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以Doty数学模型为基础，对定向井杆柱、液柱进行了受力分析，给出了描述定向井有杆抽油系统的数学模型；采用两步二阶显示差分格式对模型进行求解，得到了满意的结果。从而解决了定向井有杆抽油系统的数位模拟问题。同时指出了定向井数学模型与会在井数学模型的区别。从模拟结果看，定向并与直井的地面示功国和泵示功图均有较大的差异，因此在对定向井进行设计时要采用适合于定向井的数学模型。
Based on the Doty mathematical model, the force analysis of directional wellbore and liquid column is carried out. The mathematical model describing the rod pumping system of directional well is given. The model is solved by two-step second-order difference display format Satisfied with the results. Thus solving the problem of digital simulation of sucker rod pumping system in directional well. At the same time, it points out the difference between mathematical model of directional well and mathematical model of well in well. From the simulation results, it is found that there is a big difference between the orientation direction and the ground-state power system and the pump dynamometer of the vertical well. Therefore, the mathematical model suitable for the directional well should be adopted when designing the directional well.