Abstract：To simulate the evolution of wellbore creep accurately, predict and prevent severe accidents such as borehole wall sloughing, casing collapse and sticking of the drill, based on previous studies, the springpot element was introduced into the classical element model and the creep compliances of the fractional constitutive models were deduced. The good fitting effect of fractional constitutive model was verified. The study shows the fractional constitutive model can simulate creep with high accuracy and less input parameters, and the physical significance of the input parameters are clearer. According to the correspondence principle of viscoelastic theory, a wellbore creep model including drilling and killing processes was built up. By adjusting the value of fractional orders, the model can transform between the models of ideal elastic material and standard solid, which implies the classical wellbore shrinkage model based on standard solid model and ideal elastic model are just special cases of this model. If the fractional order is adjusted, the creep curve will change asymmetrically, which can be can be regulated by the speeding up of the transient creep and lowering the rate of steady creep, which can not be accomplished by adjusting one parameter in the classical models. The fractional constitutive model can fit complicated non-linear creep experiment data better than other models.
彭瑀, 赵金洲, 李勇明. 基于分数阶黏弹性本构方程的井眼蠕变模型[J]. 石油勘探与开发, 2017, 44(6): 982-988.
PENG Yu, ZHAO Jinzhou, LI Yongming. A wellbore creep model based on the fractional viscoelastic constitutive equation. Petroleum Exploration and Development, 2017, 44(6): 982-988.
[1] 赵贤正, 杨延辉, 孙粉锦, 等. 沁水盆地南部高阶煤层气成藏规律与勘探开发技术[J]. 石油勘探与开发, 2016, 43(2): 303-309. ZHAO Xianzheng, YANG Yanhui, SUN Fenjin, et al. Enrichment mechanism and exploration and development technologies of high rank coalbed methane in south Qinshui Basin, Shanxi Province[J]. Petroleum Exploration and Development, 2016, 43(2): 303-309. [2] CHANG C, ZOBACK M D. Creep in unconsolidated shale and its implication on rock physical properties[C]. San Francisco: American Rock Mechanics Association, 2008. [3] LIU X, BIRCHWOOD R, HOOYMAN P J. A new analytical solution for wellbore creep in soft sediments and salt[C]. San Francisco: American Rock Mechanics Association, 2011. [4] 郭彤楼. 中国式页岩气关键地质问题与成藏富集主控因素[J]. 石油勘探与开发, 2016, 43(3): 317-326. GUO Tonglou. Key geological issues and main controls on accumulation and enrichment of Chinese shale gas[J]. Petroleum Exploration and Development, 2016, 43(3): 317-326. [5] SCHOENBALL M, SAHARA D P, KOHL T. Time-dependent brittle creep as a mechanism for time-delayed wellbore failure[J]. International Journal of Rock Mechanics and Mining Sciences, 2014, 70(9): 400-406. [6] 吴超, 刘建华, 张东清, 等. 基于地震波阻抗的预探井随钻井壁稳定预测[J]. 石油勘探与开发, 2015, 42(3): 390-395. WU Chao, LIU Jianhua, ZHANG Dongqing, et al. A prediction of borehole stability while drilling preliminary prospecting wells based on seismic impedance[J]. Petroleum Exploration and Development, 2015, 42(3): 390-395. [7] CAO Y, DENG J, YU B, et al. Analysis of sandstone creep and wellbore instability prevention[J]. Journal of Natural Gas Science and Engineering, 2014, 19(7): 237-243. [8] NOPOLA J R, ROBERTS L A. Time-dependent deformation of Pierre Shale as determined by long-duration creep tests[C]. Houston: American Rock Mechanics Association, 2016. [9] MIGHANI S, TANEJA S, SONDERGELD C H, et al. Nanoindentation creep measurements on shale[C]. San Francisco: American Rock Mechanics Association, 2015. [10] ORLIC B, BUIJZE L. Numerical modeling of wellbore closure by the creep of rock salt caprocks[C]. Minneapolis: American Rock Mechanics Association, 2014. [11] RASSOULI F S, ZOBACK M D. A comparison of short-term and long-term creep experiments in unconventional reservoir formations[C]. Houston: American Rock Mechanics Association, 2016. [12] 陈文. 力学与工程问题的分数阶导数建模[M]. 北京: 科学出版社, 2010. CHEN Wen. Fractional differential modeling of the problems of mechanics and engineering[M]. Beijing: Science Press, 2010. [13] UCHAIKIN V V. Fractional derivatives for physicists and engineers[M]. Berlin: Springer, 2013. [14] YIN D, WU H, CHENG C, et al. Fractional order constitutive model of geomaterials under the condition of triaxial test[J]. International Journal for Numerical & Analytical Methods in Geomechanics, 2013, 37(8): 961-972. [15] PALOMARES-RUIZ J E, RODRIGUEZ-MADRIGAL M, CASTRO LUGO J G, et al. Fractional viscoelastic models applied to biomechanical constitutive equations[J]. Revista Mexicana De Física, 2015, 61(4): 261-267. [16] WU F, LIU J F, WANG J. An improved Maxwell creep model for rock based on variable-order fractional derivatives[J]. Environmental Earth Sciences, 2015, 73(11): 6965-6971. [17] ZHOU H W, WANG C P, HAN B B, et al. A creep constitutive model for salt rock based on fractional derivatives[J]. International Journal of Rock Mechanics and Mining Sciences, 2011, 48(1): 116-121. [18] 张千贵, 梁永昌, 范翔宇, 等. 基于能量守恒定律对西原模型的改进与验证[J]. 重庆大学学报(自然科学版), 2016, 39(3): 117-124. ZHANG Qiangui, LIANG Yongchang, FAN Xiangyu, et al. A modified Nishihara model based on the law of the conservation of energy and experimental verification[J]. Journal of Chongqing University (Natural Science Edition), 2016, 39(3): 117-124. [19] MUSTO M, ALFANO G. A fractional rate-dependent cohesive-zone model[J]. International Journal for Numerical Methods in Engineering, 2015, 103(5): 313-341. [20] PAOLA M D, PIRROTTA A, VALENZA A. Visco-elastic behavior through fractional calculus: An easier method for best fitting experimental results[J]. Mechanics of Materials, 2011, 43(12): 799-806. [21] 殷德顺, 任俊娟, 和成亮, 等. 一种新的岩土流变模型元件[J]. 岩石力学与工程学报, 2007, 26(9): 1899-1903. YIN Deshun, REN Junjuan, HE Chengliang, et al. A new rheological model element for geomaterials[J]. Chinese Journal of Rock Mechanics and Engineering, 2007, 26(9): 1899-1903. [22] CHRISTENSEN R M. Theory of viscoelasticity: An introduction[M]. New York: Academic Press, 1982. [23] 陈德坤. 钢-混凝土组合结构的应力重分布与蠕变断裂[M]. 上海: 同济大学出版社, 2006. CHEN Dekun. Stress redistribution and creep rupture of integral structure of steel and concrete[M]. Shanghai: Tongji University Press, 2006. [24] 李卓. 粘弹性分数阶导数模型及其在固体发动机上的应用[D]. 北京: 清华大学, 2000. LI Zhuo. Viscoelastic fractional derivative model and its application on solid rocket motor[D]. Beijing: Tsinghua University, 2000. [25] 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. Petroleum engineering rock mechanics[M]. Beijing: Science Press, 2008.
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