Unsteady Flow Of Power-law Fluid In Eccentric Annuli With The Inner Cylinder Reciprocating Axially

For the case of deep oil well, pumping rod is eccentric in oil tube during the oil recovery. The flow of the fluid produced by means of polymer-driving in a well can be seen as unsteady flow of power-law fluid in eccentric annuli with the inner cylinder reciprocating axially.Unsteady flow of power-law fluid in eccentric annuli with the inner cyinder reciprocating axially is studied in this paper.Power-law fluid is used to describe the Non-newtonian rheological property of the produced fluid in a polymer-driving well; the governing equations, boundary and initial equations of power-law fluid in eccentric annuli with the inner cylinder reciprocating axially is established in bipolar coordinates system; formulas of instantaneous flow rate and stress distribution on the outwall of the inner cylinder of the unsteady flow of power-law fluid in eccentric annuli with the inner cylinder reciprocating axially are established.Taking HPAM solutions as an example , the unsteady flow of power-law fluid in eccentric annuli with the inner cylinder reciprocating axially is calculated; the distribution of velocity, flow rate and:stress distribution on the outwall of the inner cyinder is obtained; the effect of eccentricity, stroke and frequency on distribution of velocity is analysed; the effect of eccentricity and axial movement on stress distribution on the outwall of the inner cylinder is analysed too.Through the laboratory flow experiments with aqueous solution of varied consistency of HPAM ,the average flow rates calculated with the theoretical formulae are compared with those meassured in the experiments , and it shows that the numerical method of the unsteady flow of power-law fluid in eccentric annuli with the inner cylinder reciprocating axially in the paper is correct.The above results provide theoretical basis for researching and prevnting the eccentric wear of pumping rod and optimizing the working parameters.