Abstract: Based on the theory of skin effect and the coupling of electriomagnetic and temperature fields,a calculation model to describe the principle of electric heating system for oil production was established by the use of the finite element method. The hypothesess were based on that the characteristics of electriomagnetic field is the same in every cross section along the whole hollow sucker rods and the continuous cable,and the magnetic leak in atmosphere is omitted in this calculation model. By using this calculation model and finite element method,the coupling of electromagnetic field along hollow sucker rods and the cable in sucker rods was simulated and analyzed. The current density distributions under different frequence were obtained. The relationship between the depth of skin effect and frequence was gotten. The calculation shows that the bigger the electric frequence is,the smaller the skin effect depth will be. The heating equipment can be applied safely,because the electric current is mainly distributed on the inner surface along the hollow sucker rods.

Key words: heavy oil exploitation, hollow sucker rod, electric heating system, finite element method, skin effect, electromagnetic field, numerical calculation model

摘要： 基于集肤效应原理及电磁场有关耦合理论,利用有限元方法,推导了描述交流电加热井下原油的数学物理模型。在数值计算中,假设在同一级空心抽油杆和杆内电缆在每个截面上的电磁场完全相同,并忽略空气中的漏磁。根据建立的模型,对加热系统中空心抽油杆及杆内电缆的电磁场进行了模拟和分析,得出了在不同的操作频率下,空心抽油杆及杆内电缆的电流密度分布情况以及频率与集肤深度的关系。计算结果表明,电流频率越高,集肤深度越小。对空心抽油杆而言,电流主要分布在杆体的内表面上,因而该装置使用安全。

关键词: 稠油开采, 空心抽油杆, 电加热系统, 有限元法, 集肤效应, 电磁场, 数值计算模型