Unsteady Flow Of Viscoelastic Fluid In Eccentric Annuli With Inner Cylinder Reciprocating Axially

Since the industrial application of polymer flooding in the Daqing Oil Field, a preferable driving effect has been achieved. At the same time, there exist a lot of problems in the rod-pumped wells of polymer flooding compared with water flooding, such as greater ergogram, lower pumping efficiency, eccentric wear of the sucker rod, shorter period of pump checking, etc. The occurrence of these problems is greatly related with the viscoelastic property of the produced fluid. And the sucker rod reciprocating axially is always in a condition of eccentric, which will even aggravate the mentioned problems. The flow law in the eccentric annuli with inner cylinder reciprocating axially of the produced fluid in the polymer flooding wells is studied in this paper. It's obviously that the study has a significant engineering meaning in the optimizing of the parameters of the pumping unit and in the prevention of the eccentric wear of the sucker rod. The second order fluid with variable coefficients is used to describe the rheological property of the produced fluid in the polymer flooding wells, and the unsteady flow of such a fluid in the eccentric annuli with inner cylinder reciprocating axially is studied in this paper. The basic equations of the unsteady flow of second order fluid with variable coefficients in the eccentric annuli with inner cylinder reciprocating axially in rectangular and bipolar coordinate are established respectively in this paper, and the formula of normal stress on the inner cylinder is given. The basic equations of the unsteady flow of second order fluid with variable coefficients in the eccentric annuli with inner cylinder reciprocating axially are dispersed with the doublelayer Crank-Nicholson latent difference scheme. By the using of the left divide of Matlab, the sparse system of linear equations is numerically calculated, and the numerical solution of the unsteady flow of second order fluid in the eccentric annuli with inner cylinder reciprocating axially is obtained. By the numerical calculation of the equations of motion, the velocity distribution, the instantaneous flow rate distribution, the average flow and the normal stress distribution on the inner cylinder of second order fluid with variable coefficients in the eccentric annuli with inner cylinder reciprocating axially are obtained; and the influences of eccentricity, stroke and frequency of the inner cylinder on the velocity distribution, the instantaneous flow rate distribution, the average flow and the normal stress distribution on the inner cylinder are analyzed; the velocity distribution, the instantaneous flow rate distribution, the average flow and the normal stress distribution on the inner cylinder of second order fluid with variable coefficients in the eccentric annuli with the inner cylinder reciprocating axially are compared with that of the power-law fluid under the same flowing condition. The results show that, the velocity and instantaneous flow rate distribution of second order fluid with variable coefficients differ greatly from the ones of the power-law fluid; the average flow of second order fluid with variable coefficients is smaller than that of the power-law fluid under the same condition; and as the existence of the second normal stress coefficient in the model of second order fluid with variable coefficients, there is a concentric effect in the upstroke and a eccentric effect in the down stroke, but there is no such a effect for the power-law fluid or for the Weissenberg fluid. The unsteady flow experiments of the HPAM aqueous solution of two kinds of different mass concentration in the eccentric annuli with inner cylinder reciprocating axially are carried out. The calculated flow rate neglected the elastic item is compared with the experimental flow rate, and the results show that they are coinsistent well. It can be considered that the basic equations and numerical method presented in this paper are correct.