A Uniform and Reduced Mathematical Model for Sucker Rod Pumping

Abstract

Abstract. The dynamic mathematical models were greatly developed to describe the motion of the sucker-rod pumping system since 1960s and various mathematic models based on different assumptions were presented. This paper does a study in three sides. First, a mathematical model is presented to describe the sucker-rod string with longitudinal and transverse vibrations, and coupled with longitudinal vibration of the tubing and fluid columns in a deviated well. Second, the relations of several kinds of mathematical models in sucker-rod pumping systems are discussed, and the model made in this paper, when based on different assumptions, can become different models made by people these years, which are presented in important references. Third, a method of characteristics is used to transform the set of partial differential equations which describe the vibration of the sucker-rod string, and coupled with vibrations of tubing and liquid columns in the sucker-rod pumping system. Through the transformation, a diagonal partial differential equations set is obtained. Hence a relatively complex model is transformed into a reduced model which is easy to solve. This model has basic meaning for using the technique of pattern recognition to make automatic diagnosis of sucker rod pumping system.

Ensuring the operational-technological characteristics of the new design solution of the sucker-rod pumping unit

“…The technical factors include the mechanical transfer characteristic axis dimensions of the pumping unit, such as the effective area of the sucker's cross-section and the plunger stroke, the working pressure of the pumping unit, and its transmission. The economic factors include the increase in the power of transfer that can be achieved by using the balanced pumping unit compared to the unbalan ced analogous mechanism, the capital costs, exploitation expenses, and other related factors [15][16][17].…”

Determining the parameters of oscillation dissipation in a column of sucker rods

“…The algorithm of numerical calculation of rod columns of DRPI was proposed. Dynamics of the motion of a SR column in the twisted column of PCP is described in [6]. The mathematical model is presented in the form of a system of differential equations of motion with partial derivatives and geometric equations of a spatial curve.…”

Dynamic Behavior of the Polished Rod for the Coalbed Methane Pumping Installations

“…And four methods available have generally been used for the operators to predict dynamic loadings on polished rod for the specific pumping installation. American Petroleum Institute (API) offered a complete solution of the rod motion problem [7,8]. But this method had limiting assumptions such as simplified polished rod motion and full pump.…”