رفتار سازه های لوله قابل ارتقا جامد تحت فرآیند گسترش شعاعی - تحلیلی، روش های عددی و تجربی

Today’s structures have to meet increasingly rigorous requirements during operation. The economic and human costs of failure during service impose a great responsibility on organizations and individuals who develop new products as well as those who select/integrate products in a final engineering design. A crucial aspect for successful product development and/or inclusion is the careful selection of the best material(s), derived from an informed awareness of the capabilities and opportunities afforded by all candidate materials, together with a design that takes full benefit of those competencies. Thick-wall tubular is an example where all these issues are playing a major role in deciding their industrial applications. Given for their desirable features of high strength and geometrical shape, they are widely used in aerospace, marine, military, automotive, oil and gas, and many other fields. This paper focuses on developing analytical solution to investigate the structural response of thick-wall tubulars undergo plastic deformation due to expanding them using a rigid mandrel of conical shape. Volume incompressible condition together with the Levy–Mises flow rule were used to develop the equations which relate the expansion ratio of the tubular to the length and thickness variations. Besides, Tresca’s yield criterion was used to include the plastic behavior of the tubular material. Further to this, a numerical model of the tubular expansion process was also developed using the commercial finite element software ABAQUS. Experiments of tubular expansion have been conducted using a full-scale test-rig in the Engineering Research Laboratory at Sultan Qaboos University to validate the analytical and numerical solutions. The developed analytical and numerical models are capable of predicting the stress field in the expansion zone, the force required for expansion, as well as the length and thickness variations induced in the tubular due to the expansion process. Comparison between analytical, experimental, and simulation results showed that a good agreement has been attained for various parameters.

The continuously increasing demands for petroleum products have forced the petroleum companies from all around the world to search for new reservoirs or to revitalize the existing ones, which are difficult to access and/or maintain a profitable production level. Current well drilling and operation technologies cannot provide cost effective solutions for emerging challenges in this field. The well-bore tubular technology has gained significant importance in every well with maturation in oil and gas industry. The conventional well-bore tubular technology has progressed over decades of research work including laboratory experiments and field trials that produced satisfactory results. Currently, telescoping of well size, from wellhead down to the reservoir, is a result of conventional well construction methods. This ends up in high cost of surface casing, wellheads and operating equipments. At times, the method also results in an unworkable small hole size at the target depth. This could lead to unprofitable production or in worst cases failure to reach the desired target. The conventional well-bore tubular technology is still unable to provide solutions for many problems such as deep drilling, conservation of hole size during hydraulic isolation processes, and accessing of new reservoirs that currently cannot be reached economically. These issues as well as many others are not only long-standing but have far-reaching consequences in the oil and gas industry. They involve one of the industry’s most fundamental technologies: well-bore tubulars. The revolutionary new Solid Expandable Tubular (SET) Technology has successfully addressed some of the above-mentioned issues. It provides mechanical stability in situations where conventional casing strings cannot be installed due to geometrical restrictions. Further to this, larger diameters can be attained at terminal depths for enhanced production from a single well. Thus, it has gained momentum and attracted the attention of operators and researchers, and is rapidly expanding its horizon of applications. The notion of using this technology in the oil and gas industry started to take place in the late 1990s, driven by operators’ aspiration to trim down the telescopic effect in casings design as the wells are drilled deeper. The basic idea was studied in several papers published during the last decade. The concept of SET Technology is simple to understand and consists of a down-hole in situ expansion of the tubular inner diameter that is attained by hydraulic and/or mechanical forces to pull/push a solid mandrel from the bottom up that permanently deforms the tubular to the required size as shown in Fig. 1. Since then, the technology has continued to grow in acceptance and use, where in a period of two years, the reliability of the technology has improved from an average of 67% in 2000 to over 95% in 2002 (Escobar et al., 2003). This has lead to the development of a collection of products that can be utilized as solutions for an ample range of drilling, completion, and production problems. Many different designs and processes have been created over the years, and as the oil industry continues to grow and change, expandables are also evolving to generate new and innovative solutions to the ever-shifting issues that operators’ deal with. The ultimate goal is to realize the drilling of slim to mono-diameter oil and gas wells as opposed to the current practices of drilling telescopic wells as shown in Fig. 2. Reducing the telescopic nature of the conventional wells would allow a much smaller surface casing to be used and subsequent casings could be reduced in diameter. Additionally, with the aid of this technology, operators will be able to reduce the amount of resources required to construct the well, as well as reaching target depths with bigger diameter. Several economic evaluations have been performed to show the cost effectiveness of this new technology (Owoeye et al., 2000, Benzie et al., 2000 and Dupal et al., 2001). Through field trials and case studies Dupal et al., 2001 and Gusevik and Merritt, 2002 and other researchers (Benzie et al., 2000) showed that open-hole solid expandable tubular have the potential to reduce the overall well construction cost. An interesting case was reported in Campo et al. (2003) showed that the mono-diameter system provides 48% cost reduction in well construction as compared to the fifth generation drillship cost and 33% cost reduction when compared with high specification semisubmersible. The environmental benefits are also substantial. Campo et al. (2003) reported a remarkable environmental impact of solid expandable tubular due to lesser requirement of consumables for well construction. The study showed 44% reduction in drilling fluid volume, 42% in cement volume and 42% in casing tonnage. These environmental impacts prove that the energy industry can fulfill world’s demand for hydrocarbon products with an environmentally friendly process.Much of the activities accompanying the introduction of SET Technology in petroleum industry were related to the effect of the expansion process on the material properties (Filippov et al., 1999, Mack et al., 1999, Stewart et al., 1999 and Mack et al., 2000). Solid tubulars having adequate material properties characterized by collapse and burst strength, ductility, impact toughness, resistance to wear and environmental cracking must be carefully selected for down-hole applications. An API Grade L-80 expandable steel tubular of 5–1/2 in diameter was tested to determine the effect of expansion on the mechanical properties (Filippov et al., 1999 and Mack et al., 1999). The results showed that the ultimate tensile strength increases, the elongation tends to decrease and the collapse rating decreases. The test data reveal no detrimental effect on burst strength. Benzie et al., 2000 and Ruggier et al., 2001 attributed the decrease in collapse pressure to the length and thickness variation, Bauschinger effect, and residual stresses. The expansion process does not affect burst pressure because the plastic work during expansion, which increases the strength of tubular; compensate the losses in wall thickness (Dupal et al. 2001). Klever and Stewart, 1998 and Stewart and Klever, 1998 developed a mathematical model which describes the effects of irregularities on the burst strength of the subjected tubular. Later, Stewart et al. (1999) extended the mathematical model to solid expandable tubular and conducted a laboratory test at Aachen University of Technology using a 3–1/2 in (OD) Grade B tubular following X42 ASTM A106 standards. The results showed that the yield strength increases in the order of 70% and the ultimate tensile strength increases in the order of 30%, whereas the elongation at fracture decreases in the order of 50% and the uniform strain decreases from 19.4% to 1.4%. Enventure Global Technology performed the first commercial application of Solid Expandable Tubular Technology in November 1999. The results of this successful expansion showed a decrease of 4.2% in length, a minor reduction as well in wall thickness and a reduction of 50% in collapse pressure (Mack et al., 2000). Much less effect on the burst pressure is observed. In Oman, the research on expandable tubing technology started lately with the support from the local oil companies. This is due to the need to know how to best adopt expandable tubular applications for well drilling and remediation in the Sultanate. The goals are to produce from difficult reservoirs, increase oil production, reduce unwanted production of water, and lower the cost of expandable tubular technology. However, oil recovery in Omani reservoirs is often impaired by zones of high permeability i.e., fractures, fault-related fracture corridors, karstied parts of the reservoir, etc. (Fokker et al., 2005, Lighthelm et al., 2006, Marketz et al., 2005 and Ozkaya and Richard, 2006) which can span from an aquifer to the wellbore. Several carbonate aquifers in Oman have been developed by horizontal wells, which are often intersected by these fractures, resulting in severe losses. Drilling through fractured reservoir sections causes drilling losses that have to be cured to be able to place cement in the annulus. As well, fractures may become potential avenues for the injected water to bypass large volumes of oil resulting in a poor sweep efficiency of the conventional water flooding operations and thus the water is cycled without any improvement in oil production (Chilingraian et al., 1996). In order to avoid this shortcut between the aquifer-formation interfaces (initial oil–water contact), hydro-isolation is usually carried out by cementing, chemical treatment, and installation of scab liners in the vicinity of the wellbore-fracture intersections. However, these mechanical and chemical techniques implemented in fractured carbonate reservoirs in a series of wells had limited success owing to drilling losses, high cost of gels, intensive seepage around the short seal of external casing packers, etc. (Al-Dhafeeri and Nasr-El-Din, 2007). Therefore, expandable tubular and swelling elastomer sealing technologies have been introduced for wells drilling as an alternative to cemented liners. This is done to provide zonal isolation which is critical for profile control, eliminate the need for curing losses and liner cementation, and slim down the well design, i.e., reduce the size of the top hole to reduce footprints. This non-invasive or invasive technique, depending on the use of elastomers, is applied in several wells with water rates reduction up to 40% and oil gains up to 45 m3 per day per well (Welling et al., 2007). Nevertheless, still a lot of issues need to be resolved before this technology can be used to its full potential for well drilling and remediation. In this contest, the research in Oman at the early stages was focused on developing semi-analytical and finite element models that address different issues of this emerging technology. However, the capacity of the research has been strengthened with the inauguration of the expandable tubular test-rig at Sultan Qaboos University (SQU) in 2009 which has helped local operators to use this technology with confidence. The research activities tackled many essential issues including: simulation of tubular expansion in well drilling using nonlinear explicit finite element method to study the effect of different expansion ratios, friction coefficients and mandrel angles on the tubular expansion process (Pervez et al., 2005), simplified mathematical model for tubular expansion process (Seibi et al., 2005), analytical solution for wave propagation due to pop-out phenomenon (Seibi et al., 2006), post-expansion tube response under mechanical and hydraulic expansion – a comparative study (Seibi et al., 2007), research on possibility of using aluminum as expandable tubular instead of steel (Pervez et al., 2008), dynamic effects of mandrel–tubular interaction in down-hole tubular expansion process (Seibi et al., 2009), experimental and numerical investigation of expandable tubular structural integrity for well applications (Pervez, 2010 and Pervez et al., 2012b), simulation of tubular expansion in irregularly shaped boreholes (Pervez et al., 2011), and finite element analysis of tubular ovality in oil wells (Pervez and Qamar, 2011). The results showed that tubular wall thickness decreases with an increase in mandrel angle, expansion ratio, and friction coefficient. In addition, the tubular length often shortens for expansion under tension for most of the loading mechanisms. However, it elongates at high friction levels due to the resistance that opposes the interface materials from flowing smoothly over each other creating some tension in the tubular. Developing a mathematical model that represents the tubular expansion process is a powerful tool that would help in alleviating the need for conducting the costly experiments or even the time consuming simulation practices via the finite element method. With a set of mathematical equations, a program that could help field engineers in amassing data on the expandable tubular technology could be created which would helps in reducing time with regard to the experimental and simulation practices, and brings down the effort and cost involved. A review of selected literature on developing analytical solution for thick-wall tubulars revealed the availability of many papers that attempted to study the elastic–plastic behavior of thick-wall cylindrical shells subjected to different types of loading (Hausenbauer and Lee, 1966, Perry and Aboudi, 2003, Gao, 2003, Ayob et al., 2009 and Darijani et al., 2009). However, there are only a few studies dealing with the plastic deformation of thick cylindrical shells, and even fewer studies that deal with the behavior of these structures under plastic deformation due to expanding them using a mandrel. Recently, plasticity and membrane theories were used to develop analytical models for expansion of thin-walled tubulars with a conical expansion tool (Al-Hiddabi et al., 2002 and Ruan and Maurer, 2005). The models demonstrate the variation in the force required for expansion with respect to expansion ratio, friction coefficient, mandrel geometry, and tubular material’s yield strength. Karrech and Seibi (2010) developed a model to predict the stress field in the expanded zone and the dissipated energy due to the expansion process. However, when the cylinder has an inner-radius-to-wall-thickness ratio of less than 10, thin-walled cylinder equations are no longer hold since stresses vary significantly between inside and outside surfaces and shear stress through the cross section can no longer be neglected. Thus, the need for the current work, which focuses on developing analytical solution for thick-walled solid expandable tubular subjected to large plastic deformations (where the tubular expands up to 30% of its original inner diameter). The paper is divided into six major sections. Section 2 includes the mathematical formulations of the developed analytical model. Development of a finite element model of the tubular expansion process is presented in Section 3, followed by a description of the experimental work is discussed in Section 4. Section 5 consists of the results and discussion part, followed by the conclusions in Section 6.

Analytical and numerical models describing the expansion process of a thick-wall solid tubular have been developed based on kinematics and equilibrium conditions. In addition, tubular expansion tests have been conducted in the expandable tubular test-rig at SQU, to validate the developed analytical and numerical models. It was found that the results for expansion force, thickness reduction and length shortening under various expansion ratios from both models are in good agreement with the experimental observations. It is also evident from the comparison that the expansion of the tubular by 16%, 20%, and 24% expansion ratios result in thickness reduction of approximately 6.67%, 10.3%, and 13.16%, and length shortening of approximately 4.4%, 5.7%, and 6.2%, respectively. Also, the expansion force increases as the expansion ratio and the friction coefficient increases while it decreases as the mandrel angle increases due to the reduction in contact area. Tubular wall thickness decreases as the expansion ratio and the friction coefficient increases while the reduction in wall thickness reduces as the mandrel angle increases. Also, it has been observed that the tubular length shortens for most of the loading mechanisms. However, it elongates sometimes at higher values of friction coefficient (i.e., greater than 0.4) and small mandrel angles (i.e., less than 10°). This can be attributed to the difficulty that opposes the interface materials from flowing over each other smoothly creating some tension in the tubular. Finally, it is worthwhile to state that the developed analytical and numerical models are capable of providing excellent approximation for the actual experimental results, which consequently would help in reducing the trial and error operations in the selection of tools and processes design and thereby reduce material waste and lead-time to drill new wells.