基于有杆抽油系统Gibbs模型中泵功图的计算研究

Research on the Calculation of Pump Diagram in Gibbs Model Based on Rod Oil Pumping System

计算泵功图的关键就是求解Gibbs模型中的波动方程。采用分离变量法和傅里叶级数展开方法进行求解,其中系数的求解由初始条件与边界条件决定;对于多级杆泵功图,需要对抽油杆的载荷做分级计算,将前一级杆末端的载荷与位移作为后一级杆的初始及边界条件,直至求出最后一级末端的载荷与位移,得出最终的泵功图。

The key to calculating pump diagram is to solve wave equation in Gibbs Model. Separation variables method and Fourier series expansion method are used to solve pump diagram, among which the solution to the coefficient is determined by the initial condition and boundary condition, the solution to multistage pump diagram needs classified computation for the load of sucker-rod, by end as the initial and boundary condition of the are solved and then the ultimate pump diagram taking the load and displacement of the former stage rod later stage rod, until the load and displacement of the last stage end is obtained.