多孔固体充满黏性流体时的边界条件

M·D·夏玛

doi:10.3879/j.issn.1000-0887.2009.07.002

多孔固体充满黏性流体时的边界条件

doi: 10.3879/j.issn.1000-0887.2009.07.002

M·D·夏玛

库鲁克西查大学数学系,136 119,印度

详细信息

中图分类号: O347.4⁺¹;O357.3
计量
- 文章访问数: 1725
- HTML全文浏览量: 152
- PDF下载量: 749
- 被引次数: 0
出版历程
- 收稿日期: 2008-07-29
- 修回日期: 2009-04-28
- 刊出日期: 2009-07-15

Boundary Conditions for Porous Solids Saturated With Viscous Fluid

M. D. Sharma

Department of Mathematics, Kurukshetra University, India-136 119

摘要

摘要: 基于物理学基本原理和能量守恒定律的精确检查，导出充满黏性流体多孔固体边界呈连续性要求的边界条件．当孔隙流体具有黏性时，多孔弹性固体就是一个耗散的充满黏性流体的多空固体．孔隙流体的黏性造成的耗散应力准确地表达了边界条件．边界上两种固体连接的不完全，导致孔隙流体的流出，多孔骨料两边微粒运动的不平衡．导出多孔-多孔固体界面孔隙局部连接时的数学模型．在该界面上，滑移的松-紧，以及孔隙开-合，能造成一部分应变能的耗散．数值结果表明，在水和饱和油砂岩之间的界面上，修正的边界条件将影响各向同性多孔介质中折射波的能量．
- 多孔固体 /
- 耗散 /
- 边界条件 /
- 流-固耦合问题 /
- 广义Darcy定律
Abstract: Boundary conditions were derived to represent the continuity requirements at the boundaries of a porous solid saturated with viscous fluid.These were derived from the physically grounded principles with a mathematical check on the conservation of energy.The poroelastic solid is a dissipative one,for the presence of viscosity in inter stitial fluid.The dissipative stresses due to the viscosity of pore-fluid,are well represented in the boundary conditions.The unequal particle motions of two constituents of porous aggregate at a boundary between two solids were explained interms of drainage of pore-fluid leading to imperfect bonding.Mathematical model was derived for the partial connection of surface pores at the porous-porous interface.At this interface,the loose-contact slipping and partial pore opening/connection may dissipate a part of strain energy.Numerical example shows that,at the interface between water and oil-saturated sandstone,the modified boundary conditions do affect the energies of the waves refracting into the isotropic porous medium.
- porous solid /
- dissipative /
- boundary conditions /
- fluid-solid coupling /
- Darcy law

HTML全文

参考文献(21)

[1]	Biot M A. The theory of propagation of elastic waves in a fluid-saturated porous solid—Ⅰ：low~frequency range；Ⅱ：higher frequency range[J].J Acoust Soc Am,1956,28(2):168-191. doi: 10.1121/1.1908239
[2]	Biot M A. Mechanics of deformation and acoustic propagation in porous media[J].J Appl Phys,1962,33（4）:1482-1498. doi: 10.1063/1.1728759
[3]	Biot M A. Generalized theory of acoustic propagation in porous dissipative media[J].J Acoust Soc Am,1962,34（9A）:1254-1264. doi: 10.1121/1.1918315
[4]	Deresiewicz H, Skalak R. On uniqueness in dynamic poroelasticity[J].Bull Seism Soc Am,1963,53（4）:793-799.
[5]	Dutta N C, Ode H. Seismic reflections from a gas-water contact[J].Geophysics,1983,48（2）:148-162. doi: 10.1190/1.1441454
[6]	Lovera O M. Boundary conditions for a fluid-saturated porous solid[J].Geophysics,1987,52（2）:174-178. doi: 10.1190/1.1442292
[7]	De La Cruz V, Spanos T J T.Seismic boundary conditions for porous media[J].J Geophys Res, 1989,94（B3）:3025-3029. doi: 10.1029/JB094iB03p03025
[8]	Sharma M D, Saini T N. Pore alignment between two dissimilar saturated poroelastic media:reflection and refraction at the interface[J].Int J Solids Struct,1992,29（11）:1361-1377. doi: 10.1016/0020-7683(92)90084-7
[9]	Gurevich B, Schoenberg M. Interface conditions for Biot′s equations of poroelasticity[J].J Acoust Soc Am,1999,105（5）:2585-2589. doi: 10.1121/1.426874
[10]	Denneman A I M, Drijkoningen G G, Smeulders D M J,et al.Reflection and transmission of waves at a fluid/porous medium interface[J].Geophysics,2002,67（1）:282-291. doi: 10.1190/1.1451800
[11]	Auriault J L. Dynamic behavior of a porous medium saturated by a Newtonian fluid[J]. Int J Engng Sci,1980,18（6）:775-785. doi: 10.1016/0020-7225(80)90025-7
[12]	Burridge R, Keller J B. Poroelasticity equations derived from microstructure[J].J Acoust Soc Am,1981,70（4）:1140-1147. doi: 10.1121/1.386945
[13]	Pride S R, Gangi A F, Morgan F D. Deriving the equations of motion for porous isotropic media[J].J Acoust Soc Am,1992,92（6）:3278-3290. doi: 10.1121/1.404178
[14]	Deresiewicz H, Rice J T. The effect of boundaries on wave propagation in a liquid-filled porous solid—Ⅲ：reflection of plane waves at a free plane boundary (general case)[J].Bull Seism Soc Am,1962,52（3）:595-625.
[15]	Chen J. Time domain fundamental solution to Biot′s complete equations of dynamic poroelasticity—part Ⅰ:two-dimensional solution[J].Int J Solids Struct,1994,31（10）:1447-1490. doi: 10.1016/0020-7683(94)90186-4
[16]	Sharma M D. 3-D wave propagation in a general anisotropic poroelastic medium:reflection and refraction at an interface with fluid[J].Geophys J Int,2004,157（2）:947-957. doi: 10.1111/j.1365-246X.2004.02226.x
[17]	Sharma M D. Wave propagation in a general anisotropic poroelastic medium with anisotropic permeability:phase velocity and attenuation[J].Int J Solids Struct,2004,41（16/17）:4587-4597. doi: 10.1016/j.ijsolstr.2004.02.066
[18]	Morse P M, Feshbach H.Methods of Theoretical Physics[M].New York：McGraw-Hill, 1953.
[19]	Vashisth A K, Sharma M D, Gogna M L. Reflection and transmission of elastic waves at a loosely bonded interface between an elastic solid and liquid-saturated porous solid[J]. Geophys J Int,1991,105(3):601-617. doi: 10.1111/j.1365-246X.1991.tb00799.x
[20]	Borcherdt R D. Reflection-refraction of type-Ⅱ S waves in elastic and inelastic media[J].Bull Seism Soc Am,1977,67:43-67.
[21]	Rasolofosaon P N J, Zinszner B E. Comparison between permeability anisotropy and elasticity anisotropy of reservoir rocks[J].Geophysics,2002,67(1):230-240. doi: 10.1190/1.1451647