Modeling and characteristic analysis of viscous resistance in annulus gap of coalbed gas well drainage pump

Abstract

The viscous resistance caused by the relative motion of plunger and pump barrel is an important factor in the dynamic analysis of the drainage and production mechanism during coalbed methane exploitation. Existing studies mostly focus on deep well (1000–3000 m) large-displacement pump (usually 80–300 m3/d), and the interstitial medium is mainly crude oil. Regression fitting is mainly carried out based on empirical formula or experimental simulation method, without considering the characteristics of shallower coalbed gas well (400–800 m) small-displacement pump (<10 m3/d). The variation of the clearance between plunger and barrel and the variation of viscous resistance between plunger and barrel are not revealed. Based on the Navier-Stokes equation and Newton's internal friction law, a mathematical model of the annular viscous resistance between the plunger and the pump barrel is established, and an analytical method is used to describe the influence of stroke times, annular clearance, and differential pressure between the upper and lower plungers on the viscous resistance. The results show that the plunger stroke is directly proportional to the variation range of viscous resistance, and low stroke is beneficial to reduce the viscous resistance. The effect of differential pressure between upper and lower plunger of rod pump on viscous resistance of small displacement coalbed gas well is significantly greater than that of plunger running speed. The annular clearance is directly proportional to the differential pressure between the upper and lower parts of the plunger, the inertia force of the plunger, and the shear force of the moving fluid. The annular viscous resistance model between plunger and pump barrel is helpful to improve the calculation accuracy of suspending point load of coalbed gas well pumping unit, analyze the working condition of coalbed gas drainage gas production process, and provide basis for the optimization design of coalbed gas well rod pump clearance.