含两种不相混流体的饱和孔隙介质的波场模拟(英文)
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摘要
文中对含两种不相混流体的饱和孔隙介质模型进行了波场模拟,该模型基于封闭型系统假设,考虑了流相与固相的相对运动和孔隙率、饱和度(毛细管压力)的松弛机制,可以较好的模拟波场的数值衰减。与目前常用的等效流体方法和基于开敞系统假设的非饱和孔隙介质模型相比,更符合勘探阶段的实际情况。前人对该介质模型平面波的速度和衰减做了一定的研究,但对整个波场的计算研究还未见报道。本文推导了该模型包含毛细管压力和孔隙度松弛机制的波动方程,并利用有限元的方法进行了波场模拟,并对波场特征进行了分析。数值模拟结果表明,在地震频段,非湿相位移波场中慢波p3较为清晰;毛细管压力(饱和度)和孔隙度的松弛效应对非湿相流体位移有较大影响,随松弛系数的增大,位移减小。
Wavefields in porous media saturated by two immiscible fluids are simulated in this paper.Based on the sealed system theory,the medium model considers both the relative motion between the fluids and the solid skeleton and the relaxation mechanisms of porosity and saturation(capillary pressure).So it accurately simulates the numerical attenuation property of the wavefields and is much closer to actual earth media in exploration than the equivalent liquid model and the unsaturated porous medium model on the basis of open system theory.The velocity and attenuation for different wave modes in this medium have been discussed in previous literature but studies of the complete wave-field have not been reported.In our work,wave equations with the relaxation mechanisms of capillary pressure and the porosity are derived.Furthermore,the wavefield and its characteristics are studied using the numerical finite element method.The results show that the slow P3-wave in the non-wetting phase can be observed clearly in the seismic band.The relaxation of capillary pressure and the porosity greatly affect the displacement of the non-wetting phase.More specifically,the displacement decreases with increasing relaxation coefficient.
Wavefields in porous media saturated by two immiscible fluids are simulated in this paper.Based on the sealed system theory,the medium model considers both the relative motion between the fluids and the solid skeleton and the relaxation mechanisms of porosity and saturation(capillary pressure).So it accurately simulates the numerical attenuation property of the wavefields and is much closer to actual earth media in exploration than the equivalent liquid model and the unsaturated porous medium model on the basis of open system theory.The velocity and attenuation for different wave modes in this medium have been discussed in previous literature but studies of the complete wave-field have not been reported.In our work,wave equations with the relaxation mechanisms of capillary pressure and the porosity are derived.Furthermore,the wavefield and its characteristics are studied using the numerical finite element method.The results show that the slow P3-wave in the non-wetting phase can be observed clearly in the seismic band.The relaxation of capillary pressure and the porosity greatly affect the displacement of the non-wetting phase.More specifically,the displacement decreases with increasing relaxation coefficient.
引文
Auriault,J. L.,Boutin,C.,Royer,P.,and Schmitt,D.,2002,Acoustics of a porous medium saturated by a bubbly fluid undergoing phase changes: Transport Porous media,46,43 - 76.
Ba,J.,Cao,H.,Yao,F. C.,Nie,J. X.,and Yang,H. Z.,2008,Double-porosity rock model and squirt flow in thelaboratory frequency band: Applied Geophysics,5(4),261 - 276.
Bedford,A.,and Stern,M.,1982,A model for wave propagation in gassy sediments: J. Acoust. Soc. Am.,73,409 - 417.
Berryman,J. G.,Thigpen,L.,and Chin,R.,1988,Bulk elastic wave propagation in partially saturated porous solids: J. Acoust. Sco. Am.,84 (1),360-373.
Biot,M. A.,1956,Theory of propagation of wave in fiuid-saturated porous solid: J. Acoust. Soc. Am.,28(2),168 - 178.
Carcione,J. M.,Helle,H. B.,and Pham N. H.,2003,White’s model for wave propagation in partially saturated rocks: comparison with poroelastic numerical experiments: Geophysics,68,1389 - 1398.
Carcione,J. M.,Cavalini,F.,Santos,J. E.,Ravazzoli,C. L.,and Gauzellino,P. M.,2004,Wave propagation in partially saturated porous media: simulation of a second wave: Wave Motion,39,227 - 240.
Chao,G.,Smeulders,D. M.,and Dongen,M. E. H.,2006,Dispersive surface waves along partially saturated porous media: J. Acoust. Soc. Am.,119(3),1347 - 1454.
Ciz,R.,and Gurevich,B.,2005,Amplitude of Biot’s slow wave scattered by a spherical inclusion in a fluid-saturated poroelastic medium: Geophys. J. Int.,160,991 - 1005.
Garg,S. K.,and Nayfeh,A. H.,1986,Compressional wave propagation in liquid and/or gas saturated elastic porous media: J. Appl. Phys.,60,3045 - 3055.
Johnson,D. L.,2001,Theory of frequency dependent acoustics in patchy-saturated porous media: J. Acoust. Soc. Am.,110(2),682 - 694.
Lee,M. W.,2004,Elastic velocities of partially saturated unconsolidated sediments: Marine and Petroleum Geology,21,641 - 650.
Lu,J. F.,and Hanyga,A.,2005,Linear dynamic model for porous media saturated by two immiscible fluids: International Journal of Solid and Structure,42,2689 -2709.
Li,X. J.,Liao,Z. P.,and Du,X. L.,1992,An explicit finite difference method for viscoelastic dynamic problem: Journal of Earthquake Engineering and Engineering Vibration (in chinese),12(4),74 - 79.
Liu,Y.,and Wei,X. C.,2008,Finite-difference numerical modeling with even-order accuracy in two-phase anisotropic media: Applied Geophysics,5(2),107 - 114.
Lu,J. F.,Hanyga,A.,and Jeng,D. S.,2007,A mixture-theory-based dynamic model for a porous medium saturated by two immiscible fluids: Journal of Applied Geophysics,62,89 - 106.
Mavko,G.,and Nolen-Hoeksema,R.,1994,Estimating seismic velocities at ultrasonic frequencies in partially saturated rocks: Geophysics,59(2),252 - 258.
Mochizuki,S.,1982,Attenuation in partially saturated rocks: J. Geophys. Res.,87,8598 - 9604.
Santos,J. E.,Corbero,J. M.,and Douglas,J.,1990a,Static and dynamic behavior of a porous solid saturated by a two-phase fluid: J. Acoust. Soc. Am.,87,1428 - 1438.
Santos,J. E.,Douglas,J.,Corbero,J. M.,and Lovera,O. M.,1990b,A model for wave propagation in a porous medium saturated by a two-phase fluid: J. Acoust. Soc. Am.,87,1439 - 1448.
Santos,J. E.,Ravazzoli,C. L.,Gauzellino,R. M.,Carcione,J. M.,and Cavallini,F.,2004,Simulation of waves in poro-viscoelastic rocks saturated by immiscible fluids: numerical evidence of a second slow wave: Journal of Computational Acoustics,12(1),1 - 21.
Smeulders,D. M. J.,and Van Dongen,M. E. H.,1997,Wave propagation in porous media containing a dilute gas-liquid mixture: theory and experiments: J. Fluid Mech.,343,351 - 373.
Wang,E. L.,Han,L. G.,and Wang,D. L.,2007,Multi-azimuth three-component surface seismic modeling for viscoelastic cracked monoclinic media: Applied Geophysics,4(1),16 - 24.
Wang,Z. J.,He,Q. D.,and Wang,D. L.,2008,The numerical simulation for a 3D two-phase anisotropic medium based on BISQ model: Applied Geophysics,5(1),24 - 34.
Wei,C. F.,and Muraleetharan,K. K.,2002,A continuum theory of porous media saturated by multiple immiscible fluids: I. Linear poroelasticity: International Journal of Engineering Science,40,1807 - 1833.
White,J. E.,1975,Computed seismic speeds and attenuation in rocks with partial gas saturation: Geophysics,40(2),224 - 232.
White,J. E.,Mikhaylova,N. G.,Lyakhovitskiy,F. M.,1975,Low-frequency seismic waves in fluid saturated layered rocks: Physics of the Solid Earth,11,654 - 659.
Zhao,H. B.,2007,Acoustic wave field in porous media saturated with two immiscible fluids: PhD Dissertation,Institute of Acoustics,Chinese Academy of Sciences.
Zienkiewicz,O.C.,and Morgan,K.(writer),Tao,Z. Z.(translator) 1989,Finite elements and approximation,Chinese Communications Press(in chinese),Beijing,46 - 48.
Zou,Z. H.,and Yu,W. H.,2006,Wave field forward modeling and theoretical analysis of weakness in discrete media: Applied Geophysics,3(2),75 - 81.
Ba,J.,Cao,H.,Yao,F. C.,Nie,J. X.,and Yang,H. Z.,2008,Double-porosity rock model and squirt flow in thelaboratory frequency band: Applied Geophysics,5(4),261 - 276.
Bedford,A.,and Stern,M.,1982,A model for wave propagation in gassy sediments: J. Acoust. Soc. Am.,73,409 - 417.
Berryman,J. G.,Thigpen,L.,and Chin,R.,1988,Bulk elastic wave propagation in partially saturated porous solids: J. Acoust. Sco. Am.,84 (1),360-373.
Biot,M. A.,1956,Theory of propagation of wave in fiuid-saturated porous solid: J. Acoust. Soc. Am.,28(2),168 - 178.
Carcione,J. M.,Helle,H. B.,and Pham N. H.,2003,White’s model for wave propagation in partially saturated rocks: comparison with poroelastic numerical experiments: Geophysics,68,1389 - 1398.
Carcione,J. M.,Cavalini,F.,Santos,J. E.,Ravazzoli,C. L.,and Gauzellino,P. M.,2004,Wave propagation in partially saturated porous media: simulation of a second wave: Wave Motion,39,227 - 240.
Chao,G.,Smeulders,D. M.,and Dongen,M. E. H.,2006,Dispersive surface waves along partially saturated porous media: J. Acoust. Soc. Am.,119(3),1347 - 1454.
Ciz,R.,and Gurevich,B.,2005,Amplitude of Biot’s slow wave scattered by a spherical inclusion in a fluid-saturated poroelastic medium: Geophys. J. Int.,160,991 - 1005.
Garg,S. K.,and Nayfeh,A. H.,1986,Compressional wave propagation in liquid and/or gas saturated elastic porous media: J. Appl. Phys.,60,3045 - 3055.
Johnson,D. L.,2001,Theory of frequency dependent acoustics in patchy-saturated porous media: J. Acoust. Soc. Am.,110(2),682 - 694.
Lee,M. W.,2004,Elastic velocities of partially saturated unconsolidated sediments: Marine and Petroleum Geology,21,641 - 650.
Lu,J. F.,and Hanyga,A.,2005,Linear dynamic model for porous media saturated by two immiscible fluids: International Journal of Solid and Structure,42,2689 -2709.
Li,X. J.,Liao,Z. P.,and Du,X. L.,1992,An explicit finite difference method for viscoelastic dynamic problem: Journal of Earthquake Engineering and Engineering Vibration (in chinese),12(4),74 - 79.
Liu,Y.,and Wei,X. C.,2008,Finite-difference numerical modeling with even-order accuracy in two-phase anisotropic media: Applied Geophysics,5(2),107 - 114.
Lu,J. F.,Hanyga,A.,and Jeng,D. S.,2007,A mixture-theory-based dynamic model for a porous medium saturated by two immiscible fluids: Journal of Applied Geophysics,62,89 - 106.
Mavko,G.,and Nolen-Hoeksema,R.,1994,Estimating seismic velocities at ultrasonic frequencies in partially saturated rocks: Geophysics,59(2),252 - 258.
Mochizuki,S.,1982,Attenuation in partially saturated rocks: J. Geophys. Res.,87,8598 - 9604.
Santos,J. E.,Corbero,J. M.,and Douglas,J.,1990a,Static and dynamic behavior of a porous solid saturated by a two-phase fluid: J. Acoust. Soc. Am.,87,1428 - 1438.
Santos,J. E.,Douglas,J.,Corbero,J. M.,and Lovera,O. M.,1990b,A model for wave propagation in a porous medium saturated by a two-phase fluid: J. Acoust. Soc. Am.,87,1439 - 1448.
Santos,J. E.,Ravazzoli,C. L.,Gauzellino,R. M.,Carcione,J. M.,and Cavallini,F.,2004,Simulation of waves in poro-viscoelastic rocks saturated by immiscible fluids: numerical evidence of a second slow wave: Journal of Computational Acoustics,12(1),1 - 21.
Smeulders,D. M. J.,and Van Dongen,M. E. H.,1997,Wave propagation in porous media containing a dilute gas-liquid mixture: theory and experiments: J. Fluid Mech.,343,351 - 373.
Wang,E. L.,Han,L. G.,and Wang,D. L.,2007,Multi-azimuth three-component surface seismic modeling for viscoelastic cracked monoclinic media: Applied Geophysics,4(1),16 - 24.
Wang,Z. J.,He,Q. D.,and Wang,D. L.,2008,The numerical simulation for a 3D two-phase anisotropic medium based on BISQ model: Applied Geophysics,5(1),24 - 34.
Wei,C. F.,and Muraleetharan,K. K.,2002,A continuum theory of porous media saturated by multiple immiscible fluids: I. Linear poroelasticity: International Journal of Engineering Science,40,1807 - 1833.
White,J. E.,1975,Computed seismic speeds and attenuation in rocks with partial gas saturation: Geophysics,40(2),224 - 232.
White,J. E.,Mikhaylova,N. G.,Lyakhovitskiy,F. M.,1975,Low-frequency seismic waves in fluid saturated layered rocks: Physics of the Solid Earth,11,654 - 659.
Zhao,H. B.,2007,Acoustic wave field in porous media saturated with two immiscible fluids: PhD Dissertation,Institute of Acoustics,Chinese Academy of Sciences.
Zienkiewicz,O.C.,and Morgan,K.(writer),Tao,Z. Z.(translator) 1989,Finite elements and approximation,Chinese Communications Press(in chinese),Beijing,46 - 48.
Zou,Z. H.,and Yu,W. H.,2006,Wave field forward modeling and theoretical analysis of weakness in discrete media: Applied Geophysics,3(2),75 - 81.
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