应力松弛对颗粒物质弹性性质的影响及等效介质模型校正研究
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最偏高的剪切模量值.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/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 seismic exploration,the effective medium theories based on Hertz-Mindlin contact model were often used to predict the seismic elastic properties of unconsolidated sands.But those theories often give 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 with the aim to study the insufficiencies of those effective medium theories from the level of microscale of particle size and mesoscale of force chain.The simulation indicates that stress relaxation resulting from the rotation and rearrangements of particles has negligible 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/R were advocated to calibrate those effective medium theories based on Hertz-Mindlin contact model to accounting for the influence of relaxation in contact area and grain angularity.
In seismic exploration,the effective medium theories based on Hertz-Mindlin contact model were often used to predict the seismic elastic properties of unconsolidated sands.But those theories often give 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 with the aim to study the insufficiencies of those effective medium theories from the level of microscale of particle size and mesoscale of force chain.The simulation indicates that stress relaxation resulting from the rotation and rearrangements of particles has negligible 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/R were advocated to calibrate those effective medium theories based on Hertz-Mindlin contact model to accounting for the influence of relaxation in contact area and grain angularity.
引文
[1]Mindlin R D.Compliance of elastic bodies in contact.Journal of Applied Mechanics,1949,16:259--268
[2]Walton K.The effective elastic moduli of a random packing of spheres.Journal.Mech.Phys.Solids.,1987,35(2): 213-226
[3]Winkler K W.Contact stiffness in granular and porous materials:comparison between theory and experiment. Geophysical Research Letters,1983,10:1073-1076
[4]Zimmer M A,Prasad M,Mavko G,Nut A.Seismic velocities of unconsolidated sands:Part1-Presssure trends from 0.1 to 20 MPa.Geophysics,2007,72(1):1-13
[5]Makse H A,Gland N,Johnson D L,et al.Granular packing:nonlinear elasticity,sound propagation and collective relaxation dynamics.Physical Review E,2004,70 (061302):1-19
[6]Johnson D L,Makse H A,Gland N,et al.Nonlinear elasticity of granular media.PhysicaB,2000,279:134-138
[7]Bachrach R,Dvorkin J,Nur A.Seismic velocities and Poisson's ratio of shallow unconsolidated sands.Geophysics, 2000,65:559-564
[8]Cundall P A,Strack O D L.A discrete numerical method for granular assemblies.Geotechnique,1979,29(1):47--65
[9]Majaudar T S,Behringer R P.Contact force measurements and stress-induced anisotropy in granular materials.Nature, 2005,23:1079-1082
[10]徐泳,孙其诚,张凌等.颗粒离散元法研究进展.力学进展,2003,33(2):250-260 Xu Y,Sun Q C,Zhang L,et al.Advances in discrete element methods for particulate materials.Advances in Mechanics(in Chinese),2003,33(2):250-260
[11]孙其诚,王光谦.静态堆积颗粒中的力链分布.物理学报, 2008,57(8):4668-4674 Sun Q C,Wang G Q.Force distribution in static granular matter in two dimensions.Acta Physiea Sinica(in Chinese), 2008,57(8):4668-4674
[12]陈颙,黄庭芳.岩石物理学.北京:北京大学出版社,2001 Chen Y,Huang T F.Rock Physics(in Chinese).Beijing: Peking University Press,2001
[13]Mavko G,Mukerji T,Dvorkin J.The Rock Physics Handbook:Tools for Seismic Analysis in Porous Media.New York:Cambridge University Press,1998.106- 160
[14]Norris A N,Johnson D L.Non-linear elasticity of granular media.Journal of Applied Mechanics,1997,64:39-49
[15]Thornton C,Barnes D J.Computer simulated deformation of compact granular assemblies.Acta Mechanica,1986,64(1): ??45-61
[16]Brilliantov,Spahn F,Hertzsch J,et al.Model for collisions in granular gases.Physical Review E,1996,53(5):5382- 5392
[17]邓继新,韩德华,王尚旭.未固结砂岩地震弹性性质的岩石物理模型表征研究.石油地球物理勘探,2010,45(2):249- 235 Deng J X,Han D H,Wang S X.Rock physics modeling characteristic studies on seismic elastic properties of unconsolidated sandstone.Oil Geophysical Prospecting, 2010,45(2):249--235
[18]Kruyt N P,Rothenburg L.Kinematic and static assumptions for homogenization in micromechanics of granular materials. Mechanics of Materials,2004,36:1157-1173
[19]Prasad M,Meissner R.Attenuation mechanisms in sands: laboratory versus theoretical(Biot) data.Geophysics,1992, 57:710--719
[20]Tittmann B,Abdel-Gawad M,Salvado C.A brief note on the effect of interface bonding on seismic dissipation. Proceedings of the 12th Lunar and Planetary Science Conference,1981:1737-1745
[21]Deng J X,Wang S X,Han D H.The velocity and attenuation anisotropy of shale at ultrasonic frequency.J. Geophys.Eng.,2009,6:269--278
[2]Walton K.The effective elastic moduli of a random packing of spheres.Journal.Mech.Phys.Solids.,1987,35(2): 213-226
[3]Winkler K W.Contact stiffness in granular and porous materials:comparison between theory and experiment. Geophysical Research Letters,1983,10:1073-1076
[4]Zimmer M A,Prasad M,Mavko G,Nut A.Seismic velocities of unconsolidated sands:Part1-Presssure trends from 0.1 to 20 MPa.Geophysics,2007,72(1):1-13
[5]Makse H A,Gland N,Johnson D L,et al.Granular packing:nonlinear elasticity,sound propagation and collective relaxation dynamics.Physical Review E,2004,70 (061302):1-19
[6]Johnson D L,Makse H A,Gland N,et al.Nonlinear elasticity of granular media.PhysicaB,2000,279:134-138
[7]Bachrach R,Dvorkin J,Nur A.Seismic velocities and Poisson's ratio of shallow unconsolidated sands.Geophysics, 2000,65:559-564
[8]Cundall P A,Strack O D L.A discrete numerical method for granular assemblies.Geotechnique,1979,29(1):47--65
[9]Majaudar T S,Behringer R P.Contact force measurements and stress-induced anisotropy in granular materials.Nature, 2005,23:1079-1082
[10]徐泳,孙其诚,张凌等.颗粒离散元法研究进展.力学进展,2003,33(2):250-260 Xu Y,Sun Q C,Zhang L,et al.Advances in discrete element methods for particulate materials.Advances in Mechanics(in Chinese),2003,33(2):250-260
[11]孙其诚,王光谦.静态堆积颗粒中的力链分布.物理学报, 2008,57(8):4668-4674 Sun Q C,Wang G Q.Force distribution in static granular matter in two dimensions.Acta Physiea Sinica(in Chinese), 2008,57(8):4668-4674
[12]陈颙,黄庭芳.岩石物理学.北京:北京大学出版社,2001 Chen Y,Huang T F.Rock Physics(in Chinese).Beijing: Peking University Press,2001
[13]Mavko G,Mukerji T,Dvorkin J.The Rock Physics Handbook:Tools for Seismic Analysis in Porous Media.New York:Cambridge University Press,1998.106- 160
[14]Norris A N,Johnson D L.Non-linear elasticity of granular media.Journal of Applied Mechanics,1997,64:39-49
[15]Thornton C,Barnes D J.Computer simulated deformation of compact granular assemblies.Acta Mechanica,1986,64(1): ??45-61
[16]Brilliantov,Spahn F,Hertzsch J,et al.Model for collisions in granular gases.Physical Review E,1996,53(5):5382- 5392
[17]邓继新,韩德华,王尚旭.未固结砂岩地震弹性性质的岩石物理模型表征研究.石油地球物理勘探,2010,45(2):249- 235 Deng J X,Han D H,Wang S X.Rock physics modeling characteristic studies on seismic elastic properties of unconsolidated sandstone.Oil Geophysical Prospecting, 2010,45(2):249--235
[18]Kruyt N P,Rothenburg L.Kinematic and static assumptions for homogenization in micromechanics of granular materials. Mechanics of Materials,2004,36:1157-1173
[19]Prasad M,Meissner R.Attenuation mechanisms in sands: laboratory versus theoretical(Biot) data.Geophysics,1992, 57:710--719
[20]Tittmann B,Abdel-Gawad M,Salvado C.A brief note on the effect of interface bonding on seismic dissipation. Proceedings of the 12th Lunar and Planetary Science Conference,1981:1737-1745
[21]Deng J X,Wang S X,Han D H.The velocity and attenuation anisotropy of shale at ultrasonic frequency.J. Geophys.Eng.,2009,6:269--278
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心