Underwater Technology 37.3 by SUT

Vol. 37 32 No. No. 3 3 2 2020 2014 Vol.

UNDERWATER TECHNOLOGY Underwater Technology in China Special Issue

Frank Lim and Stephen Hall

Kang Yongtian, Xiao Wensheng, Zhang Dagang, Zhang Liang, Zhou Chouyao and Li Mingang

103

A Personal View... China - reaping the rewards of long-term investment in capability and education Study on microscopic growth mechanism of emulsion system hydrate

Jin Zhang, An Chen and Menglan Duan

Numerical simulation of creep behaviour of flexible riser inner liner

Jiayu Zhang, Junpeng Liu, Kexuan Duan, Wenbo Li and Menglan Duan

Reliability analysis of an umbilical under ultimate tensile load based on response surface approach

Xia Ran, Zhang Yu, Zheng Lijun, Zhang Zhou and Guo Jiangyan

Performance validation and dynamic response analysis of a deepwater cable bending restrictor

Optimal design of buckling resistance for a large deepwater functional tank (DFT)

Wang Yi, Zhang Fangfang and Xu Fan

111

Development of next generation subsea production system (NextGen SPS) design and analysis for ultra-deepwater applications

ISSN 1756 0543

Xing-wei Zhen, Yue Han, Qiu-yang Duan, Jia-hao Wu and Yi Huang

119

Book Review Marine Robotics and Applications

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UNDERWATER TECHNOLOGY Editor Dr MDJ Sayer Scottish Association for Marine Science Assistant Editor E Azzopardi SUT Editorial Board Chairman Dr MDJ Sayer Scottish Association for Marine Science Gavin Anthony, GAVINS Ltd Dr MA Atamanand, National Institute of Ocean Technology, India LJ Ayling, Maris International Ltd Commander Nicholas Rodgers FRMetS RN (Rtd) Prof Ying Chen, Zhejiang University Jonathan Colby, Verdant Power Neil Douglas, Viper Innovations Ltd, Prof Fathi H. Ghorbel, Rice University G Griffi ths MBE, Autonomous Analytics Prof C Kuo FRSE, Emeritus Strathclyde University Dr WD Loth, WD Loth & Co Ltd Craig McLean, National Ocean and Atmospheric Administration Dr S Merry, Focus Offshore Ltd Prof Zenon Medina-Cetina, Texas A&M University Prof António M. Pascoal, Institute for Systems and Robotics, Lisbon Dr Alexander Phillips, National Oceanography Centre, Southampton Prof WG Price FRS FEng, Emeritus Southampton University Dr R Rayner, Sonardyne International Ltd Roland Rogers CSCi, CMarS, FIMarEST, FSUT Dr Ron Lewis, Memorial University of Newfoundland Prof R Sutton, Emeritus Plymouth University Dr R Venkatesan, National Institute of Ocean Technology, India Prof Zoran Vukić, University of Zagreb Prof P Wadhams, University of Cambridge Cover Image (top): zoonar.com/syrist Cover Image (bottom): Steve Crowther Cover design: Quarto Design/ kate@quartodesign.com

Society for Underwater Technology Underwater Technology is the peer-reviewed international journal of the Society for Underwater Technology (SUT). SUT is a multidisciplinary learned society that brings together individuals and organisations with a common interest in underwater technology, ocean science and offshore engineering. It was founded in 1966 and has members in more than 40 countries worldwide, incIuding engineers, scientists, other professionals and students working in these areas. The Society has branches in Aberdeen, London and South of England, and Newcastle in the UK, Perth and Melbourne in Australia, Rio de Janeiro in Brazil, Beijing in China, Kuala Lumpur in Malaysia, Bergen in Norway and Houston in the USA. SUT provides its members with a forum for communication through technical publications, events, branches and specialist interest groups. It also provides registration of specialist subsea engineers, student sponsorship through an Educational Support Fund and careers information. For further information please visit www.sut.org or contact: Society for Underwater Technology 2 John Street, London WC1N 2ES e info@sut.org

Scope and submissions The objectives of Underwater Technology are to inform and acquaint members of the Society for Underwater Technology with current views and new developments in the broad areas of underwater technology, ocean science and offshore engineering. SUT’s interests and the scope of Underwater Technology are interdisciplinary, covering technological aspects and applications of topics including: diving technology and physiology, environmental forces, geology/geotechnics, marine pollution, marine renewable energies, marine resources, oceanography, salvage and decommissioning, subsea systems, underwater robotics, underwater science and underwater vehicle technologies. Underwater Technology carries personal views, technical papers, technical briefings and book reviews. We invite papers and articles covering all aspects of underwater technology. Original papers on new technology, its development and applications, or covering new applications for existing technology, are particularly welcome. All papers submitted for publication are peer reviewed through the Editorial Advisory Board. Submissions should adhere to the journal’s style and layout – please see the Guidelines for Authors available at www.sut.org.uk/journal/default.htm or email elaine.azzopardi@sut.org for further information. While the journal is not ISI rated, SUT will not be charging authors for submissions.

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China - reaping the rewards of long-term investment in capability and education Following the foundation of the China National Offshore Oil Corporation (CNOOC) in 1982, China began its foray into offshore oil and gas production from shallow-water, fixed platforms. These early oil fields, many of them still operational and expanding, were commissioned in Bohai Bay and East China Sea in water depths less than 90 m. By 1996 CNOOC had ventured into ‘deep’ water in the South China Sea with Amoco and Kerr-McGee when Liuhua 11-1 came on stream. This was China’s first subsea production system in a depth of 310 m. While Liuhua continues to expand to this day, several subsea production systems have since been installed in neighbouring Panyu and Lufeng. China’s leap beyond 1000 m water depth came in 2014 with Liwan 3-1, a gas field in 1300 m water depth operated by Husky. CNOOC is preparing to operate its own 1400 m deep Lingshui 17-2 gas field, which is currently under construction. China has thus far relied on the importation of subsea production hardware from established foreign suppliers, such as Cameron, Aker, DrilQuip and GE, for wellheads, trees, manifolds, connectors, subsea control modules, control umbilicals and multiphase flow meters. Understandably, there is an ongoing effort to reduce this dependency, and therefore significant investments have been channelled in the past decade to develop ‘made in China’ products with varying degrees of success. However, the biggest obstacle to China’s progress on this is the mindset that foreign products are superior and more reliable.

Simultaneously, there is an underlying suspicion that domestic products lack testing and may suffer from enthusiastic design specifications boasting exaggerated performances. As a result of this skepticism, projects continue to import and fail to bring the many ‘successful’ domestic prototypes into operation. Project leaders simply do not want to be held responsible for taking the risk. When project decisions are made by expert committees in China, risks are not ranked and it is deemed that all are to be avoided. Quantitative risk assessment is virtually unknown and therefore not practiced. In order to train enough engineers to serve the domestic oil and gas industry, China has a number of specialised petroleum universities. Most notable are two universities, both named ‘China University of Petroleum’, run independently in Beijing and Qingdao. Although traditionally focused on onshore petroleum engineering, these universities have been diversifying into offshore and subsea engineering subjects in recent years. Quite distinct from the Western norm where technologies tend to be developed by the industry with universities only playing a supporting role, the Chinese offshore industry relies heavily on universities to give them technical creditability to commercialise their products. The bond between industry and academia in China is strong. There is no shortage of manufacturers who, attracted to the enormity of the potential subsea market, take advantage of both

central and local government funding to collaborate with universities to develop products they hope to sell. The government also funds the building of impressive experimental facilities, such as wave tanks and hyperbaric chambers that outshine any outside China. A common problem these universities face, however, is the fact that the research is carried out mostly by students, and therefore continuity is often lost when experienced students leave after graduation. Thankfully, things are changing with a new breed of entrepreneurial academics setting up companies to further these research and development efforts professionally. CNOOC has now made plans to add domestic subsea production components in a systematic manner to their future field developments, starting from lower risk applications. Their successful implementations would fuel confidence, and the subsequent track record would likely negate their inferiority complex. China’s subsea industry will not be confined to oil and gas: there is rising enthusiasm about methane hydrates and rare element mineral reserves dotted around the seabed close to China. President Xi Jinping remarked at a national science conference in 2016:

A Personal View...

doi:10.3723/ut.37.067 Underwater Technology, Vol. 37, No. 3, pp. 67–69, 2020

‘The deep sea contains treasures that remain undiscovered and undeveloped, and in order to obtain these treasures we have to control key technologies in getting into the deep sea, discovering the deep sea, and developing the deep sea’.

Frank Lim and Steve Hall. China - reaping the rewards of long-term investment in capability and education

such facility in the world, and the pervasive myth that ‘the moon shines brighter in the West’ could be out of the window! Professor Frank Lim, Chair SUT China, Member of SUT Council

Frank Lim has served as Global Director of 2H Offshore, a company that has pioneered technologies for riser systems that are now deployed in deepwater regions around the world. He now assumes the role of Principal Advisor and is also a Professor at the China University of Petroleum in Beijing. Frank’s offshore engineering career began in 1983 after gaining a PhD in the UK, and continued through numerous oil and gas projects in the North Sea, Gulf of Mexico, West Africa and Brazil. In the mid-2000s, he turned his interests to deepwater projects in the Asia Pacific, supporting these from the 2H Kuala Lumpur and Beijing offices he set up in the region. Since 2007, he has been leading all 2H projects in seabed mining riser design in different parts of the world, including Papua New Guinea, Pacific Ocean, Black Sea and South Indian Ocean. A fellow of SUT, Institution of Mechanical Engineers (IMechE) and Royal Institution of Naval Architects (RINA), Frank is a regular author of technical papers and speaker at international conferences. Frank was a member of the SUT Subsea Engineering and Operations Committee from 1992 to 1994, and has represented 2H Offshore as a corporate member of the Society since 2004. He has been the chairman of the SUT China Branch since 2017, and is currently a member of the SUT International Committee. He was elected an SUT Council Member in late 2019.

This ties in with a plan announced the same year by the science ministry that China would build a manned, deep-sea experimental station under the South China Sea that would host dozens of crew members who could remain underwater for up to a month. Once in use, it will be the first 68

I first visited China before I joined the Society for Underwater Technology as CEO. At the time, I was vice-Chair of UNESCO’s Intergovernmental Oceanographic Commission, which opened many doors to me that might have normally remained closed to a foreigner. I was treated as a VIP and invited to meet the Directors of China’s prestigious marine research institutions in Qingdao and elsewhere, and saw first hand the extraordinary progress that China was making in marine science, technology and engineering. China’s technical universities were full of bright, highly motivated students looking forward to contributing their talents to drive forward China’s advances in ocean technology, engineering, science, fisheries, mining, marine spatial planning, as well as the closely-linked aspects of marine policy and law. In addition to the huge effort by China’s own excellent universities, I learned that there were thousands of Chinese postgraduate students enrolled on courses in the West. The vast majority of them return to China, bringing with them state-of-the-art knowledge in science and engineering, enabling China to advance at the extraordinary pace we have seen in the last couple of decades. When I first visited China, there were many areas where their science and technology were behind the West, but today I strongly believe they have caught up with us in many areas – and in some they are already ahead. With so much resource dedicated to education and investment in

Before joining SUT as CEO, Steve Hall spent over 26 years with the Natural Environment Research Council (NERC), carrying out a range of duties including tracer chemistry in the wild seas of the Southern Ocean, and managing the NERC Autosub Science Missions thematic programme from 1997 to 2002. He spent a decade as a marine policy specialist, becoming Head of the International and Strategic Partnerships Office of the National Oceanography Centre, the UK’s and Overseas Territories’ tsunami warning focal point, and Head of the UK’s delegation to UNESCO’s Intergovernmental Oceanographic Commission, where he was elected Vice-Chair from 2015 to 2017. Steve joined SUT in the 1990s, serving on the Education and Training Committee and later the Policy Advisory Committee, and was twice elected to SUT Council, serving as Honorary Secretary and Chair. He is a Fellow of SUT and the Institute of Marine Engineering, Science and Technology (IMarEST), a Chartered Marine Scientist and author of children’s books about the ocean and policy briefings to government on topics from renewable energy and nuclear submarine decommissioning to scallop dredging. When not working for SUT he enjoys cycling and walking with his family in the hills near his home in Wales. Steve will be moving on to a new CEO role in west Wales after December 2020.

training and technology, it won’t be long before Western customers are choosing Chinese products not only for items such as the hulls of ships or offshore platforms, but also for the high-end electronics, sensors, software and computers that currently comprise the bulk of the cost of many offshore systems.

Underwater Technology Vol. 37, No. 3, 2020

On a visit to Hainan in 2019, I had a fascinating conversation with a local businessman who had a company that imported and sold Western oceanographic instruments. He took me across the exhibition trade hall to show me his other booth of the subsidiary of his company manufacturing Chinese systems, which did a similar job but retailed at a lower cost. I asked him if his systems were as good as the Western ones. He replied that they weren’t yet, but soon would be – his limiting factor had been a lack of access to high-accuracy calibration and test facilities. He smiled as he explained that the local government was helping to finance the construction of a full-specification calibration and testing laboratory, and that once it was ready, he was confident that he could build equipment that was as good as the big brand-name sensors. He added that his young engineers had gained experience working with US, Canadian and European manufacturers during their PhD studies and knew exactly what needed to done.

I hear similar stories from across the spectrum of technology, science and engineering sectors – and crucially I now see examples of original thinking and innovation, not just skilled copying of products from other countries. There are autonomous underwater vehicles that are ‘biomimetic’ – designs based on examples found in nature, with imaginative uses of new materials, new ways of working – and some evidence suggests that China may be ahead of the West in harnessing quantum systems for subsea communications. China is aware that their own rapid development has come at an environmental cost, and we are beginning to see signs that as the country pulls itself well outside of ‘developing nation’ status, it is already beginning to pay attention to repairing some of that collateral damage. President Xi Jinping has committed China to becoming carbon neutral by 2060, and China is constructing renewable energy systems at an impressive rate – not only to wean China off the need to

import fuel from abroad, but also to address the chronically bad air quality that plagues many Chinese cities that have until now relied on burning coal or lignite to meet their energy requirements. The controversial new installations that China has been constructing in the South China Sea are all part of the move towards securing future energy supplies, marine space, access to fisheries and ‘defence in depth’. Coupled with the maritime Belt and Road initiative, these point to a China that is confident, strong and ready to emerge as the world’s dominant power – at least in economic terms – of this century. Ocean resources, energy and commerce will be a key part of China’s way forward, and sharing knowledge via learned societies such as SUT will be an important part of ensuring that we can all work together in peace, and in support of sustainable use of resources, in the future. Stephen Hall, SUT CEO 2017–2020

Society for Underwater Technology International multidisciplinary learned society This non-aligned membership-based organisation seeks to further the dissemination of knowledge and lessons learned in the underwater environment through networking, events and publications

Its membership covers the following activity areas: n defence n diving and manned submersibles n environmental forces n marine policy n marine renewable energies n ocean resources n offshore site investigation and geotechnics n salvage and decommissioning n subsea engineering and operations

For further information For events, membership, publications or general enquires, contact: e info@sut.org e events@sut.org

n underwater robotics n underwater science n underwater vehicles

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doi:10.3723/ut.37.071 Underwater Technology, Vol. 37, No. 3, pp. 71–77, 2020

Study on microscopic growth mechanism of emulsion system hydrate Jin Zhang, An Chen* and Menglan Duan College of Safety and Ocean Engineering, China University of Petroleum Beijing, Beijing, China

Technical Paper

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Received 31 October 2019; Accepted 3 July 2020

Abstract In order to master the microscopic growth mechanism of natural gas hydrate, a series of experiments were carried out using a high-pressure hydrate flow loop. The microscopic physical information of the growth of hydrates in the emulsion system is captured by advanced microscopic equipment and the phenomena of the experiments show that: 1) not all water droplets instantaneously generate a hydrate shell, but only a few of the water droplets gradually generate a hydrate shell when reaching the conditions of the hydrate formation; and 2) the coalescence and shear do occur in the hydrate formation process, and the distribution of hydrate particle size has changed. Keywords: natural gas hydrate, particle size, coalesce, high-pressure flow loop

1. Introduction Under the external conditions of low temperature and high pressure, natural gas molecules and water molecules will form cage crystal compounds, which are natural gas hydrates, in a certain proportion. Natural gas hydrate, commonly known as combustible ice, is similar to ice crystals in appearance, but its crystal structure differs. Its simple chemical formula can be expressed as nGas· mH2O. Natural gas hydrate is widely used in natural gas storage and transportation, carbon dioxide deep-sea storage and other industries because of its unique physical and chemical properties. However, the formation of hydrate can easily lead to pipeline blockage in the process of oil and gas transportation, posing a threat to the normal exploitation and safe transportation of oil and gas. Therefore, mastering the microscopic growth mechanism of natural gas hydrate not only provides a good theoretical research basis for the development of effective * Contact author. Email address: anchen@cup.edu.cn

kinetic mechanisms to control the formation rate of natural gas hydrates, but is also important to establish a hydrate microscopic growth model. In water-in-oil emulsion, the nucleation process of natural gas hydrate is first observed at the interface between water droplets and the oil phase around the water droplets, and the rapid formation of natural gas hydrate membrane is observed around the water droplets. The further growth of hydrate is controlled by heat and mass transfer, and the influence of mass transfer will gradually increase. As shown in Fig 1, during the hydrate growth process, the hydrate shell gradually thickens until all the droplets are converted into hydrate particles. Turner et al. (2005) found that water droplets entrained in the oil phase can be converted into hydrate particles, which provides a theoretical reference for realizing the transportation of hydrate particles in the oil phase in the form of slurry. Kobayashi et al. (2001) found that the surface of hydrate crystals formed under the flow condition is not only not smooth but is also porous. The growth mechanism of hydrate is complex, and researchers have put forward various growth models by different simplifications (Skovborg et al., 1993; Englezos et al., 1987; Kono and Budhijanto, 2002; Kvamme, 2002). Vysniauskas et al. (1983; 1985) proposed the hydrate growth kinetics semi-empirical model. The CSMHyK model proposed by Kinnari et al. (2008) only considers intrinsic dynamics and disregards the influence of heat transfer and mass transfer. Most researchers only consider mass transfer or heat transfer as the control factor in the process of establishing hydrate growth models and make a series of assumptions, leading to narrow applicability. Gong et al. (10) established an inward hydrate shell model that considers the three control factors comprehensively. However, the model has a significant disadvantage because the hydrate growth parameters are 71

Zhang et al. Study on microscopic growth mechanism of emulsion system hydrate

Fig 1: Schematic of the hydrate particle formation

Fig 2: Schematic diagram of hydrate inward and outward growth shell model

difficult to determine. On the basis of Gong’s ’s model, Shi et al. (2011) gave the calculation methods of water molecule permeation rate and hydrate guest molecule concentration change and established an inward and outward hydrate shell model (Fig 2). However, many parameters of the model depend on a large number of hydrate growth kinetics experimental data. At present, there are two main problems in the international research on the growth mechanism of natural gas hydrate. Firstly, the laboratory puts forward high requirements on experimental equipment to study natural gas hydrate because it can only be formed under harsh conditions of high pressure and low temperature. Therefore, most researchers study the growth mechanism of natural gas hydrate by studying the growth rules of other hydrates. Secondly, current hydrate research is mostly carried out in reactors or in low-pressure experimental loops, which cannot truly simulate the formation of natural gas hydrate in deep-sea pipelines. In view of the above shortcomings, the present paper adopts a high-pressure flow loop to more accurately simulate the hydrate formation process in the emulsion system and uses advanced microscopic equipment to capture the microscopic physical information of the growth of hydrates. Through the analysis of the experimental phenomena, the microscopic mechanism of natural gas hydrate is obtained.

2. Experiments 2.1. High-pressure hydrate experimental loop As shown in Fig 3, the hydrate experiments were carried out in the high-pressure hydrate experimental 72

loop constructed in the China University of Petroleum (Beijing). The 30 m stainless steel test section comprises two rectilinear horizontal lengths joined together to form a pipe with 2.54 cm (1 in) internal diameter, and a 5.08 cm (2 in) diameter jacket circulating a water glycol blend surrounds the test section. The process temperature control ranges from -20 °C to 100 °C. The vacuuming system mainly includes a vacuum pump and a vent valve; the air sucked by the vacuum pump is discharged into the atmosphere through the vent valve. The oil-water emulsion is sent to the experimental loop by the magnetic centrifugal pump through the liquid outlet at the bottom of the separator. The flow rate can be judged by observing the mass flowmeter at the outlet of the pump, and the flow rate can be adjusted by adjusting the rotating rate of the centrifugal pump. The gas is sent to the experimental loop after being compressed by a compressor. Natural gas and oilwater emulsion are mixed by a gas-liquid mixer, and a dosing port is arranged at the outlet of the gasliquid mixer. Experimental reagents are injected into the experimental loop by an electric metering pump. To better simulate the low-temperature environment in the deep sea, the experimental loop is equipped with four thermostatic circulators to control the temperature of the test pipeline, and the laboratory is equipped with high-power air conditioner. The formation process of hydrate in the emulsion system can be observed through the highpressure window. 2.1.1 FBRM As shown in Fig 4, the growth and distribution of hydrate are measured by (focused beam reflectance measurement (FBRM), an online particle analyser manufactured by Mettler-Toledo Company. Since the scanning speed of laser beam (2 m/s to 8 m/s) is much higher than the passing speed of the hydrate particles, it can be considered that particles are basically in a static state. When the focused beam reaches one end of the particle, FBRM will detect the reflected scattered light and the signal will continue to grow until the beam reaches the other end of the particle. FBRM can clearly observe the morphology of droplets or particles during hydrate formation and accurately measure the particle size of hydrate, thus enabling the study of the microscopic growth mechanism of natural gas hydrate. 2.1.2. PVM As shown in Fig 5, particle video microscope (PVM) is a probe-type observation tool that can provide instant information to assist researchers in observing

Underwater Technology Vol. 37, No. 3, 2020

Fig 3: Schematic of the high-pressure hydrate experimental loop

Fig 5: Schematic of PVM

2.2. Experimental procedure Fig 4: Schematic of FBRM

the formation process of natural gas hydrate. The particle monitoring range of PVM is 2 μm to 1 mm, and ten pictures can be continuously and dynamically stored per second. PVM can give images of solid particles suspended in continuous phases such as crude oil or emulsion, providing a visual basis for the morphological study of hydrate formation process. 2.1.3. Experimental fluid The experimental fluid is deionised water, -20# diesel and civil natural gas (Table 1). The mixed inhibitor of emulsifier-Span 20 is used in the experiment. 2.1.4. Experimental condition The pressure ranges from 3 MPa to 6 MPa and the temperature range is from -5 °C to 50 °C.

1) The experimental loop is vacuumed to make the vacuum degree reach 0.09 MPa. Diesel and water are injected into the separator through the feed inlet of the separator by self-suction. 2) The e data acquisition system is opened and the temperature controller turned on to adjust the temperature to 30 °C. Then, the magnetic pump is turned on, and the added oil and water are fully stirred for approximately three hours to form a relatively stable water-inoil emulsion. 3) After opening the makeup valve to increase the system pressure to the experiment pressure, the FBRM and PVM are started to monitor the change of particle size of the water droplets in the experimental loop. After the average chord length parameter is monitored by FBRM and remains constant, the hydrate experiment is conducted. 73

Zhang et al. Study on microscopic growth mechanism of emulsion system hydrate

Table 1: The composition of natural gas (mol %) Composition Mol%

Composition Mol%

N2 CO CO2 C1 C2

C3 iC4 iC5 nC6+

1.50 2.06 0.91 89.30 3.10

2.80 0.30 0.04 0.01

4) The temperature control system is adjusted to a specific experimental temperature to cool the entire experimental loop. The data collected by the data collection system is recorded, and the particle data is monitored by FBRM and PVM. 5) The hydrate slurry rheology experiment and the hydrate slurry multiphase flow experiment are carried out when the temperature, pressure and flow rate in the experimental loop are almost stable. 6) After the rheology experiment and multiphase flow experiment are complete, the system temperature is reset to 30 Â°C to carry out the hydrate slurry decomposition experiment. The date and experiment stop being recorded when the temperature, pressure and flow rate of the system are stable. 7) After the hydrate experiments are complete, the experimental gas is recovered and the liquid in the experimental loop is discharged. The experimental loop is cleaned, and the compressed air is used to sweep the experimental loop. Nitrogen is used to replace the gas in the experimental loop.

3. Results and discussion 3.1. Study on microscopic morphology of emulsion system hydrate The microscopic growth mechanism of emulsion system hydrate is complex, and most researchers make a simplification that all water droplets dispersed in the continuous oil phase rapidly nucleate and transform into hydrate particles when reaching the conditions of the hydrate formation, and the subsequent coalescence is only the interaction among the formed hydrate particles. In the present study, a series of experiments were carried out in the high-pressure hydrate flow loop, and the following microscopic physical information of the growth of hydrates in the emulsion system was captured by FBRM and PVM. Firstly, there is a certain proportion of nucleation of the water droplets in the emulsion system, and its nucleation process deviates from the assumption that all water droplets nucleate. Not all water droplets instantaneously generate a hydrate shell, but only a few of the water droplets gradually generate a 74

Fig 6: Schematic of the formation of natural gas hydrate

Fig 7: Schematic of the coalescence of natural gas hydrate

hydrate shell when reaching the conditions of the hydrate formation (Fig 6). Secondly, in the process of nucleation, the energy required for the further growth of the shell of nucleated water droplets may be less than that required for the nucleation of nonnucleated water droplets. There are still non-nucleated water droplets in the system when the hydrate growth proceeds. Third, the hydrate particles coalesce and form larger hydrate particles with the continuous formation of hydrates (Fig 7). Affected by the hydrate particle and droplet collision, fragmentation, coalescence and shear, the coalescence forms between the hydrate particles and droplets are more complex. Finally, large particles are sheared into small particles under the stronger shearing action (Fig 8). As such, the coalescence of natural gas hydrate particles is the main reason for the blockage of hydrate slurry transportation.

3.2. Law of distribution of hydrate particle size In the present work, a series of experiments were carried out in the high-pressure hydrate flow loop, and the distribution of hydrate particle size in the

Underwater Technology Vol. 37, No. 3, 2020

Fig 10: Schematic of the number of particles with the size less than 10 μm Fig 8: Schematic of the shear of natural gas hydrate particles

Fig 11: Schematic of the number of particles with the size ranging from 10~50 μm Fig 9: Schematic of the change of square-weighted chord length

emulsion system was captured by FBRM and PVM. As shown from Figs 9 to 14, the following phenomena can be found. Firstly, the square-weighted chord length remains substantially constant before the hydrate generation. Secondly, once the hydrates start to form after the two-hour experiment, the squareweighted chord length of particles rises immediately, the number of particles with the size less than 10 μm and with the size ranging from 10 μm~50 μm reduces sharply, the number of particles with the size ranging from 50 μm~150 μm and with the size ranging from 150 μm~300 μm increases sharply, and the number of particles with the size ranging from 300 μm~1000 μm increases slightly. Thirdly, when the experiment is carried out for three hours, the square-weighted chord length of particles reduces immediately, the number of particles with the size ranging from 50 μm~150 μm and with the size ranging from 150 μm~300 μm reduces sharply, and the number of particles with the size ranging from 300 μm~1000 μm reduces slightly. From the above phenomena, the following conclusions can be made. Firstly, once the hydrates start to form after the two-hour experiment, the

number of small particles reduces sharply and the number of large particles increases sharply, because the hydrate particles coalesce and form larger hydrate particles with the continuous formation of hydrates. Secondly, there are two main reasons that can explain the experimental phenomena when the experiment is carried out for three hours: 1) a stronger shearing action caused by the increased slurry viscosity breaks the gathered large particles of the hydrate, or 2) the wettability of hydrate particles reduces and the degree of subcooling for the reaction increases along with the hydrate further formation, resulting in the reduced cohesive force between hydrate particles. The chord length distribution of particles at three different time points in the experiment is shown in Fig 15. When the experiment is carried out for two hours, the chord length distribution is on the right and is concentrated in the range of 50 μm~300 μm, and the number of large particles is significant. This reflects that the hydrate particles coalesce and form larger hydrate particles with the continuous formation of hydrates. When the experiment is carried out for three hours, the chord length distribution starts to move to the left. When the experiment is carried out for four hours, the chord length distribution shifts to the 75

Zhang et al. Study on microscopic growth mechanism of emulsion system hydrate

Fig 12: Schematic of the number of particles with the size ranging from 50~150 μm

Fig 15: Schematic of the chord length distribution of particles at three different time points in the experiment

formation process. Mastering the microscopic growth mechanism of natural gas hydrate not only provides a good theoretical research basis for the development of effective kinetic mechanisms to control the formation rate of natural gas hydrates, but also is of great importance to establish a hydrate microscopic growth model.

4. Conclusions

Fig 13: Schematic of the number of particles with the size ranging from 150~300 μm

Fig 14: Schematic of the number of particles with the size ranging from 300~1000 μm

left and is concentrated in the range of 50 μm ~100 μm, and the number of large particles reduces sharply. This also reflects the stronger shearing action and reduced cohesive force between hydrate particles. Regardless of the change of the number of hydrate particles with different particle size or the chord length distribution at different time points, the conclusions drawn are consistent with the microscopic morphology captured by FBRM and PVM in the hydrate formation process, showing that the coalescence and shear occur in the hydrate

In the present work, a series of natural gas hydrate experiments were carried out in the high-pressure flow loop, and the microscopic physical information of the growth of hydrates was captured by advanced microscopic equipment. Through the analysis of the experimental phenomena, the following conclusions are obtained: 1) Not all water droplets instantaneously generate a hydrate shell, but only a few of the water droplets gradually generate a hydrate shell when reaching the conditions of the hydrate formation. The coalescence and shear occur in the hydrate formation process. 2) In the process of hydrate growth, the distribution of hydrate particle size changes. Firstly, the square-weighted chord length remains substantially constant before the hydrate generation. Secondly, once the hydrates start to form, the square-weighted chord length of particles rises immediately, and the number of large particles increases. This reflects that the hydrate particles coalesce and form larger hydrate particles with the continuous formation of hydrates. Thirdly, when the hydrate growth is stable, the squareweighted chord length of particles and the number of large particles reduce immediately. There are two main reasons that can account for this phenomenon: 1) a stronger shearing action breaks the gathered large particles of the hydrate, or 2) the cohesive force between hydrate particles reduces.

Underwater Technology Vol. 37, No. 3, 2020

Acknowledgements The present paper is supported by the National Key Research and Development Plan (No. 2016YFC0303704) and the National Natural Science Foundation of China (No. 51879271).

References Englezos P, Kalogerakis N, Dholabhai D and Bishnoi PR. (1987). Kinetics of formation of methane and ethane gas hydrates. Chemical Engineering Science 42: 2647–2658. Gong J, Shi B and Zhao J. (2010). Natural gas hydrate shell model in gas-slurry pipeline flow. Journal of Natural Gas chemistry 19: 261–266. Kinnari K, Labes-Carrier C, Lunde K, Hemmingsen PV, Davies SR, Boxall JA, Koh CA and Sloan ED. (2008). Hydrate plug formation prediction tool – an increasing need for flow assurance in the oil industry. In: Proceedings of the 6th International Conference on Gas Hydrates, 6–10 July, Vancouver, Canada. Kobayashi I, Ito Y and Mori YH. (2001). Microscopic observations of clathrate-hydrate films formed at liquid/liquid interfaces. I. Morphology of hydrates films. Chemical Engineering Science 56: 4331–4338.

Kono HO and Budhijanto B. (2002). Modeling of gas hydrate formation process by controlling the interfacial boundary surface. In: Proceedings of the 4th International Conference on Gas Hydrates, 19–23 May, Yokohama, Japan. Kvamme B. (2002). Initiation and growth of hydrate. In: Proceedings of the 4th International Conference on Gas Hydrates, 19–23 May, Yokohama, Japan, 42–45. Shi BH, Gong J, Sun CY, Zhao J-K, Ding Y and Chen G-J. (2011). An inward and outward natural gas hydrates growth shell model considering intrinsic kinetics, mass and heat transfer. Chemical Engineering Journal 171: 1308– 1316. Skovborg P, Ng HJ, Rasmussen P and Mohn U. (1993). Measurement of induction times for the formation of methane and ethane gas hydrates. Chemical Engineering Science 48: 445–453. Turner D, Kleehammer D, Miller K, Koh C, Dendy E and Talley L. (2005). Formation of hydrate obstructions in pipelines: hydrate particle development and slurry flow. In: Proceedings of the fifth international conference on gas hydrates, 12–16 June, Trondheim, Norway. Vysniauskas A and Bishnoi PR. (1983). A kinetic study of methane hydrate formation. Chemical Engineering Science 38: 1061–1072. Vysniauskas A and Bishnoi PR. (1985). Kinetics of ethane hydrate formation. Chemical Engineering Science 40: 299–303.

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Numerical simulation of creep behaviour of flexible riser inner liner Jiayu Zhang1, Junpeng Liu1*, Kexuan Duan1, Wenbo Li2 and Menglan Duan1 1 College of Safety and Ocean Engineering, China University of Petroleum, Beijing 102249, China 2 Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian116024, China

Technical Paper

doi:10.3723/ut.37.079 Underwater Technology, Vol. 37, No. 3, pp. 79–86, 2020

Received 31 October 2019; Accepted 4 April 2020

Abstract The creep behaviour of an inner liner, one of the reasons for carcass tearing, may affect the structural integrity of flexible risers. This has been previously discussed without conclusive results owing to complex structure and time-dependent material properties. The present paper proposes a numerical model for predicting creep responses by means of the finite element method. In this model, series coefficient is used to characterise the viscoelastic properties of material. Consequently, the influence of geometric parameters such as span of the carcass layer and thickness of the inner layer on the deformation is observed. Moreover, a threedimensional model assembling the carcass and inner liner was established for mechanical analysis, during which the viscoelasticity of inner liner and the internal friction of the carcass are considered, after which the stress and strain distribution on each layer under the combined external pressure and axial tensile force generated by the inner liner are obtained. Additionally, the effect of external pressures on the stress distribution of the carcass cross-section was found through sensitivity analysis. Keywords: flexible riser, inner liner, carcass layer, creep, viscoelastic

1. Introduction The performance of non-bonded flexible risers is a key factor restricting the development of offshore oil and gas production systems in deep water. Nonbonded flexible risers are mainly composed of metal spiral layers and polymer cylindrical shell layers (Farnes et al., 2013; see Fig 1). Once a flexible riser fails, it will bring significant environmental hazards and economic losses. Farnes et al. (2013) conducted a detailed analysis of the axial failure of the carcass layer at the * Contact author. Email address: liujp@cup.edu.cn

2013 International Conference on Ocean, Offshore & Arctic Engineering (OMAE), indicating that the axial force in the inner liner affects the axial failure of the carcass layer. Usually, the axial force of the carcass layer is transmitted by the frictional force between the layers and is carried by the tensile armor layer. The inner liner wrapped on the outside of the carcass layer is made by the polymer, and under external pressure over a long period of time the inner liner will creep and ‘embed’ into the groove of the carcass layer. This creates a gap with the outer layer, so that the axial force acting on the carcass layer cannot be transmitted outward through the interlayer contact. Owing to the occurrence of creep, the inner liner will exert the axial force suffered on the carcass layer, and as a result the excessive axial forces cause the tearing of the carcass layer. These pipes are exposed to large pressure and temperature changes during start-up, shut-down and pressure testing which cause changes in the polyvinylidene fluoride (PVDF) material wrapped outside the carcass layer and result in multiple axial carcass failures (Kristensen et al., 2017). Tear failure occurs most often in the weld at the top of the carcass layer, as shown in Fig 2. The present paper simulates the failure of the carcass layer when the pipeline undergoes creep after long-term use, under conditions of shut-down. In recent related research, many scholars mainly study the interaction between the carcass layer and inner liner by combining numerical simulation and experiment. Kristensen et al. (2014) considered the two-layer structure of the carcass layer and inner liner and established the functional relationship between the modulus of the inner liner material and temperature.

Zhang et al. Numerical simulation of creep behaviour of flexible riser inner liner

Fig 1: Flexible riser structure

Hansen et al. (2015) analysed the contact relationship between the inner liner and carcass layer under the influence of temperature. Liu and Vaz (2016) investigated the structural response of a flexible riser with viscoelasticity in the time and frequency domains when subjected to external loads. However, these studies did not consider the viscoelasticity of the inner liner material, and there is no simulated inner liner embedded into the carcass layer. In the present paper, the finite element method is proposed for the creep model of the inner liner under external pressure. The model considered the change of the viscoelastic material modulus with time and temperature, and realised its viscoelastic properties in the finite element software. Finally, a 3D model was used to simulate the axial loading on the carcass and its failure mechanism.

Fig 3: Inner liner embedded in carcass (Farnes et al., 2013)

2.2. Creep stress-strain relationship The inner liner is a viscoelastic material whose creep behavior stress-strain curve depends on three variables: stress, time and temperature. In the current work, the creep stress-strain curve expression used is: ε = C 1 ∗ σC 2 ∗ t (1−C 3) ∗ e −C 4 /T /(1 − C 3) , (1)

where, C1, C2, C3 andC4 are four material coefficients; C4 relates to the change in ambient temperature (Qiu and Zhang, 2006). As the groove temperature does not change significantly during the operation, and as the inner liner is thin, it can be assumed that the temperature is constant with satisfactory accuracy (Qiu and Zhang, 2006). C4 can then be taken as 0, thus eliminating temperature from the expression. C3 represents the effect of strain rate on time. The relationship between C3 and strain rate is shown from the derivative of Equation 2 versus time: dε

2. Numerical simulation of inner liner creep 2.1. Creep model description In practical engineering, the flexible riser is subjected to high seawater pressure, temperature pressure, and long-term application. These factors are the cause of creep and relaxation of the viscoelastic inner liner, as shown in Fig 3. Based on the viscoelastic material, the inner liner creep model was simulated by commercial finite element software ABAQUS.

dt = C 1 ∗ σ

C2 represents the applied stress correlation coefficient. When C2 = 1, it means that there is a linear relationship between stress-strain, that is, the stress increments are equal, and the corresponding strain increments should also be equal. Conversely, if C2 ≠ 1, the stress increment is constant and the strain increments are not equal, showing a certain nonlinearity. For nonlinear materials, C2 should generally be greater than 1.

Fig 2: Tear of carcass profile beneath carcass weld (Farnes et al., 2013)

∗ t (−C 3) (2)

Underwater Technology Vol. 37, No. 3, 2020

Fig 4: Carcass layer groove model simplification

C1 primarily affects the global position between the stress-strain curves, mainly measured by experiments. In the present paper, the data given in reference is selected, in which C1 = 1.2 * 10–9, C2 = 1.829, and C3 = 0.88. After determining these coefficients, the viscoelastic material can be numerically simulated in the finite element software.

2.3. Parameter setting of PVDF material modulus The creep modulus and relaxation modulus of viscoelastic materials are both related to time and temperature. In order to better demonstrate the viscoelastic behaviour of materials in practical engineering, the N-order Maxwell model is used to describe the creep response and relaxation response. Since engineering applications involve long-time scales, and experimental constraints do not allow measuring the full-time range of the relaxation function at certain temperatures, a time-temperature superposition model can be used to describe the viscoelastic behaviour (Shaw and MacKnight, 2005): G(t ,T ) = G(t / αT ,T0 ) , (3)

where aT is the time conversion factor, which is obtained by the WLF equation (Williams et al., 1955): log αt =

C1(T −T0 ) , (4) C 2 + T −T0

where C1 and C2 are arbitrary material constants and can be measured by experiment. Therefore, on condition of temperature T, based on the expression of relaxation modulus at the reference temperature T0 the extended Prony series becomes: n

G(t ,T )= E ∞ + ∑ Ei e

−

t αt τ Ri

Table 1: Material modulus in ABAQUS g_iProny

k_iProny t_iProny

0.397350993 0.079470199 0.033112583 0.066225166 0.039735099 0.026490066 0.026490066 0.033112583 0.039735099 0.039735099 0.026490066 0.01986755

0 0 0 0 0 0 0 0 0 0 0 0

1.25 8.5 1*102 1.2*103 1.5*104 6*104 2.8*105 4*106 4*107 6.5*107 3.5*1010 1.5*1012

b) k_iProny: The modulus ratio of the first term in the Planone expansion series of bulk relaxation modulus. If the material is incompressible, this value is ignored; and c) t_iProny: The relaxation time of the first term in the expanded series. The material parameters in ABAQUS are then calculated according to the constants of relaxation modulus and creep modulus measured by the experiment by Junpeng (2016) as shown in Table 1.

2.4. Two-dimensional numerical simulation 2.4.1 Model parameter setting For the viscoelastic simulation of the polymer inner liner, because the analysis focuses on the mechanical relationship between the inner liner and carcass layer at the groove, it is only necessary to simulate the groove portion. In the present study, the local structure was simplified into a twodimensional cross-section model, and three full strips of the carcass were considered to capture the precise locking mechanism of the carcass as

(5)

i =1

In ABAQUS, the extended Prony series can be used to represent the viscoelastic properties of the PVDF. The parameters should be set as follows: a) g_iProny: The modulus ratio of the first term in the Planone expansion series of the shear relaxation modulus;

Fig 5: 2D model and grid diagram

Zhang et al. Numerical simulation of creep behaviour of flexible riser inner liner

Fig 6: Stress distribution of PVDF inner liner

seen in Fig 4. The model can clearly determine the shape of the inner liner creep, show the influence distribution on the cross-section of the carcass layer, and reduce complexity, which is useful for calculation results to converge. Both the inner liner and carcass layer are divided by the 2D grid unit. Since the inner liner creeps under the action of external force, the inner liner grid needs to be encrypted and divided to obtain more accurate results. The boundary conditions in the fixed Y direction were established at the innermost side of the carcass layer, as shown in Fig 5. The two contact portions were disposed so as not to take into account the frictional limited sliding, and the top of the inner liner was loaded with a constant external pressure of 4 MPa. The analysis step was set to viscoelastic analysis, and the 20-year creep of the inner liner was calculated by the analysis step setting. 2.4.2 Analysis of calculation results The present study first simulated the creep process of the liner for 20 years, and obtained a cloud map of the stress distribution, which is compared with the solid (non-viscoelastic) inner layer to highlight the effect of the viscoelastic behaviour of polymer on the results. Secondly, the parameters that affect the creep of the inner liner are altered and the law is explored. Finally, an axial force was set on the

Fig 7: Stress distribution of solid inner liner

creeped inner liner to simulate the stress distribution on the carcass. Figs 6 and 7 are the calculated stress clouds of PVDF inner liner and solid inner layer after simulating the creep of the inner liner for 20 years with a constant external pressure of 4 MPa. It can be seen from the PVDF stress cloud diagram that the maximum stress occurs at both sides of the groove, where the stress concentration is highest at the first contact of the inner liner with the carcass, and the remaining stress is minor. It can be seen from the cloud diagram that the inner liner is partially deformed and squeezed into the groove of the carcass; this is consistent with the phenomenon of crowding in actual engineering. Fig 7 shows the stress distribution of a non-viscoelastic liner under the same experimental conditions. From a numerical point of view, the stress value of the solid model is less than that of the PVDF model. The difference is owing to the material property, which results in different deformation methods and resulting internal stress. Fig 8 compares the nodes with the highest strain on the two inner liners; it can be seen that under constant external pressure, the strain of the viscoelastic material shows an increasing trend with time and reaches a larger strain value. This phenomenon is consistent with polymer creep property. Although

Underwater Technology Vol. 37, No. 3, 2020

Fig 8: The strain-time relation of two types of inner liners

Fig 10: Effect of different spans on creep strain

there is a strain distribution on the solid inner liner, the maximum value is only 0.0002, and the strain does not change with time.

carcass to reduce the groove span can effectively avoid the occurrence of creep. Fig 11 illustrates the thickness of the inner liner as uniformly increased from 1 mm to 4 mm, and the strain as non-uniformly reduced. The thickness of the different inner liner shows a significant nonuniform change when the inner liner thickness is 1 mm. Here, the strain of the inner liner increases sharply. A thinner inner liner can reduce the weight of the pipe, but insufficient thickness will lead to increased creep. Therefore, choosing an inner liner with a thickness of 3 mm – 4 mm has good economic practicality.

2.4.3. Parametric analysis of creep Under the premise that the material parameters of the PVDF inner liner are unchanged, the three basic parameters corresponding to the creep strain are analysed, including the external pressure, the span of the carcass groove and the thickness of the inner liner. Fig 9 shows that the external pressure of the inner liner is uniformly increased from 2 MPa to 6 MPa; the creep also shows a uniform increase. The strain increases sharply at the initial loading of external pressure, and the strain growth trend gradually increases when time slows down. It can be seen that the creep of the inner liner is sensitive to the response of the pressure change, and therefore during the start-up, shut-down and pressure testing sudden changes in pressure will affect the polymer layer. Fig 10 shows the the carcass layer span as uniformly increased from 4 mm to 10 mm. With the increase of the groove span, the strain of the inner liner also shows a non-linear increase. Therefore, appropriate adjustment of the structural size of the

Fig 9: Effect of different external pressures on creep strain

2.4.4. Simulation of the axial force of D inner liner The present study considered one of the main reasons for the tearing of the carcass as the axial force applied by the inner liner, and therefore the calculated axial force was added to the model after creep. According to Liu and Vaz. (2016), the magnitude of the axial force on the flexible riser is: F = 500 + 50 sin[(π / 8)t −(π / 2)]KN (6)

Fig 11: Effect of different thickness on creep strain

Zhang et al. Numerical simulation of creep behaviour of flexible riser inner liner

Fig 12: Stress cloud diagram when an axial force is applied

By substituting known parameters about geometry, material and load conditions into the axisymmetric viscoelastic cylinder model, the axial force in the inner lining can be calculated. The result is a dynamic response that changes with time. To simplify the model, the axial force was set to the average value of 3600 N (Liu and Vaz, 2016). Fig 12 is a stress cloud diagram simulating the axial force of the inner liner. It can be seen that the stress on both sides of the groove is relatively large. This is caused by the inner liner having a greater squeezing and pulling effect on the carcass layer after it is embedded into the groove. However, as the stress in other parts is relatively small, it was observed that the creep behaviour has a significant effect on the carcass layer. Although the 2D plane model can intuitively show the creep process and force situation, there are limitations in the ABAQUS simulation. For example, the 2D plane is a shell model, and it is not possible to use solid contact methods. In the simulation process of stretching the carcass layer by applying an axial force, it is not possible to show more realistically the stress and displacement of the carcass being stretched. Therefore, a solid model of the carcass layer and inner liner was established. Emphasis was placed on simulating the influence of the axial force on the carcass when the inner liner is embedded.

3. Numerical simulation of the mechanical behavior of the carcass layer 3.1. Three-dimensional embedded model description The present paper establishes a real carcass layer model; the carcass layer section is shown in Fig 13. According to the ‘S’ section structure, the present paper establishes a carcass layer with an inner diameter of 127 mm as the research object. Table 2 gives the specific parameter values of the carcass layer section (Nogueira and Netto, 2010). 84

Fig 13: Carcass layer cross-sectional view

Since the carcass layer structure is an ‘S’ type spiral wound structure, the model is relatively complex, and the contact between the inner liner and carcass layer is nonlinear. Therefore, solving the problem that the complex model calculation does not converge, and improving the calculation accuracy and optimising the simulation effect, is difficult. Because the model is only affected by axisymmetric loads and does not consider bending loads, the mesh elements can use fully integrated elements, i.e. C3D8 elements. C3D8 refers to an eight-node linear hexahedral element. This element shows good mechanical properties when subjected to axial loads. However, when the model is subjected to bending and torsion, and torque, the mesh element is distorted, affecting the calculation accuracy and convergence of the model. Therefore, when the model is subjected to only Table 2: Carcass layer section parameters (Nogueira and Netto, 2010) Parameter

Value

Parameter

Value

E/GPa

190

Poisson’s ratio

0.3

L1/mm

q1/°

L2/mm

q2/°

L3/mm

q3/°

L4/mm

R1/mm

L5/mm

R2/mm

L6/mm

2.25

R3/mm

2.5

L7/mm

Rtip/mm

Underwater Technologyâ&#x20AC;&#x192; Vol. 37, No. 3, 2020

Fig 16: Carcass layer displacement cloud

Fig 14: Model grid diagram and loading schematic

axial loads and no bending loads, calculations can be performed using fully integrated elements. The boundary conditions limit the inner liner to the X-axis negative direction to be completely constrained. The analysis step is set up using a combination of viscoelastic analysis and implicit analysis. According to the results calculated by the theoretical model, an external pressure of 4 MPa was applied to the outer surface of the inner liner, and the 3600N axial force was applied to the point where the end portion of the inner liner was coupled in the positive direction of the X-axis (shown in Fig 14).

3.2. Carcass layer axial stress/strain analysis Figs 15 and 16 show calculated carcass stress cloud and deformation cloud, respectively. In Fig 15, the carcass layer stress is mainly distributed in the interaction area with the inner liner. The stress distribution of the adjacent â&#x20AC;&#x2DC;Sâ&#x20AC;&#x2122; cross-section of the carcass layer is similar, and the larger stress appears on the surface of the carcass layer and the groove, mainly owing to the large frictional force with the inner liner on the surface of the carcass layer, and creeping of part of the inner liner material into the groove of the carcass layer. Fig 16 reflects the axial deformation of the carcass layer under the axial load of the inner liner. Because of the fixed

Fig 15: Assembly model stress cloud

Fig 17: Loading path on carcass cross-section

Fig 18: Stress distribution of the carcass layer under different external pressures

constraint at the end of the carcass layer, the axial displacement approaches 0, and the displacement in the upper end region reaches 4.3 mm. The displacement of the carcass layer is gradually changed along the spiral direction owing to its spiral winding structure. To demonstrate the stress distribution of the carcass layer section more clearly, the present paper creates a path on the carcass layer section and analyses the change along it. The red arrow represents the direction of the path as seen in Fig 17. Fig 18 shows the stress distribution of the crosssection of the lining layer under different external pressures; the stress of the main force-bearing area of the carcass layer gradually increases with the increase of external pressure. Because the larger external pressure will make the inner liner have more contact with the carcass layer, the deformation of the inner liner between the grooves and the friction of the contact region will become increasingly larger. Therefore, a distinct stress gradient is formed at the two peaks. 85

Zhang et al. Numerical simulation of creep behaviour of flexible riser inner liner

4. Conclusion Based on the phenomenon that the inner liner of the flexible riser is exposed to external pressure and temperature, the present paper simulated creep behaviour during long-term operation. Combined with the mechanism of tearing failure of the carcass layer, the influence of the inner liner creep behaviour on the carcass was investigated. The establishment of the two-dimensional model focused on the simulation analysis of the creep behaviour of viscoelastic materials. The creep characteristics of viscoelastic materials were affected by parameters such as time, temperature and pressure. Therefore, based on the theoretical model, the present paper established a finite element calculation model and drew a stress and strain cloud diagram that visually shows the creep form of the inner liner for 20 years. The present study overcame the calculation and test problems of long-term use of pipelines in engineering, and analysed the basic parameters affecting the creep of the inner liner. The conclusions of the present study are: a) the creep of the inner liner is sensitive to the response of the pressure change, but change is linear; b) with the increase of the groove span, the strain of the inner liner shows a non-linear increase; and c) the thickness of the different inner liner shows a significant non-uniform change. These conclusions play a guiding role in the structural design of the carcass layer and the inner liner. In the 3D model, the defects of the 2D shell structure model are well compensated and contact between the inner liner and the carcass layer is more accurately established. It reflected the stress and strain distribution of the inner liner and the carcass layer under the combined external and axial forces. It was determined that the position where the carcass layer is subjected to the most stress is the groove (path length is 14 mm), where the inner liner is squeezed into the groove. The axial force generated in the inner liner is passed to the carcass layer by way of being ‘embedded’. Here, the region will be subject to greater mises stress. The second mises stress peak appeared in the area where the two layers are closely attached (path length is 30 mm). In this area, the two layers are fully in contact with the external pressure, and the forces will be transmitted to the carcass layer through friction. In the subsequent path, the crosssection of the carcass layer is nested inside the next

carcass layer in a spiral wound structure and is no longer used as the main bearing area.

Acknowledgements The present authors acknowledge the support from the China National Key Research and Development Plan (Grant No.2016YFC0303702), National Natural Science Foundation of China (51809276) and Science Foundation of China University of Petroleum, Beijing (No.2462017YJRC040).

References Farnes KA, Kristensen C, Kristoffersen S, Muren J and Sødahl N. (2013). Carcass failures in multilayer PVDF risers. In: Proceedings of the ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering, 9–14 June, Nantes, France. Hansen R, Lyckegaard A, Cappeln C, Mcgeorge D, Sødahl N and Bendiksen E. (2015). Carcass tearing in flexible pipes. In: Proceedings of ASME 2015, International Conference on Ocean, Offshore and Arctic Engineering, 31 May–5 June, St. John’s, Newfoundland, Canada. Junpeng L. (2016). Axial viscoelastic damping behavior of flexible risers. Doctoral thesis, Federal University of Rio de Janeiro. Kristensen CE, Muren J, Gjendal A, Hanssen EB, Melve B, Sødahl N, Engh B and Søfferud M. (2017). Full-scale validation of axial carcass loads in flexible pipe structure from cyclic pressure and temperature. In: Proceedings of ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering, 25–30 June, Trondheim, Norway. Kristensen CE, Muren J, Skeie G, Skjerve H, and Sødahl N. (2014). Carcass tear out load model for multi-layer pressure sheath risers. In: Proceedings of ASME 33rd International Conference on Ocean, Offshore and Arctic Engineering, 8–13 June, San Francisco, USA. Liu J and Vaz MA. (2016). Axisymmetric viscoelastic response of flexible pipes in time domain. Applied Ocean Research 55: 181–189. Nogueira VPP and Netto TA. (2010). A simple alternative method to estimate the collapse pressure of flexible pipes. In: Proceedings of ASME 29th International Conference on Ocean, Offshore and Arctic Engineering, 6–11 June, Shanghai, China. Qiu L and Zhang J. (2006). Creep analysis for an unbonded flexible pipe barrier. In: Proceedings of ASME 25th International Conference on Offshore Mechanics and Arctic Engineering, 4–9 June, Hamburg, Germany. Shaw MT and MacKnight WJ. (2005). Introduction to polymer viscoelasticity, third edition. Hoboken, NJ: John Wiley & Sons, 316 pp. Williams ML, Landel RF and Ferry JD. (1955). The temperature dependence of relaxation mechanisms in amorphous polymers and other glass forming liquids. Journal of the American Chemical Society 77: 3701–3707.

doi:10.3723/ut.37.087â&#x20AC;&#x201A; Underwater Technology, Vol. 37, No. 3, pp. 87â&#x20AC;&#x201C;93, 2020

Reliability analysis of an umbilical under ultimate tensile load based on response surface approach Xia Ran1, Zhang Yu1*, Zheng Lijun2, Zhang Zhou1 and Guo Jiangyan2 1 China University of Petroleum, Beijing, Beijing, China 2 China National Offshore Oil Corporation Research Institute, Beijing, China

Technical Paper

www.sut.org

Received 31 October 2019; Accepted 3 July 2020

Abstract The umbilical is one of the most important components of a subsea production system. Processing errors and environmental load deviations may occur during the manufacturing process, and the deterministic design based on safety factors is often unable to meet the needs of engineering. In the present paper, the random distribution law of the umbilical geometry parameters is considered to analyse the reliability of the umbilical under the ultimate tensile load by combining the response surface approach of reliability analysis with the finite element analysis. Keywords: umbilical, tensile failure, reliability analysis, response surface approach

1. Introduction The umbilical is one of the most important components of offshore production. It is a composite cable consisting of pipes, cables and fillers. It functions as a connection of the underwater production system and control system, providing the underwater production system with electrical power, hydraulic power and chemicals necessary for its normal operation, and transmitting control data signals to it. The umbilical plays an important role in ensuring the safety and stability of offshore oil and gas development (Guo, 2016). The typical structure of spirally wound and mutually non-bonded contact umbilical with multi-unit and multi-layer is shown in Fig 1. However, there are limitations of the traditional metal armor in the umbilical with increase of application depth. In order to overcome these challenges, carbon fibre rods and stranded wire can be used to replace metal armor (Yu and Su, 2008; Zhang et al., 2019). The section of umbilical strengthened by carbon fibre rods and stranded wire is shown in Fig 2. *â&#x20AC;&#x201A; Contact author. Email address: zhangyu@cup.edu.cn

During installation and in-position operation, the top of the umbilical is subjected to large tensile load as water depth increases, and umbilical damage caused by tensile load may occur. Tang et al. (2014) studied the tension behaviour of an umbilical by finite element analysis and compared this with the corresponding analytical results; the results verified the accuracy and validity of the finite element model. Uttings and Jones (1987a; b) considered the Poisson effect of armored steel wire and the friction, extrusion and contact between components, and analysed the tensile behaviour of the cable. The results showed that friction has little effect on the tensile performance of spiral components. Li et al. (2018) established two types of finite element models of umbilical, no-filling and partialfilling, and explored the effect of filling on the tensile properties of an unarmored umbilical. Previous research on the tensile behaviour of umbilicals has mainly focused on mechanical analysis, not reliability analysis. However, there is some existing reliability analysis and optimisation for marine pipelines. Yang and Zhen (2011) analysed the reliability of a deep-sea steel catenary riser by the agent model and Monte Carlo methods. Sen (2006) studied the fatigue reliability of a steel catenary riser and applied the probability of failure to re-determine the safety factor to guide its design. Song et al. (2011) applied the moving least square response surface approach to optimise the reliability of a floating production storage and offloading (FPSO) riser and provided a reliable method for the design of an offshore riser. Wang et al. (2011) used the approximate model method to analyse the fatigue reliability and optimise the design of the bending stiffener, obtaining reasonable optimisation results. Therefore, existing research about umbilicals mainly focuses on mechanical analysis, and further 87

Ran et al. Reliability analysis of an umbilical under ultimate tensile load based on response surface approach

Fig 1: Section of the typical structure of the umbilical

Fig 3: Integral configuration of the umbilical

The applied depth of the umbilical studied in the present paper is 2000 m, and its configuration is slow waveform, as shown in Fig 3. The tensile load of the umbilical can be calculated from the marine environment (located in the northern sea area of Qiongdongnan Basin), as shown in Table 2, and the umbilical weight can be calculated using the software Orcaflex. From the distribution of tensile load (shown in Fig 4), the maximum tensile load of the umbilical can calculated as 120 kN. Fig 2: Section of the umbilical strengthened by the carbon fibre and stranded wire

research about reliability is still required. The umbilical is a multi-component and non-bonded structure with a complex manufacturing process; it can cause structural size errors owing to a number of factors including operational reasons, process accuracy and environmental impact. In order to ensure the safety performance of the umbilical structure, it is therefore necessary to calculate the reliability of the umbilical by considering the randomness of the structural size parameters.

2. Mechanical model of the umbilical 2.1. Global analysis of the umbilical The umbilical is mainly composed of: tube, cable, fibre and filling units; the material properties of each element of the umbilical are shown in Table 1. The linear density of an umbilical in water can be calculated as 13.3 kg/m.

2.2 Local analysis of the umbilical The local umbilical is shown in Fig 5; all steel tubes are made of s-super duplex stainless steel and covered with high-density polyethylene (HDPE), and the stranded wire simplified into a cylinder. The cable unit is simplified to HDPE filled with copper wire, and the fibre unit can be simplified to HDPE cylinder. The internal clearance is filled with high-density polyethylene, which is tangent to the surrounding elements. The material of the outer protective layer is also HDPE. The dimensional parameters of each component in the mechanical model of the umbilical are shown in Table 3. The contact type of the model is regular, and the contact attribute is hard (Xu et al., 2019). Uttings and Jones (1987a; b) reported that friction has little effect on umbilical elongation, and therefore the tangential contact of the coulomb friction coefficient is 0 in the model. In order to load effectively, reference points can be set up at one end of the model. The loaded end and reference point are constrained by motion coupling, and degrees of

Table 1: Material properties

Unit

Material

Steel tube Stranded wire Filling and sheathing

Super duplex stainless steel 20 600 Steel 195 000 High-density polyethylene 1 200

Elastic Modulus (MPa)

0.33 0.33 0.48

Cable Carbon fibre rod

Copper Carbon fibre

0.33 0.307

110 800 210 000

Poissonâ&#x20AC;&#x2122;s ratio

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Table 2: Marine environment

Maximum wave height (m) Period of maximum wave height (s) Surface flow velocity (m/s) Underflow velocity (m/s)

Once per 100 years

Once per year

16.9 15.9 2.4 0.4

13.4 14.7 2.04 0.4

6.3 12.1 1.09 0.25

Table 3: Dimension of the model Unit

Outer Thickness Quantity diameter (mm) (mm)

High-pressure steel tube Low-pressure steel tube Stranded wire Carbon fibre rod Power cable

12.7

1.3

19.06

1.3

Control cable Fibre-optical

Fig 4: Distribution of the tension load

freedom of the loaded end are controlled by the reference point. The mechanical model of the umbilical is constrained at one end, and the coupling point at the other end exerts a concentrated force of 120 kN. The stress analysis results of the umbilical and its units are shown in Fig 6. The failure priority of each component of the umbilical can be obtained by Equation 1 (Zhang et al., 2015):

19 24.4 185 mm2 (conductor cross-section) 24.4 16.6

2 2 1 2 1

1.5 p , (1) Sy

where p is the maximum Mises stress and Sy is the yield stress. For steel pipes, stranded wires and carbon fibre rods, it can be calculated that N1 ≈ 0.93, N2 ≈ 0.48, N3 ≈ 0.25. The failure probability of steel tubes is therefore much greater.

3. Random distribution of geometric parameters of the umbilical The umbilical is manufactured based on deterministic design schemes that contain uncertainties owing to process defects. Since the carbon fibre rod, stranded wire and steel tube are the main tensile components, the thickness of the steel tube, and diameters of the stranded wire and carbon fibre rod are taken as variables. Random variables follow normal distribution (ASTM International, 2020), and their probability density and cumulative distribution functions are shown in Equations 2 and 3, respectively: f X (X ) =

 1 x − µ  2  1   (2) exp −   2  σ   2πσ

 x − µ  (3) FX (X ) = Φ    σ  Fig 5: Three-dimensional model of the umbilical

Detailed statistical characteristics of each variable are shown in Table 4. 89

Ran et al. Reliability analysis of an umbilical under ultimate tensile load based on response surface approach

Fig 6: Stress analysis results of the umbilical and its elements: (a) stress nephogram of the umbilical; (b) stress nephogram of the low-pressure steel tube; (c) stress nephogram of the high-pressure steel tube; (d) stress nephogram of the stranded wire; and (e) stress nephogram of the carbon fibre rod

4. Reliability analysis of tensile failure of the umbilical 4.1. Design of random variables based on the Box-Behnken method The Box-Behnken method (Ferreira et al., 2007) extracts three points with different probabilities from each random variable, and the midpoint of the edges and center points are selected as samples. Fig 7 illustrates the principle of the Box-Behnken method for extracting samples of three random variables. Equation 4 (Box and Behnken, 1960) can be used to select samples for arbitrarily distributed random variables: xs

â&#x2C6;Ť f (x )dx = p

â&#x2C6;&#x2019;â&#x2C6;&#x17E;

, n = 1, 2, 3 , (4)

where f(x) is the probability density function of random variable; pn is probability; p1 is 0.002; p2 is 0.5; and p3 is 0.998. In the present paper, only the dimensions of the main tension component are considered: the thickness of steel tube t, the diameter of stranded wire d1 and the diameter of carbon fibre rod d2. The midpoints and center points can be selected by Equation 4 (a total of 13 samples are shown in Table 5).

4.2. Fitting of response surface function According to Equation 1, failure probability of the steel tube is much greater than the other components, and therefore in the present analysis the maximum Mises stress of the steel tube was taken as the response value. The same mechanical analysis was carried out on the 13 samples, and their maximum Mises stress are shown in Table 6.

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Table 4: Probability distribution characteristics of random variables Random variable Distribution

Mean value

Coefficient of variation

Standard deviation

Thickness of steel tube Diameter of stranded wire Diameter of carbon fibre rod Tensile strength of steel tube

Normal distribution

1.3 mm

0.03

0.039

Normal distribution

19.0 mm

0.02

0.380

Normal distribution

24.4 mm

0.01

0.244

Normal distribution

650 MPa

0.03

18.67

analyse the influence of three random variables on the response value. The function of tensile failure of the umbilical can be fitted as: 1 S y − 7055.88 + 13.33t + 19.58d1 1.5 (6) + 508.82d2 − 0.79td1

+ 2.28td2 − 0.81d1d2 − 10.59t 2 + 0.23d12 − 9.90d22 The correction coefficient of the fitting function is R2 = 0.93, which shows that the model fits well, and can be used for preliminary analysis and prediction of the failure of the steel tube under ultimate tensile load.

Fig 7: Samples of the Box-Behnken method

According to the failure conditions of the steel tube, the conditions for its safe operation are: Z=

1 S y − p > 0 , (5) 1.5

where the safety factor is 1.5; Sy is the yield stress of the super duplex stainless steel; and p is the maximum stress of the steel tube in the finite element analysis. Taking t, d1 and d1 as basic random variables, based on the multi-variate binomial mathematical model, the least square method is used to fit and

4.3. Reliability calculation The methods of calculating reliability in practical engineering include the first-order second-moment (FOSM) and Monte Carlo methods (Yin, 2014). The FOSM method is used to calculate the reliability of the umbilical under ultimate tensile load, and the results are compared with the Monte Carlo method. The basic principle of the FOSM method can be seen in Equation 7 (Zhu, 2007), which uses the mean and standard deviation of random variables to calculate the reliability index of structures:

Table 5: Parameters of 13 samples Sample Thickness of steel Diameter of stranded Diameter of carbon tube (mm) wire (mm) fibre rod (mm) 1 2 3 4 5 6 7 8 9 10 11 12 13

1.300 1.495 1.105 1.300 1.105 1.495 1.300 1.105 1.495 1.105 1.495 1.300 1.300

19.000 20.140 19.000 20.140 19.000 17.860 20.140 20.140 19.000 17.860 19.000 17.860 17.860

24.400 24.400 25.132 23.668 23.668 24.400 25.132 24.400 25.132 24.400 23.668 25.132 23.668

Ran et al. Reliability analysis of an umbilical under ultimate tensile load based on response surface approach

Table 6: Response values of 13 samples Sample

Thickness of steel tube (mm)

Diameter of stranded Diameter of carbon Maximum Mises stress wire (mm) fibre rod (mm) of steel tube (MPa)

1 2

1.300 1.495

19.000 20.140

24.400 24.400

403.4 385.8

1.105

19.000

25.132

381.9

1.300

20.140

23.668

403.5

1.105

19.000

23.668

419.1

1.495

17.860

24.400

402.2

1.300

20.140

25.132

383.5

1.105

20.140

24.400

397.8

1.495

19.000

25.132

385.5

1.105

17.860

24.400

421.5

1.495

19.000

23.668

411.7

1.300

17.860

25.132

400.1

1.300

17.860

23.668

421.7

Z (µx1 , µx2 ,..., µxn ) µ , β≈ Z = 1 (7) σZ 2 2  n  ∂Z      ∑ i =1 ∂X µσxi    i    where b is reliability index; Z is limit-state function; m is average value; s is standard deviation; and Xi are independent random variables. The reliability index b = 2.99 can be obtained by Equation 7, and the reliability of the umbilical under ultimate tensile load becomes 0.995. The reliability parameters, such as failure rate and reliability index, are calculated through 1 million sampling analysis of Equation 6. Table 7 shows the comparison of results from the two methods. The reliability difference between the two methods is 0.002 %, demonstrating that the method can effectively calculate the reliability of the umbilical, which is effective and practical for engineering application. It also provides a reference for reliability design of other ocean structures.

5. Conclusion In the present paper, the reliability model of the stranded wire and carbon fibre reinforced umbilical under ultimate tension load was established by combining the finite element analysis and response surface approach. The reliability of the umbilical was then calculated by the FOSM and Monte Carlo methods. In the present study, the global and local mechanical analysis model of the stranded wire and carbon fibre reinforced umbilical was established. The mechanical analysis of the umbilical under the ultimate tensile load was carried out, 92

Table 7: Comparisons of calculation results

Reliability b

FOSM method

Monte Carlo Difference method

0.9986 2.99

0.9968 2.73

0.002 % 8.6 %

and the results show that the steel tube fails first. Based on the Box-Behnken method, the geometric parameters of an umbilical were selected and designed. The limit-state function of the umbilical under ultimate tension load was established by finite element analysis and least square method. The limit-state function of an umbilical was calculated by the FOSM method, and the reliability of the umbilical under the ultimate tension load was obtained. Through comparison with the Monte Carlo method, the result shows that the reliability calculation is accurate.

Acknowledgement The present research was supported by the National Natural Science Foundation of China (grant number No. 51779266) and National Key Research and Development Plan (grant numbers No. 2016YFC0303705)

References ASTM International. (2020). ASTM A789 / A789M – 20: Standard Specification for Seamless and Welded Ferritic/ Austenitic Stainless Steel Tubing for General Service. DOI: 10.1520/A0789_A0789M-20. Available at: http://www.astm.org/cgi-bin/resolver.cgi?A789A789M, last accessed <13 September 2020>. Box G and Behnken D. (1960). Some new three level designs for the study of quantitative variables. Technometrics 2: 455–476.

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Ferreira SLC, Bruns RE, Ferreira HS, Matos GD, David JM, Brandão GC, da Silva EGP, Portugal LA, dos Reis PS, Souza AS and dos Santos WNL. (2007). Box-Behnken design: An alternative for the optimization of analytical methods. Analytica Chimica Acta 597: 179–186. Guo HZ. (2016). Key technologies of umbilical design, manufacture and testing for underwater production system. Beijing: Petroleum Industry Press. 223 pp. Li XY, Guo HY, Zhu YY and Zhang T. (2018). Finite element analysis considering the tensile behavior of filled steel tube umbilical. Journal of China Ocean University 48: 182–187. DOI: CNKI:SUN:QDHY.0.2018-S1-022. Sen TK. (2006). Probability of fatigue failure in steel catenary risers in deep water. Journal of Engineering Mechanics 132: 1001–1006. Song CY, Lee J and Chuong JM. (2011). Reliability-based design optimization of an FPSO riser support using moving least squares response surface meta-models. Ocean Engineering 38: 304–318. Tang MG, Yan J, Wang Y and Yue Q. (2014). Tensile stiffness analysis on ocean dynamic power umbilical. China Ocean Engineering 28: 259–270. Utting WS and Jones N. (1987a). The response of wire rope strands to axial tensile loads – Part I. Experimental results and theoretical predictions. International Journal of Mechanical Sciences 29: 605–619. Utting WS and Jones N. (1987b). The response of wire rope strands to axial tensile loads – Part II. Comparison of experimental results and theoretical predictions.

International Journal of Mechanical Sciences 29: 621– 636. Wang AJ and Yang HZ. (2011). Reliability optimization analysis of bending strengtheners. In: Proceedings of the 15th China Ocean (Coastal) Engineering Symposium (II), 3-6 August, Tai Yuan, China. Xu SX, Su ZT and Wu J. (2019). Analysis on sealing performance of VL seals based on mixed lubrication theory. Industrial Lubrication and Tribology 71: 54–60. Yang HZ and Zheng W. (2011). Metamodel approach for reliability-based design optimization of a steel catenary riser. Journal of Marine Science and Technology 16: 202–213. Yin J. (2014). The performance comparison of reliability analysis algorithm based on MATLAB. Sichuan Building Mater 40: 69–71. DOI: 10.3969/j.issn.1672-4011.2014.02. 031. Yu BF and Su F. (2008). New application of carbon fiber composites in deep sea oil and gas field development. Material Engineering s1: 000176–179. DOI: 10.3969/j. issn.1001-4381.2008.z1.034. Zhang Y, Cheng NY, Zhao Y and Zhang P. (2019). Analysis of mechanical properties of carbon fiber reinforced spiral rod in umbilical. UK. In: Proceedings of 38th ASME International Conference on Ocean, Offshore and Arctic Engineering (OMAE 2019), 9–14 June, Glasgow, UK. Zhang Y, Cao XP, Wang CF and Zhang WC. (2015). Mechanics of materials, Chinese edition. Beijing: Tsinghua University Press. Zhu XD. (2007). A comparative study of calculation methods for reliability of engineering structures. China Shipping 7: 110–111.

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Performance validation and dynamic response analysis of a deepwater cable bending restrictor Kang Yongtian1,2,*, Xiao Wensheng1, Zhang Dagang2, Zhang Liang2, Zhou Chouyao2 and Li Mingang2 1 Department of Mechanical and Electronic Engineering, China University of Petroleum (East China), Qingdao, 266000, China 2 Qingdao DMAR Engineering INC.,Qingdao, 266000, China

Technical Paper

doi:10.3723/ut.37.095 Underwater Technology, Vol. 37, No. 3, pp. 95–101, 2020

Received 31 October 2019; Accepted 3 July 2020

Abstract The deepwater cable bending restrictor is an important protective device for risers, umbilicals and cables in offshore engineering, protecting cable structure by controlling minimum bending radius. Its mechanical properties are analysed based on the numerical analysis model and finite element analysis (FEM) of ø175. The sensitivity analysis of using quantity of bending restrictors is also performed to show the effect of the quantity on bending stiffness. A testing scheme of bending stiffness of the bending restrictor is then formulated based on its structure. From numerical analysis results through test simulation, the tolerance is less than 3 %, which verifies the reliability of the numerical analysis model. Performance of the bending restrictor and dynamic response are analysed according to environmental parameters that occur once per 100 years from offshore wind power farms and pipein-pipe models, respectively. The results show the bending restrictor can effectively protect cable structure, and the pipein-pipe model is suitable for calculating mechanical properties of interaction between the bending restrictor and cable. Keywords: bending restrictor, structural analysis, sensitivity analysis, test simulation, pipe-in-pipe model

1. Introduction The bending restrictor, a cable-protecting device widely used in deepwater offshore engineering, can effectively protect deepwater risers, umbilicals and power cables from damage. It can be used within the range of certain bend radius. Guo (2016), Zhang et al. (2013), Lu et al. (2011) and Kang et al. (2020) the show the connection type of the bending restrictor and cable. The bending restrictor is mainly used to avoid damage on cables as a consequence of * Contact author. Email address: kang402@126.com

cable overbending. Normally, the bending restrictor is connected with pipeline, with a connector on the other end to a subsea manifold or distribution units. ISO1328-5:2009 (International Organization for Standardization, 2009) states that the bending restrictor consists of some units with self-locking structures. The units can bear some external pressure, from which a smooth arc is formed in the bending restrictor system; the arc radius is the lock radius of the bending restrictor. When a bending restrictor is elected, its lock radius should be larger than the minimum bending radius of cable. Application of a bending restrictor is shown in Fig 1. The mechanical performance of the bending restriction through mechanical form analysis has been previously studied. Xue et al. (2016) and Yang and Zheng (2011) calculate the bending form of risers or umbilicals via numerical simulation and propose the demand for bending stiffness of the bending restrictor. Witz (1996) and Probyn et al. (2007) simplify the calculation on structures of the riser and bending restrictor by beam unit, and analyse pipeline structure and stress state of the bending restrictor via the member element method. When all units of the bending restrictor are locked, a certain bending radius is formed, which bears the bending moment from the external load. In this way, the cable structure can be effectively protected from damage. Zhang et al. (2012) and Kang et al. (2015) analyse the interaction between the riser and drill pipe based on the pipe-in-pipe mechanical model, and calculate the bending radius, ultimate bearing capacity and other factors. In the present paper, the bending restrictor of ø175 was analysed and its numerical model built

Yongtian et al. Performance validation and dynamic response analysis of a deepwater cable bending restrictor

Fig 2: Bending restrictor after docking connection

Fig 1: Application of bending restrictor in offshore wind power project

using the finite element ABAQUS. As a result, the mechanical analysis method of the bending restrictor was obtained and sensibility analysis using the number of bending restrictors performed. A stiffness test based on its mechanical property was then performed, and the reliability of the numerical model verified. Finally, the mechanical properties and performance were shown through analysis of the interaction between the bending restrictor and cable via the pipe-in-pipe mechanical method and the application of projects using bending restrictors in shallow-water wind power platforms.

2. Structure of the bending restrictor The bending restrictor is a cable protection device made of non-metal material normally polyurethane and high-density polyethylene. Under special conditions, stainless steel can also be used to reinforce the framework for complex working conditions. The material trademark for the bending restrictor of Ă¸175 in the present paper is HYPERLAST 7983170, and its properties are shown in Table 1. The bending restrictor is designed with a semicircular structure, making it easy to install on a cable Table 1: Properties of HYPERLAST 7983170

No.

Property

Value

Unit

1 2 3 4 5

Tensile strength Strain limit Ceiling temperature Impact strength specific gravity

50 12 78 15 1.15

MN/M2 % Â°C KJ/m2 kg/m3

structure. During its design, the bending radius of a locked bending restrictor should be taken into consideration and contact surface of curvature control set to create the ideal lock radius. The structure of the bending restrictor is illustrated in Fig 2. Bolts are used for the docking connection between one half of the bending restrictor and the other, with the bending restrictor locked externally on cables. The upper boss of the bending restrictor can move at some angle in the groove of the other half, forming a bending radius. In order to protect cable structure, the number of pairs of bending restrictors used will vary according to different water depths, sea conditions and cable layout structure.

3. Analysis of the structure of the bending restrictor 3.1. Theoretical analysis Finite element analysis (FEM) is built for the bending restrictor according to bending conditions. Point A is bent to point B (surface-to-surface contact with 4Â° offset). The bending displacement of the bending restrictor is shown in Fig 3. The present analysis supposes the bending restrictor initially as a cantilever beam structure, where bending forms owing to an external bending moment after connection. After being bent, the bending restrictor is still in a plane according to the Bernoulli-Euler theory, and therefore Equation 1 can be obtained: M=

EI , (1) R

where M is the bending moment, E is the elastic modulus of material 800 MPa, and I and R are the

Underwater Technology Vol. 37, No. 3, 2020

unit is subject to a bending moment, and its load model is shown in Fig 4. It can then be calculated that:

Fig 3: Finite element analysis (FEM) displacement of the bending restrictor

π(OD 4 − ID 4 ) , (2) 64

where OD is the hypothetical outside diameter of the cross-section of the bending restrictor, 0.22 m, and OD is the inside diameter, 0.175 m. The relationship between the arc length and radius is: L = R * α*π / 180 (3) The offset angle a of the bending restrictor is 4°, and its length is 0.38 m. The arc length is then: L = 0.38 m

sinφ =

dx (7) dL

ε=

(5)

When Equations 5 and 2 are applied to Equation 1, the bending moment is calculated as: M = 10 116 n ⋅ m. The bending restrictor with an offset angle of 4° is mechanically analysed, and the bending restrictor unit is simplified into a small unit according to the Bernoulli-Euler theory. The lower part of small

OD (8) 2R(L )

The tension from the bending moment is: F=

2M (9) OD

As a result of horizontal stress balance:

Fsinφ = Tcosφ (10) Applying Equation 9 to Equation 10, the following calculation is then made:

(4)

When Equation 4 is applied to Equation 3, the following calculation is derived: R = 5.45 m

dy (6) dL

The strain from bending is:

sectional moment of inertia and bending radius, respectively. I=

cosφ =

2M tanφ (11) OD

From Equation 1, the mechanical equation of a certain unit is: M (L ) =

EI (L ) (12) R(L )

According to Equations 3 and 12, curvature can be obtained by: k=

dφ M (L ) , (13) = dL EI (L )

where R(L) is the unit radius; EI(L) is the unit bending stiffness; and M(L) is the bending moment. Based on the bending moment equilibrium equation, it can be concluded that: dM − F cos φdx + F sin φdy −T cos φdy −T sin φdy = 0 (14)

When Equations 6 and 7 are applied to Equation 14, it can be derived that: dM = T (15) dL When Equation 11 is applied to Equation 15, then:

Fig 4: Load model of the bending restrictor

dM 2M = tanφ (16) dL OD

Yongtian et al. Performance validation and dynamic response analysis of a deepwater cable bending restrictor

When the initial bending angle of 4° and Equation 13 are applied to Equation 16, it can be concluded after derivation that:  dk 1  2M = tan(φ + 4)− kdEI (L ) (17)   dL EI (L ) OD When Equation 8 is applied to Equation 17, then:

dε Mtan(φ + 4) kdEI (L ) OD = − ⋅ (18) dL EI (L ) EI(L) 2 The partial differential equation of the bending restrictor under bending conditions is solved according to Equations 6, 7 and 3. The bending moment and strain curves are illustrated in Fig 5.

Fig 6: Finite element analysis (FEM)

Fig 5: Bending moment and strain curves

3.2. Finite element analysis (FEM) FEM is built through the finite element software ABAQUS. Owing to through-holes and surfaces in the model, tetrahedron element is more suitable for mesh generation. Second-order-tetrahedron element is more accurate than first-order-tetrahedron element but involves a large amount of computation. First-order-tetrahedron is advantageous because of its high accuracy and low computation cost. Therefore, after mesh generation, hexahedron element and tetrahedron element can be used to build the model to analyse the main part and minor part, respectively, based on the main contact position. The FEM is shown in Fig 6. The simulation results show that a 12 % tensile strain limit appears before a 50 MPa tensile stress (tensile strength). The red part in Fig 7 is the position of maximum stress. Meanwhile, stress concentration occurs when the bending restrictor is bent downward leading to higher stress. In applications, multiple bending restrictors are combined to share bending of internal tubes, and therefore stress is not large. Maximum stress in the neck is chosen as the maximum value in the analysis. The reaction bending moment is extracted according to material properties of the bending restrictor when the strain reaches 12%. At this moment, the 98

Fig 7: Strain analysis result for structure of the bending restrictor

bending moment is at its maximum. The minimum bending radius can be calculated after the rotation angle is extracted according to Equation 3. The calculation result is shown in Table 2.

3.3. Sensitivity analysis of simulation quantity of bending restrictor As position changes of multiple restrictor models are complex, it is necessary to analyse sensitivity of the required quantity of bending restrictor models. Multiple bending restrictor models are built according to their changes during the bending process, and analysis of the mechanical state and sensitivity to bending of the bending restrictors is performed. 3-pair and 9-pair bending restrictor models are built for comparison of the mechanical Table 2: Calculation results Conditions

Safety factor

Bend moment (kN.m)

Operation limit

0.67 1

11.05 15.23

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Fig 8: Displacement analysis result of 6-pair bending restrictors

Fig 11: Test schematic diagram of stiffness

Fig 9: Displacement analysis result of 7-pair bending restrictors

Fig 10: Bending moment-strain relationship comparison

state of different quantities. Analysis results of the bending restrictors are shown in Figs 8 and 9. Fig 10 indicates that the quantity of bending restrictors has little effect on the result, thus demonstrating that finite analysis is reliable.

4. Bending moment test Test methods are developed according to the mechanical properties of the simulated bending moment of the bending restrictor. One end of the bending restrictor is fixed, and the middle part is connected to a hydraulic cylinder with rope through a pulley. This results in the bending restrictor under the state of bending by means of hydraulic traction. The strain is then measured, and performance of the different bending moments is extracted. The test principle is shown in Fig 11. As shown in Figs 12 and 13, strain gauges are attached evenly on the sides of the bending restrictor, and the changes are monitored when bent. When strain reaches 12 %, the bending moment can be calculated by reading the hydraulic cylinder.

Fig 12: Simulation test of ultimate bending moment

In this way, bending moments under different states can be obtained. To eliminate errors, three-times measured values are averaged as the final test value. The result of the bending test is obtained from the previously mentioned test data. Through

Fig 13: Installation of strain gauges

Yongtian et al. Performance validation and dynamic response analysis of a deepwater cable bending restrictor

Table 3: Environmental conditions name wind (m/s) current (m/s) wave (m) period (s) value

37.7

2.3

14.22

9.1

Fig 14: Simulation test of the ultimate bending moment

comparison of the results from finite element analysis and test analysis as shown in Fig 14, it can be concluded that the results are similar, with less than 3 % tolerance. In addition, through FEM analysis it can be concluded that there is no damage on the surface of the bending restrictor, with 12 % strain. Therefore, the material can bear more bending moment; further study on the material is to be performed.

5. Dynamic response analysis of the bending restrictor The bending restrictor is used in dynamic environments in marine engineering. Subject to tensile and bending moment, the bending restrictor bears external bending moment and maintains a certain bending radius, protecting the cable structure from damage. The software Orcaflex is used to model the bending restrictor and pipe-in-pipe cable. The cable is simulated by one beam element of the software, and the other beam element from the cable outer layer is used to simulate the bending restrictor, with two-layer elements defined by friction contact. The analysis model is built based on applications in a shallow-water platform.

Fig 15: Relative positions of the bending restrictor and J-tube

100

Fig 16: Bending moment changes along arc length

According to relative positions of the bending restrictor and J-tube as shown in Fig 15, the cable enters into the J-tube through the bending restrictor and reaches the upper part of the platform. After it is connected to the wind power generator, the beam element is used for analysis. Stress conditions of the pipe-in-pipe model are obtained from structure analysis, and sea conditions that occur once per 100 years are then analysed, as shown in Table 3. Stress results of external and internal tubes of the pipe-in-pipe model are compared and analysed (see Figs 16 and 17). The bending restrictor bears bending moments and the inside cable bears tensile force. Stress tendency coincides with Figs 16 and 17, and calculation results of the pipe-in-pipe model are satisfactory. Therefore, the pipe-in-pipe model is suitable for simulation analysis of bending restrictors in risers. During simulation, the bending restrictor shows a positive protective effect. The bending moment will be larger when the bottom of the bending

Fig 17: Curvature changes alone arc length

Underwater Technology Vol. 37, No. 3, 2020

restrictor is driven and its upper end is embedded into soil. The bending radius of the cable structure is controlled by the bending restrictor. The maximum bending curvature is 0.38 l/m, which is lower than the required 0.42 l/m, thus meeting the application conditions of the cable.

Acknowledgment The present paper was funded by the High-tech Shipping Research Project from the Ministry of Industry and Information Technology of the People’s Republic of China, ‘Research of full life-cycle reliability guarantee technology system for subsea oil and gas production system’ (2018GXB01-02-003).

6. Conclusion The present paper aims to present the mechanical properties, bending moment, strain and other influence factors of the bending restrictor by means of theoretical analysis and finite element analysis. Sensitivity analysis of the effect on bending performance based on models of different quantities is also performed. The structure of 3-pair bending restrictors meets the calculation requirements; meanwhile, the ultimate bending moment of different pairs coincides with that of 3-pair ones. Therefore, it can be concluded that the quantity of bending restrictors has little effect on their bending resistance performance. Bending stiffness and bending strength are tested by simulating the bending shape of the bending restrictor. Comparisons between bending test results and numerical analysis results show less than 3 % tolerance. Therefore, the bending restrictor has some bending resistance effect. Dynamic response of the bending restrictor and risers based on pipe-in-pipe models is analysed. The interaction dynamic conditions are well simulated, showing consistent movement between bending restrictor and risers. In this way, cable structure is well protected. Therefore, friction and interaction between the bending restrictor and cable structure can be well simulated by the pipe-in-pipe mechanical model.

Data availability statement The data used to support the findings of the present study are available from the corresponding author upon request.

References Guo HZ. (2016). Key technologies of umbilical design, manufacture and testing for underwater production system. Beijing: Petroleum Industry Press. International Organization for Standardization. (2009). ISO 13628-5:2009: Petroleum and natural gas industries – design and operation of subsea production systems – Part 5: subsea umbilicals. Available at: https://www.iso.org/ standard/41322.html, last accessed <13 September 2020>. Kang YT, Xiao WS, Wang QB, Zhang D and Zhao J. (2020). Suppression of Vortex-Induced Vibration by Fairings on Marine Risers. Journal of Ocean University of China 19: 298– 306. DOI: 10.1007/s11802-020-4033-0. Kang Z, Zhang L, Zhang L and He N. (2015). Parameter sensitivity analysis of top tensioned riser pipe in pipe structure. Ship & Ocean Engineering 44. DOI: 10.3963/j. issn.1671-7953.2015.04.025. Lu Q, Xiao N and Yan J. (2011). Finite element analysis of bending stiffness of steel umbilical. Computer Assisted Engineering 16: 19-38. DOI: 10.3969/j.issn.1006-0871.2011.02.004. Probyn I, Dobson A and Martinez M. (2007). Advances in 3D FEA techniques for metallic tube umbilicals. In: Proceedings of International Society of Offshore and Polar Engineers ISOPE-2007, 1–6 July, Lisbon, Portugal. Witz JA. (1996). A case study in the cross-section analysis of flexible risers. Marine Structures 9: 885–904. Xue S, Peng Y, Liu Z, Chen X and Zhang Y. (2016). Study on the analysis and layout technology of flexible pipe. China’s New Technology Products 9: 81–83. DOI: 10.13612/j. cnki.cntp.2016.09.053. Yang HZ and Zheng WQ. (2011). Metamodel approach for reliability-based design optimization of a steel catenary riser. Journal of Marine Science and Technology 16: 202–203. Zhang DG, Wybro P and Kang YT. (2013). Deeper water oil and gas field development in South China Sea. Engineering Sciences 11: 1–5. Zhang Q, Huang Y and Zhao B. (2012). Nonlinear time domain analysis of TTR structure by pipe in pipe model. Ship Engineering 90: 93–97. DOI: 10.13788/j.cnki. cbgc.2012.04.002.

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Optimal design of buckling resistance for a large deepwater functional tank (DFT) Wang Yi, Zhang Fangfang1* and Xu Fan School of Safety and Ocean Engineering, China University of Petroleum (Beijing), Beijing, Beijing, China

Technical Paper

doi:10.3723/ut.37.103â&#x20AC;&#x201A; Underwater Technology, Vol. 37, No. 3, pp. 103â&#x20AC;&#x201C;109, 2020

Received 31 October 2019; Accepted 24 August 2020

Abstract Buckling resistance is a major challenge in the design of a large deepwater functional tank (DFT), and internal stiffeners are commonly used to strengthen its shell. In the present paper, the influence of various stiffener parameters on the stability of the DFT was studied via the finite element method. The strengthening scheme of the DFT was optimised by the orthogonal test method, by which the influence of various parameters on the shell mass, internal volume and stability of the structure was evaluated. The optimal buckling resistance scheme can be obtained using the comprehensive balance method based on the orthogonal assessment results. Keywords: deepwater functional tank, reinforced structure, orthogonal assessment method, multi-objective, structure optimisation

1. Introduction A new underwater production system is proposed involving a large deepwater functional tank (DFT) to overcome problems of high installation and disassembly costs, inconvenient emergency maintenance and monitoring. As one of the key components in the underwater production system, the DFT connects production equipment and oil pipelines, and provides a dry enclosure for ensuring the normal operation of underwater facilities such as oil tree and separator. The main design challenge of the DFT is withstanding high external hydrostatic pressure. The buckling resistance of the tank is a concern owing to its large size. Timoshenko and Gere (1964) and Bazant and Cedolin (2010) introduced the elastoplastic stability theory of rod, beam, plate and shell structures, providing a foundation for the study of structural stability. Liang et al. (2004) used the extended interior penalty function (EIPF) and Davidon-Fletcher-Powell (DFP) methods to study *â&#x20AC;&#x201A; Contact author. Email address: 1399724381@qq.com

the optimisation of the design of the large depth multi-spherical shell. Liu et al. (2015) studied the secondary development of CATIA software and its communication with Abaqus software to achieve the parametric design of the pressure spherical shell. Leon (1971) studied the influence of the annular rib of the double-spherical titanium alloy pressure shell on its failure load. He et al. (2009) discussed the strength and stability of the underwater external pressure shell by changing various parameters, including the radius and thickness of the shell and the spacing of the ribs. Zhu et al. (2005) proposed a semi-circular, shell-type, ribreinforced cylindrical shell structure, and established a design calculation method based on theoretical and model experiments. Lv (2006) compared the stability of various types of rib-reinforced cylindrical shells on the theoretical analysis. The present paper analyses a DFT for use in 1000 m water depth, comprising a 3 m outer radius, 10 m height and 0.1 m shell thickness, for the stability of the large shell structure; the DFT analysed is a combined structure of hemi-sphere and cylinder, as shown in Fig 1. Parameters such as shell thickness, the cross-sectional shape of the stiffener and the web length are used to study the buckling resistance of the DFT. The DFT is assessed by the orthogonal test method to achieve the optimal strengthening scheme based on the criteria of small mass, large internal volume and high stability.

2. Numerical model of the DFT Owing to the structural complexity of the DFT, a simplified combined structure of hemi-sphere and cylinder is selected for the numerical analysis (Huang and Chen, 2015), as shown in Fig 2. According to the design requirements, high-strength steel is selected for the material of the DFT, with elastic 103

Yi et al. Optimal design of buckling resistance for a large deepwater functional tank (DFT)

250000

Shell weight Critical buckling load 200000

150000

Shell weight /kg

Critical buckling load /MPa

100000

Fig 1: Vertical layout of the DFT

100

150

Shell thickness /mm

Fig 3: Effect of shell thickness on buckling load and shell weight

3.2. Influence of the stiffener Arranging the stiffeners inside the DFT is a common method for improving the stability and overall rigidity of the DFT. The following analyses the influence of various parameters of the stiffener and arrangement methods on the stability of the DFT.

Fig 2: Numerical model of pressure shell

modulus E = 2.06 Ă&#x2014; 105 MPa, Poissonâ&#x20AC;&#x2122;s ratio m = 0.3, and yield strength = 785 MPa. The working pressure is 10 MPa external; the bottom of the DFT is fixed; the general finite element software Abaqus is used to build the model and perform buckling analysis; and the grid unit type is C3D8R.

3. Parameter analysis for stability of the DFT 3.1. Influence of the shell thickness In order to obtain the influence of the thickness of the shell on the buckling result and the weight of the DFT, the thickness of the shell is selected as 50 mm, 75 mm, 90 mm, 100 mm, and 110 mm respectively. This ensures that the variation range is sufficient to obtain an ideal value. Fig 3 shows the variation of the critical buckling load and weight of the DFT under various shell thicknesses. It can be seen that as the shell thickness increases, the critical buckling load and weight of the DFT also increase, and that there is a positive correlation between the two parameters. However, the growth trend of the shell weight is greater than the growth trend of the critical buckling load, which also increases the difficulty of welding. Therefore, to obtain higher shell stability, it is unreasonable and uneconomical to increase the thickness of the shell. 104

3.2.1. Effect of the shape of the stiffener In order to study the influence of the cross-sectional shape of the stiffener on the buckling resistance of the DFT, the cross-sectional area is a fixed value of 0.009 m2. The cross-sectional shapes of the stiffener are selected as rectangular, L-shaped, I-shaped and T-shaped, respectively. The critical buckling load of the DFT under different stiffener section parameters is shown in Table 1. Fig 4 shows the critical buckling load of the DFT under various cross-sectional shapes of the stiffener. It can be seen that when the crosssectional area is the same, the I-shaped stiffener has the best buckling resistance, and hence the highest stability. 3.2.2. Effect of the length of the I-shaped stiffener web Five ring horizontal I-shaped stiffeners are evenly arranged inside the DFT, with a spacing of 1.5 m, Table 1: Critical buckling load of the DFT with different stiffener cross-section shapes Section shape L h h

t L L L

t t t

L/mm

h/mm

t/mm

Critical buckling load / MPa

120

25.9

120

105

26.5

120

27.1

120

28.6

Underwater Technology Vol. 37, No. 3, 2020

Fig 6: Schematic diagram of the angle α 23.5

Fig 4: Critical buckling load of the DFT for different stiffener shapes

3.2.3. Effect of the arrangement of stiffener In order to study the influence of the ring stiffener angle α (as shown in Fig 6) on the buckling load of the DFT, only one ring stiffener is arranged inside the DFT, and the axial position of the stiffener is fixed and placed at the position of 3500 mm from the bottom of the DFT. The angle of α is selected from 0, 5, 10, 15, 20, 25, 30, 35, and 40 degrees, respectively. Fig 7 shows the change of the critical buckling load of the DFT when the angle of the stiffener is Internal volume Critical buckling load

Critical buckling load /MPa

and the length of the web L is selected as 30 mm, 60 mm, 90 mm, 120 mm, 150 mm, 180 mm, 210 mm, 240 mm, respectively. Fig 5 shows the critical buckling load and internal volume variation for the DFT at different web lengths. It can be seen that the effect of the web length on the buckling load of the DFT is still large. As the length of the web increases, the buckling resistance of the DFT increases, while the internal volume of the DFT decreases.

23.0

22.5

22.0

21.5

21.0

20.5

Reinforcement angle /䚹

Fig 7: Critical buckling load value of the DFT under different stiffener angles

changed. It can be seen that the buckling resistance of the DFT tends to decrease as the angle increases. When the angle is increased from 0 to 40 degrees, the critical buckling load of the pressure shell decreases by 10.3 %. Therefore, changing the angle of the ring stiffener reduces the stability of the DFT, and thus it is not preferable to obtain high stability by changing the angle of the ring stiffener. In order to study the influence of the ring stiffener position on the buckling load of the DFT, only

170

165 30 160

155

150

22 0

100

200

Internal volume /m3

Critical buckling load /MPa

145 300

Web length /mm

Fig 5: Critical buckling load value and internal volume of the DFT

Fig 8: Schematic diagram of the position H

105

Yi et al. Optimal design of buckling resistance for a large deepwater functional tank (DFT)

stiffeners on the stability of the DFT is studied. Fig 10 shows the change in the critical buckling load value of the DFT as the number of longitudinal stiffeners changes. It can be seen that adding the number of longitudinal stiffeners inside the DFT can improve the stability, but when the number of stiffeners exceeds six, the growth trend is slowed.

Critical buckling load /MPa

24 23 22 21 20

4. Optimisation design of the DFT based on orthogonal assessment method

19 18

1000

2000

3000

4000

5000

6000

7000

Reinforcement position /mm

Fig 9: Critical buckling load value of the DFT under different stiffener positions

one ring stiffener is arranged inside the DFT, and the axial position of the stiffener H (as shown in Fig 8) is gradually moved from the bottom of the DFT to the top at intervals of 1000 mm. The value H of the ring stiffeners is selected from 500 mm, 1500 mm, 2500 mm, 3500 mm, 4500 mm, 5500 mm, and 6500 mm, respectively. Fig 9 shows the change of the critical buckling load of the DFT when the position of the stiffener is changed. It can be seen that when the position of the stiffener moves gradually from the bottom to the top, the critical buckling load of the DFT first increases, and then decreases. When the position is 4500 mm, the buckling resistance of the DFT is maximised, and therefore it is preferable to arrange the stiffener in the upper middle area of the DFT. 3.2.4. Effect of longitudinal stiffeners The general method of reinforcement for large shell structures is ring stiffener. In the present paper, longitudinal stiffeners are evenly arranged inside the DFT, and effect of the longitudinal 22.5

Critical buckling load /MPa

22.0 21.5 21.0 20.5 20.0 19.5

4.1. Orthogonal assessment method design Before the structural optimisation, the parameters of the DFT are selected as follows: the shell thickness of DFT is 100 mm; the length of the web is 120 mm; the reinforcement method is ring and longitudinal stiffeners; the shell mass is 1.73 Ă&#x2014; 105 kg; the internal volume is 211.46 m3; and the critical buckling load is 23 MPa. The structure of the DFT was optimised by the orthogonal assessment method. The three factors to be controlled in the assessment were the shell thickness, reinforcement method and length of the web. Each factor takes three levels, as shown in Table 2. The blank column is set in the orthogonal table to reflect the error caused by random factors; the blank column is often called the error column in the analysis of variance. This column is a comprehensive of unexamined interactions and other Table 2: DFT factor level table

19.0

Factor (A) Shell (B) Reinforcement (C) Web level thickness/mm method length/mm

18.5 0

Number of longitudinal stiffeners

Fig 10: Relationship between the number of longitudinal stiffeners and critical buckling load of the DFT

106

While there are various methods that can be used to improve the stability of the DFT, analysing the combination of numerous different factors takes a significant amount of time. In order to determine the optimal solution quickly, the present study uses the orthogonal assessment method. The orthogonal assessment method is a mathematical statistical method that uses orthogonal tables to arrange and analyse multi-factor samples. The advantage of this method is that the influence of factors on the objective function and its influence law can be obtained through a small number of assessments, and the best assessment condition can then be inferred (He et al., 2015; Chen et al., 2008). Therefore, in the present study, the orthogonal assessment method is used to optimise the structure of the DFT, and the solution with the smallest mass, largest volume and greatest stability is obtained.

1 2 3

90 100 110

Longitudinal Ring Ring + longitudinal

90 120 150

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Table 3: DFT orthogonal assessment plan No. A

Empty Shell Internal Critical buckling weight/kg volume/m3 load/MPa

1 2 3 4 5 6 7 8 9

1 2 3 1 2 3 1 2 3

1 2 3 2 3 1 3 1 2

1 2 3 3 1 2 2 3 1

1 1 1 2 2 2 3 3 3

1.52e5 1.57e5 1.59e5 1.69e5 1.73e5 1.74e5 1.85e5 1.88e5 1.91e5

unknown influencing factors. The error obtained from the blank column contains the combined error of experiment and interaction, and is an estimate. Corresponding with the optimisation goal i.e.to meet the stability requirements with the lightest weight and largest volume, Table 3 is the orthogonal assessment scheme table of the DFT.

4.2. Analysis of assessment results In the orthogonal table, A, B, C represent three independent variable factors; 1, 2, 3 represent three levels under each factor; Ki is the test index of the same level of each factor; and Ki is the average of the test index of the same level of each factor. The factor order represents each factor the influence of a target is arranged from large to small, and the best solution gives the optimal solution for a single target. The sum Ki of the three factor values at each level is calculated, and the average value Ki Table 4: Analysis of orthogonal assessment results Index A Shell weight K1 4.68 K2 5.16 Ă&#x2014;105/kg K3 5.64 K1 1.56 K2 1.72 K3 1.88 R 0.32 Factor order Best solution Internal K1 640.24 634.41 volume/m3 K2 K3 628.60 K1 213.40 K2 211.47 K3 209.53 R 3.87 Factor order Best solution Critical K1 62.90 K2 75.87 buckling K3 81.61 load/MPa K1 20.97 K2 25.29 K3 27.21 R 6.24 Factor order Best solution

B 5.06 5.18 5.24 1.69 1.73 1.75 0.06

C 5.14 5.17 5.17 1.71 1.72 1.72 0.01 ABC A1B1C1 634.46 645.05 634.40 634.38 634.39 623.82 211.49 215.02 211.35 211.46 211.46 207.94 0.14 7.08 CAB A1B1C1 58.34 68.57 79.90 74.84 82.13 76.96 19.45 22.86 26.63 24.95 27.38 26.65 7.93 3.79 BAC A3B3C3

Empty 5.16 5.16 5.16 1.72 1.72 1.72 0 634.44 634.43 634.38 211.48 211.47 211.46 0.02 74.18 72.79 73.40 24.73 24.26 24.47 0.47

216.98 213.40 209.86 211.46 207.94 215.01 206.02 213.06 209.52

14.54 23.35 25.01 20.69 28.84 26.33 23.11 27.70 30.80

of each level corresponding factor is used as an important parameter to evaluate the sensitivity of the influencing factors. The calculation results are shown in Table 4. The magnitude of the range R reflects the degree of influence of the corresponding factors in the experiment on each index (Li and Hu, 2008). The larger the range R of the factor, the more obvious the influence of the factor on the index, and the weaker the opposite. Corresponding to a single index, the primary and secondary factors affecting the target, and the best combination plan, can be determined. Fig 11 shows the range of each indicator under different factors.

4.3. Determine the optimal solution As the optimisation considers multiple factors which cannot directly choose the optimal solution, an integrated balance method is used to determine the optimal solution. The visual analysis of each indicator is performed separately for each indicator, and the optimal level combination of the primary and secondary order of the influencing factors of each indicator is obtained. Then the overall balance is performed to find out the best combination of each factor for each indicator: 1) Shell thickness. For the mass and internal volume of the shell, it is better to select A1 for the factor, and to take A3 for the critical buckling load of the shell. It can be seen from the table that the influence of this factor on the three objectives is relatively large. Since the shell quality is the most important factor affecting the shell thickness, this should be considered. The factor level is therefore taken as A1. 2) Reinforcement method. For the mass and internal volume of the shell, the reinforcement method is a relatively minor factor. For the critical buckling load of the shell, the reinforcement method is the main factor; the critical buckling load is the most important index among the three indicators. Therefore, the factor level is taken as B3. 3) The length of the I-shaped stiffener web. As the length of the web of the stiffener increases, the values of the three targets also tend to increase. It can 107

Yi et al. Optimal design of buckling resistance for a large deepwater functional tank (DFT)

0.4

the reinforcement method is ring plus longitudinal reinforcement; and the length of the web is 90 mm. The shell weight of this solution is 1.58 × 105 kg, and the internal volume is 216.97 m3. Comparing the stability requirements with the structural parameters before optimisation, the shell weight was reduced by 8.7 %, and the internal volume was increased by 2.6 %.

(a)

Shell weight R /kg

0.3

0.2

0.1

5. Conclusion

0.0

-0.1

Empty

Factor

Critical buckling load R /MPa

(b)

0 A

Factor 8

(c)

Internal volume R /m3

Acknowledgement 2

Empty

Factor

Fig 11: The extreme difference of the mean of the indicators under various factors: (a) the magnitude of R under factor of shell weight; (b) the magnitude of R under factor of internal volume; and (c) the magnitude of R under factor of critical buckling load

be seen from Table 4 that this factor is the main factor affecting the internal volume. The factor level is taken as C1. For the shell mass and critical buckling load, this factor is a secondary factor, and C1 and C3 are best. When the factors take C1 and C3, the shell mass and critical buckling load are similar. Therefore, this factor takes C1. By synthesising the analysis, the optimal solution is A1B3C1, i.e., the thickness of the casing is 90 mm; 108

In the present study, the orthogonal assessment method was successfully applied to the optimal design of buckling resistance for large shell structures such as the DFT, and the influence of different parameters was obtained by numerical simulation. The present paper has shown that the orthogonal assessment method is efficient and useful in helping to select the optimal design parameters with the smallest mass, the largest volume and the best stability. It was found that the stability of the I-shaped reinforced structure is the best under the same cross-sectional area. The thickness of the shell and length of the web are positively correlated to the stability of the shell, whereas the angle of the stiffener is negatively correlated with the stability of the shell. Moreover, it can be concluded that the orthogonal method can be used in optimal design of buckling resistance for the DFT. The optimal solution can be obtained by analysing the orthogonal assessment results and using the comprehensive balance method.

The present paper was funded by the National Key Research and Development Plan (Grant no. 2016YFC0303708), and the Open Project Program of Beijing Key Laboratory of Pipeline Critical Technology and Equipment for Deepwater Oil & Gas Development (Grant No. BIPT2018005).

References Bazant ZP and Cedolin L. (2010). Stability of structures: elastic, inelastic, fracture and damage theories. New York: World Scientific Publishing, 1040 pp. Chen G, Zhan M, Yang H, Li H and Huang L. (2008). FEA of power spinning of complicated thin-walled shell based on orthogonal optimization. Journal of Plasticity Engineering 15: 67–71. He FZ, Ma JJ and Wan ZQ. (2009). Analysis on structure strength and stability of submersible pressure tank. Journal of Ship Mechanics 13: 915–922. He X, Liu X and Guo Z. (2015). Structural optimization design of pressure-resistant shell of submersible based on orthogonal experiment. Mechanical Science and Technology 34: 8–12. DOI: 10.13433/j.cnki.1003-8728.2015.0102

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Huang J and Chen J. (2015). Strength and stability analysis of wide flat ring rib cylindrical shell. Ship Science and Technology 37: 7–11. DOI: 10.3404/j.issn.1672-7649.2015.09.002 Leon GF. (1971). Intersecting titanium spheres for deep submersibles. Journal of the Engineering Mechanics Division 97: 981–1006. Li Y and Hu C. (2008). Experiment design and data processing. Beijing: Beijing Chemical Industry Press. Liang CC, Shiah SW, Jen CY and Chen HW. (2004). Optimum design of multiple intersecting spheres deep-submerged pressure hull. Ocean Engineering 31: 177–199. Liu F, Wang LF, Han DF and Yao J, (2015). Parametric design and stability analysis of pressure-resistant spherical

shell of manned submarine. Journal of Ocean Technology 34: 32–37. Lv C, Wang X, Yao W and Liang C. (2006). Study on structural stability of pressure cylindrical shell strengthened by various types of ribs. Ship Mechanics 113–118. DOI: 10.3969/j.issn.1007-7294.2006.05. 016 Timoshenko SP and Gere JM. (1964). Theory of elastic stability. New York: McGraw-Hill, 541 pp. Zhu B, Wan Z, Xu B and Shao D. (2005). Study on structural stability of pressure cylindrical shell strengthened by semi-ring shell ribs. Ship Mechanics 79–83. DOI: 10.3969/j. issn.1007-7294.2005.01.012

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Development of next generation subsea production system (NextGen SPS) design and analysis for ultra-deepwater applications Xing-wei Zhen*, Yue Han, Qiu-yang Duan, Jia-hao Wu and Yi Huang School of Naval Architecture and Ocean Engineering, Dalian University of Technology (DUT), NO-116024 Dalian, China

Technical Briefing

doi:10.3723/ut.37.111 Underwater Technology, Vol. 37, No. 3, pp. 111–117, 2020

Received 31 October 2019; Accepted 25 May 2020

Abstract The present paper describes a new offshore field development solution, Next Generation Subsea Production System (NextGen SPS), that aims to overcome the technical and commercial limitations of the current offshore field development concepts (dry tree or subsea tree) in ultra-deep water (more than 1500 m). The key developments of the NextGen SPS, including its main characteristics, stability characteristics and optimal design on the riser system, are presented and discussed. The series of studies demonstrates that the NextGen SPS offers improved technical and commercial performance, higher levels of safety, reduced interface complexity and improved development flexibility for field development in ultra-deep water. Keywords: NextGen SPS, stability characteristics, hydrodynamic characteristics, optimal design, risk control, ultra-deep water

1. Introduction In China, large offshore petroleum fields are placed in deep and ultra-deep water, where the challenges are characterised by water depth, remoteness and harsh environmental conditions. Currently, the offshore petroleum fields in deep and ultra-deep water are developed by dry tree units, subsea tree systems or a combination of both, as illustrated in Fig 1 (Barton et al., 2018). However, both dry tree and subsea tree developments have limitations when aiming to overcome the challenges of offshore field development in deep and ultra-deep water, as illustrated in Table 1 (Lim, 2009). Aiming at meeting the challenges of offshore field development in deep and ultra-deep water, the current studies mainly focus on * Contact author. Email address: zhenxingwei@dlut.edu.cn

the development of new offshore platforms (Srinivasan et al., 2006; Roberts, 2007; Murray et al., 2008; Zhang et al., 2007; Ocker et al., 2010; Li et al., 2011) and riser systems (Alliot and Legras, 2005; Franciss, 2005; Karunakaran et al., 2009; Tellier and Thethi, 2009). Nonetheless, it can be found that the current studies are still in the domain of dry tree and subsea tree developments, whose limitations are not overcome essentially. It is therefore necessary to develop a new offshore field development solution to overcome the technical and commercial limitations of the existing offshore field development concepts in deep and ultra-deep water. In 2011, Dalian University of Technology (DUT) initiated research activities to develop a new offshore field development solution for 3000 m water depth based on artificial seabed technology, termed NextGen SPS (Zhen et al., 2012). Fig 2 presents the general arrangement of the NextGen SPS at the present stage. Thus far, a series of studies have been carried out to confirm the advantages of the NextGen SPS over the existing offshore field development solutions, including working principle, structural design, layout design, hydrodynamic behaviour, global response and optimal design (Zhen et al., 2013; Zhen et al., 2014; Huang et al., 2014; Zhen et al., 2017; Zhen et al., 2018a; Zhen et al., 2018b; Zhen et al., 2018c; Han et al., 2019; Wu et al., 2019). In addition, a study of the NextGen SPS safety in the operational phase (Zhen et al., 2018d; 2020) has been carried out by DUT in collaboration with the Norwegian University of Science and Technology (NTNU). The present paper describes the main characteristics of the NextGen SPS and describes its key developments, including stability characteristics and optimal design on the riser system. 111

Zhen et al. Development of next generation subsea production system (NextGen SPS) design and analysis for ultra-deepwater applications

Fig 1: Current deepwater system types (dry tree units or subsea tree systems; Barton et al., 2018)

2. Main characteristics of the NextGen SPS Fig 2 shows a general view of the NextGen SPS, which consists of the following components. The artificial seabed is composed of the monocolumn platform (MCP) and internal buoyancy can (IBC). The MCP guides the mid-water well system so that all rigid risers move collectively, thus reducing the collision risk. The IBC provides a stable platform for holding the mid-water X-mas tree in place. In contrast to the geological seabed, the artificial seabed, which is positioned certain distances below mean water level (MWL) to minimise the effects of direct loads from surface waves and currents, is established to support shallow-water rated well completion equipment and technology for the development of large oil and gas fields in ultra-deep water. In the current design, the MCP can support four wells which are intended to drill from the MCP. The mid-water well system comprises casing programs, well completion assemblies, wellheads and X-mas trees. The casing program consists of all casing and liner strings. The well completion assembly comprises production tubing, tubing hanger, downhole safety valve (DHSV) and production packer to ensure efficient and safe access from the artificial seabed to the reservoir. The wellhead is the mid-water/subsea termination of a wellbore in

the distributed antenna system (DAS). The subsea wellhead incorporates internal profiles for support of the casing strings and isolation of the annuli, while the mid-water wellhead incorporates internal profiles for support of the rigid riser and isolation of the annuli. The mid-water wellhead system also incorporates facilities for guidance, mechanical support and connection of the systems, such as blowout preventer (BOP) and X-mas tree, which are used to drill and complete the well. The midwater tree system includes a tubing hanger and tree, which provide the barriers between the reservoir and the environment in the production phase. The mid-water manifold system is a system of headers and branched piping used to gather and distribute fluids. The flexible jumpers connect the manifold to the floating production unit (FPU) and comprise a slack catenary shape to isolate the artificial seabed from FPU motions. It should be noted that the FPU can be any existing floating platform, such as floating production storage and offloading (FPSO) unit, semi-submersible platform, spar platform, etc., and that the mid-water manifold system will simplify the riser/vessel interface and reduce the risk of flexible jumper clashing. The mooring system comprises vertically loaded tendons connecting the artificial seabed to the

Table 1: Features of subsea vs dry tree developments (Lim, 2009)

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Feature

Dry tree development

Subsea tree development

Drilling cost

From facility

Requires MODU

OPEX cost

From facility

Requires MODU

Facilities CAPEX cost

High cost hull

Choose least cost hull

Offshore construction

Heavy lift requirements

Depends on riser system

Development flexibility

Restricted due to hull form

Minimal vessel impact

Riser/vessel interfaces

Complex interaction

Simpler interaction

Vessel flexibility

Restricted to Spar or TLP

Full range

Shut in location

In well bay close to people

Seabed isolation and offset

Flow assurance

Shortest flow path

Potentially long tie flowlines

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Fig 2: General arrangement of the DAS system

anchor piles. The function of the mooring system is to restrain the artificial seabed horizontally and vertically. The tendon assemblies consist of successive sections of chain and spiral strand wire rope. The anchor pile is a suction pile transferring the horizontal and vertical loads to the seabed. The present paper describes the key features of the NextGen SPS, which are summarised in Table 2. The NextGen SPS offers both technical and commercial advantages over the current offshore field development concepts.

3.1. Jumper length influences Flexible jumpers connect the artificial seabed to the FPU. The most significant challenge is how to set the critical length criterion of the flexible jumper. The flexible jumper length should be long enough so as to be in a slack catenary shape for the de-coupled effect. However, flexible jumpers are considerably expensive, and therefore design length values should be as short as possible. As a result, the critical length is defined as the minimum length 1500

3. Stability characteristics

near

1250 1000

T (kN)

Stability is important for the NextGen SPSâ&#x20AC;&#x2122;s operation safety. If large movement of the artificial seabed or tether failure occur, the stability behaviour of the NextGen SPS would be compromised. This could result in the breakdown of the NextGen SPS, possibly causing damage and hydrocarbon release. Hence, jumper length, artificial seabed location and mooring pattern have been taken into consideration as influence factors to guarantee the stability of the NextGen SPS.

mean

far

l=350 m l=380 m l=430 m l=530 m l=630 m l=731 m

750 500 250 150 170 200

250

300

350

400

450

500 530 550

s (m)

Fig 3: Effects of horizontal span on top tension (d = 300 m)

Table 2: Features of the DAS system Feature

NextGen SPS

Drilling cost OPEX cost Facilities CAPEX cost

From facility From facility

Offshore construction Development flexibility Riser/vessel interfaces Vessel flexibility Shut in location Fatigue damage Emergency response Flow assurance

Choose least cost hull/shallow-water rated mid-water well completion technology and equipment can be applied Pre-installation before FPU on site Minimal vessel impact Simpler interaction Full range Downhole & artificial seabed isolation and offset Less sensitive Disconnectable between FPU and flexible jumpers Shortest flow path

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1500

min

1250 1000

T (kN)

max l=420 m l=460 m l=500 m l=580 m l=620 m l=667 m

750 500 250 100

150

200

250

300

350

400

450

500

d (m)

Fig 4: Effects of submerged depth on top tension (s = 350 m)

that can maintain the equilibrium between the de-coupled property and economics of the flexible jumper. It should be noted that the critical jumper length relates to not only its maximum span but also the submerged water depth of the artificial seabed. The effects of horizontal span and submerged depth on the top tension are illustrated in Figs 3 and 4. In the present study, a highly effective analytical approach for determining the critical jumper length is proposed, and the validity is confirmed by numerical parametric studies. The critical arc-length of the flexible jumper that corresponds to the minimum tension condition is obtained as follows: lcrit ≅ 1.5818S 2far + d 2 , (1)

where, lcrit is the critical arc-length of the flexible jumper; Sfar is the maximum span that occurs in the far situation; and d is the submerged depth of the artificial seabed.

3.2. Artificial seabed location influences The submerged depth of the artificial seabed is determined by: (1) the direct loading from the surface wave and current and (2) the access for manual intervention. Hence, to ensure that the effects of the direct loading from the surface wave and current are minimised, the submerged depth of the artificial seabed should be as shallow as possible. In the present study, a wave attenuation index is developed to determine the submerged depth of the artificial seabed, as illustrated in Fig 5:

Fig 5: Effects of the direct loading from surface waves on the heave motion amplitude of the artificial seabed

3.3. Mooring pattern influences In order to investigate the mooring pattern effects on the STLP stability, sensitivity studies on the top inclined angle and tether numbers were carried out. Figs 6 and 7 present the effects of the top inclined angle on the trim and offset of the artificial seabed, respectively. The top inclined angle is defined as the angle between the top of the tether and the vertical direction and offset of the artificial seabed is expressed as a percentage of water depth. The results indicate that in order to meet the requirements of artificial seabed stability and optimise the seabed layout, the mooring pattern of vertically loaded tethers should be selected. Fig 8 shows the mooring patterns with different tethers, with signs and numbers used to indicate the arrangement of tethers. The stability performance of the NextGen SPS under extreme storm conditions (wave: Hs = 15 m, Tz = 10.4 s) with the return period of 100 years in the South China Sea (SCS) was studied, and current data is shown in Table 3. Table 4 presents the effects of tether numbers on the offset of the artificial seabed. It can be seen that the maximum offset of the artificial seabed

2   2H  H  e k z    , (2)    T  

where H is the wave height; T is the wave zero crossing period; k is the wave number; z is the submerged depth; and L is the wave length. 114

Fig 6: Inclined angle effects on the trim of the artificial seabed

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Table 4: Effects of tether numbers on the offset of the artificial seabed 3 tethers 4 tethers 6 tethers 8 tethers Maximum 2.20%WD 1.91%WD 1.54%WD 1.33%WD horizontal offset relative to the water depth (WD) (%)

Table 5: Static motions of the artificial seabed with four tethers owing to tether failure Failed tether No. Rotation (deg) Fig 7: Inclined angle effects on the offset of the artificial seabed

1 (2)

1 11.56

2 10.76

3 -4.31

3 (4)

10.41

-0.80

1,3 (2,4)

0.17

-10.17 0.83

-0.03

4. Optimisation design on the riser system

Fig 8: Mooring patterns with different tether numbers

can be significantly reduced when the number of tethers is increased, which is of importance for the requirements of pre-drilling operations. Table 5 presents the static motions of the artificial seabed with four tethers after one or two tethers have failed. The artificial seabed will have a large tilt when one tether is broken. When two opposite tethers are broken, the artificial seabed moves upward but remains flat. If a large tilt is found unacceptable in one tether failure condition, an alternative mooring system can be designed, i.e. two tethers at each corner. Table 3: Current data with the return period of 100 years Depth/m

Speed m/s

Depth/m

Speed m/s

0 10 20 50 100 150

2.05 1.99 1.98 1.77 0.93 0.94

200 300 500 1000 3000

0.74 0.74 0.60 0.43 0.32

The main objective of the present study is to develop an efficient design method for the riser system of NextGen SPS based on optimisation techniques. In the optimisation process, the evaluation of the structural behaviour of each candidate configuration requires dynamic analysis under environmental loadings and FPU motions. The process is time consuming and would be difficult to conduct. To overcome this, a series of surrogate models developed by back propagation neural network (BPNN) were used to replace the dynamic analysis. According to the input values of design variables, these surrogate models can forecast structural responses rapidly and with sufficient accuracy. Moreover, the definition of the NextGen SPSâ&#x20AC;&#x2122;s riser system depends on several design variables. In general, as the number of design variables increases, the required size of the sample used for training the surrogate models increases. This implies a rise of the time and computational cost. Consequently, design of experiments (DOE) analysis was conducted to explore the design space before the optimisation process. This analysis arranges the parametric sensitivity study on the behaviour of NextGen SPSâ&#x20AC;&#x2122;s riser system through DOE method. The DOE results clarify how design variables affect the riser system behaviour and give directions to reduce the number of design variables in the optimisation process. The proposed methodology consists of the following steps, as shown in Fig 9: 1) Identify all relevant operation states, limit states, environmental loads and input design variables; 2) Define design variables, constraints and objective functions; 3) Define the cases by DOE method and perform the dynamic analysis on such cases; 4) Analyse the obtained data by statistical method;

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Zhen et al. Development of next generation subsea production system (NextGen SPS) design and analysis for ultra-deepwater applications

Fig 9: Main aspects of the proposed optimisation methodology

5) Generate a reasonable distribution of sample points throughout the design space using Latin hypercube sampling (LHS) method; 6) Obtain the responses of each sample point through dynamic analysis; 7) Develop the surrogate model based on part of the sample, and assess the model accuracy using the other part of the sample; and 8) Perform the optimisation procedure using back propagation neural network (BPNN) model and particle swarm optimisation (PSO) algorithm. In the present study, the cost of the riser system, which is the sum of the rigid risers cost and the flexible jumpers cost, is taken as the objective function. The cost of rigid risers can be valued by the amount of material being used (including the stress joint and keel joint). The cost of the flexible jumper is related to its length: f = 4mC1 + 2l f C 2 , (3) where, m is weight of rigid riser; lf is flexible jumper length; C1 and C2 are cost weight associated to rigid riser and flexible jumper, respectively. This result achieves a reduction of 46 % for the cost of the riser system (46 % reduction for flexible jumper cost, and 40 % reduction for rigid riser cost). The flexible jumper cost is significantly higher than the rigid riser cost; hence, reducing the length of the flexible jumper is the main direction to reducing the cost of the riser system. DOE and surrogate techniques improve the efficiency of

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optimisation design, as DOE results reduce the number of design variables and the application of surrogate model avoids the time-consuming dynamic analysis in the optimisation process.

5. Conclusions Aiming to overcome the technical and commercial limitations of the current offshore field development concepts in ultra-deep water, the present paper presents a new concept of NextGen SPS based on artificial seabed technology. Furthermore, the key developments of NextGen SPS design and analysis for ultra-deepwater applications are discussed, and conclusions can be summarised as follows: 1) There exists a critical flexible jumper length that corresponds to the minimum condition of the top tension. It has been demonstrated that the critical flexible jumper length relates to not only its maximum span, but also the submerged water depth of the artificial seabed. 2) The mooring configuration with vertical loaded tethers should be selected in order to meet the requirements of artificial seabed stability and optimise the seabed layout. If a large tilt is found unacceptable in one tether failure condition, an alternative mooring system can be designed, i.e. two tethers at each corner. 3) DOE and surrogate techniques improve the efficiency of optimisation design, as DOE results can be used to reduce the number of design variables, and the application of surrogate model

Underwater Technology Vol. 37, No. 3, 2020

avoids the time-consuming dynamic analysis in optimisation process. In conclusion, the NextGen SPS improves technical and commercial performance, and provides higher levels of safety, reduced interface complexity and improved development flexibility. It can therefore provide an effective offshore field development solution for ultra-deep water.

Acknowledgements The present research has been financially supported by the National Natural Science Foundation of China (No.51709041), China Postdoctoral Science Foundation (2017M610178, 2018T110224), Natural Science Foundation of Liaoning Province (No. 20170540185).

References Alliot V and Legras J-L. (2005). Lessons learned from the evolution and development of multiple-lines hybrid riser towers for deep water production applications. Offshore Technology Conference, 2–5 May, Houston, USA. Barton C, Hambling H, Albaugh EK, Mahlstedt B and Davis D. (2018). Deepwater solutions and records for concept selection. Offshore Magazine. Available at: https://www.offshore-mag.com/resources/maps-posters/whitepaper/14034382/wood-2018-deepwater-solutions-recordsfor-concept-selection, last accessed <15 September 2020>. Franciss R. (2005). Subsurface buoy configuration for rigid risers in ultra deepwater. Proceedings of the 24th International Conference on Offshore Mechanics and Arctic Engineering, June 12-17, Halkidiki, Greece. Han Y, Zhen XW and Huang Y. (2019). Drift-off safety limits of dynamic positioned FPSO on the NextGen SPS. In: Proceedings of the Twenty-ninth International Ocean and Polar Engineering Conference, 16–21 June, Honolulu, Hawaii, USA. Huang Y, Zhen XQ, Zhang Q and Wang WH. (2014). Optimum design and global analysis of flexible jumper for an innovative subsurface production system in ultra-deep water. China Ocean Engineering 28: 239–247. Karunakaran D, Lee D and Mair J. (2009). Qualification of the Grouped SLOR Riser System. Offshore Technology Conference, 4–7 May, Houston, USA. Li B B, Ou J P and Teng B. (2011). Numerical investigation of damping effects on coupled heave and pitch motion of an innovative deep draft multi-spar. Journal of Marine Science and Technology 19: 231–244. Lim, F. (2009). Dry or wet trees in deepwater developments from a riser system perspective. In: Proceedings of the 3rd ISOPE International Deep-Ocean Technology Symposium, ISOPE-D-09-006, 28 June–1 July, Beijing, China, 50–54. Murray J, Yang C K, Chen C Y and Nah E. (2008). Two Dry Tree Semisubmersible Designs for Ultra Deep Water

Post-Katrina Gulf of Mexico. Proceedings of the 27th International Conference on Offshore Mechanics and Arctic Engineering, 15–20 June, Estoril, Portugal. Ocker C and Bordlee C. (2010). Mirage Field Multi-Column Deep Draft Floating Platform: Graving Dock Construction and Hull Fabrication. Offshore Technology Conference, 3-6 May, Houston Texas, USA. Roberts B. (2007). The Extendable Draft Platform-a Construction Friendly Dry Tree Semi. Petromin 11: 40–46. Srinivasan N, Chakrabarti S and Radha R. (2006). Response Analysis of a Truss-Pontoon Semi-Submersible with Heave-Plates. Journal of Offshore Mechanics and Arctic Engineering 128: 100–107. Tellier E and Thethi R. (2009). The Evolution of Freestanding Risers. Proceedings of the 28th International Conference on Offshore Mechanics and Arctic Engineering, 31 May- 5 June, Honolulu, USA. Wu JH, Zhen XW, Liu G and Huang Y. (2019). Optimization design on the riser system of next generation subsea production system with the assistance of DOE and surrogate model techniques. Applied Ocean Research 85: 34–44. Zhang F, Yang J M, Li R P and Chen G. (2007). Numerical and Experimental Research on the Global Performances of Cell-Truss Spar Platform. China Ocean Engineering 21: 567–576. Zhen XW, Huang Y, Zhang Q and Wang WH. (2012). Concept design of an innovative ultra-deep water oil production device. In: Proceedings of Ship Mechanics Conference, Shaoxing, China. Zhen XW, Huang Y, Wang WH and Zhang Q. (2013). Investigation of hydrodynamic coefficients for artificial buoyancy seabed unit. Journal of Ship Mechanics 17: 1381–1391. Zhen XW, Huang Y, Zhang Q and Wang WH. (2014). Parametric study on the effects of flexible jumpers on the global behavior of the rigid riser based on an innovative subsurface tension leg platform. Journal of Ship Mechanics 18: 711–723. Zhen XW and Huang Y. (2017). Parametric study on the behavior of an innovative subsurface tension leg platform in ultra-deep water. China Ocean Engineering 31: 589–597. Zhen XW, Han Y, Huang Y, Yao JJ and Wu JH. (2018a). Analytical approach for the establishment of critical length criterion for the safe and economical design of the flexible jumper in deepwater applications. Applied Ocean Research 75: 193–200. Zhen XW, Huang Y and Zhang Q. (2018b). Investigations on the mechanical behavior of an innovative subsurface tension leg platform in ultra-deep water (Part I). Journal of Ship Mechanics 22: 311–324. Zhen XW, Wu JH, Huang Y, Han Y and Yao JJ. (2018c). Parametric dimensional analysis on the structural response of an innovative subsurface tension leg platform in ultradeep water. China Ocean Engineering 32: 482–489. Zhen XW, Moan T, Gao Z and Huang Y. (2018d). Risk assessment and reduction for an innovative subsurface well completion system. Energies 11: 1306. Zhen XW, Vinnem JE, Han Y, Peng C, Yang X and Huang Y. (2020). New risk control mechanism for innovative deepwater artificial seabed system through online risk monitoring system. Applied Ocean Research 95: 1–9.

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CALL FOR PAPERS Underwater Technology: InternaƟonal Journal of the Society for Underwater Technology The Society for Underwater Technology is calling for papers for its internaƟonal journal, Underwater Technology. The journal publishes peer-reviewed technical papers on all aspects and applicaƟons of underwater technology, including: • • • • • • • • • • • • •

diving technology and physiology environmental forces geology/geotechnics marine polluƟon marine renewable energies marine resources oceanography subsea systems underwater acousƟcs underwater roboƟcs underwater science underwater vehicle technologies salvage and decommissioning

Original papers on new technology, its development and applicaƟons, and papers covering new applicaƟons for exisƟng technology, are parƟcularly welcome. Submissions should adhere to the journal’s guidelines available at www.sut.org/publicaƟons/underwater-technology/guidelines-for-authors/ For more informaƟon or to make a submission, please contact the Assistant Editor, Elaine Azzopardi, at Elaine.Azzopardi@sut.org

Marine Robotics and Applications Edited by Luc Jaulin, Andrea Caiti, Marc Carreras, Vincent Creuze, Frédéric Plumet, Benoît Zerr and Annick Billon-Coat Published by Springer eBook edition, 2018 ISBN 978-3-319-70724-2 188 pages Marine Robotics and Applications is a Springer volume composed of nine ocean engineering papers (listed as individual chapters) related to the Monitoring Quantitatif de l’Environnement SousMarin (MOQESM) Conference held in Brest, France in 2016. MOQESM, or Quantitative Monitoring of Underwater Environment Conference, is a biannual international conference that joins coastal hydrography and marine robotics specialists from industry and academia. This book was edited by a team of French, Italian and Spanish researchers: Luc Jaulin, Andrea Caiti, Marc Carreras, Vincent Creuze, Frédéric Plumet, Benoît Zerr, and Annick Billon-Coat, most of whom coauthored at least one of the chapters in the volume. The chapters relate to several current autonomous underwater vehicle (AUV) research and development themes: • Underwater acoustics: sonar track registration; • Multi-vehicle operations: securing an area with AUVs and

performing adaptive sampling with autonomous sail boats; • Platform localisation and navigation: simultaneous localisation and mapping (SLAM), range only localisation, interval analysis for trajectory estimation and electric sense for navigation; and • Development: propulsion system optimisation and AUV design and control. The chapters range from 15–20 pages each, with the exception of a much longer final chapter to conclude the volume. I am not sure if this was deliberate on the part of the editors, but there is a part of me that appreciates this sort of balance in paper lengths within a book or journal. I understand that disseminating results or ‘telling the story’ shouldn’t be determined by a word or page count; however, it is nice when content is presented in similar-sized digestible portions. There is a reasonable mix of figures, graphs, plots and images to support the text in each chapter. In most cases, the mathematics presentation is tidy and notation isn’t confusing or overly complex. The first chapter is the sole chapter in the volume under the underwater acoustics/sonar theme. ‘Fast Fourier-Based BlockMatching Algorithm for Sonar Tracks Registration in a Multiresolution Framework’ is focused on sonar image registration to support change detection for applications such as automatic target recognition (ATR). Nicolas et al. describe the underpinning mathematics and methods, and follow with an application of their elastic registration algorithm to a previously collected dataset. They

www.sut.org

demonstrate that their methods show positive results with respect to registration. The stated processing time is approximately one minute which is entirely reasonable for ATR applications, but might not quite meet the threshold for a real-time autonomous navigation implementation. There are two chapters related to multi-vehicle operations: ‘Adaptive Sampling with a Fleet of Autonomous Sailing Boats Using Artificial Potential Fields’ and ‘Secure a Zone from Intruders with a Group Robots’. One might notice a typo in the second title; unfortunately, that was not my or our editor’s mistake. More about this later. The fleet optimisation paper by Saoud et al. is a simulation-based paper that shows how potential fields can be used to maintain a formation of three vessels while following a path in the presence of marine currents and winds. The zone securing chapter by Vencatasamy et al. is the seventh chapter in the volume and is based on a scenario of a group of generic robots to maintain a military picket type formation or chain to act as a barrier against an intruder. Set theory and interval analysis are used to show in a simulated, two-dimensional environment that it is possible to force multiple agents into a desirable formation. The paper concludes with a result that uses the Bay of Biscay as the real-world backdrop for the simulation. In the acknowledgements, there is a link to a video of the simulation. The link worked and I found it added value to the chapter. Unfortunately, and somewhat disappointingly, both of these chapters (two and seven) suffer from some inconsistencies

Book Review

doi:10.3723/ut.37.119 Underwater Technology, Vol. 37, No. 3, pp. 119–121, 2020

119

Luc Jaulin et al. Marine Robotics and Applications

and errors that may distract a discerning reader. The second chapter follows a different referencing style than the first chapter of the text. Instead of citations in numerical order in the text, references are listed alphabetically, and as a result citations do not follow a natural ordering. There are some grammatical errors in Chapter 2 that I assume are a result of non-native English authors. That can be a distraction for some. The illustrations and figures in Chapter 7 are not appropriately labelled in multiple cases, e.g. no axes, units or titles. Both of these chapters are interesting and credible, and I quite like the mathematics. However, if one is going to go through the effort to write a sound paper, then they should see it through to the end and spend the effort on figures and citations. Yes, it can be a pain, but to do otherwise can diminish the value of the overall product. The platform localisation and navigation theme includes four chapters. Chapter Three, Bazeille et al.’s ‘Underwater Robots Equipped with Electric Sense of the Exploration of Unconventional Aquatic Niches’, is a highly interesting read on a heterogeneous fleet of marine robots tasked with environmental data collection under conditions not conducive to vision or acousticbased navigation. At the core of the paper is development and lab-scale testing of electric sense. The overall goal is to determine whether electric sense is suitable for reactive navigation, obstacle avoidance, exploration and submerged object shape estimation. The paper presents a sound foundation on electric sense in this context and is realistic in terms of its strengths, weaknesses and ideal applications. It will be fascinating to see how this work evolves over time. ‘Estimating the Trajectory of Low-Cost Autonomous Robots 120

Using Interval Analysis: Application to the euRathlon Completion’ by Le Bars et al. describes a method based on interval analysis/set membership to overcome the lack of GPS or range measurements onboard an AUV. A postprocessing software applied to real-world data from an AUV in the euRathlon competition shows positive results. It is a well written paper, but exhibits some figure inconsistencies similar to Chapter 3. It also has some inconsistent and incomplete references. ‘Marine Robots in Environmental Surveys: Current Developments at ISME – Localisation and Navigation’ by Caiti et al. summarises work from the Interuniversity Center of Integrated Systems for the Marine Environment in Italy. Specifically, the work focuses on results in simultaneous AUV navigation and current estimation, cooperative navigation using acoustics positioning systems and acoustic SLAM. The paper is cleanly written and includes a decent set of references, which is a key element of a quality survey paper. Nicola and Jaulin’s ‘Comparison of Kalman and Interval Approaches for the Simultaneous Localization and Mapping of an Underwater Vehicle’ examines the effect of poor initial estimates and outliers on SLAM in the traditional Kalman filter context using a commercial off-the-shelf hardware: a coupled inertial navigation system/Doppler velocity log system and acoustic beacons for range only measurements. The authors describe the underlying set theory based on interval filtering and show that it offers advantages over the Kalman approach when there is minimal prior knowledge of acoustic beacon positions. The methods are applied to real ship-based data (as a surrogate for an AUV). It is always nice to see actual data used when it is available. The chapter

has a nice balance of figures, graphs, mathematics and text, but unfortunately there are scattered grammatical and typographical errors. There are two chapters related to AUV development. ‘Design and Control of an Autonomous Underwater Vehicle (AUV – UMI)’ by Manzanilla et al. describes aspects of the development of a rover type autonomous underwater vehicle/ remotely operated vehicle. It proposes the physical layout and control architecture for a platform including some preliminary simulated motion control results. It is a good reference paper and would benefit any group looking to develop a small underwater vehicle platform from scratch. ‘Evolutionary Dynamic Reconfiguration of AUVs for Underwater Maintenance’ by Chocron et al. is the final and longest chapter in the volume. It commences with a survey on vehicle propulsion techniques and follows with an exposition on genetic algorithms from first principles. The authors adapt propulsion development and control to the development of a genetic and evolutionary framework. Several applications are used to drive the need for a reconfigurable propulsion-control subsystem: seabed inspection, driving toward a water turbine, and tomography. For a reader with interest in new ways to develop propulsion systems, this is a relatively comprehensive, but accessible work. These geneticevolutionary methods will be relevant for future advanced uses of AUV technology that require greater autonomy for broaderbased applications and tasks. Classic approaches like the design spiral or parametric design will likely fail to be robust when there is a need for AUV in-mission adaptability. A physical copy of the book was not made available by the publisher so it is difficult to

Underwater Technologyâ&#x20AC;&#x192; Vol. 37, No. 3, 2020

comment on the volume as a total package. The clarity of certain graphics and plots were not ideal for grayscale in certain cases. I find it difficult to read and process comprehensive material from soft copy; it was necessary in multiple cases to go back and forth between hard copy printed in grayscale and onscreen PDF. Good graphics and plots should be easy to interpret in colour as well as grayscale. There were a number of grammatical and typographical

errors, as well as inconsistencies and errors with referencing, throughout the book. The MOQESM Conference covers research and applications that employ novel approaches and new perspectives to one of the fundamental areas for autonomous marine robotics. Marine survey is an ideal area for autonomy. This book is a very good set of papers from academic and industrial voices from a strong marine robotic development community in western Europe.

It includes sophisticated concepts and mathematics presented in a relatively accessible manner. I would definitely recommend it for any underwater vehicle research and development individuals or groups.

(Reviewed by Dr Ron Lewis, Groundfish Section, Science Branch, Fisheries and Oceans Canada, Northwest Atlantic Fisheries Centre, Newfoundland and Labrador)

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The SUT is still operating during these difficult times We will continue to work online around the world, serving our members and the subsea community. The SUT has a new collection of online offerings whilst business is not as usual, helping us keep connected with our members and the subsea community. • Technical webinars, fortnightly every Monday, live via Zoom or watch later. See www.sut.org/events/ for details of upcoming seminars or see www.youtube.com/user/SUTMedia to watch later. • The Underwater Technology Podcast, released weekly covering a range of topics of interest to members. Listen to the podcast at sut.buzzsprout.com/ or via iTunes/ Apple Podcasts, Stitcher & Spotify – search for ‘Underwater Technology Podcast’. • Gadgets and Widgets, short videos uploaded to our social media - an excellent opportunity for corporate members with a service or product they would like to highlight to the SUT membership, see www.youtube.com/user/SUTMedia. Keep connected with the SUT via social media for the latest updates and news: Twitter – @SUT_news Facebook – www.facebook.com/sut.org Instagram – societyforunderwater Linkedin – www.linkedin.com/company/sutevents Youtube – www.youtube.com/user/SUTMedia Website – www.sut.org

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UT2 covers a focused range of underwater subjects including offshore, marine renewables, subsea engineering, ocean resources, diving and manned submersibles, underwater science and robotics. The magazine is represented at all the many exhibitions around the world at which the Society both co-organises and attends. Furthermore, the magazine is distributed at the many subsea training courses that are organised by the Society, ensuring it reaches tomorrowâ&#x20AC;&#x2122;s engineers and technologists.

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UT3 is the online magazine of the Society for Underwater Technology, and covers the subsea industry.

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It consists of the content of the print magazine UT2, greatly expanded with other information.

UT2 and UT3 are available online at http://issuu.com/ut-2_publication www.sut.org

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