Pressure Gradient Of Power Law Fluid Flowing In Annulus With The Inner Cylinder Executing A Planetary Motion

Under the behavior of production by screw pump, the pump rod rotates not only around its own axis but also around the axis of the oil tube, for the effects of its self-weight and decentralization. The flow of produced liquid in annulus between the pump rod and the oil tube could be regarded as flow of non-Newtonian fluid in annulus with the inner cylinder executing a planetary motion. So, research on the pressure gradient of flow of non-Newtonian fluid in annulus with the inner cylinder executing a planetary motion is of certain theoretical instruction significance for optimizing and designing the parameters of pump in screw pump production well.In this paper, the rheological properties of the produced liquid in screw pump production well were described by the model of power law fluid. The kinematic equations of flow of power law fluid in annulus with the inner cylinder executing a planetary motion were transformed by the method of undetermined coefficient, and then the relation expressions among stream function, axial velocity and pressure gradient were obtained. The mathematical model of the pressure gradient of flow of power law fluid in annulus with the inner cylinder executing a planetary motion was established and then calculated by finite difference method. Through the correlation analysis between the analytical solutions and the numerical solutions of the pressure gradient of flow of Newtonian fluid in annulus with the inner cylinder executing a planetary motion, it is known that the formula and the numerical calculation method of the pressure gradient given in this paper are accurate. The effects of the rotation and revolution velocities of the inner cylinder, the eccentricity and the flux on the pressure gradient were analyzed respectively when Newtonian and power law fluid flow in annulus with the inner cylinder executing a planetary motion. The results indicate that, for the flow of Newtonian fluid in annulus with the inner cylinder executing a planetary motion, the eccentricity and the flux are the main effects to the pressure gradient, while the rotation and revolution velocities have no effect on it; for the flow of power law fluid in annulus with the inner cylinder executing a planetary motion, the eccentricity and the flux are the main effects to the pressure gradient, while the rotation and revolution velocities have less effect on it.