This paper describes new theoretical results for predicting the buckling behavior of pipe in horizontal holes. Pipe buckling in horizontal holes occurs initially in a sinusoidal mode along the low side of the hole and at higher axial compression a helix is formed. Equations are given for computing the forces required to initiate these different buckling modes. Simple laboratory experimental results are also used to confirm the theory. Results presented in this paper can have applications in friction modeling of buckled tubulars to help predict when pipe can be forced to move along a long section of a horizontal well. Introduction Many analyses have been performed on the mechanics of pipe in oil and gas wells since 1950. Lubinski, et al. [1] defined the helical buckling behavior of pipes in vertical wells. However, the postbuckling behavior of pipe is different for horizontal wells than in nearly vertical wells. Knowledge of the configuration of buckled tubulars is important to prevent costly failures and to predict whether a tool can be forced along a horizontal well. This paper provides methods for use in analyzing these problems. Two modes of buckling can occur for tubulars in horizontal or steeply inclined wells: a helical mode and a sinusoidal mode. The axial compressive force required to buckle the pipe into a sinusoidal configuration depends on stiffness and weight of the pipe and on hole size in a manner similar to a beam on elastic foundation. As the axial force is increased the buckling mode changes from sinusoidal to helical. Model experiments confirm the results of the analysis. (Equation available in full paper)

Summary. This paper describes new theoretical results for predicting the buckling behavior of pipe in horizontal holes. Pipe buckling in horizontal holes occurs initially in a sinusoidal mode along the low side of the hole; at higher axial compression a helix is formed. Equations are given for computing the forces required to initiate these different buckling modes. Simple experimental laboratory results confirm the theory. Results presented in this paper apply to friction modeling of buckled tubulars to help predict when pipe can be forced to move along a long section of a horizontal well. Introduction Since 1950, many analyses have been performed on the mechanics of pipe in oil and gas wells. Lubinski et al. defined the helical buckling behavior of pipes in vertical wells. However, the postbuckling behavior of pipe in horizontal wells is different from that in nearly vertical wells. Knowledge of the configuration of buckled tubulars is important to prevent costly failures and to predict whether a tool can be forced along a horizontal well. This paper provides methods to analyze these problems. Two modes of buckling can occur for tubulars in horizontal or steeply inclined wells: helical and sinusoidal (Fig. 1). The axial compressive force required to buckle the pipe into a sinusoidal configuration depends on pipe stiffness and weight and on hole size in a manner similar to a beam on an elastic foundation. As axial force is increased, the buckling mode changes from sinusoidal to helical. Model experiments confirm the results of the analyses.

The helical postbuckled configuration of a weightless, circular column confined within a cylinder was used by Lubinski et al. in 1962 to develop frequently applied equations describing the deformation of oilfield tubing. This paper presents an extension of their work in the form of another expression for the relation between applied force and helical pitch in the buckled state. Based on simple laboratory experiments and stability arguments it appears that the previous force-pitch equation applies during load application and the one given in this paper applies during unloading. Introduction The helical postbuckled configuration of a radially confined tubular is a phenomenon of significant import to the petroleum industry. For the case phenomenon of significant import to the petroleum industry. For the case of smaller tubulars such as most tubing, the radial clearance boundary can be large enough to both allow significant axial shortening and induce bending stresses of a magnitude sufficient to yield the tube body. For larger tubulars such as casing, large radial clearances normally are associated only with washed out or overgauge sections of the wellbore. However, even for small radial clearances, and with particular regard to intermediate casing strings, the helical configuration can present a hazard to the integrity, of the well by promoting wear during drilling operations. The majority of recent work on helical buckling can be traced to the classic paper by Lubinski et al. on helical buckling of tubing sealed in packers. Applications of this early work to a variety of downhole packers. Applications of this early work to a variety of downhole configurations have appeared in the literature; however, with the exception of some recent work on the influence of the packer on the helical configuration, the basic relation between applied compressive axial force and helical pitch has remained unaltered since its introduction. The intent of our study is to reconsider the helical postbuckled configuration by applying the principle of virtual work to deviation of the column from its straight, prebuckled configuration. The result of this effort will be two force-pitch relations (one of which is the relation derived by Lubinski et al.) that differ by a factor of two. The remainder of the discussion is then devoted to the significance of the a alternate solutions and the effect of the dual solution on tubular designs. A description of the postbuckled configuration of a tubular can be quite complex. In fact, if one includes from the outset the axial component of stress arising from the distributed weight of the tubular along its length, the resulting expressions become unwieldy. As an alternative, this discussion is restricted to an analysis of the postbuckled geometry of a weightless rod. Adjustment of the results of this analysis to include the effects of both the distributed weight of the tubular and internal and external pressure are covered in detail in Ref. 1. Geometry of the Helix At the instant a compressed, straight rod buckles, the lateral displacements will be sinusoidal in nature. However, if the lateral displacements are constrained to be less than or equal to some predetermined value (i.e., a wall constraint concentric with the undeformed predetermined value (i.e., a wall constraint concentric with the undeformed position of the rod), contact of the buckled rod with the constraint will position of the rod), contact of the buckled rod with the constraint will induce a rearrangement of the rod such that it assumes the form of a helix. Consider Fig. 1, which illustrates the geometry of a representative length of the helically buckled rod and several important variables to be used throughout the analysis. Notice in particular the definition of the pitch being the length between repetitions of the helical configuration. pitch being the length between repetitions of the helical configuration. Since the rod is assumed here to be weightless and infinite in length, the pitch will be constant throughout. pitch will be constant throughout. Now let a cartesian coordinate system be placed at some representative point along the length of the helix. point along the length of the helix. SPEJ p. 467

A laboratory investigation of the behavior of casing subjected to salt loading indicates that it is not economically feasible to design casing for the most severe situations of nonuniform loading. When the annulus is completely filled with cement, casing is subjected to a nearly uniform loading approximately equal to the overburden pressure, and, although the modes of failure may be different, the design of casing to withstand uniform salt pressure can be computed on the same basis as the design of casing to withstand fluid pressure. Failure of casing by nonuniform loading in inadequately cemented washed-out salt sections should be considered a cementing problem rather than a casing design problem. Introduction Casing failures in salt zones have created an interest in understanding the behavior of casing subjected to salt loading. The designer must know the magnitudes and types of loading to be expected from salt flow and he must be able to calculate the reaction of the casing to these loads. In the laboratory study reported in this paper, short-time experimental measurements of the load required to force steel cylinders into rock salt are used as a basis for computing the salt loading on casing. These results must be considered to be qualitative only since rock salt behaves differently under down-hole and atmospheric conditions and also may vary in strength at different locations. The beneficial effects ofcement around casing,a liner cemented inside of casing, andfluid pressure inside of casing in resisting casing failure are considered. ROCK SALT BEHAVIOR UNDER STRESS The effects of such factors as overburden loading, internal fluid pressure, and temperature on the flow of salt around cavities have been studied extensively at The U. of Texas. Brown, et al. have concluded that an opening in rock salt can reach a stable equilibrium if the formation stress is less than 3,000 psi and the temperature is less than 300 deg. F. At higher temperatures and pressures an opening. in salt can close completely. These results indicate that calculations based upon elastic and plastic equilibrium for an open hole in salt should be applied only at depths less than 3,000 ft. In most oil wells the temperature will be less than 300 deg. F in the salt sections, therefore no appreciable temperature effects are anticipated. Serata and Gloyna have reported an investigation of the structural stability of salt. They assume that the major principal stress is due to the overburden. Other stresses can be superimposed if additional lateral pressures are known to be acting in a particular region. In the present analysis an isotropic state of stress is assumed to exist in the salt before the hole is drilled, since salt regions are generally at rest. This assumption is partially verified from formation breakdown pressure data taken during squeeze- cementing operations in salt. Experimental measurements of the elastic properties of rock salt indicate a value of 150,000 psi for Young's modulus and a value of approximately 0.5 for Poisson's ratio. A value of 1/2 for Poison's ratio with finite Young's modulus would indicate that the, material was incompressible. Values ranging from 2,300 to 5,000 psi have been reported' for the unconfined compressive strength of salt. These variations may be due to differences in the properties of the salt from different locations or at least partially to differences in testing techniques. Salt is very ductile, even under relatively low confining pressures. For example, in triaxial tests reported by Handin strains in excess of 20 to 30 per cent were obtained without fracture. When casing is cemented in a hole through a salt section, the casing must withstand a load from the formation if plastic flow of the salt is prevented. To determine the forces which salt can impose on casing, circular steel rods were forced into, Hockley rocksalt with the longitudinal axis of the rods parallel to the surface of the salt. The force required to embed rods 0.2 to 1 in. in diameter and 1/2 to 1 in. long to a depth equal to the radius of the rods was found to be (1) where D is the diameter, and L is the length of the rod. CASING STRESSES Since an open borehole through salt at depths greater than 3,000 ft will tend to close, cemented casing which prevents closure of the hole will be subjected to a pressure approximately equal to the horizontal formation stress after a sufficiently long time. As a first approximation the horizontal stress can be assumed to be equal to the overburden pressure, This is in agreement with the suggestion by Texter that an adequate cement job can prevent plastic flow of salt and result in a pressure on the casing approximately equal to the overburden pressure. JPT P. 1069ˆ

Distinguished Author Series articles are general, descriptive representations that summarize the state of the art in an area of technology by describing recent developments for readers who are not specialists in the topics discussed. Written by individuals recognized as experts in the area, these articles provide key references to more definitive work and present specific details only to illustrate the technology. Purpose: to informthe general readership of recent advances in various areas of petroleum engineering. Introduction Maintaining a stable wellbore is of primary importance during drilling and production of oil and gas wells. The shape and direction of the hole must becontrolled during drilling, and hole collapse and solid particle influx must be prevented during production. Wellbore stability requires a proper balance between production. Wellbore stability requires a proper balance between the uncontrollable factors of earth stresses, rock strength, and pore pressure, andthe controllable factors of wellbore fluid pore pressure, and the controllable factors of wellbore fluid pressure and mud chemical composition. pressure andmud chemical composition. Wellbore instabilities can take several forms (Fig.1). Hole size reduction can occur when plastic rock is squeezed into the hole, and hole enlargement can be caused by caving shales or hard rock spalling. If the wellbore fluid pressure is too high, lost circulation can occur as a resultof unintentional hydraulic fracturing of the formation; if it is too low, the hole may collapse. Excessive production rates can lead to solid particlein flux. Hole instabilities can cause stuck drill pipe as well as casing or liner collapse. These problems can result in side tracked holes and abandoned wells. Since 1940 considerable effort has been directed toward solving rock mechanics problems associated with wellbore instabilities, and much progress has beenmade during the past 10 years toward providing predictive analytical methods. Some of the literature representative of this work is discussed in thisarticle. Emphasis here is on understanding factors that influence wellbore stability in open holes, prediction of wellbore failures, and applications of rock mechanics concepts to control wellbore stability, A brief historical overview is followed by discussion of various types of wellbore instabilities and descriptions of studies of field wellbore stability problems. Stresses Around Wellbores H.M. Westergaard published a paper entitled "Plastic State of Stress Arounda Deep Well" in 1940. This now-classic paper defined the wellbore stability problem as follows. The analysis that follows is a result of conversations with Dr. KarlTerzaghi who raised this question: What distributions of stress are possible inthe soil around an unlined drill hole for a deep well? What distributions of stress make it possible for the hole not to collapse but remain stable for sometime, either with no lining or with a thin "stove pipe" lining of small structural strength? Westergaard uses stress functions in cylindrical coordinates to solve the elastic-plastic wellbore problem for zero pressure in the hole and all normal stress components equal to the overburden far from the hole. Hooke's law was applied for the elastic region and a Coulomb yield condition* where "the limiting curve for Mohr's circle is a straight line" was assumed for the plastic region. His conclusions were: The plastic action makes it possible for the great circumferential pressures that are necessary for stability to occur not at the cylindrical surface of the hole but at some distance behind the surface, where they may be combined with sufficiently great radial pressures. The formulas that have been derived serveto explain the circumstances under which the drill hole for a deep well may remain stable. Westergaard's elasticity solution agrees with the Lame solution for a thick-walled cylinder subjected to the same boundary conditions. Hubbert and Willis (1957) demonstrated how earth stresses can vary from regions of normal faulting to those with thrust faulting. On the basis of a Coulomb failure model, they suggest that the maximum value of the ratio of the maximum to the minimum principal stress in the earth's crust should be about 3:1. JPT P. 889