Static And Dynamic Behavior Analysis Of Oil And Gas Pipe Rods Based On Fractional Derivative Viscoelastic Model

In this paper,the deformation of oil and gas well pipe rods are considered as viscoelasticity.Combined with elastic mechanics and fractional derivative theory,the static dynamic behavior of oil and gas well tubulars in horizontal wells obeying fractional Kelvin viscoelastic model is studied.The main work is as follows:(1)Considering the pipe model as a horizontal viscoelastic circular section beam model,then combined with the elastic dynamics and fractional derivative theory,the static torsion governing equation of the viscoelastic pipe rod obeying the fractional Kelvin model is established.The analytical solution of the stress and displacement components with non-zero is carried out.Based on the numerical examples,analyzed the static torsion problem of viscoelastic pipe rods.The results show that the magnitude of the fractional order can significantly affect the vertical and circumferential stresses of the pipe.And the magnitude of the hoop displacement value,the external torque value,the length of the pipe rod and the model constant ratio have obvious influence on the stress and displacement components of the pipe rod;the influence of the pipe bar thickness on the stress and displacement is relatively small.(2)Based on the fractional derivative and elastic mechanics theory,the pipe model is simplified to the viscoelastic cylindrical tube model,and the motion control equation of the incompressible viscoelastic cylindrical tube under axial symmetry is established.The displacement solution is directly obtained from the incompressibility assumption.The Laplace transformation is used to obtain the circumferential displacement and stress analytical solution of the pipe.Through numerical examples,the results show that the fractional value and the thickness of the outer casing have a significant effect on the displacement of the pipe;the inner and outer radius of the pipe the ratio,the Poisson's ratio of the casing and the elastic modulus have little effect on the radial displacement;the material constant has a greater influence on the radial displacement;the fractional value has a greater influence on the stress generated at the inner diameter of the pipe;the model constant has small influence of the radial stress;the elastic modulus of the casing will significantly affect the stress value of the pipe;the Poisson's ratio does not change the distribution of the radial stress,and has little effect on the vertical stress;the change of the ratio of the inner and outer radius of the pipe rod will significantly affect the stress distribution of the pipe rod.(3)Considering the compressibility of viscoelastic pipe rods and ignoring the influence of inertia effect,the equilibrium equation of compressible viscoelastic pipe rods is established,and the quasi-static response of compressible viscoelastic pipe rods is analyzed.Numerical examples show that the larger the fractional order value,the larger the initial stress at the inner wall of the corresponding pipe rod;the larger the Poisson's ratio of the outer casing,the smaller the radial displacement value;the elastic modulus of the casing has less influence on the radial displacement.The larger the model constant ratio and the outer radius,the larger the radial displacement value;the larger the fractional order value,the larger the radial and hoop stress values at the inner wall of the cylindrical tube,and the higher the corresponding vertical stress rise,the vertical stress stability of the pipe rod is larger;the larger the model constant ratio,the radial and hoop stress values are large;the larger the casing thickness,the smaller the radial stress;the thickness of the outer casing is large,the influence of hoop stress on the inner wall of the column tube is small;the Poisson's ratio of the casing has a significant effect on the radial stress value;the larger the Poisson's ratio of the casing,the smaller the corresponding radial stress value is,the effect of the Poisson's ratio size on hoop stress is not obvious;The amount of the elastic mode of the outer casing has little effect on the hoop stress;the larger the ratio of the inner and outer radii,the greater the radial stress on the inner wall and the decrease in the vertical stress.