| Polymer displacement technique may obviously increase the recovery ratio of crude oil, at the same time the serious deviating-fraction of sucker rod results in the decrease of pump repairing cycle and the reduce of compositive economic benefit. How to diagnose these problems, for example the rod wear and tear in polymer displacement well, etc, is the main thing of stabilizing crude oil production and increasing economic benefit of oil field development. Now, the wave equation and statics theory is the basis of the trouble diagnostic method and technique adopted by oil field, and it cannot basically meet with the demand of new production technique field. Production engineering domain urgently need new diagnostic method and experimental technique, and investigate and solve the new diagnostic method of down-hole working conditions on polymer displacement rod pumping system in order to increase crude oil output and ensure the secure and normal production of rod pumping system. The paper well combines basic theoretical and experimental study with application techniques and sets up new diagnostic method, which will have definite theoretical meanings for perfecting the trouble diagnostic techniques of rod pumping system. These enrich the trouble diagnostic theories of rod pumping system and let the development of correlative subjects fly farther.Adopting polymer displacement technique makes down-hole working conditions more complicated. The paper is involved in many sorts of subjects, for instance petroleum engineering, solid mechanics, hydrodynamics and so on, and it is the coupling problem of geometric nolinearities, contact nolinearities and structure dynamics. By the mechanical analysis, mechanical model of rod pumping system equipment is set up in this paper. Kirchhoff balance equation and transient dynamics balance equation of sucker rod are set up by using momentum theorem and dynamics principle in the scope of finite distortion. Non-embed measurement equation of contact surface is derived according to the design value and movement condition and the weak style of balance equation is derived according to variational principle and updated Lagrange format. Augmented Lagrange multiplier method is adopted, and momentum equation in the interface between sucker rod and tubing is set up. The relational expression is determined between the movement velocity of sucker rod and the damping forces, which are produced between sucker rod and well liquids, between oil well pump and well liquids and so on. At last, it is solved by using Newton-Raphson method, load increment method, augmented Lagrange multiplier method, Newmark on the basis of adopting finite element method, and the computer programs are edited to calculate the force and deformation law of rod pumping system down-hole equipment in the conditions of multiple coupling.The frictional resistance state (the down stroke resistance change law of oil well pump plunger, pump barrel, travel valve and so on; the on-way resistance coefficient changing law when sucker rod moving in the well liquids; local resistance coefficient changing law when coupler and centraliser of sucker rod moving in the well liquids; local resistance changing law when well liquids flowing through travel valve) is clear by force analysis and experimental research, which the down-hole equipments of polymer displacement rod pumping system moves in well liquids, and all damp coefficients of diagnostic method are determined in term of experimental results, it establishes the basis for quantificationally calculating down-hole working conditions (especially the rod wear and tear, rupture and dropout) of polymer displacement rod pumping system.The new diagnostic method of rod pumping system down-hole working conditions is set up and it cancalculate the down-hole sucker rod and tubing deformation law (including the sucker rod axial force, contact location, contact force and contact time of sucker rod and tubing, and so on) of polymer displacement well rod pumping system at any time an...
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