Research On Contact Nonlinear Buckling Of Concentric Tubular Strings In Vertical Pipe

Oil and gas well rod string is an important channel to obtain underground oil and gas resources.At the same time,it also plays the role of protecting and supporting oil wells,which is equivalent to the position of spine and central nerve in human body.The buckling deformation of rod and pipe string after instability will have an adverse impact on many operations such as drilling,completion,fracturing,logging,oil production and so on.Different from the classical Euler compression rod,the buckling of oil and gas well rod string becomes more complex due to the radial constraint of external pipe.Especially for downhole multi-layer concentric tubular string,the post buckling configuration and contact state are more complex.Therefore,the buckling of rod and pipe string is one of the key and difficult problems in the field of oil and gas drilling and production engineering.In this paper,the analytical mathematical model of helical buckling of pipe string is obtained based on the buckling differential equation,and the analytical expressions of post buckling parameters such as helical pitch,bending moment,shear force and contact force caused by axial force are derived,which provides a theoretical basis for the follow-up study of numerical methods.Aiming at the double nonlinear problems of geometry and contact,the equilibrium equation of static buckling of pipe column is established by using geometric nonlinear beam element and contact nonlinear gap element theory.At the same time,the virtual transient dynamic finite element method is proposed to solve the problems of convergence difficulty and unstable algorithm in the process of static buckling solution.Taking the single-layer contact concentric tubular column as the research object,the nonlinear buckling mechanical model of tubular column is established.Based on the combination of spatial beam element and contact gap element,the transient dynamic method is introduced,the Newmark integral method is adopted,the appropriate damping and certain analysis time are selected,and finally the stable static buckling solution is obtained.The effects of damping,element length and direction of disturbing force on the post buckling of pipe string are studied.The results show that damping has a great influence on the post buckling configuration of pipe string;The element length has no obvious effect on the post buckling configuration of pipe string,but affects the calculation efficiency;The direction of disturbing force affects the direction of helical buckling of pipe string.On this basis,six post buckling configurations of pipe string under axial force are calculated,and the structural characteristics,contact state and distribution law of post buckling mechanical parameters of different post buckling configurations are studied.In addition,the indoor experimental platform is built and the bar column buckling experiment is carried out.The experimental results are basically consistent with the theoretical results,which proves the positive determination of the theoretical method.The curve equations of sinusoidal and helical buckling of double-layer contact concentric string are established in Cartesian coordinate system.Using the small deformation assumption and based on the energy method,an analytical mathematical model describing the post buckling behavior of concentric tubular columns is established,and the analytical expressions of post buckling parameters such as spiral pitch,bending moment,shear force and contact force caused by axial force are derived,which provides a theoretical basis for subsequent research.A nonlinear finite element method combining beam element and double-layer contact gap element is proposed to solve the post buckling problem of double-layer contact concentric tubular columns in pipes.The double-layer contact nonlinear buckling mechanical model of concentric pipe string is established.Eight characteristic post buckling configurations of concentric pipe string under axial force are obtained by transient dynamic method.The structural characteristics,contact state and distribution of mechanical parameters of different post buckling configurations of inner tube and middle tube are studied.In addition,the structural characteristics of the transition section between the inner tube and the middle tube under the complete helical buckling configuration are studied.It can be found that the transition section at the end of the inner tube has only the first suspended section,and the transition section of the middle tube has the first suspended section and the second suspended section.Combined with the engineering background of oil and gas wells,the single-layer contact nonlinear buckling mechanical model of tubing in casing is established.Six post buckling configurations of tubing string under bottom hole axial pressure are calculated by transient dynamic method.The structural characteristics,contact state and distribution law of post buckling mechanical parameters of different post buckling configurations are studied.The effects of string length on the structural characteristics,post buckling mechanical parameters and buckling critical load of tubing complete helical buckling are studied.The results show that with the continuous increase of string length,the critical load of tubing complete helical buckling gradually decreases and tends to be stable,and its dimensionless value finally stabilizes at about 7.46.On this basis,ignoring the influence of cementing conditions,the double-layer contact nonlinear buckling mechanical model of concentric casing string in wellbore is established and calculated by finite element method.Considering only the dead weight of the string,the relationship between the length of concentric string and the number of helical pitches is studied.Considering the influence of tubing tension section and casing buckling,the effects of concentric string length on the structural characteristics,post buckling mechanical parameters and buckling critical load of tubing are studied.The results show that with the continuous increase of concentric string length,the critical load of complete helical buckling of tubing string gradually decreases and tends to be stable,and its dimensionless value finally stabilizes at about 8.20.In the same well injection-production system of downhole oil-water separation,two-stage packers are used to separate the injection layer from the production layer.The bridge channel between the two-stage packers and the external casing form a "three body two-layer contact" system,and the pipe string will buckle under the action of large axial force load.The structure is simplified and the mechanical model of post buckling analysis of string between packers is established and the effects of different loads and lengths on post buckling of string are studied.Aiming at the wear problem of pipe string in field application,the pipe string is improved and designed.The field test is carried out with the improved string,and the continuous operation time is more than one year,which eliminates the eccentric wear of the string,and proves the rationality of the string design.The research results of this paper provide a theoretical basis and reference basis for the further study of multi-layer contact nonlinear buckling of concentric tubular string.At the same time,it has important reference value and engineering practical significance for string design,process parameter optimization and popularization of horizontal well,multi branch well,extended reach well and coiled tubing technology.