Based on these principles, a methodology of quasi-static analysis of single and multi-component mooring systems in deep-water has been developed by several authors. In this work was developed a relation of the effective cost District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the of a mooring line with minimum catenary suspended length. Proposed method was applied to know the mooring costs of a new greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat single mooring line and compared with the mooring line of the FPSO Glen Lyon in the Schiehallion Field. Costs will be compared sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, as well as minimum length and vessel mooring line offset. prolonging the investment return period. The main scope of this paper is to assess the feasibility of using the heat demand – outdoor temperature function for heat demand © 2017 The Authors. Published by Elsevier Ltd. forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 Peer-review under responsibility of the scientific committee of the 4th International Conference on Energy and Environment buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district Research. renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were comparedCaternary with results fromsystem; a dynamic heat demand model, previously developed and validated by the authors. Keywords: mooring mooring lines; offshore anchoring. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). 1. Introduction The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and The upstream industry is always for new methods improvements for lowering the price renovation scenarios considered). On evolving the other and hand,searching function intercept increased and for 7.8-12.7% per decade (depending on the ofcoupled hydrocarbons production [2]. For onshore and shallow water production, many options are available, however scenarios). The values suggested could be used to modify the function parameters for the scenarios considered,for and deep andthe ultra-deep waters the solutions are based most of the times on stand-alone facilities or tie-back field improve accuracy of heat demand estimations. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Tel.: +251-275-329-732; fax: +251-275-329-768. E-mail address: [email protected] Keywords: Heat demand; Forecast; Climate change
1876-6102 © 2017 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of the scientific committee of the 4th International Conference on Energy and Environment Research. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 4th International Conference on Energy and Environment Research. 10.1016/j.egypro.2017.10.303
Paulo A. Figueiredo et al. / Energy Procedia 136 (2017) 456–462 M. Brójo et al. / Energy Procedia 00 (2017) 000–000
457
connected to a FPSO [2]. Nomenclature 𝜔𝜔 𝜑𝜑
AE TH Tz h 𝜌𝜌
g F, D 𝑙𝑙 𝑙𝑙𝑠𝑠 𝑥𝑥 V H 𝑖𝑖
Weight per unit length Angle between mooring line and horizontal Axial Stiffness per unit length (Area multiplied by Young Modulus) Horizontal tension Vertical tension Height of each line segment Density of sea water Gravity acceleration Current force and drag Seabed mooring length Suspended catenary length Horizontal scope (projected horizontal distance from fairlead to touch down point) Vertical fairlead Horizontal force for a given fairlead tension Segment of mooring line
FPSO’s are widely used for deep waters and ultra-deep waters in oil and gas exploration and production. Y. Wang et al [3] have studied the structural reliability based dynamic positioning of Turret Moored FPSOs in extreme seas. S. Santos et al [4] defined the 6 phases of the life cycle of the methodology of a product. The authors analysed the cost of a floating wind farm mooring system. In this study, a mooring static analysis was performed with ORCAFLEX with the same conditions as the ones already installed in Glen Lyon (FPSO, mooring lines and risers). After quasi-static and dynamic analysis, an algorithm was implemented using MATLAB to generate the equivalence outputs for the static simulation. After this step, a new analysis of the whole system was performed with ORCAFLEX to verify the difference in vessels offset to meet the requirements from DNV GL [5, 6, 7, 8]. The aim of this study is to define a relation to evaluate the cost of a mooring line with minimum catenary suspended length. In the context of this study a multi component mooring line with 5 segments will be analysed. The effective total length of the catenary and suspended weight will be the same so the suction piles stay in the actual position. The diameters of the chain links and the wires will be compared as well as each segment length. A range of chain and wire diameters will be used. In the analysis, the chosen diameters will be 133, 137, 142, 147, 152 and 157 [mm]. The mooring wire diameters in analysis will be 121, 127, 133, 140, 144, 146, 153 and 156 [mm]. 1.1. Schiehallion field This fields have been discovered in 1993, it is estimated that there are recoverable reserves of about 350-500 million barrels and is approximately 130 km west of Shetland and 35 km east from Faroe-UK. Schiehallion field has been in production since 1998 through the Schiehallion FPSO. Recent studies on the existing wells have confirmed that a significant oil potential remain to be exploited from these reservoirs [9]. The former FPSO has deteriorated through the years due to production operation, therefore Schiehallion FPSO was replaced. The new FPSO was designed for 25 years. Glen Lyon FPSO has 270 m length, 52 m breadth and 30 m depth and arrived at west Shetland in June 2016, it has the storage capacity of 800,000 barrels of oil and is expected to process 130 thousand barrels of oil and 220 million cubic feet of gas per day [10]. Glen Lyon has 20 catenary mooring lines and 24 pliant wave risers. The schematic of the system can be seen in figure 1. Glen Lyon will passively weathervane with no thruster assistance. The design is based on R3S/R4S studless chain, of no more than 158.75 mm of diameter and sheathed spiral strand wire. 1.2. Catenary theory For deep water, mooring lines are usually composed of several segments. These segments are a combination of
Paulo A. Figueiredo et al. / Energy Procedia 136 (2017) 456–462 M. Brójo et al. / Energy Procedia 00 (2017) 000–000
458
chain and rope/wire. This combination increases the stiffness in the mooring system, meanwhile getting a much more lighter cable system. Tension forces in the cables, which are the means of applying restraining forces on the floating structure are due the cable weight and elastic properties [11]. The Catenary equations in offshore environment have been developed in the last decades due to the need to anchor Vessels. In the preliminary design, the static catenary method is selected to anchoring a floating vessel, this method is based in the following assumptions [12]: • The seabed is flat and horizontal; • Bending stiffness of the mooring line can be neglected; • The mooring lines are on a vertical plane comprising x-z coordinates only. Several authors have been studying multi component mooring systems, this field is usually analysed using two main approaches, inelastic catenary approach and elastic catenary approach. In this paper, only the elastic approach will be used. Figure 2 shows on detail a mooring line element and the force components applied to that element.
Fig. 1. Glen Lyon mooring scheme (CATIA V5)
Fig. 2. 2D forces acting on mooring line element [13]
The axial tension of the mooring line segment of figure 2, in static equilibrium condition can be estimated by the following equations; 𝑑𝑑𝑑𝑑 − 𝜌𝜌𝜌𝜌𝜌𝜌𝜌𝜌𝜌𝜌 𝜌 𝜌𝜌𝜌 𝜌𝜌𝜌 𝜌𝜌 𝜌 𝜌𝜌𝜌𝜌 𝜌
𝑇𝑇
𝐴𝐴𝐴𝐴
(1)
] 𝑑𝑑𝑑𝑑
𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑇𝑇𝑇𝑇𝑇𝑇 𝑇𝑇 𝑇𝑇𝑇
𝑇𝑇
𝐴𝐴𝐴𝐴
) 𝑑𝑑𝑑𝑑
To solve the equation, the marine current effects are ignored, then the equation becomes 𝑇𝑇 ′ =𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇
Solving the equation above, the segment tension of the mooring line become as follow 𝑇𝑇𝑇𝑇𝑇𝐻𝐻 +𝜔𝜔𝜔 𝜔 (𝜔𝜔𝜔𝜔𝜔𝜔𝜔𝜔𝜔)𝑧𝑧
(2) (3) (4)
The vertical tension of the mooring can be written as (5) 𝑇𝑇𝑧𝑧 =𝜔𝜔𝜔𝜔𝑠𝑠 If the maximum external load Tmax is known, the minimum mooring line length, lmin, required to ensure the whole mooring line resistance can be calculated by the following equation or
𝑙𝑙𝑚𝑚𝑚𝑚𝑚𝑚 =ℎ(2
𝑇𝑇𝑚𝑚𝑚𝑚𝑚𝑚 𝜔𝜔𝜔
− 1)
2
(6)
𝑥𝑥
𝑙𝑙𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑎𝑎 ∗ sinh 𝑎𝑎 The full projected seabed length is 𝑋𝑋 𝑋𝑋𝑋𝑋𝑋𝑋𝑠𝑠 + 𝑥𝑥𝑥 𝑋𝑋 𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑋
𝑇𝑇𝐻𝐻
𝜔𝜔𝜔
1 2
) +
𝑇𝑇𝐻𝐻 𝜔𝜔
cosh (1+
(7) (8) 𝜔𝜔𝜔 −1 𝑇𝑇𝐻𝐻
)
The projected height of the mooring lines can be expressed as 𝑥𝑥 ℎ= 𝑎𝑎 𝑎𝑎𝑎𝑎𝑎𝑎 ) − 1] 𝑎𝑎 Where 𝑇𝑇 𝑎𝑎 𝑎 𝐻𝐻 𝜔𝜔 The maximum tension in the cable can be written as 𝑇𝑇𝑚𝑚𝑚𝑚𝑚𝑚 =𝑇𝑇𝐻𝐻 +𝜔𝜔𝜔𝜔
(9)
(10) (11) (12)
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1.3. Multi component theory According to Umaru Ba [14], for multi-component mooring line equations, the number of configurations depends on: • The number of components making up the mooring line; • The type of anchoring and mooring systems. In recent studies Yassir et al 2010 [4] have defined an implicit iterative solution of catenary equations to analyse a multi-component catenary mooring system. The authors analysed the relationship for three analysis models, positive, negative and vertical excursions. K. Ansari [15] defined for a uniform segment hanging freely under its own weight w, that the governing differential equations is 𝑑𝑑 2 𝑧𝑧
𝑤𝑤 𝑑𝑑𝑑𝑑
= (13) 𝐻𝐻 𝑑𝑑𝑑𝑑 ds is the infinitesimal element of the cable, for the horizontal projection Xc and catenary height hc. For each segment, they can be expressed by 𝑑𝑑𝑑𝑑 2
𝑋𝑋𝑐𝑐 = 𝑎𝑎𝑖𝑖 ∗ [sinh
𝜔𝜔𝑖𝑖 𝑙𝑙𝑠𝑠 +𝑉𝑉
− sinh
𝐻𝐻 𝜔𝜔𝑖𝑖 𝑙𝑙𝑠𝑠 +𝑉𝑉
𝑉𝑉 −1
𝐻𝐻
]
𝑉𝑉 −1
(14) 𝑉𝑉 −1
(15)
+ sinh ) − cosh (sinh )] ℎ𝑐𝑐 = 𝑎𝑎𝑖𝑖 ∗ [cosh ( 𝐻𝐻 𝐻𝐻 𝐻𝐻 The total vertical tension is 𝑇𝑇𝑧𝑧 = ∑𝑖𝑖1 𝜔𝜔𝑖𝑖 𝑙𝑙𝑠𝑠 𝑖𝑖 The total depth for multi component catenary is ℎ𝑡𝑡 = ∑𝑖𝑖1 ℎ𝑐𝑐 The full seabed length of a multi component catenary line can be expressed as 𝑋𝑋 𝑋 ∑𝑖𝑖1 𝑙𝑙𝑖𝑖 − ∑𝑖𝑖1 𝑙𝑙𝑠𝑠 𝑖𝑖 + ∑𝑖𝑖1 𝑥𝑥𝑖𝑖
(16) (17) (18)
1.4. Standard catenary conditions
A mooring line (Figure 3) can be divided in 5 segments. Segments (1 e 2) are lying on the seabed, segment 3 has one part lying on the seabed and other part suspended, segments 4 and 5 are completely suspended making and angle with the seabed. The 5 segments have the following characteristics: Table 1. Multi component mooring line [15] Segment
1
2
3
4
5
Type
Chain
Wire
Chain
Wire
Chain
Diameter [m]
0.157
0.144
0.152
0.144
0.152
Weight [kg/m]
426.1
84.0
399.4
84.0
399.4
Length [m]
10.0
390.0
940.0
490.0
50.0
The full length of the catenary is 1880 m and the anchor radius is approximately 1700 m [16].
Fig. 3. Multi component mooring line
To estimate the cost of the mooring line a quotation price for the components was obtained from some companies through personal communication. The quotation price for R4S was 2.33-2.85 €/kg for stud less chain with 126/136
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Paulo A. Figueiredo et al. / Energy Procedia 136 (2017) 456–462 M. Brójo et al. / Energy Procedia 00 (2017) 000–000
[mm] in October 2016. The quotation price for sheathed spiral strand, including certification/testing and transportation reels: 8 off 100 m 133/155 [mm] 1.4 – 1.5 M€. 2. Methodology For the development of this study the methodology presented on the flowchart of figure 4 was applied Start
Set Mooring Line Initial Properties
For i = 1 to Number of Segments
Evaluate Type of Segments (Chain/Wire) Diameter of chain links/ wire Full Catenary Length Max Horizontal and Vertical tension Length of Segments Costs
Update Type of Segments (Chain/Wire) Diameter of chain links/ wire Full Catenary Length Max Horizontal and vertical tension Length of Segments
For i = 1 to Number of Nodes Evaluate Minimum suspended catenary and full mooring line cost
No
Convergence Achieved? Yes End
Fig. 4. Methodology flowchart
3. Results and validation Results have been obtained taking in account the FPSO Glen Lyon located at Schiehallion Field, which will sustain environmental forces applied, anchoring, mooring conditions and FPSO’s dimensions. The results obtained from the relation between minimum catenary suspended length and effective cost are given through the cloud-point of figure 5.
Fig. 5. Minimum catenary suspended length vs Mooring cost
A new model of mooring line segments was created using the results presented on figure 5. The new mooring line
Paulo A. Figueiredo et al. / Energy Procedia 136 (2017) 456–462 M. Brójo et al. / Energy Procedia 00 (2017) 000–000
461
has the following properties: Table 2. Updated multi component mooring line Segment
1
2
3
4
5
Type
Chain
Wire
Chain
Wire
Chain
Diameter [m]
0.157
0.133
0.137
0.133
0.137
Weight [kg/m]
357.0
72.4
324.5
72.4
324.5
Length [m]
10.0
408.0
922
490.0
50.0
The 3D offset of the mooring line can be seen in figure 6 (a) and 2D offset in figure 6 (b). Difference on Offset off reference proposed and reference catenary is smaller enough to ne neglected.
Fig. 6. (a) 3D Offset position case 1 [16] and new mooring line (Table 2); (b) 2D Offset position case 1 [16] and new mooring line (Table 2)
4. Conclusions An algorithm was used to create a point cloud generating a relation between minimum suspended catenary length and cost of that multi segmented catenary. The reference catenary has a minimum suspended length of 589.3 m with a quotation price of 2.8 M€ while the new catenary has a minimum length of 603.02 m with a cost of 2.1 M€. After the new analysis with ORCAFLEX of the new mooring line the offset of quasi-static analysis of the reference mooring line at the top was 12.75 m and dynamic analysis was 58.55 m. The offset of the quasi static analysis of the new catenary at the top was 12.75 m and the dynamic analysis was 59.89 m. Acknowledgements The authors are grateful to Karl C. Strømsem for all the help and to ORCINA team, especially Ms. Yvonne Morgan for the software loan agreement. The current study was funded in part by Fundação para a Ciência e Tecnologia (FCT), under project UID/EMS/00151/2013 C-MAST, with reference POCI-01-0145-FEDER-007718. References [1] Y. Bai, Q. Bai. Subsea Engineering Handbook. Elsevier (2010). [2] Castro-Santos, L., Ferreño González, S. and Diaz-Casas. Methodology to calculate mooring and anchoring costs of floating offshore wind devices. International Conference on Renewable Energies and Power Quality, Bilbao (2013). [3] Y. Wang, C. Zou. Structural reliability based dynamic positioning of turret-moored FPSOs in extreme seas. Hindawi Publishing Corporation, (2014). [4] M. Yassir, V. Kurian, I. Harahap and A. Nabilah. Design of automatic thruster assisted position mooring systems for ships. The Asia Pacific Offshore Conference. Kuala Lumpur (2010). [5] DNV. Offshore Mooring steel wire rope. DNV-OS-E304. 04/2009. [6] DNV. Position Mooring. DNV-OS-E301. 10/2010.
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[7] API. Recommended practice for design, manufacture, installation, and maintenance of synthetic fiber ropes for offshore mooring. 03/2001. [8] DNV. Offshore Mooring Chain. 10/2008. [9] BP. Schiehallion and Loyal Decommissioning Programmed Phase. 12/2012. [10] http://www.bp.com/en_gb/united-kingdom/media/press-releases/new-glen-lyon-fpso-sets-sail-for-west-of-shetland.html, accessed February (2017). [11] M. O. Chrolenko. Dynamic analysis and design of mooring lines. MSc Thesis, Norwegian University of Science and Technology (2013). [12] C. Siow, J. Koto, H. Yasukawa, A. Matsuda, D. Terada, C. Soares, and Muhamad Zameri bin Mat Samad. Strength Analysis of FPSO’s Mooring Lines. The 1st Conference on Ocean, Mechanical and Aerospace. Pekambaru (2014). [13] O. Faltinsen. Sea Loads on Ships and Offshore Structures, Cambridge University Press (1990). [14] U. Ba. Analysis of Mooring and Steel Catenary Riser System in Ultra Deep Water. PhD Thesis. Newcastle University (2011). [15] K. Ansari. Mooring with Multicomponent Cable System., Journal of Energy Resources Technology 102.12: (2009): 62-69. [16] BP. QD-BP-MR-SPE-0002. Model Basin Test Specification - Phase 1 Concept Assessment. (2008).
ScienceDirect Availableonline onlineatatwww.sciencedirect.com www.sciencedirect.com Available Energy Procedia 00 (2017) 000–000
ScienceDirect ScienceDirect
www.elsevier.com/locate/procedia
Energy (2017) 000–000 456–462 EnergyProcedia Procedia136 00 (2017) www.elsevier.com/locate/procedia
4th International Conference on Energy and Environment Research, ICEER 2017, 17-20 July 2017, Porto, Portugal 15thof International Symposium on District Heating Parametric The study multicomponent mooring linesand atCooling catenary form in terms of anchoring cost Assessing the feasibility of using the heat demand-outdoor Paulo A. Figueiredo, Francisco M. Brójo temperature function for a long-term district heat* demand forecast Universidade da Beira Interior, Departamento de Ciências Aeroespaciais, Covilhã 6200-001, Portugal
I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc a
IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France
Abstract
The process of anchoring FPSOs (floating production storage offloading) is one of the most important parameters in the preparation for exploitation of new oilfields in terms of capital expenditures [1] (CAPEX). Precise position and the motion control are indispensable factors for offshore platforms. Mooring passive systems are the most reliable and common devices to obtain the Abstract required position and control. Based on these principles, a methodology of quasi-static analysis of single and multi-component mooring systems in deep-water has been developed by several authors. In this work was developed a relation of the effective cost District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the of a mooring line with minimum catenary suspended length. Proposed method was applied to know the mooring costs of a new greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat single mooring line and compared with the mooring line of the FPSO Glen Lyon in the Schiehallion Field. Costs will be compared sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, as well as minimum length and vessel mooring line offset. prolonging the investment return period. The main scope of this paper is to assess the feasibility of using the heat demand – outdoor temperature function for heat demand © 2017 The Authors. Published by Elsevier Ltd. forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 Peer-review under responsibility of the scientific committee of the 4th International Conference on Energy and Environment buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district Research. renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were comparedCaternary with results fromsystem; a dynamic heat demand model, previously developed and validated by the authors. Keywords: mooring mooring lines; offshore anchoring. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). 1. Introduction The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and The upstream industry is always for new methods improvements for lowering the price renovation scenarios considered). On evolving the other and hand,searching function intercept increased and for 7.8-12.7% per decade (depending on the ofcoupled hydrocarbons production [2]. For onshore and shallow water production, many options are available, however scenarios). The values suggested could be used to modify the function parameters for the scenarios considered,for and deep andthe ultra-deep waters the solutions are based most of the times on stand-alone facilities or tie-back field improve accuracy of heat demand estimations. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Tel.: +251-275-329-732; fax: +251-275-329-768. E-mail address: [email protected] Keywords: Heat demand; Forecast; Climate change
1876-6102 © 2017 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of the scientific committee of the 4th International Conference on Energy and Environment Research. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 4th International Conference on Energy and Environment Research. 10.1016/j.egypro.2017.10.303
Paulo A. Figueiredo et al. / Energy Procedia 136 (2017) 456–462 M. Brójo et al. / Energy Procedia 00 (2017) 000–000
457
connected to a FPSO [2]. Nomenclature 𝜔𝜔 𝜑𝜑
AE TH Tz h 𝜌𝜌
g F, D 𝑙𝑙 𝑙𝑙𝑠𝑠 𝑥𝑥 V H 𝑖𝑖
Weight per unit length Angle between mooring line and horizontal Axial Stiffness per unit length (Area multiplied by Young Modulus) Horizontal tension Vertical tension Height of each line segment Density of sea water Gravity acceleration Current force and drag Seabed mooring length Suspended catenary length Horizontal scope (projected horizontal distance from fairlead to touch down point) Vertical fairlead Horizontal force for a given fairlead tension Segment of mooring line
FPSO’s are widely used for deep waters and ultra-deep waters in oil and gas exploration and production. Y. Wang et al [3] have studied the structural reliability based dynamic positioning of Turret Moored FPSOs in extreme seas. S. Santos et al [4] defined the 6 phases of the life cycle of the methodology of a product. The authors analysed the cost of a floating wind farm mooring system. In this study, a mooring static analysis was performed with ORCAFLEX with the same conditions as the ones already installed in Glen Lyon (FPSO, mooring lines and risers). After quasi-static and dynamic analysis, an algorithm was implemented using MATLAB to generate the equivalence outputs for the static simulation. After this step, a new analysis of the whole system was performed with ORCAFLEX to verify the difference in vessels offset to meet the requirements from DNV GL [5, 6, 7, 8]. The aim of this study is to define a relation to evaluate the cost of a mooring line with minimum catenary suspended length. In the context of this study a multi component mooring line with 5 segments will be analysed. The effective total length of the catenary and suspended weight will be the same so the suction piles stay in the actual position. The diameters of the chain links and the wires will be compared as well as each segment length. A range of chain and wire diameters will be used. In the analysis, the chosen diameters will be 133, 137, 142, 147, 152 and 157 [mm]. The mooring wire diameters in analysis will be 121, 127, 133, 140, 144, 146, 153 and 156 [mm]. 1.1. Schiehallion field This fields have been discovered in 1993, it is estimated that there are recoverable reserves of about 350-500 million barrels and is approximately 130 km west of Shetland and 35 km east from Faroe-UK. Schiehallion field has been in production since 1998 through the Schiehallion FPSO. Recent studies on the existing wells have confirmed that a significant oil potential remain to be exploited from these reservoirs [9]. The former FPSO has deteriorated through the years due to production operation, therefore Schiehallion FPSO was replaced. The new FPSO was designed for 25 years. Glen Lyon FPSO has 270 m length, 52 m breadth and 30 m depth and arrived at west Shetland in June 2016, it has the storage capacity of 800,000 barrels of oil and is expected to process 130 thousand barrels of oil and 220 million cubic feet of gas per day [10]. Glen Lyon has 20 catenary mooring lines and 24 pliant wave risers. The schematic of the system can be seen in figure 1. Glen Lyon will passively weathervane with no thruster assistance. The design is based on R3S/R4S studless chain, of no more than 158.75 mm of diameter and sheathed spiral strand wire. 1.2. Catenary theory For deep water, mooring lines are usually composed of several segments. These segments are a combination of
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chain and rope/wire. This combination increases the stiffness in the mooring system, meanwhile getting a much more lighter cable system. Tension forces in the cables, which are the means of applying restraining forces on the floating structure are due the cable weight and elastic properties [11]. The Catenary equations in offshore environment have been developed in the last decades due to the need to anchor Vessels. In the preliminary design, the static catenary method is selected to anchoring a floating vessel, this method is based in the following assumptions [12]: • The seabed is flat and horizontal; • Bending stiffness of the mooring line can be neglected; • The mooring lines are on a vertical plane comprising x-z coordinates only. Several authors have been studying multi component mooring systems, this field is usually analysed using two main approaches, inelastic catenary approach and elastic catenary approach. In this paper, only the elastic approach will be used. Figure 2 shows on detail a mooring line element and the force components applied to that element.
Fig. 1. Glen Lyon mooring scheme (CATIA V5)
Fig. 2. 2D forces acting on mooring line element [13]
The axial tension of the mooring line segment of figure 2, in static equilibrium condition can be estimated by the following equations; 𝑑𝑑𝑑𝑑 − 𝜌𝜌𝜌𝜌𝜌𝜌𝜌𝜌𝜌𝜌 𝜌 𝜌𝜌𝜌 𝜌𝜌𝜌 𝜌𝜌 𝜌 𝜌𝜌𝜌𝜌 𝜌
𝑇𝑇
𝐴𝐴𝐴𝐴
(1)
] 𝑑𝑑𝑑𝑑
𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑇𝑇𝑇𝑇𝑇𝑇 𝑇𝑇 𝑇𝑇𝑇
𝑇𝑇
𝐴𝐴𝐴𝐴
) 𝑑𝑑𝑑𝑑
To solve the equation, the marine current effects are ignored, then the equation becomes 𝑇𝑇 ′ =𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇
Solving the equation above, the segment tension of the mooring line become as follow 𝑇𝑇𝑇𝑇𝑇𝐻𝐻 +𝜔𝜔𝜔 𝜔 (𝜔𝜔𝜔𝜔𝜔𝜔𝜔𝜔𝜔)𝑧𝑧
(2) (3) (4)
The vertical tension of the mooring can be written as (5) 𝑇𝑇𝑧𝑧 =𝜔𝜔𝜔𝜔𝑠𝑠 If the maximum external load Tmax is known, the minimum mooring line length, lmin, required to ensure the whole mooring line resistance can be calculated by the following equation or
𝑙𝑙𝑚𝑚𝑚𝑚𝑚𝑚 =ℎ(2
𝑇𝑇𝑚𝑚𝑚𝑚𝑚𝑚 𝜔𝜔𝜔
− 1)
2
(6)
𝑥𝑥
𝑙𝑙𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑎𝑎 ∗ sinh 𝑎𝑎 The full projected seabed length is 𝑋𝑋 𝑋𝑋𝑋𝑋𝑋𝑋𝑠𝑠 + 𝑥𝑥𝑥 𝑋𝑋 𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑋
𝑇𝑇𝐻𝐻
𝜔𝜔𝜔
1 2
) +
𝑇𝑇𝐻𝐻 𝜔𝜔
cosh (1+
(7) (8) 𝜔𝜔𝜔 −1 𝑇𝑇𝐻𝐻
)
The projected height of the mooring lines can be expressed as 𝑥𝑥 ℎ= 𝑎𝑎 𝑎𝑎𝑎𝑎𝑎𝑎 ) − 1] 𝑎𝑎 Where 𝑇𝑇 𝑎𝑎 𝑎 𝐻𝐻 𝜔𝜔 The maximum tension in the cable can be written as 𝑇𝑇𝑚𝑚𝑚𝑚𝑚𝑚 =𝑇𝑇𝐻𝐻 +𝜔𝜔𝜔𝜔
(9)
(10) (11) (12)
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1.3. Multi component theory According to Umaru Ba [14], for multi-component mooring line equations, the number of configurations depends on: • The number of components making up the mooring line; • The type of anchoring and mooring systems. In recent studies Yassir et al 2010 [4] have defined an implicit iterative solution of catenary equations to analyse a multi-component catenary mooring system. The authors analysed the relationship for three analysis models, positive, negative and vertical excursions. K. Ansari [15] defined for a uniform segment hanging freely under its own weight w, that the governing differential equations is 𝑑𝑑 2 𝑧𝑧
𝑤𝑤 𝑑𝑑𝑑𝑑
= (13) 𝐻𝐻 𝑑𝑑𝑑𝑑 ds is the infinitesimal element of the cable, for the horizontal projection Xc and catenary height hc. For each segment, they can be expressed by 𝑑𝑑𝑑𝑑 2
𝑋𝑋𝑐𝑐 = 𝑎𝑎𝑖𝑖 ∗ [sinh
𝜔𝜔𝑖𝑖 𝑙𝑙𝑠𝑠 +𝑉𝑉
− sinh
𝐻𝐻 𝜔𝜔𝑖𝑖 𝑙𝑙𝑠𝑠 +𝑉𝑉
𝑉𝑉 −1
𝐻𝐻
]
𝑉𝑉 −1
(14) 𝑉𝑉 −1
(15)
+ sinh ) − cosh (sinh )] ℎ𝑐𝑐 = 𝑎𝑎𝑖𝑖 ∗ [cosh ( 𝐻𝐻 𝐻𝐻 𝐻𝐻 The total vertical tension is 𝑇𝑇𝑧𝑧 = ∑𝑖𝑖1 𝜔𝜔𝑖𝑖 𝑙𝑙𝑠𝑠 𝑖𝑖 The total depth for multi component catenary is ℎ𝑡𝑡 = ∑𝑖𝑖1 ℎ𝑐𝑐 The full seabed length of a multi component catenary line can be expressed as 𝑋𝑋 𝑋 ∑𝑖𝑖1 𝑙𝑙𝑖𝑖 − ∑𝑖𝑖1 𝑙𝑙𝑠𝑠 𝑖𝑖 + ∑𝑖𝑖1 𝑥𝑥𝑖𝑖
(16) (17) (18)
1.4. Standard catenary conditions
A mooring line (Figure 3) can be divided in 5 segments. Segments (1 e 2) are lying on the seabed, segment 3 has one part lying on the seabed and other part suspended, segments 4 and 5 are completely suspended making and angle with the seabed. The 5 segments have the following characteristics: Table 1. Multi component mooring line [15] Segment
1
2
3
4
5
Type
Chain
Wire
Chain
Wire
Chain
Diameter [m]
0.157
0.144
0.152
0.144
0.152
Weight [kg/m]
426.1
84.0
399.4
84.0
399.4
Length [m]
10.0
390.0
940.0
490.0
50.0
The full length of the catenary is 1880 m and the anchor radius is approximately 1700 m [16].
Fig. 3. Multi component mooring line
To estimate the cost of the mooring line a quotation price for the components was obtained from some companies through personal communication. The quotation price for R4S was 2.33-2.85 €/kg for stud less chain with 126/136
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[mm] in October 2016. The quotation price for sheathed spiral strand, including certification/testing and transportation reels: 8 off 100 m 133/155 [mm] 1.4 – 1.5 M€. 2. Methodology For the development of this study the methodology presented on the flowchart of figure 4 was applied Start
Set Mooring Line Initial Properties
For i = 1 to Number of Segments
Evaluate Type of Segments (Chain/Wire) Diameter of chain links/ wire Full Catenary Length Max Horizontal and Vertical tension Length of Segments Costs
Update Type of Segments (Chain/Wire) Diameter of chain links/ wire Full Catenary Length Max Horizontal and vertical tension Length of Segments
For i = 1 to Number of Nodes Evaluate Minimum suspended catenary and full mooring line cost
No
Convergence Achieved? Yes End
Fig. 4. Methodology flowchart
3. Results and validation Results have been obtained taking in account the FPSO Glen Lyon located at Schiehallion Field, which will sustain environmental forces applied, anchoring, mooring conditions and FPSO’s dimensions. The results obtained from the relation between minimum catenary suspended length and effective cost are given through the cloud-point of figure 5.
Fig. 5. Minimum catenary suspended length vs Mooring cost
A new model of mooring line segments was created using the results presented on figure 5. The new mooring line
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has the following properties: Table 2. Updated multi component mooring line Segment
1
2
3
4
5
Type
Chain
Wire
Chain
Wire
Chain
Diameter [m]
0.157
0.133
0.137
0.133
0.137
Weight [kg/m]
357.0
72.4
324.5
72.4
324.5
Length [m]
10.0
408.0
922
490.0
50.0
The 3D offset of the mooring line can be seen in figure 6 (a) and 2D offset in figure 6 (b). Difference on Offset off reference proposed and reference catenary is smaller enough to ne neglected.
Fig. 6. (a) 3D Offset position case 1 [16] and new mooring line (Table 2); (b) 2D Offset position case 1 [16] and new mooring line (Table 2)
4. Conclusions An algorithm was used to create a point cloud generating a relation between minimum suspended catenary length and cost of that multi segmented catenary. The reference catenary has a minimum suspended length of 589.3 m with a quotation price of 2.8 M€ while the new catenary has a minimum length of 603.02 m with a cost of 2.1 M€. After the new analysis with ORCAFLEX of the new mooring line the offset of quasi-static analysis of the reference mooring line at the top was 12.75 m and dynamic analysis was 58.55 m. The offset of the quasi static analysis of the new catenary at the top was 12.75 m and the dynamic analysis was 59.89 m. Acknowledgements The authors are grateful to Karl C. Strømsem for all the help and to ORCINA team, especially Ms. Yvonne Morgan for the software loan agreement. The current study was funded in part by Fundação para a Ciência e Tecnologia (FCT), under project UID/EMS/00151/2013 C-MAST, with reference POCI-01-0145-FEDER-007718. References [1] Y. Bai, Q. Bai. Subsea Engineering Handbook. Elsevier (2010). [2] Castro-Santos, L., Ferreño González, S. and Diaz-Casas. Methodology to calculate mooring and anchoring costs of floating offshore wind devices. International Conference on Renewable Energies and Power Quality, Bilbao (2013). [3] Y. Wang, C. Zou. Structural reliability based dynamic positioning of turret-moored FPSOs in extreme seas. Hindawi Publishing Corporation, (2014). [4] M. Yassir, V. Kurian, I. Harahap and A. Nabilah. Design of automatic thruster assisted position mooring systems for ships. The Asia Pacific Offshore Conference. Kuala Lumpur (2010). [5] DNV. Offshore Mooring steel wire rope. DNV-OS-E304. 04/2009. [6] DNV. Position Mooring. DNV-OS-E301. 10/2010.
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[7] API. Recommended practice for design, manufacture, installation, and maintenance of synthetic fiber ropes for offshore mooring. 03/2001. [8] DNV. Offshore Mooring Chain. 10/2008. [9] BP. Schiehallion and Loyal Decommissioning Programmed Phase. 12/2012. [10] http://www.bp.com/en_gb/united-kingdom/media/press-releases/new-glen-lyon-fpso-sets-sail-for-west-of-shetland.html, accessed February (2017). [11] M. O. Chrolenko. Dynamic analysis and design of mooring lines. MSc Thesis, Norwegian University of Science and Technology (2013). [12] C. Siow, J. Koto, H. Yasukawa, A. Matsuda, D. Terada, C. Soares, and Muhamad Zameri bin Mat Samad. Strength Analysis of FPSO’s Mooring Lines. The 1st Conference on Ocean, Mechanical and Aerospace. Pekambaru (2014). [13] O. Faltinsen. Sea Loads on Ships and Offshore Structures, Cambridge University Press (1990). [14] U. Ba. Analysis of Mooring and Steel Catenary Riser System in Ultra Deep Water. PhD Thesis. Newcastle University (2011). [15] K. Ansari. Mooring with Multicomponent Cable System., Journal of Energy Resources Technology 102.12: (2009): 62-69. [16] BP. QD-BP-MR-SPE-0002. Model Basin Test Specification - Phase 1 Concept Assessment. (2008).