Analysis Of The Forces On The Inner Cylinder With A Planetary Motion By Viscoelastic Fluid Flowing In Annulus

During drilling process for special wells, the drillpipe not only rotates around its own axis but around the axis of wellbore as well, because of its own gravity and eccentricity. Therefore, the flow of drilling fluid in the annulus between the drillpipe and wellbore can be regarded as flow of viscoelastic fluid in the annulus with the inner cylinder performing a planetary motion. Likewise, in a polymer flooding production well by screw pump, the flow of the produced fluid in the annulus between pumping rod and oil tube can also be regarded as the same flow pattern. Research on the forces exerted on the inner cylinder by viscoelastic fluid flowing in annulus with the inner cylinder performing a planetary motion is of great theoretical significance for special well trajectory control of drilling and preventing drillpipe sticking, as well as for analyzing and controlling eccentric wear and breakage of pump rod, optimizing and designing the parameters of pump in screw pump production wells by polymer flooding.In this paper, the rheological properties of the viscoelastic fluid are described by the model of second order fluid with variable coefficients. The calculation formulae of normal stress difference, tangential stress and moment, exerted on the inner cylinder by the second order fluid with variable coefficients flowing in the annulus with the inner cylinder performing a planetary motion, are derived; and corresponding calculation methods of numerical solution of are given. The effects of rotation and revolution velocities of the inner cylinder, eccentricity and pressure gradient on normal stress difference, tangential stress and moment acted on the inner cylinder when second order fluid with variable coefficients flows in annulus with the inner cylinder executing a planetary motion are calculated and analyzed. The results indicate that as to the flow of second order fluid with variable coefficients in annulus with the inner cylinder performing a planetary motion, the influences of rotation and revolution velocities and eccentricity on normal stress difference, tangential stress and moment acted on the inner cylinder are obvious; the influence of pressure gradient on normal stress difference, tangential stress and moment is weak; using the results of numerical calculation, normal stress difference, tangential stress and moment exerted on the inner cylinder as to the second order fluid with variable coefficients in annulus with the inner cylinder performing a planetary motion are compared with those as to the power law fluid under the same conditions, and the results of which show that if the elasticity of second order fluid with variable coefficients is small, the influence of elasticity of the fluid on normal stress difference, tangential stress and moment is weak; if the elasticity of second order fluid with variable coefficients is large, the influence of elasticity of the fluid on normal stress difference is obvious while on tangential stress and moment is weak. The comparison between the analytical solutions and the numerical solutions of normal stress difference, tangential stress and moment exerted on the inner cylinder as to the flow of Newtonian fluid in annulus with the inner cylinder performing a planetary motion, shows that they match perfectly. This indicates that the calculation formulae and numerical calculation methods of normal stress difference, tangential stress and moment exerted on the inner cylinder by the viscoelastic fluid given in this paper are correct.