为解决石油天然气钻井、地热钻井中深部地层井眼稳定问题,基于连续介质弹性力学建立深部地层井眼稳定平面应变问题的基本微分方程,采用边界元理论推导了井周应力和位移的边界元求解方法;通过建立井眼稳定物理模型、划分边界单元,将求解出的井周应力结果与解析解进行对比;分析了四川某油田深部地层井眼的稳定性情况。结果表明:BEM 求解应力分布与解析解吻合较好,其误差小于0.82%;实例井2500~3500 m 井段井眼稳定性分析结果与实际情况基本一致,实际钻井液密度低于坍塌压力当量密度,导致井眼扩大率普遍达到20%以上,适当提高钻井液密度能够维持井眼稳定,进一步验证了BEM 方法的准确性。该方法为井眼稳定分析提供了一种新的手段和方法。
To study the borehole stability problem of oil and gas drilling and geothermal drilling in deep formations, a basic differential equation of plane strain problem for borehole stability in deep formation is proposed on the basis of the continuum mechanics of elasticity, and a BEM calculation method of stress and displacement distribution around the wellbore is derived by using the BEM theory. To test the correctness of the BEM method, a physical model and the boundary elements of borehole stability problem are established, then the stress solution around the wellbore is compared with the analytical solution. By analyzing the borehole stability problem of deep formation in a certain oilfield of Sichuan, it is shown that the stress distribution with the BEM method is in good agreement with analytical solution, and its error is less than 0.82%. The borehole stability analysis results are basically in accord with the actual situation at 2500-3500 m in the example well, the actual drilling fluid density is lower than the equivalent density of the collapse pressure, and the hole expanding rate is above 20%. Increasing the density of drilling fluid can maintain wellbore stability, thus the accuracy of the BEM method is further verified. This method provides a new means for wellbore stability analysis.
[1] 郤保平, 赵阳升. 高温高压下花岗岩中钻孔围岩的热物理及力学特性试验研究[J]. 岩石力学与工程学报, 2010, 29(6): 1245-1253. Xi Baoping, Zhao Yangsheng. Experimental study of thermophysicomechanical property of drilling surrounding rock in granite under high temperature and high pressure[J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 29(6): 1245-1253.
[2] 苏德辰, 杨经绥. 国际大陆科学钻探(ICDP)进展[J]. 地质学报, 2010, 84(6): 873-886. Su Dechen, Yang Jingsui. Advances of international continental scientific drilling program[J]. Acta Geologica Sinica, 2010, 84(6): 873- 886.
[3] 郤保平, 赵金昌, 赵阳升, 等. 高温岩体地热钻井施工关键技术研究[J]. 岩石力学与工程学报, 2011, 30(11): 2234-2243. Xi Baoping, Zhao Jinchang, Zhao Yangsheng, et al. Key technologies of hot dry rock drilling during construction[J]. Chinese Journal of Rock Mechanics and Engineering, 2011, 30(11): 2234-2243.
[4] 陈勉, 金衍, 张广清. 石油工程岩石力学[M]. 北京: 科学出版社, 2008. Chen Mian, Jin Yan, Zhang Guangqing. Rock mechanics on petroleum engineering[M]. Beijing: Science Press, 2008.
[5] Lu Y H, Chen M, Jin Y, et al. Influence of porous flow on wellbore stability for an inclined well with weak plane formation[J]. Petroleum Science and Technology, 2013, 31(6): 616-624.
[6] 崔杰, 焦永树, 曹维勇, 等. 各向异性地层中井孔周围应力场的研究[J]. 工程力学, 2011, 28(7): 31-36. Cui Jie, Jiao Yongshu, Cao Weiyong, et al. A study on the stress field around a borehole in anisotropic formation[J]. Engineering Mechanics, 2011, 28(7): 31-36.
[7] 殷有泉, 陈朝伟. 用稳定性理论和方法研究井壁坍塌问题[J]. 北京大学学报: 自然科学版, 2009, 45(4): 559-564. Yin Youquan, Chen Zhaowei. Study on wellbore collapse using the theory and method of stability[J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2009, 45(4): 559-564.
[8] Roshan H, Rahman S S. The effect of water content on stress changes around a wellbore drilled in a chemically active elastoplastic formation[J]. Petroleum Science and Technology, 2013, 31(20): 2118-2126.
[9] 盛金昌, 廖秋林, 刘继山, 等. 基于FEMLAB的钻井过程中流固热耦合响应分析[J]. 工程力学, 2008, 25(2): 219-223, 229. Sheng Jinchang, Liao Qiulin, Liu Jishan, et al. Analysis of coupled porothermoelastic response of a wellbore by using a FEMLAB-based simulator[J]. Engineering Mechanics, 2008, 25(2): 219-223, 229.
[10] 王倩, 周英操, 王刚, 等. 泥页岩井壁稳定流固化耦合模型[J]. 石油勘探与开发, 2012, 39(4): 475-480. Wang Qian, Zhou Yingcao, Wang Gang, et al. A fluid-solid-chemistry coupling model for shale wellbore stability[J]. Petroleum Exploration and Development, 2012, 39(4): 475-480.
[11] 屈平, 申瑞臣, 付利, 等. 三维离散元在煤层水平井井壁稳定中的应用[J]. 石油学报, 2011, 32(1): 153-157. Qu Ping, Shen Ruichen, Fu Li, et al. Application of the 3D discrete element method in the wellbore stability of coal-bed horizontal wells[J]. Acta Petrolei Sinica, 2011, 32(1): 153-157.
[12] Zhao H, Chen M, Li Y, et al. Discrete element model for coal wellbore stability[J]. International Journal of Rock Mechanics and Mining Sciences, 2012, 54: 43-46.
[13] 王炳印, 邓金根, 邹灵战, 等. 物理-化学耦合作用下泥页岩坍塌周期应用研究[J]. 石油学报, 2006, 27(3): 130-132. Wang Bingyin, Deng Jingen, Zou Lingzhan, et al. Applied research of collapse cycle of shale in wellbore using a coupled physico-chemical model[J]. Acta Petrolei Sinica, 2006, 27(3): 130-132.
[14] 屈平, 申瑞臣, 付利, 等. 煤层井壁稳定的时间延迟效应探讨[J]. 煤炭学报, 2011, 36(2): 255-260. Qu Ping, Shen Ruichen, Fu Li, et al. Time delay effect on wellbore stability in coal seam[J]. Journal of China Coal Society, 2011, 36(2): 255-260.
[15] 邹灵战, 邓金根, 徐显广, 等. 山前高陡构造节理围岩的井壁失稳机制研究[J]. 岩石力学与工程学报, 2008, 27(增1): 2733. Zhou Lingzhan, Deng Jingen, Xu Xianguang, et al. Study on wellbore collapse mechanism in jointed rock masses of high- dip- structures before mountains[J]. Chinese Journal of Rock Mechanics and Engineering, 2008, 27(Suppl 1): 2733.
[16] 申光宪. 边界元法[M]. 北京: 机械工业出版社, 1998. Shen Guangxian. Boundary element method[M]. Beijing: China Machine Press, 1998.
[17] 邓琴, 郭明伟, 李春光, 等. 基于边界元法的边坡矢量和稳定分析[J]. 岩土力学, 2010, 31(6): 1971-1976. Deng Qin, Guo Mingwei, Li Chunguang, et al. Vector sum method for slope stability analysis based on boundary element method[J]. Rock and Soil Mechanics, 2010, 31(6): 1971-1976.
[18] 张志增, 李仲奎. 横观各向同性岩体中圆形巷道反分析的惟一性[J]. 岩土力学, 2011, 32(7): 2066-2072. Zhang Zhizeng, Li Zhongkui. Uniqueness of displacement back analysis of a circular tunnel in transversely isotropic rock mass[J]. Rock and Soil Mechanics, 2011, 32(7): 2066-2072.
