Summary The buckling behavior of tubulars inside wellbores is the subject of many articles. This paper presents a general overview on most of the literature available on the subject and also comments on the different, and sometimes conflicting, solutions presented in various works. Different aspects of the phenomenon are discussed, including sinusoidal (lateral) and helical buckling and the influence of torque. Introduction A good understanding of the buckling behavior of pipes in oilwell operations is very important in the petroleum industry. The significance of this matter can be measured by the great number of papers presented on the subject in the last 50 years. Since Lubinski's1 first theoretical approach to sinusoidal buckling for vertical wells, buckling of tubing, drillpipe, casing, and coiled tubing has been studied by a number of authors. There are publications covering almost every particular buckling case, such as helical buckling; torque effect; and the influence of wellbore inclination, friction, and wellbore curvature. The differential equation representing the configuration of a rod buckled because of the action of an axial load, F, was first presented by Euler in 1744.2 The solution of that differential equation indicated that a weightless rod will buckle, provided the following inequality is satisfied. Equation 1 In Eq. 1, n=a factor that depends on the end conditions. In 1881, Greenhill2 studied this problem, considering the influence of the weight of the rod. Later, in 1883,2 he considered the influence of torque and produced the following inequality as a condition for the instability of long, weightless rods. Equation 2 Last century, the stability of long rods under various conditions of loading and support were investigated by many authors, among whom Goodier,3,4 Hoff,5 Timoshenko,6 and Langhaar7 should be mentioned. Those works, although fundamental to understanding the elastic stability theory, did not deal with tubulars confined within another circular cylinder. The problem of laterally constrained pipes presents different and somehow more complex characteristics than the unconstrained situation, mainly for cases in which inclined or curved configurations exist. A summary of the most noted studies of pipe buckling inside wellbores follows. Literature Review This section presents comments on a number of papers published in the last 50 years. Although not all papers available in the literature are mentioned in this review, the majority of the most important contributions on tubular buckling inside wellbores are referred to here. As mentioned previously, the first rigorous treatment of drillstring stability was presented by Lubinski.1 In that pioneering work, an analysis of 2D drillpipe buckling in vertical wells and its effects on bit inclination, string shape, wall contact force, and bending moments were presented and discussed thoroughly. Lubinski's solution for the critical buckling load used a power series to solve the differential equation governing the instability problem. Lubinski's method leads to a very precise result expressed in the form of a power series. However, the terms of the series become very large for long strings, and after a certain length, the calculations may lead to inaccurate results. As an approximation for practical purposes, Lubinski proposed that the critical load for the first buckling mode of long strings should be calculated as: Equation 3 Wang8 proposed that the exact factor in Eq. 3 to produce the critical load of buckling for an infinite pipe inside a vertical well should be 1.018793. Equation 3a Later, with a nonlinear regression method, Guo9 combined Lubinski's results for short strings with the result for infinite columns to produce a function that gives approximated results for the critical buckling load of strings of any size. During the 1950s, Lubinski10,11 published other important papers analyzing tubular buckling in oilwell operations. Among other interesting features, those papers have derivations showing the influence of fluid density (inside and outside the pipe) on the buckling process and also how buckling could affect operations in pumping wells. In 1962, Lubinski et al.12 published another fundamental paper, in which the helical buckling of production tubing was studied for the first time. Also for the first time, the effect of fluid flow on buckling was presented. In that paper, the equation for the force-pitch relationship was derived as: Equation 4 In addition, expressions for displacement length, bending moments, and the strain energy of bending and compression were developed. Note that for the first time, this paper observed a differentiation between the beginning of the buckling process, normally called sinusoidal buckling (also known as lateral or 2D buckling), and the more severe case of helical buckling. The differences between these two situations are analyzed in the next section. The interested reader can find the most important works of Arthur Lubinski in Ref. 13.

This paper describes new theoretical results for prediction of buckling behavior of tubulars in inclined wellbores. Using conservation of energy and the principle of virtual work improved equations for buckling and post-buckling conditions are derived. The effect of torque on the buckling process is considered. Practical examples are provided showing the influence of torque on the critical buckling force. The equations for critical buckling force reduce to those previously derived when torque is set to zero and weightless strings are considered. Introduction The understanding of the buckling process of tubulars in oil-wells is very important for the oil industry. This critical phenomenon can be present in drilling. completion and production operations. Some of the issues that must be considered in design and performance predictions of tubular goods for oilwell operations are: string shortening, bending stresses evaluation, estimation of lock-up and critical strength conditions. Among the associated problems are: drillstring failure, casing wear, casing and tubing failures and limitation on use of coil tubing. The influence of torque on the buckling process of tubulars in oilwells has been disregarded in the past and normally assumed as unimportant. Only recently some investigations have been made on the matter for the case of weightless strings. Although in these works the influence of torque on the value of the critical buckling load appeared to be small, torque should be considered when more precise calculations are needed. Practical examples have showed that, depending on the stiffness of the string and the amount of torque applied, the critical buckling force can be reduced in more than 10% when compared with the non-torque situation. CRITICAL BUCKLING FORCE AND TORQUE The following major assumptions were considered in the development of the model:–String is long so that the end conditions do not affect the force-torque-pitch relationship.–The wellbore is circular and straight.–The system is frictionless. Other important assumptions are listed in Ref. 2. Let us analyze a tubular string with bending stiffness EI and unit weight w constrained within a wellbore with inclination angle. When submitted simultaneously to a certain axial load F and a torque T the string will buckle in a shape that can be described by the following equations: (1) (2) P. 173

Thm paper was prepared for presentabon at the 19S6 SPE Intemabonal ConfereM on Hcmzontat Well Technology held m Calgary, Canada, 18-20 Novem* 19% This papr was selected for presentawan by an SPE Prqrem Committee follovmg rewew of Inlormabcm cmtamed m an abstraci Submitted by the author(s) Contents of thm papw, as presented, have not been rewewed by ths %clely of Petroleum Engineers and are subject to wrractmn by the author(s) Th!s material, as presented, does not necessarily reflect any pmbon of Ihe Scuety of ptmleum Engineers ds oficars, or membars Papers presented at SPE meettngs are subject to publcatmn rewew by Edntortal Committees of the .?,c.aety of Petroleum Engineers Penn IssIcmto capy IS restricted to an abstraci of not more than 300 words IllustratIons may not be cop!ed The abstract should contain mnsp!cvous acknowledgment of where and by whom the paper was presented Whte Libfanan, SPE, P O. Box 833=, Rchardson, TX 75083 -3e3S, U S A fax 01-214-952-9435 AbstractThis paper presents an improved mathematical model for the axial force calculations along coiled tubing (CT) while drilling in inclined and horizontal wellbores. This new mathematical model is more general as it includes three types of coiled tubing configurations: straight, postbuckling "snaking", and helical. The equations for predicting the axial force under "snaking" configuration are believed to be presented for the first time. The "snaking" configuration of CT is of practical importance as it is a stable configuration for a wide range of axial loads. Several numerical case studies are provided to show the usefulness of the proposed axial force transfer model. The influences of friction, coiled tubing and wellbore size on the axial force predictions are described and presented in graphical form. Finally, a number of laboratory experimental results validate the proposed axial force transfer model as long as the effect of residual bending is not significant.

Usual practice in drilling engineering is to determine drilling-fluid density at surface conditions assuming that drilling-fluid density does not change with changing downhole conditions. This assumption may result in inaccuracy while estimating static and dynamic pressures in the wellbore, especially when synthetic-based drilling fluids are used. Inaccurate estimation of the pressure profile in the annulus can lead to severe well problems such as kicks, drilling-fluid losses, and wellbore instability. In addition, inaccurate pressure-profile estimation can affect the success of managed-pressure-drilling (MPD) operations, which require real-time knowledge of wellbore pressures to keep wellbore pressure between formation pore and fracture pressures using a control choke placed on the return line of the annulus.Effects of pressure and temperature on volumetric behavior of two olefin-based synthetic oils are investigated in this study using a mercury-free pressure/volume/temperature (PVT) system. The olefin-based synthetic oils used in this study are C16C18 internal olefin (IO) and C12C14 linear alpha olefin (LAO). To simulate deep offshore situations, the temperature is ranged between 25 and 175°C, while the pressure is ranged between 0 and 14,000 psig.In addition, volumetric performances of olefin-based syntheticoil systems under investigation are compared with those of water, brine solution, mineral oil, diesel oil, and n-paraffin-based oil under similar conditions.The study shows that the volumetric properties of syntheticbased oils are more sensitive to pressure and temperature conditions compared to water, brine solutions, mineral oil, and diesel oil. Once emulsion systems containing synthetic-based oils are used, density change with respect to downhole conditions should be modeled to increase the reliability of pressure-profile calculations.

Currently some of the most challenging wells being drilled by our industry are located in deepwater zones in the GOM. Many of those wells are in water depths of 8,000 ft. or more and several are targeting reservoirs around 30,000 ft. and beyond.Drilling engineers face many challenges when planning drilling and completion operations for such wells. There are not many rigs available to drill in ultra-deepwater, and even the modern rigs capable of operating in this environment will present limitations ranging from the maximum mud weight possible to be used, due to riser restrictions, to the hook load capability to run very heavy intermediate casings that will easily surpass one million pounds.The well itself will present many problems including high pressure and high temperature formations, the need of multiple casing strings, unstable formations, hole cleaning, unexpected presence of tar zones, huge layers of salt, the need to underream the well, difficult to do an efficient evaluation program etc.On the completion side, the challenges can be even more demanding, with the need to complete multiple zones while trying to minimize future expensive workover operations. This paper presents some practical experiences on dealing with various of the abovementioned problems and also suggestions to make the problems manageable. It might be emphasized that we do not have a perfect solution to all problems and that we are far to have the most efficient solution to drill deep wells located in ultra-deepwater zones in the GOM. However, with daily operational costs reaching one million dollars or more, it is our intention in this paper to discuss the problems, to point out some possible directions, to show some field cases and to open a discussion that might benefit the entire industry.