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Abstract When the sinusoidal buckling of suspended tubular strings is transforming to helical buckling, the deformation changes drastically, which makes the tubular strings extremely unstable. The quantitative description of this buckling configuration in previous theoretical studies is not precise enough. In our current study, dynamic relaxation method is applied to carry out numerical simulation of buckling transition of suspended tubular strings. To obtain stable buckling configurations, larger Rayleigh damping is used to attenuate the dynamic effect. With the increase of axial compression load, the lateral buckling of the suspended strings suddenly becomes spiral shape with two contact points. As the string length increases, the position of the lower contact point remains almost at the same position. While the upper contact point gradually moves upward, and the helix angle between the two points increases and gradually tends to be constant. The maximum contact force is located at the lower contact point, the maximum shear force is located at the bottom of the strings, and the dimensionless distance between the location of the maximum bending moment and the well bottom is about 1.0. These loads, including the maximum contact force, maximum shear force and maximum bending moment, gradually decrease with the increasing string length and tend to be constant. The dimensionless critical load is reduced from 4.41 to 3.81 with the effect of string length. The critical load calculated in this paper is the minimum value when helical buckling just occurs. The results obtained in the current study have wide engineering applications, particularly in failure analysis and prevention of helical buckling. Highlights • Stable buckling configuration is obtained by using dynamic relaxation method. • Quantitative description of buckling deformation, shear force, bending moment and contact force are obtained. • The critical load obtained is the minimum one when the helical buckling just happens. [ABSTRACT FROM AUTHOR]

Helical buckling of tubular strings with connectors is divided into two sub-problems: inter-helical buckling and intra-helical buckling. The suspended section of the tubular string is depicted by beam-column model and the continuous contact section is depicted by helix. Further introducing the continuous conditions, boundary conditions and periodic conditions, the deflection curves of tubular strings can be determined. On the basis of energy stability condition, the critical helical buckling loads are deduced by introducing the potential energy factor. The contact forces on contact points and continuous contact sections and maximum bending moments on tubular strings are calculated. The above studied are further applied into a case study. At last, the supporting effect and boundary effect caused by connectors are introduced and the relationship between inter-helical buckling and intra-helical buckling modes is clarified. The results indicate that for connectors of smaller diameters, the supporting effect plays the most important role and inter-helical buckling is easier to initiate. However, for connectors of larger diameters, the constraint effect is dominant and intra-helical buckling is more likely to occur. Increasing connector diameter and decreasing the length between adjacent connectors can increase critical helical buckling loads. Both the contact forces and maximum bending moments in the intra-helical buckling mode are larger than that in the inter-helical buckling mode, so intra-helical buckling should be avoided in the optimal design of connectors on tubular strings. [ABSTRACT FROM AUTHOR]

Buckling of concentric tubular strings in pipe is an essential problem in the fields of medical, biological, and nanomaterials, especially in petroleum engineering. Completely different from the buckling of the classic Euler compression columns, the buckling of concentric tubular strings involves geometric nonlinearity and contact nonlinearity, and has more complicated geometric deformations and buckling configurations. In this paper, a finite element method combining the spatial beam element and the two-layer contact gap element is proposed, and a virtual transient dynamic method is introduced to solve the static buckling of concentric tubular strings. The internal concentric tubular strings are discretized into spatial beam elements, and the contact relationships between tubular strings are described by two-layer contact gap element. Meanwhile, the larger damping is used to attenuate the dynamic response of the system, so as to find the static part of the transient dynamic solution. Appropriate damping and element length are determined by numerical simulation. The structural characteristics and contact states of eight post-buckling configurations are studied. The helix pitch values of specific configurations are in good agreement with the theoretical solutions. In addition, the distribution of bending moment, shear force and contact force in various post-buckling configurations is studied. For the full helical buckling, it is found that there is only one non-contact section in the transition section of inner tube and two non-contact sections in the transition section of middle tube. The research results of this paper provide a theoretical basis and reference for further study on the buckling of multi-layer concentric tubular strings. • Finite element method and transient dynamics method are used to solve the static buckling of concentric tubular strings in pipe. • Eight post-buckling configurations as axial compression force increases for concentric tubular strings in pipe. • Transition section includes only one non-contact section for inner tube while includes two non-contact section for middle tube. [ABSTRACT FROM AUTHOR]

A new model depicting the buckling configuration of a tubular string in a three-dimensional curved wellbore is proposed. During modeling, the toolface angle is considered, and the sinusoidal buckling and helical buckling of the tubular string are considered on the basis of alignment with either the lower curved side or the outer curved side of the wellbore. After modeling, the energy method is used to solve the model, and the critical buckling load, which is related to the relationship between the buckling configuration and the axial load, can be obtained. The critical buckling loads calculated using the model presented in this paper are consistent with the measured data from published experiments and the trends of the He and Kyllingstad model. The results of the new model also show that with an increasing wellbore curvature, the influence of the toolface angle on the critical buckling load and the characteristic parameters of the buckling configuration (wavelength, amplitude, and pitch) decreases. Based on the expressions for the quantitative relationships between these characteristic parameters and the axial load, procedures for calculating the contact force and the bending moment are given. The results for the contact force show that the calculated values from the Johancsik et al. model and the Mitchell model are the average values calculated using the procedures presented in this paper for tubular strings under sinusoidal buckling and helical buckling, respectively. The calculation results show that the influence of the toolface angle on the bending moment of a tubular string under helical buckling is less than that under sinusoidal buckling. By using this model, not only can the critical buckling loads, contact forces and bending moments of tubular strings in three-dimensional curved wellbores be calculated, but the trends of these calculated values with the buckling configuration can also be identified to guide the selection of the control parameters for tubular strings in the field. • A buckling model for a tubular string in a three-dimensional curved wellbore is established. • The critical buckling loads and the parameters (wavelength, amplitude, and helix pitch) can be obtained by the model. • The critical buckling loads calculated by the model are consistent with the values measured in published experiments. • Based on the buckling model, the contact force and bending moment of the tubular string can be determined. [ABSTRACT FROM AUTHOR]

Oil wells typically have production tubing installed within casing strings. In the scenario of buckling, the casing string is commonly simplified to be rigid at the designing stage (Mitchell, 2012). It hasn't been fully explored by literature yet how the neglected casing string displacement impact the buckling mechanism. An improved analytical model in this paper based on Mitchell's study (2012) addressed this issue in vertical wells. The post-buckling configuration typically includes two scenarios: sinusoidal and helical buckling. This paper investigates both scenarios of concentric tubular buckling and develops an analytical model based on the minimum energy theory. The author has verified the new model with well-recognized literature before the application. Computations are also conducted to investigate the prediction improvement than previous models. This new model can find broad applications in both onshore and offshore completion/production operations. To the knowledge of the authors, there are only two existing models so far for concentric string buckling, namely Christman's model (1976) and Mitchell's model (2012). The authors find by case study that (1) Christman's model tends to overestimate the stiffness of concentric string system. (2) Mitchell assumes an unlikely transition configuration before helical buckling, where the concentric string system is independent of the wellbore. As a result, Mitchell's model ignores the wellbore restraint impact on buckling in the transition mode. The author brought up a sinusoidal buckling model for the concentric strings in the transition mode. The analytical model is derived based on the minimum energy theory. This model can evaluate the buckling induced pitch, bending moment, bending stress and total length change. The author also verified the new model with well-recognized literature by Lubinski (1962). In the end, computations investigate the prediction improvement than previous models. • There is very limited research on concentric tubular buckling regardless of its wide application onshore and offshore. • Christman (1976) overestimates the dual pipe stiffness assuming minimal inner pipe motion and evenly distributed loading. • Mitchell (2012) assumes an unrealistic dual pipe buckling configuration under small buckling force. • This new model addresses the deficiencies and provides a more reliable prediction for practical use. [ABSTRACT FROM AUTHOR]