﻿ 碳纤维连续抽油杆冲程损失计算方法

Method for Calculation of Stroke Losses in Carbon Fiber Continuous Sucker Rods
ZHANG Hao, YANG Yong, QI Yaoguang, PAN Long, MAO Zhengyi
School of Mechanical and Electrical Engineering, China University of Petroleum(Huadong), Qingdao, Shandong, 266580, China
Abstract: Carbon fiber continuous sucker rods are used extensively, but there are no techniques currently available for calculations related to the stroke losses of such rods.Conventional methods deployed for stroke losses in steel rods are characterized by significant errors.In extreme cases, such errors may lead to downhole collisions.By analyzing the materials in the carbon fiber continuous sucker rods and taking into consideration the structural features, the as well as impacts of working temperatures over carbon fiber composite materials and relevant elastic modulus, an innovative model to calculate the stroke losses in carbon fiber continuous sucker rods was developed.The model took the impact of rod vibration into account.Calculation results showed errors in calculated stroke losses were reduced from 33.1% of the conventional method to the present level of 3.6%, which can effectively satisfy accuracy requirement related to calculating stroke losses.Research results indicated the innovative calculation model could effectively remove problems related to significant errors and inaccurate adjustment of stoke tolerances in stoke loss calculation in carbon fiber continuous sucker rods.
Key words: carbon fiber     continuous sucker rod     stroke loss     structure     temperature     vibration

1 常规冲程损失计算方法存在的问题

“三抽”系统通常指抽油机、抽油杆和抽油泵，该系统中的冲程损失，是导致实际产液量小于理论产液量的重要因素[17]。在“三抽”系统中，游动阀与固定阀随着上、下冲程的变换交替开启、闭合，泵柱塞上方的液柱载荷在抽油杆柱、油管上交替转移，引起抽油杆柱和油管柱载荷的交替增减，使得上、下冲程抽油杆柱与油管柱的变形量不相等，导致抽油泵柱塞的实际行程小于抽油机的光杆冲程，该差值即为“三抽”系统的冲程损失。

“三抽”系统冲程损失的常规计算方法，是将抽油杆按照轴向划分为无数微小单元，在有液柱载荷及无液柱载荷的情况下，分别计算各微小单元变形量的总和，两者差值即“三抽”系统在作业中产生的冲程损失。

1) 给抽油杆划分微元(如图 1所示)，沿x轴向将抽油杆划分为以dx为单元的微元模型。

 图 1 碳纤维连续抽油杆微元示意 Fig.1 Schematic diagram of the micro-elements in carbon fiber sucker rod

2) 对微元积分来计算上、下冲程微元变形量总和。上冲程抽油杆变形量计算式为：

 (1)

 (2)

 (3)

 (4)

2 碳纤维连续抽油杆冲程损失计算模型 2.1 考虑结构特征的影响

 图 2 碳纤维连续抽油杆的基本结构 Fig.2 The basic structure of a carbon fiber continuous sucker rod

 (5)

F作用下，碳纤维连续抽油杆中的碳纤维复合材料和包覆层材料同时产生变形，且变形量大小相同。由此可知：

 (6)
 (7)

 (8)
 (9)

 (10)
2.2 考虑温度的影响

 图 3 聚四氟乙烯弹性模量随温度的变化曲线 Fig.3 Changes in elastic modulus of PTFE related to temperatures

 (11)

 图 4 碳纤维复合材料的弹性模量随温度的变化曲线 Fig.4 Changes in elastic modulus of carbon fiber composite materials with temperatures

 (12)

 (13)

 (14)

 (15)

 (16)

 (17)

 (18)

 (19)
 (20)

2.3 考虑振动的影响

 图 5 两级抽油杆的振动模型 Fig.5 Vibration model of the two-stage sucker rod

 (21)

k1k2并联，则其可等效为k4，因此由式(21) 可得：

 (22)

 (23)

k4k3串联，可进一步等效为k, 则：

 (24)

 (25)

 (26)

 (27)

 (28)

 (29)

 (30)
3 实例分析

 图 6 井例实测示功图 Fig.6 Measured lindicator diagram of testing well

4 结论

1) 碳纤维连续抽油杆由碳纤维复合材料和包覆材料组成，其弹性模量应为碳纤维复合材料和包覆材料复合的弹性模量。

2) 用计算钢质抽油杆冲程损失的方法计算碳纤维连续抽油杆的冲程损失时，若不考虑碳纤维连续抽油杆的结构特征而简单地用碳纤维一种材料的弹性模量，且不考虑振动对冲程损失带来的影响，则其计算结果误差较大。

3) 建立的适用于碳纤维连续抽油杆冲程损失的计算模型，其计算误差仅为3.6%，与常规计算方法的误差33.1%相比，精度明显提高，可以满足碳纤维连续抽油杆现场使用的要求。

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#### 文章信息

ZHANG Hao, YANG Yong, QI Yaoguang, PAN Long, MAO Zhengyi

Method for Calculation of Stroke Losses in Carbon Fiber Continuous Sucker Rods

Petroleum Drilling Techniques, 2017, 45(3): 95-101.
http://dx.doi.org/10.11911/syztjs.201703017