THESIS SUBMITTED IN FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

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(1)NUMERICAL ANALYSIS OF WIND INDUCED RESPONSE OF. a. SPAR-MOORING-RISER SYSTEM. M. al. ay. ABDULRAHMAN EYADA IBRAHIM. FACULTY OF ENGINEERING UNIVERSITY OF MALAYA KUALA LUMPUR. U. ni v. er. si. ty. of. THESIS SUBMITTED IN FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY. 2017.

(2) ty. si. er. ni v. U of. a. ay. al. M.

(3) NUMERICAL ANALYSIS OF WIND INDUCED RESPONSE OF SPAR-MOORING-RISER SYSTEM ABSTRACT. The search for more sources of energy has become highly urgent given the excessive oil and gas consumption in the 20th century and the depletion of most hydrocarbon. a. reservoirs in the world. In recent decades, the exploitation of hydrocarbon reservoirs. ay. under the seas and oceans has been regarded a viable alternative. Several types of floating structures are used in deep water oil and gas production. Spar platforms are the. al. latest type of platforms to be designed and utilized in deep water environments.. M. Coupled behaviour of spar–mooring–riser system under random wave, current and wind. of. loads have been studied using coupled analysis method. This study conducts nonlinear analysis of a spar–mooring–riser system. The spar hull is modelled as a rigid beam. ty. element with six degrees of freedom (DOF), with catenary mooring lines and riser pipes. si. treated as hybrid beam elements. The mooring lines are connected to the spar hull at the. er. fairlead on one end and anchored onto the seabed at the other end. In a similar manner, the riser pipe is connected at the spar keel, and its lowest end is hinged to the seabed,. ni v. which is modelled as a rigid flat surface with a large area capable of mooring contact behaviour simulation. Instantaneous damping and tension fluctuation forces of the. U. mooring–riser system, as well as other properties that vary with time have also been considered. Finite element analysis of the spar–mooring–riser system simulated as a single fully coupled integrated model using the ABAQUS/AQUA code was conducted to obtain system responses under a long crested random wave with and without current and wind inclusion. Some of the obtained results from free vibration, static and dynamic analysis are compared with well–established published experimental results. Time histories, power spectral density functions, and statistical analyses were used in iii.

(4) evaluating the system responses. Riser inclusion caused more damping to the coupled spar–mooring–riser system. The maximum values of the surge, heave and pitching motions as well as mooring top tension are decreased by 22.9%, 63.3%, 20.7% and 3.1% respectively. Current load induces a significant shift in the spar position away from its original place in the random sea state in addition to a notable reduction in the heave, pitch and riser top tension responses. The diminishing fluctuation highlights the. a. firmness and controlled oscillations of the spar platform relative to its new mean. ay. position. Aerodynamic loading induces greater lateral shifting of the spar hull with 88% due to total hydro – aerodynamic loading with respect to wave and current induced. al. surge while the heave motion reduced by 13.5% for the wind and current inclusion. The tension fluctuation caused by the wind force does not increased. of. riser system.. M. comparing with the case of current only. This fact shows the firmness of the Spar-mooring-. because of the high pretension in mooring system; however, the top tension magnitude tension and Von Mises stress are significantly increased by. ty. of the mooring, riser top. er. si. 4.77%, 27.1% and 26.3% respectively.. Keywords: Spar-mooring-riser system; Coupled dynamic analysis; Deep-water. U. ni v. structures; Moored structures; Hull-mooring interaction.. iv.

(5) NUMERICAL ANALYSIS OF WIND INDUCED RESPONSE OF SPAR-MOORING-RISER SYSTEM ABSTRAK. Pencarian lebih banyak sumber tenaga telah menjadi sangat penting memandangkan penggunaan minyak dan gas yang berlebihan pada abad ke-20 dan pengurangan. a. kebanyakan takungan hidrokarbon di dunia. Dalam dekad kebelakangan ini, eksploitasi. ay. takungan hidrokarbon di bawah laut dan lautan telah dianggap sebagai alternatif yang. al. berpotensi. Beberapa jenis struktur terapung digunakan dalam pengeluaran minyak dan gas daripada 'deep water'. Platform spar adalah jenis platform terkini yang direka bentuk. M. dan digunakan dalam persekitaran air yang dalam. Tingkah laku berganda sistem 'spar-. of. mooring-riser' di bawah gelombang rawak, beban semasa dan angin telah dikaji menggunakan kaedah analisis berganda. Kajian ini menjalankan analisis nonlinear. ty. sistem 'spar-mooring-riser'. Spar hull dimodelkan sebagai unsur rasuk tegar dengan. si. enam darjah kebebasan (DOF), dengan garis-garis tambatan catenary dan paip riser. er. diperlakukan sebagai elemen rasuk hibrid. Garis-garis tambak disambungkan ke 'spar. ni v. hull' di 'fairlead' pada satu hujung dan berlabuh ke dasar laut di hujung yang lain. Dengan cara yang sama, paip riser disambungkan pada 'spar keel', dan hujung. U. terendahnya disambung kepada dasar laut, yang dimodelkan sebagai permukaan rata yang tegar dengan kawasan luas yang mampu menghasillcan 'mooring contact behavior simulation'. Daya redaman serentak dan ketegangan yang turun naik dari 'moring riser system'. serta. sifat-sifat. dipertimbangkan.. Analisis. lain. yang. unsur. berbeza-beza. terhingga. sistem. dengan. masa. juga. telah. 'spar-mooring-riser'. yang. disimulasikan sebagai satu model gabungan yang digabungkan dengan menggunakan kod ABAQUS / AQUA telah dijalankan untuk mendapatkan respon sistem di bawah gelombang rawak yang panjang tanpa mergambil hira “current and mind inclusim”. v.

(6) Beberapa hasil yang diperoleh daripada getaran bebas, analisis statik dan dinamik dibandingkan dengan keputusan ujiliaji diperolehi daripada penertoran-penertoran batan yang terkemube. 'Time history', fungsi densiti spektrum kuasa, dan analisis statistik digunakan dalam menilai tindak balas sistem. Kemasukan Riser menyebabkan lebih redaman kepada sistem spar-mooring-riser yang digabungkan. Nilai maksima 'surge', 'heave' dan 'pitching motion' serta 'mooring top tension' berkurang masing-masing. a. sebanyak 22.9%, 63.3%, 20.7% dan 3.1%. Beban semasa mendorong pergeratan yang. ay. ketara dalam kedudukan spar dari tempat asalnya dalam keadaan laut rawak sebagai tambahan kepada pengurangan yang ketara dalam 'heave', 'pitch' dan 'riser top tension'.. al. Penurunan 'fluctuation' menonjolklan 'firmness and controlled oscillations' platform. M. spar berbanding kedudukan purata yang baru. 'Aero dynamic loading' mendorong. of. 'lateral shifting' yang lebih besar 'spar hull' dengan 88% disebabkan oleh jumlah 'hydroaerodynamic loading' yang berkaitan dengan gelombang dan lonjakar arus semasa. ty. manakala 'heave motion' berkuranga sebanyak 13.5% dengan mengambil kira angina. si. dan amir berbanding dengan kes arus sahaja berbanding dengan kes semasa sahaja.. er. Fakta ini menunjukkan kekaluan sistem 'Spar-mooring-riser'. 'Tension fluctuation' yang disebabkan oleh kuasa angin tidak meningkat disebabkan 'high pre-tension' didalam. ni v. 'mooring system', 'top tension magnitude' bagi 'mooring', 'riser top tension' dan tegasan, Von Mises meningkat dengan ketara masing-masing sebanyak 4.77%, 27.1% dan. U. 26.3%.. Keywords: Spar-mooring-riser system; Coupled dynamic analysis; Deep-water structures; Moored structures; Hull-mooring interaction.. vi.

(7) ACKNOWLEDGEMENTS. I would like to express my sincere gratitude to my supervisors Dr. Mohammed Jameel and Prof. Ir. Dr. Mohd Zamin Jumaat for their constant support, guidance and motivation. It would never have been possible for me to take this work to completion without their incredible support and encouragement.. a. I would also like to thank the researchers, lab assistants, lab technicians, UM. ay. library staff. This work was supported by the University of Malaya Research Grant [RP004E-13AET]. Provided by University of Malaya, Kuala Lumpur, Malaysia.. al. Last but not least, I gratefully acknowledge the help, encouragement,. Abdulrahman Eyada Ibrahim University of Malaya Kuala Lumpur - Malaysia. U. ni v. er. si. ty. of. M. cooperation received from my family, friends and associates.. vii.

(8) TABLE OF CONTENTS Abstract .……………………………………...………….……………………… iii Abstrak ……………………………………………………………………………v Acknowledgements.................................................................................... vii Table of Contents ..................................................................................... viii List of Figures ............................................................................................ xi List of Tables ……………………………………………………………………xv. a. List of Symbols and Abbreviations ............................................................. xvi. ay. CHAPTER 1: INTRODUCTION ……………………………………………. 1. al. 1.1. General ……………………………………………………………………...1. Fixed platform ………………… ............................................. 3. 1.2.2.. Bottom Supported Compliant Platforms ……………….. ........... 3. 1.2.3.. Floating Platforms ……………….. ......................................... 4. 1.2.4.. Spar platform ………………… ............................................... 4. 1.2.5.. of. 1.2.1.. ty. M. 1.2. Offshore Platforms types ..…………………………………………………2. si. Spar design considerations ……………….. ............................. 5. er. 1.3. Problem statement …………………………………………………...…… 8 1.4. Objectives of the study ………………………………………………….. 9 Scope of the work ……………………………………………………….. ni v. 1.5.. 9. 1.6. Thesis organization ……………………………………………………… 10. U. CHAPTER 2. LITERATURE REVIEW ………………….……….…………12 2.1. Introduction ...…………………......................................................... 12 2.2. Spar mooring system response …………………………………………..12 2.3. Spar-mooring-riser system ……………………………………………….25 2.4. Stability analysis of spar platform ……………………………………...35 2.5. Critical analysis of aerodynamic loading inclusion ……………………..44 2.6. literature summary ……………………………………………………..48. viii.

(9) CHAPTER 3: METHODOLOGY …………………………………………..51 3.1. Introduction ……………………………………………………………. 51 3.2. Spar-mooring-riser Configuration ……………………………………… 51 3.3. Spar-mooring-riser system solution approach …………………………. 53 3.4. Sources of nonlinearities ……………………………………………….. 54 Variable submergence ……………………………….………... 54. 3.4.2.. Added mass ……………….. ................................................ 55. 3.4.3.. Damping ………………. .................................................... 55. 3.4.4.. Geometric non-linearity ………………. ............................... 56. 3.4.5.. Non-linearity from the boundary condition ……………… ....... 56. 3.4.6.. Non-linearity due to forces acting on the Spar platform ……….56. M. al. ay. a. 3.4.1.. 3.5. Assumptions ……………………………………………………………..57. 3.6.1.. Equation of motion ………………. ..................................... 59. 3.6.2.. Aerodynamic force formulation …………………................... 73. 3.6.3.. ty. of. 3.6. Mathematical Formulation ……………………………………………….58. si. Wave force deterministic description …………………. .......... 80 Discretization of equations of motion …………………. .......... 86. er. 3.6.4.. Virtual work principal for discretization ………………… ....... 87. 3.6.6.. Boundary conditions ………………… .................................. 96. 3.6.7.. Numerical Application ………………… ............................... 99. U. ni v. 3.6.5.. 3.7. Finite element model …………………… ........................................ 105 3.7.1.. Solution with time Integration ………………… ................... 107. 3.8. Validation of the model …………………… ..................................... 109 3.8.1.. Validation of static behavior ………………… ..................... 109. 3.8.2.. Validation of natural time periods ………………… .............. 110. 3.8.3.. Validation of Spar response ………………… ...................... 110. 3.9. Static Equilibrium of coupled system …………………… .................. 111 3.10. Response evaluation in various sea environments ……………………. 111 ix.

(10) 3.10.1.. Effect of riser inclusion ………………………. .................... 112. 3.10.2.. Long duration random wave ……………………………… .... 112. 3.10.3.. Random waves with current …………………. ..................... 112. 3.10.4.. Wind loading …………………… ....................................... 113. CHAPTER 4: RESULTS AND DISCUSSION ………………………. ...... 114 4.1. Introduction …………………… ..................................................... 114 4.2. Spar platform simulation ……………………. .................................. 114. 4.3.2.. Validation of natural time period …………………. .............. 119. 4.3.3.. Validation of dynamic characteristics …………………. ........ 119. M. al. ay. Validation of static behavior ………………… ..................... 118. Numerical studies …………………… ............................................ 123 4.4.1.. Static equilibrium of Spar-mooring-riser system ...…………. 124. 4.4.2.. Free vibration analysis ………………… ............................. 126. of. 4.5.. 4.3.1.. Numerical results …………………………...................................... 127 Effect of riser inclusion ………………… ............................ 127. si. 4.5.1.. ty. 4.4.. a. 4.3. Validation of results with experimental behavior …………………… .. 117. Current effect in random wave sea states ………………… .... 146. er. 4.5.2. 4.5.3.. Wind effect in random wave sea states ……….. ................... 159. U. ni v. CHAPTER 5: CONCLUSIONS ……………………… ............................ 173 5.1.. Developing fully coupled integrated Spar-mooring-riser system model 173. 5.2.. Effect of riser inclusion in coupled spar………………….………. ...... 174. 5.3.. Effect of current inclusion in random wave environment .................... 175. 5.4.. Effect of aerodynamic loading inclusion in random wave environment 175. 5.5.. Future recommendation …………………………………….....……… 177. REFERENCES ...................................................................................... 178 LIST OF PUBLICATIONS ………..………………………………………. 186. x.

(11) LIST OF FIGURES. Figure 1.1: Spar platform ……………………………………………………..…..……. 2 Figure 1.2: Classic Spar platform ……………………………………………………… 6 Figure 1.3: Truss Spar Platform ……………………………………………………..… 7 Figure 1.4: Cell Spar Platform ……………………………………………………….… 8. a. Figure 3.1: Schematic diagram of Spar Platform ……………………….……………. 53. ay. Figure 3.2: Sketch of Spar-mooring-riser system …………………………………..… 59. al. Figure 3.3: Mooring line coordinate System …………………………………………. 63. M. Figure 3.4: Rigid spar hull coordinate system ……………………………………...… 70 Figure 3.5: Mooring system arrangement ………………………………………..…… 96. of. Figure 3.6: Analysis Steps involved in achieving stable configuration …………….. 107. ty. Figure 4.1: Tension comparisons authenticating present study model …………....… 118. si. Figure 4.2: Evaluation of Surge time history …………………………………….…. 120. er. Figure 4.3: Power spectrum of surge motion …………………………………….…. 121 Figure 4.4: Evaluation of Heave time history ……………………………………….. 122. ni v. Figure 4.5: Evaluation of Pitch time history ………………………………………… 123. U. Figure 4.6: Deformed shape of mooring and riser with spar due to its gravity load ... 125 Figure 4.7: Stable Spar-mooring-riser under total structural load …………………... 125 Figure 4.8: Surge time history of Spar-mooring system ……………………...…….. 128. Figure 4.9: Surge response power spectrum of Spar-mooring system ………...……. 129 Figure 4.10: Surge time history of Spar-mooring-riser system ……………………... 130 Figure 4.11: Surge response power spectrum of Spar-mooring-riser system ……….. 130 Figure 4.12: Heave time history of Spar-mooring system …………………………... 132 xi.

(12) Figure 4.13: Heave response power spectrum of Spar-mooring system ……………. 132 Figure 4.14: Heave time history of Spar-mooring-riser system …………………….. 133 Figure 4.15: Heave response power spectrum of Spar-mooring-riser system ………. 134 Figure 4.16: Pitch time history of Spar-mooring system ……………………………. 134 Figure 4.17: Pitch response power spectrum of Spar-mooring system ……………... 135 Figure 4.18: Pitch time history of Spar-mooring-riser system ……………………… 136. ay. a. Figure 4.19: Pitch response power spectrum of Spar-mooring-riser system ………... 137 Figure 4.20: Mooring line 1 top tension time history of Spar-mooring system …….. 138. al. Figure 4.21: Power spectrum of mooring line 1 top tension ………………………... 138. M. Figure 4.22: Mooring line 2 top tension time history of Spar-mooring system …….. 139. of. Figure 4.23: Power spectrum of mooring line 2 top tension ………………………... 140 Figure 4.24: Mooring line 3 top tension time history of Spar-mooring system …….. 140. ty. Figure 4.25: Power spectrum of mooring line 3 top tension ………………………... 141. si. Figure 4.26: Mooring line 1 top tension time history of Spar-mooring-riser system . 142. er. Figure 4.27: Power spectrum of mooring line 1 top tension ………………………... 142. ni v. Figure 4.28: Mooring line 2 top tension time history of Spar-mooring-riser system . 143 Figure 4.29: Power spectrum of mooring line 2 top tension ………………………... 144. U. Figure 4.30: Mooring line 3 top tension time history of Spar-mooring-riser system .. 144 Figure 4.31: Power spectrum of mooring line 3 top tension ………………………... 145 Figure 4.32: Surge time history (random wave + current) ………………………….. 147. Figure 4.33: Power spectrum of surge response (random wave + current) …………. 148 Figure 4.34: Heave time history (random wave + current) …………………………. 149 Figure 4.35: Power spectrum of heave response (random wave + current) ………… 149 Figure 4.36: Pitch time history (random wave + current) …………………………... 150 xii.

(13) Figure 4.37: Power spectrum of pitch response (random wave + current) ………….. 151 Figure 4.38: Mooring line 1 top tension time history (wave + current) …………….. 152 Figure 4.39: Power spectrum of mooring line 1 top tension (wave + current) ……… 152 Figure 4.40: Mooring line 2 top tension time history (wave + current) …………….. 153 Figure 4.41: Power spectrum of mooring line 2 top tension (wave + current) ……… 154 Figure 4.42: Mooring line 3 top tension time history (wave + current) …………….. 155. ay. a. Figure 4.43: Power spectrum of mooring line 3 top tension (wave + current) ……… 155 Figure 4.44: Riser top tension time history (wave + current) ……………………….. 156. al. Figure 4.45: Power spectrum of riser top tension (wave + current) ………………… 156. M. Figure 4.46: Riser Von Mises stress time history (wave + current) ………………… 157. of. Figure 4.47: Power spectrum of riser Von Mises stress (wave + current) ………….. 158 Figure 4.48: Surge time history (random wave + current + wind) ………………….. 160. ty. Figure 4.49: Power spectrum of surge response (random wave + current + wind) …. 161. si. Figure 4.50: Heave time history (random wave + current + wind) …………………. 162. er. Figure 4.51: Power spectrum of heave response (random wave + current + wind) … 163. ni v. Figure 4.52: Pitch time history (random wave + current + wind) …………………... 164 Figure 4.53: Power spectrum of pitch response (random wave + current + wind) …. 164. U. Figure 4.54: Mooring line 1 top tension time history (wave + current + wind) …….. 165 Figure 4.55: Power spectrum of mooring line 1 top tension (wave + current + wind) 166 Figure 4.56: Mooring line 2 top tension time history (wave + current + wind) …….. 167 Figure 4.57: Power spectrum of mooring line 2 top tension (wave + current + wind) 167 Figure 4.58: Mooring line 3 top tension time history (wave + current + wind) …….. 168 Figure 4.59: Power spectrum of mooring line 3 top tension (wave + current + wind) 169 Figure 4.60: Riser top tension time history (wave + current + wind) ………………. 170 xiii.

(14) Figure 4.61: Power spectrum of riser top tension (wave + current + wind) ………… 170 Figure 4.62: Riser Von Mises stress time history (wave + current + wind) ………… 171. U. ni v. er. si. ty. of. M. al. ay. a. Figure 4.63: Power spectrum of riser Von Mises stress (wave + current + wind) ….. 171. xiv.

(15) LIST OF TABLES Table 2.1: Recapitulated of spar-mooring system ………………...…………………. 21 Table 2.2: Recapitulated of spar-mooring-riser system ……………………………… 31 Table 2.3: Recapitulated of stability analysis ……………..…………………………. 41 Table 2.4: Recapitulated of critical analysis of aerodynamic loading inclusion ……..46 Table 4.1: Geometric properties of spar (Classic JIP Spar) ………………………... 115. a. Table 4.2: Mooring line physical properties ………………………………………... 115. ay. Table 4.3: Hydrodynamic properties ……………………………………………...... 116. al. Table 4.4: Selected environmental conditions of spar-mooring-riser system ……… 117. M. Table 4.5: Comparison of natural time periods ……………………..……………... 119 Table 4.6: Natural frequencies of present coupled Spar ………..………………….. 126. of. Table 4.7: Statistical response of Spar-mooring system under random wave ……... 129. ty. Table 4.8: Statistical response of Spar-mooring-riser system under random wave …131. si. Table 4.9: Statistics of mooring lines top tension in spar-mooring system …..…...... 141. er. Table 4.10: Statistical analysis of mooring lines top tension in spar-mooring-riser. ni v. system …………………………………………………………………...145. Table 4.11: Statistical response of Spar-mooring-riser system ……………………... 148. U. Table 4.12: Statistics of mooring lines top tension in spar-mooring-riser system ….. 153 Table 4.13: Statistics of riser top tension and Von Mises stress ……….………….... 158 Table 4.14: Statistics of Spar-mooring-riser system response under (Random wave + current + wind).....……………………………………………….……. 162 Table 4.15: Statistical analysis of mooring lines top tension in spar-mooring-riser system under (Random wave + current + wind) ………………….……...169. Table 4.16: Statistical analysis of riser top tension and Von Mises stress ..………… 172 xv.

(16) LIST OF SYMBOLS AND ABBREVIATIONS. Wave amplitude. Ai. Inner cross-section area of the mooring line. Am. Outer cross-sectional area of the mooring line. Ap. Projected area of spar and topside above mean sea level. As. Cross-sectional area of the spar hull. At. Structural cross-section area of the mooring line. b vector. Unit vector in mooring bi-normal direction at Cartesian coordinate. c. Speed of the wave traveling through the fluid. C. Shape parameter. [C]. Damping matrix. CD. Drag coefficient. CDn. Normal drag coefficient. CDt. Tangential drag coefficient. CL. Lifting coefficient. CM. Inertia coefficient. ay. al. M of. ty. si. er. Normal inertia coefficient. ni v. CMn. a. a. Tangential inertia coefficient. Cp (x,z). Wind drag coefficient at elevation z and horizontal coordinate x. d. Water depth. C. Diameter of the member. Dm. Diameter of mooring line. U. CMt. Ds. Diameter of the Spar hull. e1. Torsional strain due to Torsional moment M3. ex. Unit vector in X-axis xvi.

(17) ey. Unit vector in Y-axis. ez. Unit vector in Z-axis. 𝑒⃗t. Unit vector in the axial direction. 𝑒⃗c f. Frequency in cycles/sec.. fp. Peak frequency. FB. Buoyancy force per unit length of mooring line. F mF s. Force per unit length of mooring line. Force per unit length. {F}. Static load vector. {𝐹(𝑡)}. Total force on the spar-mooring system. G(t,z). Gust factor. H. Wave height. Hs. Significant wave height. si. ty. of. M. al. F(X,Z,t). ay. Fwind (x,z,t) Aerodynamic force on the moored spar. a. Unit vector in the current direction. I(z). Turbulence intensity. Wave number. ni v. k. er. Ixx , Iyy , Izz Moment of inertia about X,Y &Z axis respectively. Stiffness matrix. [KE]. Elastic stiffness matrix for the structure. [KG]. Geometrical stiffness matrix. L. Wave length. mi. Generalized mass. M1. Bending moment employed on CML. M2. Warping moment employed on CML. M3. Twisting moment employed on CML. U. [K]. xvii.

(18) Added mass per unit length of the structure. [M]. Mass matrix. N. Axial force variable/Normal force component on CML. Nk. Keulegan-Carpenter number. NR. Reynolds number. n vector. Unit vector in mooring normal direction at Cartesian coordinate. P. Wave period. Pi. Internal pressure related to well head pressure. Pres. Force due to hydrostatic pressure on catenary mooring. Pm. Hydrostatic external pressure around the mooring line. Pw. Pressure of the sea water. S(f). Spectral energy density. t. Instantaneous time. T. Tangential force component on CML in Cartesian coordinate system. t vector. Unit vector in mooring tangential direction at Cartesian coordinate. u. Wind velocity. uc. er. ay. al. M. of. ty. si. Current velocity. Water particle velocity. ni v. 𝑢̇. a. Ma. u̇ (𝑥, 𝑡). Water particle acceleration. uc. Current velocity normal to the Spar hull and the mooring lines. 𝑢̇ m. Maximum water particle velocity. u'. Virtual displacement. Uw(z). Mean wind velocity. U. 𝑢̈. Along wave horizontal velocity. Uw(1h,ZR) 1-h mean wind speed at the reference elevation V(𝑥,̇ 𝑡). Vertical velocity xviii.

(19) WL. Wave length. WP. Wave period. X. Point of evaluation of water particle kinematics from the origin. {X}. Structural displacement vector. �𝑋̇�. Structural velocity vector. �𝑋̈�. Z. Elevation of the wind centre of pressure above MWL. ZR. Reference elevation. ZS. Thickness of surface layer. ay. a. Structural acceleration vector. Internal virtual work done. M. 𝛿𝑊1𝐼. Wave celerity. of. 𝐶̆. al. 𝐴̆ij ,𝐵�ij ,𝐶̆ ij Constants depending on the ratio of sea depth to wave length. 𝛿𝑊1𝐸. External virtual work done. 𝛽i. Coefficients of cubic nonlinear terms. Coefficients of quadratic nonlinear terms. 𝜔. Angular velocity of wave. si. er. Natural frequency. ni v. 𝜔i. ty. 𝛼i. 𝜎 w (Z). Wind speed’s standard deviation. Phase angle. θ2. Beam curvature measures due to M2. 𝜇. Viscosity of the water. 𝜑( ). Cumulative density function. U. 𝜃. θ1. Beam curvature measures due to M1. ∆t. Time interval of data sampling. Φ( ). Cumulative distribution function. xix.

(20) ρ. Ratio of combining internal virtual works. ρw. Mass density of the sea water. ρ𝑖. Mass density of the inside fluid. 𝜌𝑎. Density of air. ρm. Mass per unit mooring line. ρ𝑡. Mass density of the mooring’s tube. ϕ(1). First-order potential of incident waves. ϕ(2). Second-order potential of incident waves. ξ. Structural damping ratio. Φ. Modal matrix. ε. Axial strain. M. al. ay. a. Mass density of the spar. U. ni v. er. si. ty. of. ρs. xx.

(21) 1. CHAPTER 1: INTRODUCTION. 1.1. General. Human settlement on lands across the globe has prompted the need for energy, which has continued to increase in recent times. The high demand for energy has resulted in the excessive use and depletion of available energy sources on the earth’s surface.. a. Hence, attention is now focused on discovering new energy alternatives, such as. ay. hydrocarbon reserves underwater. The use of this alternative necessitates the design of. al. floating structures with characteristics compatible with deep and ultra–deep water. M. environments.. A series of floating structures, such as tethered buoy towers, semi–submersibles, and. of. tension–leg, articulated leg and spar platforms have been developed. The present study deals with the spar platform, which is the newest compliant offshore floating structure,. ty. used in deep water for drilling, production and oil storage (Glanville et al., 1991; Horton. si. and Halkyard, 1992; Jameel, 2008). The spar is considered as a suitable choice in deep. er. water environment because of its economical design and better sea keeping. ni v. characteristics. The spar platforms are designed with natural frequencies away from dominated wave energy frequencies. One of the appealing characteristics of spar. U. platforms responses is its insensitivity to water depth. The small heave response design also admits the use of surface production tree. The traditional approaches of the spar response predictions are based on the uncoupled analysis using the numerical integration of the spar motion equation involving the effect of mooring–riser restoring forces. This approach can efficiently perform and predict conservative responses. However, for the oil and gas production development in deep. and ultra–deep waters, the spar–mooring–riser interaction becomes progressively significant. Various studies have observed that additional damping of slender structures 1.

(22) in deep water reduces the dynamic responses of the spar platform, especially under severe environmental loading. Hence, the coupled analysis of spar–mooring–riser has earned considerable importance. Many operational spar platforms, such as Oryx Neptune Spar, Shell’s ESSCO Brent Spar, Exxon’s Diana Spar and Chevron Genesis Spar in the North Sea and Gulf of Mexico, demonstrate the productivity, cost–effectiveness and success of this type of. a. deep water platform. Spar platforms are structurally integrated hull–mooring–riser. U. ni v. er. si. ty. of. M. al. ay. systems with six DOF as shown in Figure 1.1.. Figure 1.1: Spar platform (Mad Dog, 2005). 1.2. Offshore Platforms types. Oil and gas production in offshore regions is more complicated technically than that in land areas. Extensive theoretical and experimental studies with model testing are essential for the design, installation and operation of offshore structures utilized in energy exploration and production from hydrocarbon reservoirs underwater. Several 2.

(23) approaches for fixing platform decks have been developed to transmit static vertical forces as well as dynamic forces and moments to the seabed. Different types of offshore platform used for oil and gas exploration have also been reviewed extensively (Clauss et al., 1992; Islam Saiful, 2013; Jameel, 2008). Below is a list of the different types of offshore platforms used around the world.. ay. a. 1.2.1. Fixed platform. Fixed offshore structures are used worldwide for oil and gas production operations in. al. shallow water environments. These structures are installed on the seabed and exhibit. M. high stiffness and small displacement. Fixed offshore structures are designed with a natural period that is less than the dominant wave periods. Fixed platforms are. of. economical in shallow waters, but are not feasible in deep water environments. Jacket,. ty. hybrid, gravity and jack–up platforms are several examples of fixed platforms.. er. si. 1.2.2. Bottom Supported Compliant Platforms. ni v. These types of structures move to a limited range with the waves, wind and current and are economical for deep water conditions. Such platforms are fixed to the seabed by guy. U. lines, tension legs, flexible members or articulated joints. The elasticity force of the axially stressed legs or buoyancy force creates a restoring force. Buoyant, guyed, compliant–piled, articulated, flexible and tension buoyant towers, as well as tension leg and hybrid compliant platforms are among the certain types of bottom–supported compliant structures.. 3.

(24) 1.2.3. Floating Platforms. Both fixed and bottom–supported compliant platforms become unsuitable as oil and gas exploration moves far off the continental shelf into much deeper waters. Hence, new floating structures, such as semi–submersibles, drill ships, floating jackets, floating towers, deep draft caisson vessels and spar platforms have been suggested. These types of platforms are economical and efficient for deep water environments because of their. ay. a. lesser structural weight as compared with other types of conventional platforms. These structures are anchored to the seabed by wires, cables or chains, enabling the anchoring. al. system to provide the necessary restoring forces. The large excursion of floating. M. platforms contributes to resisting the external environmental loads, which reduces the forces acting on the structures. These production platforms are interesting because of. of. several additional advantages, such as their mobility and reusability especially for. ty. reservoirs of marginal reserves. The lag time between discovery and production can also be reduced. The platform can be disconnected swiftly in cases of extreme conditions or. ni v. er. earthquakes.. si. events. The floating platform design is not affected considerably by water depth and. U. 1.2.4. Spar platform. Spar platforms are the most recent generation of optimal floating structures for offshore hydrocarbon deposit exploration in deep and ultra–deep waters (Islam et al., 2011; Montasir and Kurian, 2011). The R/P FLIP (floating instrument platform) ship in 1962 is well recognized as the first stable ocean platform. The possible practical operation of floating spars was recognized in the offshore industry in the 1970s. Later on, the Royal Dutch Shell’s Brent Spar was erected with a design specifically intended for the storage and offloading of oil at the North Sea. Floating spars were proposed as low–cost 4.

(25) production facilities for remote sub–sea well locations Jameel and Ahmad, (2011). In 1992, the Offshore Technology Research Centre (OTRC) at Texas A&M University was launched as part of the implementation of a joint industry project to carry out a series of experiments on spar models. Two 1:55 scale models were subjected to various sea conditions in the OTRC wave basin. A number of working spar platforms in the North Sea, Gulf of Mexico, offshore Malaysia and Norway such as Shell’s ESSCO. a. Brent Spar, Exxon’s Diana Spar, Oryx Neptune Spar and Chevron Genesis Spar, have. ay. exhibited productivity, cost–efficiency and success for deep water applications. The deepest spar platform worldwide is Perdido spar platform constructed by Shell Oil. al. Company and installed in the Gulf of Mexico in 2009 at 2450 m depth of water. The. M. Perdido spar weighs 20,956 tonnes and has a total height of 173.3 m and a diameter of. of. 35.97 m. It is moored with nine taut polyester rope lines and connected with six risers. ty. (five production risers and one drilling riser).. si. 1.2.5. Spar design considerations. er. Since the first installation of a spar platform in 1996, spar technology has developed. ni v. rapidly over the last two decades (Agarwal and Jain, 2003; Zhang et al., 2006). After the first generation classic spar, spar platform has transformed into the second generation as. U. truss spar. The third generation spar platform configuration is the cell spar (Finn et al., 2003; Lim et al., 2005). The various designs of spar platforms reflect industry innovations. Each design is an amelioration of an older model and offers improved functionality at reduced costs.. 5.

(26) 1.2.5.1.. Classic Spar Platform. The classical spar platform in Figure 1.2 is a large circular cylinder with constant cross section and a large draft that supports a deck at the top side and is weighted at the bottom by a soft tank filled with high–density material to lower the platform’s centre of gravity (CG) to ensure platform stability. The platform is less affected by the hydrodynamic and aerodynamic loads because of the deep–draft concept, resulting in. a. small heave and pitch motion that enable the structure to support the subsea and dry tree. ay. developments. The surrounding cylinder serves as protection for equipment and risers.. al. The hull can also be used as oil and gas storage. The spar hull is surrounded by helical. U. ni v. er. si. ty. of. M. strakes to reduce the effects of vortex–induced motion.. Figure 1.2: Classic Spar platform (Neptune, 1996). 1.2.5.2.. Truss Spar Platform. The truss spar in Figure 1.3 is similar to the classic spar design but has shorter cylindrical hull with a truss structure connected below. The truss structure includes horizontal heave plates that provide damping to decrease vertical movement of spar platform and a relatively small keel or soft tank at the bottom. Truss spar is considered 6.

(27) an attractive alternative in the sea area at which deep current becomes a key factor causing significant drag force on the large cylindrical hull. Truss spar is also more. of. M. al. ay. a. efficient when crude storage is not required Zhang et al., (2007).. si. ty. Figure 1.3: Truss Spar Platform (Mad Dog Truss Spar, 2005). The truss spar has lower cost than the classic spar and its truss section decreases the hull. er. costs by 20%–40% (Magee et al., (2000). The truss spar is also more advantageous. ni v. because it weighs less than the classic spar, requires less steel and incurs less fabrication. U. costs.. 1.2.5.3.. Cell Spar Platform. The most recent modification of the spar is the cell spar shown in Figure 1.4, which has six pressure vessels of alternating lengths called cells surrounding a large central vessel, providing buoyancy for the platform. The soft tank is located at the bottom of the long cell containing the heavy ballasting material. These cells can be fabricated more easily through mass production and are more cost effective.. 7.

(28) a ay. M. al. Figure 1.4: Cell Spar Platform (Red Hawk Cell Spar, 2001). of. 1.3. Problem statement. The increasing global demand for oil and natural gas has prompted the need to explore. ty. deep water fields, which present a technological challenge because of the infrastructure. si. they require. The exploration of oil and gas reserves in deep waters has motivated. er. investigators to create various platforms suitable for deep water environments. Spar platform is one of the largest offshore platforms used in deep waters. A coupled. ni v. dynamic analysis of spar platforms is important because of the influence of mooring. U. lines on the response of spar–mooring–riser systems. However, the following several issues need to be explored and investigated. •. The coupled effect of riser inclusion on spar platform responses and mooring tension.. •. Evaluating spar platform responses under random waves in the presence of wind and current.. •. The impact of mean and fluctuating wind component on spar platform superstructures is the main source of wave generation in the platform region. 8.

(29) Therefore, modeling the superstructure configuration and identifying the acting wind forces are necessary. •. The frictional seabed effect on mooring lines should be evaluated to investigate its influence on spar system responses.. a. 1.4. Objectives of the study. ay. In view of the above mentioned aspects, this study focuses on the following objectives. 1. To develop a mathematical model for nonlinear dynamic analysis of sparsystem. using. the. commercial. finite. al. mooring-riser. element. code. M. ABAQUS/AQUA and verify this model with previously published experimental results.. of. 2. To assess the influence of risers on spar–mooring-riser system under random. ty. waves in deep water environments.. si. 3. To evaluate the combine effect of current and random waves on coupled spar– mooring–riser systems.. er. 4. To investigate the impact of aerodynamic loading on coupled spar–mooring–. ni v. riser systems under random waves with and without current inclusion.. U. 5. To carry out statistical analysis of random response time histories of spar, moorings and risers.. 1.5. Scope of the work. The present study aims to develop Spar-mooring-riser system in an integral model. This model study is bound by the following qualifications: 1. The spar hull is a rigid cylinder connected with mooring-riser system.. 9.

(30) 2. The mooring lines and riser are modeled as hybrid beam element in finite element environment. 3. The sea bed is modelled as a frictionless surface to simulate mooring-sea bed contact. 4. Mooring line dynamics envisages the instantaneous tension fluctuations and damping forces with time-wise variation of other properties. Coupling effect. a. of top tensioned risers in the model is included.. ay. 5. Drag, inertia and damping forces due to waves, current and wind load on mooring-riser system act simultaneously on Spar cylinder. Hence, the force,. al. displacement, velocity and acceleration are automatically attained.. M. 6. Wind loading was considered on the topside and the exposed portion of. of. cylindrical hull.. 7. The commercial finite element code ABAQUS/AQUA was used to obtain. ty. system responses under a long crested random wave with and without. er. si. current and wind inclusion.. ni v. 1.6. Thesis organization. This study consists of five chapters that deal with the different aspects of dynamic. U. response and probabilistic analysis. The brief outline is as follows: Chapter 1. Introduction. Chapter 1 includes a general introduction to deep water floating structures and presents a brief background on spar platforms. The problem statement and study objectives are subsequently discussed. The chapter is concluded with the thesis outline.. 10.

(31) Chapter 2. Literature review. Chapter 2 is aimed at conducting a critical review on the various aspects of current state-of-the-art platforms. The literature review is focused on the spar–mooring system responses, spar–mooring–riser system responses, stability analysis and critical analysis of aerodynamic loading incorporation. This chapter is concluded with a list of the main. Methodology. ay. Chapter 3. a. objectives and the scope of this study.. al. Chapter 3 presents the methodology of this study and describes the fully coupled. M. integrated spar–mooring–riser system as a single model in the finite element approach. The incorporation of aerodynamic loading is discussed. Moreover, the description of. Results and Discussion. ty. Chapter 4. of. modelling the spar–mooring–riser in the integrated system is outlined.. si. Chapter 4 deals with the dynamic responses of the coupled spar–mooring–riser system. er. under a long-crested random sea with and without wind and current forces. The. ni v. developed model is validated and the results are discussed critically. The influence of different sea states, including random waves, wind, and current, on the coupled spar–. U. mooring–riser system is evaluated. Chapter 5. Conclusion. Chapter 5 concludes the study with a discussion of the results, followed by salient conclusions. The conclusion outlines the characteristics of the spar–mooring–riser system under various aerodynamic and hydrodynamic loading environments.. 11.

(32) 2. CHAPTER 2. LITERATURE REVIEW. 2.1. Introduction. A spar platform is an offshore floating structure used for exploration, production, loading and off-loading of ocean deposits in deep and ultra-deep waters. It is the one of the most convenient and efficient choice because of its cost-effectiveness and. a. production competence. This type of floating structure consists of hull connected by. ay. long and heavy mooring lines and risers. Coupled spar–mooring–riser system. al. contributes significant inertia and damping. Hence, the accuracy of the dynamic. M. response of spar platforms in deep water plays an important role in designing costly moorings and risers. An integrated coupled analysis of a coupled spar–mooring–riser. of. system as a single model can accurately predict damping and inertia contributed by. ty. risers and moorings.. si. A detailed literature survey is carried out to review the different approaches adopted by. er. previous researchers for the dynamic analysis of spar platforms. A literature review confirms some significant aspects of existing studies, which are generally classified into. ni v. spar–mooring system responses, spar–mooring–riser system responses, stability analysis. U. and critical analysis of aerodynamic loading incorporation.. 2.2. Spar mooring system response. The design of moorings and risers connected to spar platform requires an accurate prediction of global responses of spar platform. An over prediction of responses results in expensive risers and mooring lines, whereas an under-prediction response leads to probability of disastrous failures. Therefore, accurate prediction of spar platform response is extremely essential in reducing the related cost. A spar–mooring structure 12.

(33) experiences a large–low-frequency motion excited by low-frequency wave forces. The drag forces and seabed friction acting on mooring lines result in mooring line damping which significantly decreases the slow drift response of moored semi-submersibles or ships (Rahman et al., 2006; Shah et al., 2005; Wichers and Huijsmans, 1990; Zhou et al., 2005).. Ran et al., (1996) investigated the response characteristics of a large slack-moored. a. floating spar platform in regular and irregular waves. The spar platform performance. ay. was numerically simulated and analyzed in the time domain for various wave and. al. current environments. The second-order wave body interaction theory, which. M. incorporates the influence of viscous and wave drift damping, was recommended for use in the prediction of spar platform responses. The time history response as surge and. of. pitch displacements in regular and irregular waves was investigated and compared with experimental results. The mooring inertia and damping influence was found to be. ty. important parameters in the prediction of moored compliant platform responses.. si. Jha et al., (1997) studied floating spar buoy platform motion relative to wave tank. er. experimental results. Mooring lines were treated as a set of massless linear springs.. ni v. Appropriate cases of damping and wave input were particularly investigated.. U. Ran and Kim, (1997) investigated the nonlinear response characteristics of a tethered/moored spar platform in regular and irregular waves. A 1:55 scale model was subjected to a series of experiments in OTRC’S 3D deep water model basin with current and wind combination to study the responses of the platform. The platform was moored with six spread mooring lines and supported by a vertical tether. A developed computer program was used to solve the static and dynamic characteristics of the platform. The results were evaluated on the basis of the uncoupled analysis results.. 13.

(34) Chen et al., (1999) examined the responses of a slack moored spar platform to detect the coupling influence between spar and its mooring lines by using the COUPLE code program. The results were compared with the corresponding experimental results. Ran et al., (1999) explored the nonlinear coupled response of a moored spar platform under random waves. The spar platform was assumed to be moored by four groups of taut catenary mooring lines, with each group consisting of three lines. The mooring. a. lines were connected to the platform by springs and dampers. Viscous damping was. ay. observed to be potentially over-estimated by stochastic linearization. As a result of. al. increase in viscous damping under collinear currents, the low frequency surge and pitch. M. were reduced.. Ma and Patel, (2001) inspected the hydrodynamic interaction of spar platform with. of. ocean waves and nonlinear wave components. Special focus was on centrifugal force,. ty. lower end point force of the spar, and axial divergence force. The centrifugal and axial. er. components.. si. divergence force components were found to be significant relative to the nonlinear force. Chen et al., (2001) identified the characteristics of spar platforms constrained by slack. ni v. mooring lines. Quasi-static and coupled dynamic approaches were used in modeling the. U. dynamics of the spar and mooring lines. The slow drift surge motion of the spar platform decreased due to reduction in mooring lines damping by 10% at 1,018 m water depth. The mooring line tension at the wave frequency range was eight times that found with the quasi-static approach. These results were proven to be important in predicting the fatigue strength and life span of the mooring system in deep water. Agarwal and Jain, (2003) accomplished a numerical study involving a coupled dynamic analysis of a spar platform. The spar was simulated as a rigid body with six degrees of freedom (DOFs) moored to the seabed by multi-component catenary mooring lines. The 14.

(35) mooring line was linked with the spar at the fairlead. Time domain investigations were carried out under a unidirectional regular wave. The coupling of the stiffness matrix was found to have a significant impact on the behavior of the platform. A nonlinear dynamic analysis of a multipoint slack moored buoy under the first- and second-order wave forces was performed by Umar and Datta, (2003). A hollow cylindrical buoy was moored to the seafloor with six slack mooring lines. Spar–mooring. a. system responses were sought under three regular wave groups of 5 m/5 s, 12 m/10 s,. ay. and 18 m/15 s. As expected, the investigation resulted in different types of instability,. al. such as periodic responses, symmetry breaking bifurcation, and nT sub harmonic. M. oscillations.. Classic spar heave responses were studied by Tao et al., (2004) for a variable geometry. of. case. The fixed cross-section cylindrical platform possibly showed a resonant heave. ty. under long peak periods in the environment. The authors established modifications in the cylindrical cross-section of the spar hull. They also confirmed that a variable hull. er. si. shape reduces the heave resonant response through the damping improvement. Mazaheri and Downie, (2005) submitted an artificial neural network (ANN)-based. ni v. method for the prediction of platform–mooring system responses under a multi-varied. U. alternative.. Chernetsov and Karlinsky, (2006) suggested the sub-structures spar-classic, spar-ring, and TLP-ring for the Stockman Gas Field in North West Russia. As a result of ice pressure, the spar-ring was found to be the best floating structure to be used at this environment, whereas the spar-classic and TLP-ring were regarded as inappropriate according to their characteristics.. 15.

(36) Thiagarajan and Morris-Thomas, (2006) performed a wave-induced motion evaluation of the air cushion structure at shallow water environments. Two 1:100 scale models were tested in the Western Australia University. The heave and pitch dynamic responses of models were investigated and validated with the experimental and analytical solutions. Jameel, (2008) carried out an extensive study on a coupled spar-mooring line system. a. under various wave and current cases. The spar hull was connected with mooring lines. ay. through six nonlinear springs at fairlead positions. The far end of the mooring lines was. al. anchored to the seabed. Inertia and damping forces were also considered, in addition to. M. the drag force acting on the mooring lines. The study considered diffraction theory and the reliability analysis of the spar platform.. of. A numerical method for deep water floating platforms with polyester mooring lines was. ty. proposed by Tahar and Kim, (2008). Static and dynamic analysis was performed on a classic spar platform, which included a tensioned buoy and polyester mooring lines. The. si. spar–mooring system responses were found to be significantly different from the. er. original rod theory results.. ni v. Jameel and Ahmad, (2011) conducted spar–mooring coupled analysis as an integrated. U. single model. The ABAQUS code was used to simulate the spar–mooring system to investigate its dynamic responses under a long-crested random wave in the presence of current. The first-order reliability method was used to estimate the reliability index and failure probability. The lifetime and annual sea-state reliability indicators were also studied. The spar platform motion and mooring line responses in a regular wave environment were investigated by Saiful Islam et al., (2011). The spar platform and mooring lines were coupled in harmonic mode. The study presented the dynamic responses of the 16.

(37) coupled system acting as heave, surge, and pitch displacements in time history after 1,000 and 6,000 s of storm. Jameel et al., (2011) analyzed an offshore spar platform in a regular wave sea state. The dynamic spar–mooring system responses in steady state were studied after 1 and 3 h. The damping effect of the mooring lines was observed with a fully coupled analysis of. a. the spar–mooring system.. ay. Montasir and Kurian, (2011) developed a MATLAB program called TRSPAR, which was used to calculate the influence of wave forces on slender floating structures. The. al. TRSPAR program was employed to determine the dynamic responses of a truss spar. M. platform. The obtained results were validated with the model test of a typical truss spar.. of. A coupled system comprising a deep draft multi-spar platform and its mooring lines were analyzed by SUN et al., (2011) in the time domain under a wave and current. ty. effect. The mooring lines were modeled with a nonlinear finite element approach. The. si. JONSWAP spectrum was utilized to obtain wave groups. The mooring tension and. er. platform motion responses were found to be significantly influenced by wave groups.. ni v. Zhang et al., (2012) conducted an experimental study to investigate nonlinear mooring characteristics and determine the dynamic tension when a mooring line state changes. U. from taut to taut-slack. The steady state of a mooring system was found to have the potential to transform into another state as a result of a change in system parameters, which coincided with a tension, skip of five to two times the former steady tension. The breaking of mooring line was concluded to be caused by such skip tension phenomenon. A spar platform was modeled as a fully coupled integrated single model by Jameel et al., (2013) by using the ABAQUS/AQUA code. A nonlinear dynamic analysis was performed to investigate the spar–mooring system responses after a long-duration. 17.

(38) storm. The energy content of the power spectral densities (PSDs) of the surge, heave, and pitch motions was found to be significantly reduced by long wave loading. A spar platform and mooring lines were simulated as a fully coupled integrated system by Saiful Islam et al., (2013). The spar hull and catenary mooring lines were modeled as a rigid beam element and hybrid beam element, respectively. A nonlinear analysis was performed in a severe deep sea environment under extreme wave loading. The. a. maximum tension force in the mooring lines was found to become regular an hour later. ay. under wave influence. However, the mooring tensional time history and displacements. al. of the spar hull gradually decreased because of the damping effect of the mooring. M. system, which shows the stability of spar platforms in severe sea states. Montasir et al., (2015) investigated the influence of the symmetric and asymmetric. of. configurations of a mooring system on dynamic platform responses. Dynamic response. ty. analyses of a truss spar platform in the time domain were performed. Airy wave theory was used in wave kinematic calculations, whereas a modified Morison equation was. si. utilized to determine the water wave force. The mooring system configuration was. er. significantly influenced by the offset of the initial platform, but the platform responses. ni v. were not greatly affected.. U. Shivaji and Sen, (2015) investigated the influence of linear and nonlinear stiffness of mooring lines on platform configurations. The hydrodynamic linear and nonlinear loads. caused by nonlinear incident waves were also considered. The structure response was significantly influenced by the nonlinear mooring stiffness, especially at low water. depths. The time domain solution approach was used by Sen, (2015) to study the dynamic responses of moored floating structures. A 3D numerical wave tank method was used to solve the hydrodynamic boundary value case. Linear and nonlinear sorting models were 18.

(39) utilized to simulate mooring lines. The dynamic responses of the three types of floating structures with various mooring systems were also studied. Yazid et al. (2015) identified the first– and second–order surge motion transfer functions of the truss spar platform. The wave height and surge motion data used in the identification process were obtained from 1:100 scaled down model of the truss spar. Numerical and experimental assessments for the proposed method were carried out. a. under unidirectional long–crested random waves, resulting in low frequency motion of. ay. the truss spar.. al. Lin and Sayer (2015) studied the mooring system behaviour in 300 to 3000m water. M. depths. Lumped mass and boundary element approaches were used in the investigation of mooring line characteristics and floating body hydrodynamics, respectively. The. of. investigators compared the obtained results with experimental data to present a. ty. guideline for the suitability of mooring system design approach.. si. Wu et al. (2015) conducted an analytical analysis of wave frequency and low frequency. er. tension range through a catenary mooring line consisting of homogeneous material. The authors determined that the most critical wave frequency fatigue could occur in the. ni v. lower section of mooring line or at the fairlead while low frequency fatigue damage. U. occurs near the touch–down position of a mooring line. Dymarski and Dymarski (2016) modelled a semi–submersible platform mooring system in two methods. First, the system was studied in a low–depth towing tank resembling a ‘‘Thunder Horse’’ platform in 1:100 scale. The modelled mooring system consists of 16 semi–taut mooring line arranged in star–shape and anchored to the seabed by suction piles. The tests were conducted at the towing tank of the Gdansk University of Technology. Second, numerical calculations were carried out to study the static. 19.

(40) displacement of the system under the effect of an external horizontal load. The study found that the second method was more accurate. Gutiérrez et al. (2016) presented a new time–domain model for dynamic analysis of moored floating marine devices under nonlinear environmental loads effect. A non– linear finite element approach was presented to solve the mooring system dynamics. A floater–mooring coupling model was also developed. The study also investigated the. a. effect of the mooring model on the platform dynamics and mooring lines tension. They. ay. concluded that a dynamic mooring model coupling offered practical means of predicting. al. the floating structure behaviour.. M. Teng et al. (2016) proposed two methods for calculating wave–body interaction in the time–domain under large amplitude of drift motion. The wave interaction with a spar–. of. mooring system was examined numerically in deep water. The obtained results were. ty. compared with the results of the direct expansion method. The study determined that the obtained response at the spar platform natural frequency is less than that obtained by the. er. si. direct expansion method but greater at the lower frequency. Choi et al. (2016) analysed the combination resonance characteristics between the. ni v. regular wave frequency and floating substructure natural frequencies. They derived. U. nonlinear equations of motion with two DOF by assuming that the floating structure is a rigid body with coupled heave and pitch motions. They also approximated the nonlinear term of nonlinear equations up to the second order using the Taylor series approach. The approximate model was validated through a comparison with the numerical analysis results obtained by applying ANSYS AQWA code to the full model. They concluded that combination resonance occurs between the excitation regular wave frequency and pitch frequency of the floating substructure.. 20.

(41) Studies and research that summarize spar–mooring lines are recapitulated in the following table. Table 2.1 : Recapitulated of spar-mooring system. Jha et al. (1997). Wave-drift damping influence included by improved models. Good agreement of results was observed Responses have been evaluated with the uncoupled analysis results. of. Ran and Kim (1997). Damping and mooring inertia influence were essential. a. large slackmoored floating spar platform Spar platform with Mooring lines treated as massless linear springs A scaled down tethered/moored spar platform model moored with six spread mooring lines and supported by vertical tether Slack moored spar platform. Coupled sparmooring system Spar platform moored by four groups of taut catenary mooring lines Spar platform with springs modeled mooring system spar platforms constrained by slack mooring lines. Conclusion. ay. Ran et al. (1996). Environmental state regular and irregular waves + current North Sea and the Gulf of Mexico extreme random sea environment Regular and irregular waves, with and without current and wind sea state. al. System assembly. M. Authors. U. Ma and Patel (2001). Chen et al. (2001). Nonlinear hybrid wave model. COUPLE code obtained suitable results in comparison with experimental results. Random waves condition. Over-estimated viscous damping reduced the surge and pitch low frequency under collinear current. Ocean wave with non-linear wave components Nonlinear waves condition. Centrifugal and axial divergence force components were shown as significantly influenced by wave conditions The slow drift surge motion of the spar platform reduced by 10% due to the mooring lines damping. The mooring line tension at coupled dynamic method was eight times larger than that quasi static method. ty. ni v. er. Ran et al. (1999). si. Chen et al. (1999). 21.

(42) Table 2.1, continued. Agarwal and Jain (2003b). Spar platform moored to the seabed by multicomponent catenary mooring lines Multipoint slack moored buoy Hollow cylindrical buoy moored with six slack mooring lines Classic spar platform. First and second order wave forces.. Platform-mooring system. multi-varied sea states. Three substructures SparClassic, Spar-ring and TLP-Ring. Long period of calm weather environment at Stockman gas field in North West Russia Various wave and current cases. er. si Spar-mooring system The spar hull connected with mooring lines through six nonlinear springs at fairleads position floating platforms moored by polyster mooring lines. U. ni v. Jameel (2008). Tahar and Kim (2008). Conclusion The coupling of stiffness matrix affects platform's behavior. Different types of instability expected to happen like periodic responses, symmetry breaking bifurcation and nT sub harmonic oscillations. al. M. Mazaheri and Downie (2005) Chernetsov and Karlins (2006). Variable geometry case. of. Tao et al. (2004). ty. Umar and Datta (2003). Environmental state Unidirectional regular waves. a. System assembly. ay. Authors. Large elongations and nonlinear stressstrain relations taken into consideration for polyester fibers. Variable hull shape obviously reduce the heave resonant response ANN method can reduced uncertainty level in traditional methods Spar-Ring was the best floating structure to use at Stockman gas field in North West Russia. Mooring line damping was found to be fundamental. The spar-mooring system responses quite different from the original rod theory results. 22.

(43) Table 2.1, continued. Jameel and Ahmad (2011). spar-mooring system. Environmental state Long crested random wave in presence of current case. Islam et al. (2011). spar platform and mooring lines. regular wave environment. Jameel et al. (2011). Offshore spar platform. regular wave sea state. Montasir and Kurian (2011). Truss spar platform. Wave forces. Sun et al. (2011). Deep draft multispar platform. wave and current. Yong and Mian (2012). Experimental study Mooring nonlinear characteristics Spar-mooring system fully coupled integrated Spar platform and mooring lines. The mooring line state changed from taut to taut-slack Long-duration storm. Truss spar platform symmetric and asymmetric configurations of mooring system. Wave kinematics and water wave force. U. Islam et al. (2013). Montasir et al. (2015). Reliabilities of full and segmental mooring length may significantly change if the mooring properties change along the length The dynamic responses behaviors evaluated as noticeable even for time elapse after wave hitting The damping effect of mooring lines due to the sparmooring system fully coupled analysis observed The obtained results verified by comparing with the results obtained from a model test of typical truss spar Mooring tension and platform motion responses significantly influenced by wave groups Platform breaking may be resulted by skip tension phenomenon. al. M. of. ty. si. ni v. er. Jameel et al. (2013). Conclusion. a. System assembly. ay. Authors. Severe deep sea environment under extreme wave loading. PSDs energy content of surge, heave and pitch motions significantly reduced due to long wave loading influence mooring tensional time history and spar hull displacements gradually decreased due to the mooring system damping effect, which shows spar platform stability Mooring system configuration significantly influenced by the initial platform's offset. 23.