岩石基质模量与临界孔隙度的联合预测方法（英文）
|
摘要
岩石的基质模量和临界孔隙度是岩石物理模型的两项重要输入参数,但临界孔隙度通常很难获得。本文基于有效体积模量与孔隙度的线性模型,提出一种快速计算基质模量和临界孔隙度的方法。通过对实验室或现场测量的有效体积模量与孔隙度数据进行最小二乘拟合,利用拟合系数即可计算基质模量和临界孔隙度。本文方法适用的样品孔隙度范围广,并且计算结果能够准确反映样品的粘土含量、压力大小和饱和状态的差异。粘土含量高的样品的基质模量低,临界孔隙度小。压力对基质模量影响不大,但是临界孔隙度会随着压力的升高而略微增大。饱和样品计算得到的基质模量要比干燥的更大。
The matrix modulus and critical porosity in rocks are two critical parameters to seismic rock physics models; however, the critical porosity is difficult to obtain. Based on the linear relation between the effective bulk modulus and porosity, we propose a fast method for calculating the matrix modulus and critical porosity by least square fitting of effective bulk modulus and porosity data measured in laboratory or field. The proposed method is well suited for samples with wide porosity range. The calculation results accurately reflect the differences in clay content, pressure, and saturation state. Samples with high clay content have low matrix modulus and critical porosity. The matrix modulus is independent of pressure, whereas the critical porosity increases with increasing pressure. The calculated matrix modulus for watersaturated samples is higher than that for dry rock samples.
The matrix modulus and critical porosity in rocks are two critical parameters to seismic rock physics models; however, the critical porosity is difficult to obtain. Based on the linear relation between the effective bulk modulus and porosity, we propose a fast method for calculating the matrix modulus and critical porosity by least square fitting of effective bulk modulus and porosity data measured in laboratory or field. The proposed method is well suited for samples with wide porosity range. The calculation results accurately reflect the differences in clay content, pressure, and saturation state. Samples with high clay content have low matrix modulus and critical porosity. The matrix modulus is independent of pressure, whereas the critical porosity increases with increasing pressure. The calculated matrix modulus for watersaturated samples is higher than that for dry rock samples.
引文
Avseth,P.,Mukerji,T.,and Mavko,G.,2010,Quantitative seismic interpretation:Applying rock physics tools to reduce interpretation risk,Cambridge university press.
Ba,J.,Nie,J.X.,Cao,H.,et al.,2008,Mesoscopic fluid flow simulation in double-porosity rocks:Geophysical Research Letters,35(4),228-236.
Ba,J.,Zhao,J.,Carcione,J.M.,et al.,2016,Compressional wave dispersion due to rock matrix stiffening by clay squirt flow:Geophysical Research Letters,43(12),6186-6195.
Batzle,M.L.,Han,D.H.,and Hofmann,R.,2006,Fluid mobility and frequency dependent seismic velocityDirect measurements:Geophysics,71(10),N1-N9.
Biot,M.A.,1956a,Theory of propagation of elastic waves in a fluid saturated porous solid.I.Lowfrequency range:Journal of the Acoustical Society of America,28(2),168-178.
——,M.A.,1956b,Theory of propagation of elastic waves in a fluid saturated porous solid.II.Highfrequency range:Journal of the Acoustical Society of America,28(2),179-191.
Brown,R.J.,and Korringa,J.,1975,On the dependence of the elastic properties of a porous rock on the compressibility of the pore fluid:Geophysics,40(4),608-616.
Dvorkin,J.,and Nur,A.,1993,Dynamic poroelasticity:A unified model with the squirt and the Biot mechanisms:Geophysics,58(4),524-533.
Feng,Q.,Jiang L.,Liu M.,et al.,2014,Fluid substitution in carbonate rocks based on the Gassmann equation and Eshelby-Walsh theory:Journal of Applied Geophysics,106(7),60-66.
Gassmann,F.,1951,Elastic waves through a packing of spheres:Geophysics,16,673-685.
Gor,G.Y.and Gurevich,B.,2018,Gassmann theory applies to nanoporous media:Geophysical Research Letters,45(1),146-155.
Gurevich,B.,Brajanovski,M.,Galvin,R.J.,et al.,2009,P-wave dispersion and attenuation in fractured and porous reservoirs-poroelasticity approach:Geophysical Prospecting,57(2),225-237.
Han,D.H.,Nur,A.,and Morgan,D.,1986,Effects of porosity and clay content on wave velocities in sandstones:Geophysics,51(11),2093-2107.
He,X.L.,He Z.H.,Wang R.L.,et al.,2011,Calculations of rock matrix modulus based on a linear regression relation:Applied Geophysics,8(3),155.
He,T.,Zou,C.C.,Pei,F.G.,Ren,K.Y.,Kong F.D.,and Shi G.,2010,Laboratory study of fluid viscosity induced ultrasonic velocity dispersion in reservoir sandstones:Applied Geophysics,7(2),114-126.
Jiang,L.,Wen,X.T.,He,Z.H.,et al.,2011,Pore Structure Model Simulation and Porosity Prediction in Reef-Flat Reservoirs:Chinese Journal of Geophysics,54(3),403-414.
Krief,M.,Garat,J.,Stellingwerff,J.,and Ventre,J.,1990,A petrophysical interpretation using the velocities of P-and S-waves(full waveform sonic):The Log Analyst,31(6),355-369.
Ma,X.Y.,Wang,S.X.,Zhao,J.G.,et al.,2018,Velocity dispersion and fluid substitution in sandstone under partially saturated conditions:Applied Geophysics,15(2),188-196.
Mavko,G.,and Mukerji,T.,1995,Seismic pore space compressibility and Gassmann’s relation:Geophysics,60(6),1743-1749.
Mavko,G.,Mukerji,T.,and Dvorkin,J.,2003,The rock physics handbook:tools for seismic analysis of porous media,Cambridge University Press.
Nur,A.,1992,Critical porosity and the seismic velocities in rocks:EOS,Transactions American Geophysical Union,73,43-66.
O’Connell,R.J.,and Budiansky,B.,1974,Seismic velocities in dry and saturated cracked solids:Journal of Geophysical Research,79(35),5412-5426.
Passos de Figueiredo,L.,Grana,D.,Luis Bordignon,F.,et al.,2018,Joint Bayesian inversion based on rockphysics prior modeling for the estimation of spatially correlated reservoir properties:Geophysics,83(5),1-53.
Pride,S.R.,Berryman,J.G.,and Harris,J.M.,2004,Seismic attenuation due to wave-induced flow:Journal of Geophysical Research Solid Earth,109(B1).
Reuss,A.,1929,Berechnung der fliessgrenze von mischkristallen auf grund der plastizit?tsbedingungen für einkristalle:Zeitschrift für Angewandte Mathematic und Mechanik,9,49-58.
Russell,B.H.and Smith,T.,2007,The relationship between dry rock bulk modulus and porosity-An empirical study:CREWES Research Report,19,1-14.
Saul,M.J.and Lumley,D.E.,2013,A new velocity pressure-compaction model for uncemented sediments:Geophysical Journal International,193(2),905-913.
Tang X.M.,2011,A unified theory for elastic wave propagation through porous media containing cracks-An extension of Biot’s poroelastic wave theory:Science China Earth Sciences,54(9),1441-1452.
Vernik,L.,2016,Seismic petrophysics in quantitative interpretation,Society of Exploration Geophysicists.
Walsh,J.B.,1965,The effect of cracks on the compressibility of rock:Journal of Geophysical Research,70(2),381-389.
Wang,D.X.,2016,Study on the rock physics model of gas reservoirs in tight sandstone:Chinese Journal of Geophysics,60(1),64-83.
Winkler,K.W.,1983,Frequency dependent ultrasonic properties of high-porosity sandstones:Journal of Geophysical Research,88(B11),9493-9499.
——,K.W.,1986,Estimates of velocity dispersion between seismic and ultrasonic frequencies:Geophysics,51(1),183-189
Yin,X.Y.,Zong,Z.Y.,and Wu,G.C.,2015,Research on seismic fluid identification driven by rock physics:Science China Earth Sciences,58(2),159-171.
Zhang,J.J.,Li,H.B.,and Yao,F.C.,2012,Rock critical porosity inversion and S-wave velocity prediction:Applied Geophysics,9(1),57-64.
Ba,J.,Nie,J.X.,Cao,H.,et al.,2008,Mesoscopic fluid flow simulation in double-porosity rocks:Geophysical Research Letters,35(4),228-236.
Ba,J.,Zhao,J.,Carcione,J.M.,et al.,2016,Compressional wave dispersion due to rock matrix stiffening by clay squirt flow:Geophysical Research Letters,43(12),6186-6195.
Batzle,M.L.,Han,D.H.,and Hofmann,R.,2006,Fluid mobility and frequency dependent seismic velocityDirect measurements:Geophysics,71(10),N1-N9.
Biot,M.A.,1956a,Theory of propagation of elastic waves in a fluid saturated porous solid.I.Lowfrequency range:Journal of the Acoustical Society of America,28(2),168-178.
——,M.A.,1956b,Theory of propagation of elastic waves in a fluid saturated porous solid.II.Highfrequency range:Journal of the Acoustical Society of America,28(2),179-191.
Brown,R.J.,and Korringa,J.,1975,On the dependence of the elastic properties of a porous rock on the compressibility of the pore fluid:Geophysics,40(4),608-616.
Dvorkin,J.,and Nur,A.,1993,Dynamic poroelasticity:A unified model with the squirt and the Biot mechanisms:Geophysics,58(4),524-533.
Feng,Q.,Jiang L.,Liu M.,et al.,2014,Fluid substitution in carbonate rocks based on the Gassmann equation and Eshelby-Walsh theory:Journal of Applied Geophysics,106(7),60-66.
Gassmann,F.,1951,Elastic waves through a packing of spheres:Geophysics,16,673-685.
Gor,G.Y.and Gurevich,B.,2018,Gassmann theory applies to nanoporous media:Geophysical Research Letters,45(1),146-155.
Gurevich,B.,Brajanovski,M.,Galvin,R.J.,et al.,2009,P-wave dispersion and attenuation in fractured and porous reservoirs-poroelasticity approach:Geophysical Prospecting,57(2),225-237.
Han,D.H.,Nur,A.,and Morgan,D.,1986,Effects of porosity and clay content on wave velocities in sandstones:Geophysics,51(11),2093-2107.
He,X.L.,He Z.H.,Wang R.L.,et al.,2011,Calculations of rock matrix modulus based on a linear regression relation:Applied Geophysics,8(3),155.
He,T.,Zou,C.C.,Pei,F.G.,Ren,K.Y.,Kong F.D.,and Shi G.,2010,Laboratory study of fluid viscosity induced ultrasonic velocity dispersion in reservoir sandstones:Applied Geophysics,7(2),114-126.
Jiang,L.,Wen,X.T.,He,Z.H.,et al.,2011,Pore Structure Model Simulation and Porosity Prediction in Reef-Flat Reservoirs:Chinese Journal of Geophysics,54(3),403-414.
Krief,M.,Garat,J.,Stellingwerff,J.,and Ventre,J.,1990,A petrophysical interpretation using the velocities of P-and S-waves(full waveform sonic):The Log Analyst,31(6),355-369.
Ma,X.Y.,Wang,S.X.,Zhao,J.G.,et al.,2018,Velocity dispersion and fluid substitution in sandstone under partially saturated conditions:Applied Geophysics,15(2),188-196.
Mavko,G.,and Mukerji,T.,1995,Seismic pore space compressibility and Gassmann’s relation:Geophysics,60(6),1743-1749.
Mavko,G.,Mukerji,T.,and Dvorkin,J.,2003,The rock physics handbook:tools for seismic analysis of porous media,Cambridge University Press.
Nur,A.,1992,Critical porosity and the seismic velocities in rocks:EOS,Transactions American Geophysical Union,73,43-66.
O’Connell,R.J.,and Budiansky,B.,1974,Seismic velocities in dry and saturated cracked solids:Journal of Geophysical Research,79(35),5412-5426.
Passos de Figueiredo,L.,Grana,D.,Luis Bordignon,F.,et al.,2018,Joint Bayesian inversion based on rockphysics prior modeling for the estimation of spatially correlated reservoir properties:Geophysics,83(5),1-53.
Pride,S.R.,Berryman,J.G.,and Harris,J.M.,2004,Seismic attenuation due to wave-induced flow:Journal of Geophysical Research Solid Earth,109(B1).
Reuss,A.,1929,Berechnung der fliessgrenze von mischkristallen auf grund der plastizit?tsbedingungen für einkristalle:Zeitschrift für Angewandte Mathematic und Mechanik,9,49-58.
Russell,B.H.and Smith,T.,2007,The relationship between dry rock bulk modulus and porosity-An empirical study:CREWES Research Report,19,1-14.
Saul,M.J.and Lumley,D.E.,2013,A new velocity pressure-compaction model for uncemented sediments:Geophysical Journal International,193(2),905-913.
Tang X.M.,2011,A unified theory for elastic wave propagation through porous media containing cracks-An extension of Biot’s poroelastic wave theory:Science China Earth Sciences,54(9),1441-1452.
Vernik,L.,2016,Seismic petrophysics in quantitative interpretation,Society of Exploration Geophysicists.
Walsh,J.B.,1965,The effect of cracks on the compressibility of rock:Journal of Geophysical Research,70(2),381-389.
Wang,D.X.,2016,Study on the rock physics model of gas reservoirs in tight sandstone:Chinese Journal of Geophysics,60(1),64-83.
Winkler,K.W.,1983,Frequency dependent ultrasonic properties of high-porosity sandstones:Journal of Geophysical Research,88(B11),9493-9499.
——,K.W.,1986,Estimates of velocity dispersion between seismic and ultrasonic frequencies:Geophysics,51(1),183-189
Yin,X.Y.,Zong,Z.Y.,and Wu,G.C.,2015,Research on seismic fluid identification driven by rock physics:Science China Earth Sciences,58(2),159-171.
Zhang,J.J.,Li,H.B.,and Yao,F.C.,2012,Rock critical porosity inversion and S-wave velocity prediction:Applied Geophysics,9(1),57-64.