确定地应力场边界载荷的有限元优化方法研究
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摘要
从弹性力学基本方程出发,针对煤层气储层地应力场反问题,结合对区域地应力场认识,利用阻尼最小二乘法建立了应力场反演的优化约束模型,提出了一种用于反演地应力场边界力的优化分析方法,该方法根据部分实测点的应力值进行边界力反演,并与有限元方法和有限差分法相结合,通过改变边界力参量达到优化逼近目标函数。该方法根据研究区域少量地应力实测资料进行最优化计算,使得计算应力场与实测应力达到最优拟合,以弥补回归反演方法和边界载荷调整法的不足,来提高计算精度。针对沁水盆地少数控制井的地应力大小和方向作为约束条件,计算了区域地应力场,算例证明了该方法的计算精度和可靠性,本文提出的优化方法可有效解决地应力场边界力的反演问题。
The constrained optimization model based on the least square method is established.According to the fundamental equations of elastic mechanics,an optimization inversion method of the boundary load of in-situ stress field of CBM reservoir is proposed.The method combines the finite element and the finite-difference methods together to optimize and approximate the objective function through the variation of boundary load on the basis of the stress value of partial measured points,and eventually the inverse boundary load is obtained.The optimization calculation is performed on the basis of the method which makes the calculated results agree well with the measured data of in-situ stress.This method can overcome the shortage of common back analysis method such as adjusting boundary loads and regression method,so it can improve the calculation precision.Taking the numerical magnitude and azimuth of in-situ stress in a typical well for Qinshui Basin as a constraint,the in-situ stress field has been calculated.The example shows that the proposed method is credible and has high precision,and can effectively solve the boundary load inversion of in-situ stress field.
The constrained optimization model based on the least square method is established.According to the fundamental equations of elastic mechanics,an optimization inversion method of the boundary load of in-situ stress field of CBM reservoir is proposed.The method combines the finite element and the finite-difference methods together to optimize and approximate the objective function through the variation of boundary load on the basis of the stress value of partial measured points,and eventually the inverse boundary load is obtained.The optimization calculation is performed on the basis of the method which makes the calculated results agree well with the measured data of in-situ stress.This method can overcome the shortage of common back analysis method such as adjusting boundary loads and regression method,so it can improve the calculation precision.Taking the numerical magnitude and azimuth of in-situ stress in a typical well for Qinshui Basin as a constraint,the in-situ stress field has been calculated.The example shows that the proposed method is credible and has high precision,and can effectively solve the boundary load inversion of in-situ stress field.
引文
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[16]叶建平,武强,叶贵钧,等.沁水盆地南部煤层气成藏动力学机制研究[J].地质评论,2002,48(3):320–323.(YE Jian-ping,WU Qiang,YE Gui-jun,et al.Study on the coalbed methane reservoir-forming dynamic mechanism in the Southern Qinshui Basin,Shanxi[J].Geological Review,2002,48(3):320–323.(in Chinese))
[2]陈志德,蒙启安,万天丰,等.松辽盆地古龙凹陷地应力场弹塑性增量法数值模拟[J].地学前缘,2002,9(2):483–491.(CHEN Zhi-de,MENG Qi-an,WAN Tian-feng,et al.Numerical simulation of tectonic stress field in Gulong depression in Songliao Basin using elasitic-plastic increment method[J].Earth Science Frontiers,2002,9(2):483–491.(in Chinese))
[3]王薇,王连捷,乔子江,等.三维地应力场的有限元模拟及其在隧道设计中的应用[J].地球学报,2004,25(5):587–591.(WANG Wei,WANG Lian-jie,QIAO Zi-jiang,et al.Modeling of three dimensional crustal stress field and its application in tunnel design[J].Acta Geoscien Sinica,2004,25(5):587–591.(in Chinese))
[4]GIULIO,RAFFAELE ARDITO,ROBERTO FEDELE.Inverse analysis problems in structural engineering of concrete dams[J].Computational Mechanics,2004,9:5–10.
[5]MAIER G,BOCCIARELLI M,BOLZON G,et al.Inverse analysis in fracture mechanics[J].International Journal of Fracture,2006,138:47–73.
[6]闫相祯,杨秀娟,王建军,等.基于多井约束优化方法的低渗透油藏应力场反演与裂缝预测技术及应用[C]//第一届油气田开发技术大会.北京:石油工业出版社,2005:142–148.(YAN Xiang-zhen,YANG Xiu-juan,WANG Jian-jun,et al.Stress field inversion,fracture prediction technique and application of low permeability reservoir based on multi-well constrained optimization method[C]//The Frist Oil and Gas Field Development Technology Congress.Beijing:Petroleum Industry Press,2005:142–148.(in Chinese))
[7]薛履中.工程最优化技术[M].天津:天津大学出版社,1998:50–62.(XUE Lü-zhong.Engineering optimum programming technologies[M].Tianjing:Tianjing University Press,1998:50–62.(in Chinese))
[8]傅雪海,秦勇,姜波,等.山西沁水盆地中—南部煤储层渗透率物理模拟与数值模拟[J].地质科学,2003,38(2):221–229.(FU Xue-hai,QIN Yong,JIANG Bo,et al.Physical and numerical simulations of permeability of coal reservoirs in Central and Southern part of the Qinshui Basin,Shanxi[J].Chinese Journal of Geology,2003,38(2):221–229.(in Chinese))
[9]王杏尊,刘文旗,孙延罡,等.煤层气井压裂技术的现场应用[J].石油钻采工艺,2001,23(2):58–61.(WANG Xing-zun,LIU Wen-qi,SUN Yan-gang,et al.Field testing of fracturing techanolgy in coal formed gas well[J].Oil Drilling&Production Technology,2001,23(2):58–61.(in Chinese))
[10]贺天才,秦勇.煤层气勘探与开发利用技术[M].徐州:中国矿业大学出版社,2007:64–67.(HE Tian-cai,QIN Yong.Technologies of coal bed methane exploration and develoment[M].Xuzhou:China University of Mining and Technology Press,2007:64–67.(in Chinese))
[11]刘洪林,王勃,王烽,等.沁水盆地南部地应力特征及高产区带预测[J].天然气地球科学,2007,18(6):885–890.(LIU Hong-lin,WANG Bo,WANG Feng,et al.Ground stress characteristics and prediction of hign productivity zones in South of Qinshui Basin[J].Natural Gas Geoscience,2007,18(6):885–890.(in Chinese))
[12]傅雪海,秦勇,李贵中.沁水盆地中—南部煤储层渗透率主控因素分析[J].煤田地质与勘探,2001,29(3):16–19.(FU Xue-hai,QIN Yong,LI Gui-zhong.An analysis on the principal control factor of coal reservoir permeability in Central and Southern Qin shui Basin[J].Coal Geology&Exploration,2001,29(3):16–19.(in Chinese))
[13]刘巍,赵新平,安卫平,等.山西地区的震源机制结果[J].山西地震,1993(2):7–12.(LIU Wei,ZHAO Xin-ping,AN Wei-ping,et al.Focal mechanism of Shanxi region[J].Earthquake Research in Shanxi,1993(2):7–12.(in Chinese))
[14]单学军,张士诚,李安启,等.煤层气井压裂裂缝扩展规律分析[J].天然气工业,2005,25(1):130–132.(SHAN Xue-cheng,ZHANG Shi-cheng,LI An-qi.Analyzing the fracture extended law of hydraulic fracturing in coalbed gas wells[J].Natural Gas Industry,2005,25(1):130–132.(in Chinese))
[15]张培河.沁水煤田煤储层压力分布特征及影响因素分析[J].煤田地质与勘探,2002,30(6):31–32.(ZHANG Pei-he.Characters of distribution and influencing factors about the reservoir pressure in Qinshui Coalfield[J].Coal Geology&Exploration,2002,30(6):31–32.(in Chinese))
[16]叶建平,武强,叶贵钧,等.沁水盆地南部煤层气成藏动力学机制研究[J].地质评论,2002,48(3):320–323.(YE Jian-ping,WU Qiang,YE Gui-jun,et al.Study on the coalbed methane reservoir-forming dynamic mechanism in the Southern Qinshui Basin,Shanxi[J].Geological Review,2002,48(3):320–323.(in Chinese))
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