Buckling of Tubing inside Casing

Summary Oil wells typically have multiple concentric casing strings. For a set of two concentric strings, if the inner pipe has a compressive axial force, it will typically buckle within the outer string. The buckling of pipe can be important in the analysis of a well-completion design because the buckled pipe can develop bending stresses that may be significant. Most analyses of this problem assume that the outer casing is rigid. In reality, this external casing is also elastic and would displace owing to the loads generated by contact with the inner pipe. Further, if both strings have compressive axial forces, both strings will buckle, and the resulting buckled configuration must fit together so that contact forces between the two strings are positive and the pipes do not each occupy the same space. If the two strings have an external, cylindrical rigid wellbore, then any contact forces with this wellbore must also be positive, and the buckled pipe system must lie within this wellbore. The only known solution to the multiple concentric pipe-buckling problem is that of Christman (1976), who proposed a composite pipe based on the summed properties of the individual pipes. This analysis does not conform to the requirements posed in the preceding paragraph. This paper presents the various ways that two concentric pipes can interact when one or both pipes are in compression and would then have a tendency to buckle. The contact forces between the pipes and with the external wellbore are explicitly calculated, and contact or noncontact conditions are determined. All results are analytical so that they can easily be used in spreadsheets or hand calculations. Several examples of calculations are presented to illustrate how these results might be used.

Casings can deform over the life of the well due to various reasons such as changing stress regimes, geological fault and fractures causing pinching, pressure differential created due to production, increased pressure due to injection, squeezing formations such as shale and salt, etc. A detailed casing deformation evaluation can provide insights to the operators in correlating the deformation to suitable reasons in their field. There are various methods to evaluate the innermost casing or tubing using ultrasonic and mechanical caliper measurements but there is no technology available to evaluate outer or second casing deformation without first retrieving the inner casing or tubing. This work introduces and encapsulates the novel methodology of transforming the outer or second casing third interface echo (TIE) response, obtained by advanced ultrasonic and flexural measurement inside innermost casing or tubing, into a 3D wellbore view to suitably visualize and analyze the outer or second string deformations. The work involves measuring the azimuthal radius and thickness of the innermost casing with the ultrasonic evaluation technique and computing the azimuthal annular distance between the two casings using the flexural wave TIE arrival time and its velocity in the annular fluid. The computed values are then combined to generate an array of azimuthal internal radius values of the outer or second casing and is finally converted into a 3D wellbore image for better and straight-forward visualization. To validate the methodology, a shop inspection test (SIT) was carried out where the dimensions of the inner and the outer casing were precisely measured with a mechanical caliper tool. Following that, ultrasonic and flexural measurement tool was run inside the innermost casing to obtain the response of both casings. The comparison showed a close match between the actual values and the measurements. Also, the 3D wellbore shape clearly showed the geometry of the outer string validating the methodology used in the creation of the 3D shape. The work can enable the operators to carry out time lapse outer string analysis on a periodic basis to give them early indications of any deformation in the outer or second string. This novel technique or methodology also has valuable application in plug and abandonment (P&A) where the inner tubing and casing retrieval can be hindered due to outer casing deformation. This technique can also help in designing the right drilling BHA for sidetracking based on the minimum ID of the outer pipe through which slot recovery or side-track has to be performed.

Operator-induced compressive axial forces during implant gold screw fastening

When steel moment frames are subjected to seismic forces, H-shaped beams carry the gradient flexural moment. Large cross-section beams are used as main beams to design structural members effectively in real large space structures. Long span beams may not possess the plastic strength due to lateral buckling, so that many lateral braces along the beams should be set up to prevent the lateral bucking deformation (AIJ 1998). Most oy beams in frames are connected by continuous braces such as folded-roof plates, which are effective to prevent the lateral buckling oy beams. However, in the Japanese design code, non-structural members are not considered as the braces. On the other hands, there have been many moment resisting frames with dampers to prevent damages oy main frames recently, and then H-shaped beams connected with dampers are subjected to compressive axial forces in addition to gradient flexural moment. If the beam carries the large axial force induced by the damper during earthquake, the lateral-torsional buckling behavior oy H-shaped beam becomes more unstable than that under flexural moment only. The axial force which the beams carry is possible to exceed 30% oy yield load oy the beam. Therefore, in this paper, the lateral buckling behavior for H-shaped beams with continuous braces under gradient flexural moment and compressive axial force is clarified and elasto-plastic lateral buckling stress oy the beams or lateral stiffing force and rotational stiffing moment oy continuous braces are evaluated by the energy method and numerical analyses. In this study, for H-shaped beams with continuous braces subjected to gradient flexural moment and compressive axial force, two types oy loading conditions and two types oy bracing rigidities are considered. One oy the loading conditions, which is called as Type A, is the case that the upper flange's compressive load is larger than the lower flange's one in the left side oy beam as shown in Fig. 3(a), and another, which is called as Type B, is that the upper flange's compressive load is smaller than the lower flange's one in the left side oy beam as shown in Fig. 3(b). Furthermore, the ratio oy the compressive axial force, P2 to P1 is represented as an axial force ratio ‘p’ in equation oy elastic lateral buckling load. The continuous braces are divided into the lateral braces, ku, and rotational braces, kβ, as shown in Fig. 1. In the case oy TypeA, ku is effective for preventing lateral deformation oy compressive upper flange, whereas in the case oy TypeB, kβ, is effective for preventing torsional deformation. This study is conducted by the following procedures: 1. The equations oy lateral buckling loads oy H-shaped beams with continuous braces under gradient flexural moment and compressive axial force are derived by energy method. To simplify the equations by energy method, the new equations oy lateral buckling loads are suggested with reference to the terms oy the flexural and torsional rigidities oy beams, the rigidities oy braces, and condition oy the loads. 2. The elasto-plastic buckling behaviors oy the beams are simulated by elasto-plastic large deformation analysis. The lower bound oy the elasto-plastic buckling stress oy the beams can be evaluated with the interpolated buckling curve between those oy bending member and compression member, which are provided by Recommendation for Limit State Design oy Steel Structure (AIJ), depending on the axial force ratio. 3. The upper bound oy moment and lateral force which continuous braces carry at the lateral buckling oy beams is evaluated based on the ratio oy the flexural and torsional rigidities oy beams, the rigidities oy braces, the axial force ratio, and the gradient oy flexural moment.

ABSTRACTHorizontal forces subjected to the moment resisting frame will be essentially resisted by the flexural manner of the columns. Horizontal forces are significant under seismic action; combined loading condition have a possibility to destabilize the columns. In ultimate limit state design, formation of the plastic hinge at the columns are allowed; however, it not permitted to lose its resistance. Moreover, sufficient deformation capacity at the plastic hinge should be guaranteed to fulfill the collapse mechanism of the structure. Following failure modes can occur in the column; 1) local buckling, 2) lateral torsional buckling for the open section subjected to strong axis bending, and 3) in‐plane second‐order effect instability. These failure modes should be prevented to guarantee the ductility of the plastic hinge which is formed in the column.In this paper, column instability due to second‐order effect introduced by compressive axial force is studied. Numerical simulation is used to clarify this issue and in‐plane behaviour is evaluated. Parameters selected for the analysis are cross‐section shape, slenderness ratio, compressive axial force, bending moment distribution, material strength, and initial imperfection. From the results, it was found that material strength is not a significant parameter for column instability which is caused by the second‐order effect. Finally, the formula which can guarantee a sufficient deformation capacity to the column was proposed. Proposed formula was composed by the information of cross‐section shape, slenderness ratio, bending moment distribution, and force level subjected to the column.

Behaviour and design of steel members with web openings under combined bending, shear and compression

Ensuring the integrity of oil and gas cased-wellbores is of crucial importance to operators around the world to maintain safe production and environmental compliance. While sonic and ultrasonic measurements have been developed for evaluating the well integrity of single casing strings, there is currently a gap in characterizing the cement and annular fill behind two or more casing strings due to the lack of sensitivity of the ultrasonic tools and the complexity of the sonic response. This abstract describes an experimental study to characterize the sonic response and help fill this gap in conjunction with a theoretical modeling effort that is reported elsewhere. Scaled laboratory experiments are conducted to acquire reference data used to verify the modeling approach developed to predict the guided modal characteristics of axially-propagating waves in concentric and non-concentric cylindrical structures immersed in fluid. These structures simulate the geometries and environment encountered downhole when conducting acoustical measurements to evaluate the cementation of oil and gas cased wells. Typically, cement is expected to fill the annular space between the outer string and rock formation. Nevertheless, cement damages such as fluid channels, partial cement coverage, and weak bonding interfaces, which can compromise well safety as well as environmental compliance, inevitably occur due to the harsh downhole environment and downhole operations. Measurements are made in a dual-string steel pipe of quarter scale in an immersion tank or in a sandstone formation with concentric as well as a variety of eccentric configurations. A set of samples are prepared with the cement in annulus B (the space beyond the outer casing) with purposefully introduced fluid channels in a controlled manner. A comparison of the experimental and numerical results indicates features in the sonic response that are indicative of channels in annulus B as distinguished from eccentricity effects. These results suggest a new well integrity evaluation work-flow to characterize cement quality and coverage in annulus B taking advantage of the rich acoustic features in the sonic response.

In order to enhance the pertinence of agriculture building design, the experiment and numerical simulation on cold-formed thin-walled steel members with “л” section under axial compressive force were conducted to investigate the effects of residual stress on bearing capacity of them. For the members, there are inevitably initial defects, such as initial bending, initial eccentricity and residual stress due to the manufacturing error. In the numerical simulation, initial bending and initial eccentricity of the members were considered. The results show that the residual stress affects instability forms of the members. And as the member slenderness ratio increases from 69 to 200, the bearing capacity of member with residual stress decreases from 12.8% to 84.9% of that without residual stress.

The stability of a thin elastic rod loaded with non-conservative tangentially distributed and axial compressive force is analyzed. The axial compressive force has constant and periodic component. Also it is assumed that the rod axis is extensible and shear stress effects are taken into account. The in-plane vibrations and stability of the rod are analyzed. The critical load is also determined.

Small scale effect on linear vibration of buckled size-dependent FG nanobeams

Category:Midfoot/ForefootIntroduction/Purpose:A metatarsal osteotomy is sometimes used to correct hallux valgus deformities in the foot, by placing an angular bone graft or spacer in the osteotomy wedge held together using an osteotomy plate. Information on loads through the osteotomy is essential to ensure that the device is adequately tested to perform safely. This study used a validated musculoskeletal computer model of the lower extremities [J Biomech Eng. 2015] with a detailed foot section [Carbes, ISB 2011, Brussels], for evaluating loads across the 1st metatarsal osteotomy during the stance phase of walking gait. This study also evaluates the effect of anatomic variability (osteotomy location relative to anatomical landmarks) and surgical variability (plane of the osteotomy cut) on the peak loading across the osteotomy.Methods:The foot section of the model included 26 bones and major soft tissue structures (Figure 1a), resulting in more than 75 forces acting on the 1st metatarsal. Four healthy patient specific models were analyzed (body weight: 774±73 N; foot length: 246±16 mm), for five osteotomy planes. The osteotomy plane perpendicular to the long axis of the 1st metatarsal (posterior- anterior) was considered a neutral-N osteotomy. Four additional planes were considered to capture surgical variability of 5 degrees in abduction-AB, adduction-AD, dorsiflexion-DF and plantarflexion-PF. Compressive (Fx) and shear (Fy, Fz) forces as well as three moments: varus/valgus (Mx), flexion/extension (My) and internal/external rotation (Mz) were predicted in body weight (BW) multiples. Anatomic variability (standard deviation in peak values between patients, averaged across all osteotomies) and surgical variability (Standard deviation in peak values between osteotomies, averaged across all patients) were computed for the peak force and moment components.Results:Similar trends for peak forces and moments were predicted for all patients. An average of 2.2xBW peak force was predicted along the long axis of the 1st metatarsal (Fx) at 50% gait position (Figure 1b, 1c). The predicted shear forces (Fy, Fz) were much lower than the axial compressive force (Fx). The average moment predictions were similar among all five osteotomy planes, with peak moments predicted in the internal/external direction (My) at 43% and 55% of gait positions. Thus, load variability due to patient anatomy and surgical cuts were studied for Fx and My (Figure 1c). Load variability between patients of 18% and 21% were predicted for the Fx and My, respectively. The highest surgical variability of 7% and 3% were predicted for Fx and My.Conclusion:A validated musculoskeletal computer model can be used to inform physiological loading across the 1st metatarsal osteotomy throughout gait, which can be used to evaluate the device safety. The model further helps to understand the influence of anatomical and surgical variability on the peak loading passing through the 1st metatarsal osteotomy, providing guidance in surgical planning. Although peak loading passing through the 1st metatarsal osteotomy is affected by both anatomical as well as surgical variability, it was influenced more by anatomical variability than surgical. This modeling approach can be used to evaluate loading for patients with numerous specific disorders.

This paper presents two experimental campaigns carried out on 36 reinforced concrete (RC) beams (with and without shear reinforcement) subjected to a three‐point bending loading with a shear force on the one hand, an axial compressive load and a negative bending moment applied at each end of the beams on the other hand. Such a loading configuration makes it possible to investigate the influence of both axial compression and negative bending moment on the shear capacity of RC beams. For each campaign, three values of axial compressive force were studied, and the test beams were divided into two series with low and high negative bending moment. During the tests, Digital Image Correlation technique was used to capture the cracking evolution of the specimens. Besides, the experimental shear strengths of the beams are confronted to the predictions of Eurocode 2 in order to assess its practical validity. Finally, a semi‐analytical method proposed by Wahbi et al. 2021 (A failure criterion for RC beams subjected to axial and transverse loadings) for evaluating the resistance domain of RC elements subjected to transverse and axial loads, is extended in this paper to take into account the negative bending moment and compared to the experimental results.

The buckling moment of doubly symmetric spatial beams under different types of end bending moment and compressive axial force is investigated using finite element method. A co-rotational total Lagrangian finite element formulation is employed here. An incremental-iterative method based on the Newton-Raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations. The zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state. Numerical examples are presented to investigate the effect of compressive force on the buckling moment of spatial beams under different types of bending moment.

This paper discusses concrete members reinforced internally with composite GFRP bars (Glass Fibre Reinforced Polymer). The studies are focused on members under axial force and bending moment. Experimental studies of 4 RC columns loaded with compressive axial force, longitudinally and transversally reinforced with GFRP bars were discussed. Columns had cylinder shape with the nominal diameter of 200mm and height of 600mm. Longitudinal reinforcement contained six bars with 11mm diameter and transversal reinforcement of continuous spiral bars # 4 and #8 with spacing equal to 45mm and 60mm. Studies show that the GFRP reinforcement has very good adhesion to concrete and,in failure state reaches stresses adequate to longitudinal strains of members. This paper proves that the interaction curves can be determined on the same strain state basis as used in RC members according to EC2.

This paper proposes a method of reasonable selection of the fixation scheme, and the number of intermediates supports for straight multi-span beams in order to ensure the given values of the critical load from the compressive axial force. This axial force may be an external load or may occur, for example, as a result of a change in beam temperature. An effective way of providing the first critical force of the beam is to choose the appropriate method of fixing it: the type of the main supports and, if necessary, intermediate supports. This paper proposes a method of normalizing effective length factors, which enables to obtain convenient comparable values when choosing a fixation method and, as a result, to develop a method for a reasonable selection of a support arrangement system for a straight beam. The technique is based on the well-known theory of beam stability and uses effective length factors as a criterion for selecting the fixation scheme, which is formed after solving the corresponding differential equations of the beam state and is determined only by the fixing conditions. The obtained results can be used in calculations and design of any extended beam structures to control their stability by selecting the appropriate fixation scheme.KeywordsStabilityBeamSupportEffective length factorThe first critical loadNormalizing