﻿ 温度与压力作用下页岩气井环空带压力学分析

Annulus Pressure Analysis of a Shale Gas Well under Varied Temperatures and Pressures
LIU Kui, GAO Deli, ZENG Jing, FANG Jun, WANG Yanbin
MOE Key Laboratory of Petroleum Engineering(China University of Petroleum(Beijing)), Beijing, 102249, China
Abstract: With consideration of the severe problems related to annulus pressure in shale gas wells, mechanical analysis were performed to clarify the impact of changes in temperatures and pressures during fracturing and production on the annulus pressure in shale gas wells.According to elastic mechanical theories, a mechanical model of a double casing system was established.The formula in calculating the stress of each contact surface was derived based on a displacement continuity condition.In addition, the impact of casing internal pressures, temperatures and in-situ stresses on the sealing ability of a cement sheath were reviewed.Research results suggest that the increase in temperatures, internal pressures, in-situ stresses, and elastic modulus of cement are beneficial and may improve the sealing ability of the cement sheath.On the other hand, decreasing casing thicknesses can be damaging because it increases the radial stress on the interfaces.Radial stresses on interfaces may increase with well depths, so the key to relieving the annulus pressure in the wellhead is to improve the sealing ability of the cement in the lower section of the vertical well.The first and second interfaces are the dangerous positions and they are where there is maximum risk of cementing failure.Improving the cementing quality of the first and second interfaces is helpful in reducing the risk of annulus pressure generation.
Key words: temperature     pressure     shale gas well     annulus pressure     double layer casing     cement sheath     radial stress

1 力学模型

 图 1 页岩气储层内流体流动情况示意 Fig.1 Fluid flow in a shale gas formation

 图 2 页岩气井双层套管应力分析模型 Fig.2 Stress analysis model for a double casing system in a shale gas well

2 应力计算 2.1 界面径向应力计算

 (1)

ρ1=ρ2=b时，ur1=ur2，代入式(1) 化简可得：

 (2)

ρ2=ρ3=c时，ur2=ur3，代入式(1) 化简可得：

 (3)

ρ3=ρ4=d时，ur3=ur4，代入式(1) 化简可得：

 (4)

ρ4=ρ5=e时，ur4=ur5，代入式(1) 化简可得：

 (5)

2.2 温度应力计算

 (6)

 (7)

i界面处的温度为tii=1，2，3，4。生产套管内温度为t0，地层温度为t5，圆环i的导热系数为λi(i=1，2，3，4，5)。单位长度圆筒的导热热流量Φ的计算公式为：

 (8)

 (9)

 (10)

 (11)

3 敏感性分析

3.1 温度变化对径向应力的影响

 图 3 界面径向应力与井筒内温度的关系 Fig.3 Correlation between radial stress on interfaces and casing internal temperature
 图 4 双层套管系统温度变化曲线 Fig.4 Temperature variation in adouble casing system

3.2 套管内压对径向应力的影响

 图 5 套管内压与界面径向应力的关系 Fig.5 Correlation between the radial stress on interfaces and internal pressure of casing

 图 6 地应力与界面径向应力的关系 Fig.6 Correlation between radial stress on interfaces and in-situ stress

3.3 套管壁厚对径向应力的影响

 图 7 内层套管壁厚与界面应力的关系 Fig.7 Correlation between radial stress on interfaces and thickness of internal casing
 图 8 外层套管壁厚与界面应力的关系 Fig.8 Correlation between radial stress on interfaces and thickness of external casing

3.4 水泥环弹性模量对径向应力的影响

 图 9 水泥环弹性模量与界面径向应力的关系 Fig.9 Correlation between radial stress on interfaces and elastic modulus of cement sheath

4 算例分析

 图 10 页岩气井压裂过程中界面径向应力与井深的关系 Fig.10 Correlation between radial stress on interfaces and well depth in shale gas wells during fracturing
 图 11 页岩气井生产过程中界面径向应力与井深的关系 Fig.11 Correlation between radial stress on interfaces and well depth in shale gas well during development

5 结论

1) 通过建立的双层套管系统各界面应力和温度变化计算模型，分析计算了内压及温度变化对页岩气井直井段井眼系统各界面上应力的影响。结果发现，井深越深, 水泥环封隔能力越强，提高直井段下部水泥环的封隔能力是提高整个井筒环空水泥环封隔能力的关键。

2) 温度升高、套管壁厚减小均有利于增大界面的径向应力，在满足套管强度要求的前提下可适当减小套管壁厚；增加水泥环弹性模量有利于增大界面径向应力，但同时因套管周向应力变大而发生挤毁套管的概率增大，因此，应综合考虑优选水泥环弹性模量。

3) 井深较深处第一界面和第二界面的径向应力较小，是水泥环封隔失效的危险点，提高第一界面和第二界面的固井质量，有利于降低页岩气井形成环空带压的风险。

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#### 文章信息

LIU Kui, GAO Deli, ZENG Jing, FANG Jun, WANG Yanbin

Annulus Pressure Analysis of a Shale Gas Well under Varied Temperatures and Pressures

Petroleum Drilling Techniques, 2017, 45(3): 8-14.
http://dx.doi.org/10.11911/syztjs.201703002