双重孔隙介质波传播理论与地震响应实验分析
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摘要
为调查非均匀流-固双相介质中的弹性波传播规律,本文推导了双重孔隙介质中的波传播方程,从双孔模型的设计、波动方程的推导、速度频散与衰减规律的分析、岩石物理实验的验证四个方面讨论了双孔波动理论的数学物理基础与实际意义.速度频散与衰减分析显示,双孔波动理论能兼容前人理论的所有特点.在岩石实验的验证中,本文与前人理论的对比显示,双孔波动理论能较好解释岩石内部地震波在中低频带的速度频散现象.
To investigate elastic waves' propagation laws in a heterogeneous fluid-solid 2-phase medium,this paper derived the wave propagation equations in a double-porosity model.The mathematical and physical basis and the practical significance of this theory are discussed in four aspects:model design,theoretical derivation,velocity dispersion and attenuation analysis and rock experiment verification.The velocity dispersion and attenuation analysis shows double-porosity wave theory is in good agreement with former theoretical results in all wave's characteristics.Comparisons with former theories in rock experiment verifications show that the double-porosity wave theory can provide much better prediction for the moderate-low frequency wave velocity dispersion in actual rocks.
To investigate elastic waves' propagation laws in a heterogeneous fluid-solid 2-phase medium,this paper derived the wave propagation equations in a double-porosity model.The mathematical and physical basis and the practical significance of this theory are discussed in four aspects:model design,theoretical derivation,velocity dispersion and attenuation analysis and rock experiment verification.The velocity dispersion and attenuation analysis shows double-porosity wave theory is in good agreement with former theoretical results in all wave's characteristics.Comparisons with former theories in rock experiment verifications show that the double-porosity wave theory can provide much better prediction for the moderate-low frequency wave velocity dispersion in actual rocks.
引文
1Ba J,Nie J X,Cao H,et al.Mesoscopic fluid flow simulation in double-porosity rocks.Geophys Res Lett,2008,35:L04303
2巴晶.复杂多孔介质中的地震波传播机理研究.博士学位论文.北京:清华大学,2008
3Ba J,Yang H Z,Xie G Q.AGILD seismic modelling for double-porosity media.PIERS2008in Hangzhou.Cambridge:The Electromagnetics Academy,2008
4Ba J,Cao H,Yao F C,et al.Double-porosity rock model and squirt flow in laboratory frequency band.Appl Geophys,2008,5(4):261—276
5Ba J,Cao H,Yao F C.Pore heterogeneity induces double-porosity in Guang’an sandstone.In:CPS/SEG Beijing.Beijing:Society of Petroleum Geophysics,2009.47
6刘炯,巴晶,马坚伟,等.随机孔隙介质中地震波衰减分析.中国科学:物理学力学天文学,2010,40(7):858—868
7Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid:I.Low-frequency range.J Acoust Soc Am,1956,28(2):168—178
8Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid:II.Higher frequency range.J Acoust Soc Am,1956,28(2):179—191
9Gassmann F.Uber die elastizitat poroser medien.Vier Der Natur Gesellschaft,1951,96:1—23
10White J E.Computed seismic speeds and attenuation in rocks with partial gas saturation.Geophysics,1975,40:224—232
11Johnson D L.Theory of frequency dependent acoustics in patchy-saturated porous media.J Acoust Soc Am,2001,110:682—694
12Carcione J M,Helle H B,Pham N H.White’s model for wave propagation in partially saturated rocks:Comparison with poroelastic numerical experiments.Geophysics,2003,68:1389—1398
13Pride S R,Berryman J G,Harris J M.Seismic attenuation due to wave-induced flow:J Geophys Res,2004,109:B01201
14Mavko G,Nur A.Melt squirt in asthenosphere.J Geophys Res,1975,80(11):1444—1448
15Dvorkin J,Nur A.Dynamic poroelasticity:A unified model with the Squirt and the Biot mechanisms.Geophysics,1993,58(4):524—533
16Nie J X,Yang D H.Viscoelastic BISQ model for low-permeability sandstone with clay.Chin Phys Lett,2008,25(8):3079—3082
17Nie J X,Yang D H,Yang H Z.A generalized viscoelastic Biot/squirt model for clay-bearing sandstones in a wide range of permeabilities.Appl Geophys,2008,5(4):249—260
18Johnson D L,Hemmick D L,Kojima H.Probing porous media with first and second sound.I.Dynamic permeability.J Appl Phys,1994,76(1):104—114
19Johnson D L,Plona T J,Kojima H.Probing porous media with first and second sound.II.Acoustic properties of water-saturated porous media.J Appl Phys,1994,76(1):115—125
20King M S,Marsden J R,Dennis J W.Biot dispersion for P-and S-wave velocities in partially and fully-saturated sandstones.Geophys Prosp,2000,48:1075—1089
21King M S,Marsden J R.Velocity dispersion between ultrasonic and seismic frequencies in brine-saturated reservoir sandstones.Geophysics,2002,67(1):254—258
22Dvorkin J,Nolen-Hoeksema R,Nur A.The squirt-flow mechanism:macroscopic description.Geophysics,1994,59(3):428—438
23Batzle M L,Han D H,Hofmann R.Fluid mobility and frequency-dependent seismic velocity-direct measurements.Geophysics,2006,71(1):N1—N9
24Biot M A.Mechanics of deformation and acoustic propagation in porous media.J Appl Phys,1962,33(4):1482—1498
25Barenblett G I,Zheltov Y P.Fundamental equations of filtration of homogeneous liquids in fissured rocks.Sov Phys Doklady,1960,5:522—525
26Warren J E,Root P J.The behavior of naturally fractured reservoirs.Soc Pet Eng J,1963,3:245—255
27Berryman J G,Wang H F.The elastic coefficients of double-porosity models for fluid transport in jointed rock.J Geophys Res,1995,100(B12):24611—24627
28Berryman J G,Wang H F.Double porosity modelling in elastic wave propagation for reservoir characterization.In:SPIE Conference on Mathematical Methods in Geophysical Imaging V.San Diego California:SPIE Press,1998.58—69
29Mavco G,Nur A.Wave attenuation in partially saturated rocks.Geophysics,1979,44:161—178
30Pride S R,Berryman J G.Linear dynamics of double-porosity dual-permeability materials.I.Governing equations and acoustic attenuation.Phys Rev E,2003,68:036603
31Pride S R,Berryman J G.Linear dynamics of double-porosity dual-permeability materials.II.Fluid transport equations.Phys Rev E,2003,68:036604
32Biot M A,Willis D G.The elastic coefficients of the theory of consolidation.Appl Mech Div Summer Conf,1957,24:594—601
33Johnson D L.Recent developments in the acoustic properties of porous media:Frontiers in Physical Acoustics XCIII.In:Sette D,ed.New York:North Holland Elsevier,1986.255—290
34Berryman J G,Berge P A.Critique of two explicit shemes for estimating elastic properties of multiphase composites.Mech Mater,1996,22:149—164
35Berryman J G.Effective medium theories for multicomponent poroelastic composites.J Eng Mech,2006,132(5):519—531
36Kuster G T,Toks-z M N.Velocity and attenuation of seismic waves in two-phase media:I.Thereotical formulation.Geophysics,1974,39:587—606
37Berryman J G.Thoery of elastic properties of composite-materials.Appl Phys Lett,1979,35(11):856—858
38Thompson A H,Katz A J,Krohn C E.The microgeometry and transport properties of sedimentary rock.Adv Phys,1987,36(5):625—694
39Agersborg R,Johansen T A,Jakobsen M.Velocity variations in carbonate rocks due to dual porosity and wave-induced fluid flow.Geophys Prosp,2009,57:81—98
40Winkler K.The effects of pore fluids and frictional sliding on seismic attenuation.Dissertation for the Doctoral Degree.Stanford:Stanford University,1979
41Adam L,Batzle M,Brevik I.Gassmann's fluid substitution and shear modulus variability in carbonates at laboratory seismic and ultrasonic frequencies.Geophysics,2006,71(6):F173—F183
42聂建新,杨顶辉,巴晶.含泥质低孔渗各向异性黏弹性介质中的波频散和衰减研究.地球物理学报,2010,53(2):385—392
43巴晶,卢明辉,胡彬,等.黏弹双相介质中的松弛骨架模型:地球物理学报,2008,51(5):1527—1537
44付晓飞,苏玉平,吕延防,等.断裂和裂缝的分形特征,地球科学-中国地质大学学报,2007,32(2):227—234
45Anstey N A,O'Doherty R F.Circles,layers,and reflections:Part1.Leading Edge,2002,21:44—51
46Anstey N A,O'Doherty R F.Circles,layers,and reflections:Part2.Leading Edge,2002,21:152—158
2巴晶.复杂多孔介质中的地震波传播机理研究.博士学位论文.北京:清华大学,2008
3Ba J,Yang H Z,Xie G Q.AGILD seismic modelling for double-porosity media.PIERS2008in Hangzhou.Cambridge:The Electromagnetics Academy,2008
4Ba J,Cao H,Yao F C,et al.Double-porosity rock model and squirt flow in laboratory frequency band.Appl Geophys,2008,5(4):261—276
5Ba J,Cao H,Yao F C.Pore heterogeneity induces double-porosity in Guang’an sandstone.In:CPS/SEG Beijing.Beijing:Society of Petroleum Geophysics,2009.47
6刘炯,巴晶,马坚伟,等.随机孔隙介质中地震波衰减分析.中国科学:物理学力学天文学,2010,40(7):858—868
7Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid:I.Low-frequency range.J Acoust Soc Am,1956,28(2):168—178
8Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid:II.Higher frequency range.J Acoust Soc Am,1956,28(2):179—191
9Gassmann F.Uber die elastizitat poroser medien.Vier Der Natur Gesellschaft,1951,96:1—23
10White J E.Computed seismic speeds and attenuation in rocks with partial gas saturation.Geophysics,1975,40:224—232
11Johnson D L.Theory of frequency dependent acoustics in patchy-saturated porous media.J Acoust Soc Am,2001,110:682—694
12Carcione J M,Helle H B,Pham N H.White’s model for wave propagation in partially saturated rocks:Comparison with poroelastic numerical experiments.Geophysics,2003,68:1389—1398
13Pride S R,Berryman J G,Harris J M.Seismic attenuation due to wave-induced flow:J Geophys Res,2004,109:B01201
14Mavko G,Nur A.Melt squirt in asthenosphere.J Geophys Res,1975,80(11):1444—1448
15Dvorkin J,Nur A.Dynamic poroelasticity:A unified model with the Squirt and the Biot mechanisms.Geophysics,1993,58(4):524—533
16Nie J X,Yang D H.Viscoelastic BISQ model for low-permeability sandstone with clay.Chin Phys Lett,2008,25(8):3079—3082
17Nie J X,Yang D H,Yang H Z.A generalized viscoelastic Biot/squirt model for clay-bearing sandstones in a wide range of permeabilities.Appl Geophys,2008,5(4):249—260
18Johnson D L,Hemmick D L,Kojima H.Probing porous media with first and second sound.I.Dynamic permeability.J Appl Phys,1994,76(1):104—114
19Johnson D L,Plona T J,Kojima H.Probing porous media with first and second sound.II.Acoustic properties of water-saturated porous media.J Appl Phys,1994,76(1):115—125
20King M S,Marsden J R,Dennis J W.Biot dispersion for P-and S-wave velocities in partially and fully-saturated sandstones.Geophys Prosp,2000,48:1075—1089
21King M S,Marsden J R.Velocity dispersion between ultrasonic and seismic frequencies in brine-saturated reservoir sandstones.Geophysics,2002,67(1):254—258
22Dvorkin J,Nolen-Hoeksema R,Nur A.The squirt-flow mechanism:macroscopic description.Geophysics,1994,59(3):428—438
23Batzle M L,Han D H,Hofmann R.Fluid mobility and frequency-dependent seismic velocity-direct measurements.Geophysics,2006,71(1):N1—N9
24Biot M A.Mechanics of deformation and acoustic propagation in porous media.J Appl Phys,1962,33(4):1482—1498
25Barenblett G I,Zheltov Y P.Fundamental equations of filtration of homogeneous liquids in fissured rocks.Sov Phys Doklady,1960,5:522—525
26Warren J E,Root P J.The behavior of naturally fractured reservoirs.Soc Pet Eng J,1963,3:245—255
27Berryman J G,Wang H F.The elastic coefficients of double-porosity models for fluid transport in jointed rock.J Geophys Res,1995,100(B12):24611—24627
28Berryman J G,Wang H F.Double porosity modelling in elastic wave propagation for reservoir characterization.In:SPIE Conference on Mathematical Methods in Geophysical Imaging V.San Diego California:SPIE Press,1998.58—69
29Mavco G,Nur A.Wave attenuation in partially saturated rocks.Geophysics,1979,44:161—178
30Pride S R,Berryman J G.Linear dynamics of double-porosity dual-permeability materials.I.Governing equations and acoustic attenuation.Phys Rev E,2003,68:036603
31Pride S R,Berryman J G.Linear dynamics of double-porosity dual-permeability materials.II.Fluid transport equations.Phys Rev E,2003,68:036604
32Biot M A,Willis D G.The elastic coefficients of the theory of consolidation.Appl Mech Div Summer Conf,1957,24:594—601
33Johnson D L.Recent developments in the acoustic properties of porous media:Frontiers in Physical Acoustics XCIII.In:Sette D,ed.New York:North Holland Elsevier,1986.255—290
34Berryman J G,Berge P A.Critique of two explicit shemes for estimating elastic properties of multiphase composites.Mech Mater,1996,22:149—164
35Berryman J G.Effective medium theories for multicomponent poroelastic composites.J Eng Mech,2006,132(5):519—531
36Kuster G T,Toks-z M N.Velocity and attenuation of seismic waves in two-phase media:I.Thereotical formulation.Geophysics,1974,39:587—606
37Berryman J G.Thoery of elastic properties of composite-materials.Appl Phys Lett,1979,35(11):856—858
38Thompson A H,Katz A J,Krohn C E.The microgeometry and transport properties of sedimentary rock.Adv Phys,1987,36(5):625—694
39Agersborg R,Johansen T A,Jakobsen M.Velocity variations in carbonate rocks due to dual porosity and wave-induced fluid flow.Geophys Prosp,2009,57:81—98
40Winkler K.The effects of pore fluids and frictional sliding on seismic attenuation.Dissertation for the Doctoral Degree.Stanford:Stanford University,1979
41Adam L,Batzle M,Brevik I.Gassmann's fluid substitution and shear modulus variability in carbonates at laboratory seismic and ultrasonic frequencies.Geophysics,2006,71(6):F173—F183
42聂建新,杨顶辉,巴晶.含泥质低孔渗各向异性黏弹性介质中的波频散和衰减研究.地球物理学报,2010,53(2):385—392
43巴晶,卢明辉,胡彬,等.黏弹双相介质中的松弛骨架模型:地球物理学报,2008,51(5):1527—1537
44付晓飞,苏玉平,吕延防,等.断裂和裂缝的分形特征,地球科学-中国地质大学学报,2007,32(2):227—234
45Anstey N A,O'Doherty R F.Circles,layers,and reflections:Part1.Leading Edge,2002,21:44—51
46Anstey N A,O'Doherty R F.Circles,layers,and reflections:Part2.Leading Edge,2002,21:152—158
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