Numerical Calculation For The Flow Of The Viscoelastic Fluid In Annulus With The Inner Cylinder Executing A Planetary Motion

During the exceptional well drilling process, the drill pipe rotates not only around its own axis but also around the axis of wellbore (casing tube), the flow of particular drilling fluid in eccentric annulus between the drill pipe and wellbore(casing tube) could be regarded as flow of viscoelastic fluid in annulus with the inner cylinder executing a planetary motion. Under the behavior of production by polymer flooding screw pump, the pump rod rotates not only around its own axis but also around the axis of the oil tube, the flow of production liquid in eccentric annulus formed by the pump rod and the oil tube could be regarded as flow of viscoelastic fluid in annulus with the inner cylinder executing a planetary motion. So researching on the flow rules of viscoelastic fluid in annulus with the inner cylinder executing a planetary motion has important guidance significance for analyzing the carrying debris capacity in bore hole of particular drilling fluid and optimizing production parameters of polymer flooding screw pump production wells.In this paper, the second order fluid with variable coefficients model was used to describe rheological property for the viscoelastic fluid, and the velocity distribution, the flow rate and the pressure gradient for the flow of it in annulus with the inner cylinder executing a planetary motion were numerically calculated.With the governing equations for the flow of the second order fluid with variable coefficients in annulus with the inner cylinder executing a planetary motion, the flow rate formula and the pressure gradient equation group for the flow and the relative numerical calculation method were given in this paper.Using HPAM aqueous solution which can be regarded as a second order fluid with variable coefficients, the flow rate for this flow was numerically calculated on the basis of the results of axial velocity distribution by solving numerically the governing equations menthioned above. The pressure gradient for this flow was numerically calculated on the basis of the pressure gradient equation group mentioned above. The influences on the tangential velocity distribution, the radial velocity distribution, the axial velocity distribution and the flow rate by the revolution velocity and the rotation velocity of the inner cylinder, the eccentricity and the pressure gradient in annulus, the inertia force and the elasticity of solution were analyzed. The influences on the pressure gradient by the revolution velocity and the rotation velocity of the inner cylinder, the eccentricity in annulus, the inertia force and the elasticity of solution were analyzed.The tangential velocity distribution, the radial velocity distribution, the axial velocity distribution for the flow of water, which can be regarded as a Newtonian fluid, calculated by the numerical method for the velocity distribution for the flow of the second order fluid with variable coefficients in annulus with the inner cylinder executing a planetary motion given in this paper were compared with those calculated by the analytic solutions, they coincide well. Through the experiments on the flow of HPAM solution which can be regarded as a second order fluid with variable coefficients in annulus with the inner cylinder executing a planetary motion, the flow rate values and the pressure gradient values calculated numerically were compared with those measured in the experiments, the even relative percent errors between them were both smaller than 5%, it shows that the numerical calculation methods for the velocity distribution, the flow rate and the pressure gradient for the flow of the second order fluid with variable coefficients in annuls with the inner cylinder executing a planetary motion are correct.