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)

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This paper investigates the focal location effects on the penetration depth of molten region surrounding a paraboloid of revolution-shaped cavity (i.e. keyhole of this model) irradiated by a moving focused energy beam, which profile of intensity is assumed to be Gaussian distribution. Considering the momentum balance at the base of the keyhole, a quasi-steady-state thermal model relative to a constant-speed moving high-energy beam and paraboloid of revolution-shaped cavity is developed in a parabolic coordinate system. The analytical solution is obtained for this model with the adiabatic condition directly set on the workpiece surface for semi-infinite domain instead of the image method for infinite domain using the separation-of-variables method. The analytical solution of this model gives a reasonable prediction for the cavity temperatures. The predicted relation of the penetration depth to the focal location agrees with the available measured data. The effects of focal convergence angle and spot size on the penetration depth are also discussed.

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