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根据垂直井地面驱动螺杆泵采油系统的工作特点，利用抽油杆柱的动力学分析结果，建立了抽油杆柱运动模型，并给出了其有限差分解。利用该模型，可以根据在地面测试的光杆扭矩变化规律计算出井筒中任意部位及螺杆泵处抽油杆扭矩的变化情况，也可根据螺杆泵处抽油杆扭矩变化来预测光杆扭矩的变化。为进一步研究地面驱动螺杆泵抽油杆柱的运动特性和采油系统的工作状况提供了理论基础。计算实例表明，该数学模型及其有限差分解法是有效的和稳定的。
According to the working characteristics of vertical well ground driven screw pump oil recovery system, based on the dynamic analysis results of sucker rod string, the motion model of sucker rod column was established and its finite difference solution was given. The model can be used to calculate the torque variation of sucker rod at any position in the wellbore and the screw pump according to the variation law of the polished rod torque measured on the ground. The torque variation of sucker rod rod can also be predicted according to the variation of sucker rod rod torque at the screw pump. This study provides a theoretical basis for further research on the movement characteristics of sucker rod and the working conditions of oil recovery system. The calculation example shows that the mathematical model and its finite difference method are effective and stable.