应力松弛作用对未固结砂岩等效弹性性质的影响
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摘要
未固结碎屑砂岩储层是国内外重要的油气储层类型之一,其物理本质是由离散颗粒组成的软凝聚态物质。在地震勘探中通常使用Hertz-Mindlin等效介质模型来计算未固结砂岩的地震弹性特征,但该模型在使用中通常会得到明显偏高的剪切模量值。基于3D离散元技术,对颗粒介质在单轴压缩与纯剪两种过程中的力学响应进行离散元数值模拟,从微观颗粒尺度和细观力链尺度分析等效介质模型产生预测误差的可能机制。结果表明:颗粒相对滑动、旋转、重排列等造成的应力松弛作用对体积模量计算结果的影响较弱,但在剪应力扰动下这种松弛作用所形成的细观不均匀应变对剪切模量的计算会有明显影响,是等效介质模型形成预测误差的主要原因。在此基础上给出了利用切向刚度校正因子C及组合参数R珚/R对Hertz-Mindlin等效介质模型进行修正的方法,以考虑颗粒间松弛作用及颗粒不规则性对该模型计算结果的影响,并应用于实际测井资料中验证了方法的正确性。
In the seismic exploration,effective medium theories based on Hertz-Mindlin equivalent medium model were often used to predict the seismic elastic properties of unconsolidated sands.But those theories often give relative larger shear modulus comparing to measured data.By using 3D discrete element simulation,a series of uniaxial compression and pure shear test were carried out on granular material for the sake to study the insufficiencies of those effective medium theories from the level of microscale of particle size and mesoscale of force chain.The simulation result indicates that stress relaxation getting from the rotation and rearrangements of particles has neglect influences on the calculation of bulk modulus.But the stress relaxation has significant influences on the calculation of shear modulus under the shear stress perturbation.Shear stiffness calibration factor(C) and combined parameter /R were advocated to calibration those effective medium theories based on Hertz-Mindlin equivalent medium model to accounting for the influence of relaxation in contact area and grain angularity.
In the seismic exploration,effective medium theories based on Hertz-Mindlin equivalent medium model were often used to predict the seismic elastic properties of unconsolidated sands.But those theories often give relative larger shear modulus comparing to measured data.By using 3D discrete element simulation,a series of uniaxial compression and pure shear test were carried out on granular material for the sake to study the insufficiencies of those effective medium theories from the level of microscale of particle size and mesoscale of force chain.The simulation result indicates that stress relaxation getting from the rotation and rearrangements of particles has neglect influences on the calculation of bulk modulus.But the stress relaxation has significant influences on the calculation of shear modulus under the shear stress perturbation.Shear stiffness calibration factor(C) and combined parameter /R were advocated to calibration those effective medium theories based on Hertz-Mindlin equivalent medium model to accounting for the influence of relaxation in contact area and grain angularity.
引文
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[3]Winkler K W.Contact stiffness in granular and porousmaterials:comparison between theory and experiment[J].Geophysical Research Letters,1983,10:1073-1076.
[4]Zimmer M A,Prasad M,Mavko G,et al.Seismicvelocities of unconsolidated sands:part 1.presssuretrends from 0.1to 20MPa[J].Geophysics,2007,72(1):E1-E13.
[5]Makse H A,Gland N,Johnson D L,et al.Granularpacking:nonlinear elasticity,sound propagation andcollective relaxation dynamics[J].Physical Review E,2004,70:1-19.
[6]Johnson D L,Makse H A,Gland N,et al.Nonlinearelasticity of granular media[J].Physica B,2000,279:134-138.
[7]Bachrach R,Dvorkin J,Nur A.Seismic velocities andPoisson’s ratio of shallow unconsolidated sands[J].Geophysics,2000,65:559-564.
[8]Cundall P A,Strack O D L.A discrete numerical me-thod for granular assemblies[J].Geotechnique,1979,29(1):47-65.
[9]Majaudar T S,Behringer R P.Contact force measure-ments and stress-induced anisotropy in granularmaterials[J].Nature,2005,23:1079-1082.
[10]徐泳,孙其诚,张凌,等.颗粒离散元法研究进展[J].力学进展,2003,33(2):250-260.XU Yong,SUN Qi-cheng,ZHANG Ling,et al.Advances in discrete element methods for particulatematerials[J].Advances in Mechanics,2003,33(2):250-260.
[11]孙其诚,王光谦.静态堆积颗粒中的力链分布[J].物理学报,2008,57(8):4668-4674.SUN Qi-cheng,WANG Guang-qian.Forcedistribution in static granular matter in twodimensions[J].Acta Physica Sinica,2008,57(8):4668-4674.
[12]戴文亭,陈星,张弘强.粘性土的动力学特性实验及数值模拟[J].吉林大学学报:地球科学版,2008,38(5):831-836.DAI Wen-ting,CHEN Xing,ZHANG Hong-qiang.Experiment and numerical simulation of dynamicbehavior for cohesive soils[J].Journal of JilinUniversity:Earth Science Edition,2008,38(5):831-836.
[13]陈颙,黄庭芳.岩石物理学[M].北京:北京大学出版社,2001.CHEN Yong,HUANG Ting-fang.Rock physics[M].Beijing:Peking University Press,2001.
[14]Mavko G,Mukerji T,Dvorkin J.The rock physicshandbook:tools for seismic analysis in porous media[M].New York:Cambridge University Press,1998:106-160.
[15]Norris A N,Johnson D L.Non-linear elasticity ofgranular media[J].Journal of Applied Mechanics,1997,64:39-49.
[16]Thornton C,Barnes D J.Computer simulated defor-mation of compact granular assemblies[J].ActaMechanica,1986,64(1):45-61.
[17]Brilliantov,Spahn F,Hertzsch J,et al.Model ofcollisions in granular gases[J].Physical Review E,1996,53(5):5382-5392.
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