基于岩相约束的Xu-White模型线性化近似与反演
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摘要
Xu-White模型为强非线性模型,无法直接进行线性化近似、实现储层物性线性化反演。对Xu-White模型进行正演分析,发现泥质含量是影响模型非线性强弱的关键因素。为此,提出岩相约束的岩石物理模型线性化近似方法,实现了由Xu-White模型线性化反演储层物性参数。主要有四个步骤:①利用测井曲线建立岩相模型;②利用泰勒级数展开方法,分岩相对Xu-White模型进行线性化近似;③依据贝叶斯理论建立储层物性反演目标函数,并利用最小二乘优化算法反演孔隙度、泥质含量与含水饱和度等参数;④通过不确定性分析,验证反演结果的可信程度。该方法在模型试算及实际测试中均取得了较高质量的反演结果。
The Xu-White model is a strong nonlinear model,and linearized approximation and inversion of this model cannot be directly achieved.The XuWhite forward model demonstrates that the size of clay volume is the key of the model nonlinear strength.Therefore we propose a linearized approximation based on lithofacies constraint to realize the Xu-White model linearized approximation and inversion for petrophysical property.The procedure of the proposed approach includes four steps:(1)lithofacies model building with logging data,(2)model linearized approximation on each facies with first-order Taylor series expansion,(3)petrophysical property inversion objective function establishment based on Bayesian theory,and the porosity,clay volume,and water saturation obtained with least-squares optimization algorithm,and(4)the reliability of the inversion results verification with the uncertainty analysis.Model and real data tests show the feasibility of the proposed approach,which delivers accurate results for reservoir characterization and fluid prediction.
The Xu-White model is a strong nonlinear model,and linearized approximation and inversion of this model cannot be directly achieved.The XuWhite forward model demonstrates that the size of clay volume is the key of the model nonlinear strength.Therefore we propose a linearized approximation based on lithofacies constraint to realize the Xu-White model linearized approximation and inversion for petrophysical property.The procedure of the proposed approach includes four steps:(1)lithofacies model building with logging data,(2)model linearized approximation on each facies with first-order Taylor series expansion,(3)petrophysical property inversion objective function establishment based on Bayesian theory,and the porosity,clay volume,and water saturation obtained with least-squares optimization algorithm,and(4)the reliability of the inversion results verification with the uncertainty analysis.Model and real data tests show the feasibility of the proposed approach,which delivers accurate results for reservoir characterization and fluid prediction.
引文
[1] 马淑芳,韩大匡,甘利灯,等.地震岩石物理模型综述[J].地球物理学进展,2010,25(2):460-471.MA Shufang,HAN Dakuang,GAN Lideng,et al.A review of seismic rock physics models[J].Progress in Geophysics,2010,25(2):460-471.
[2] Kuster G T,Toks?z M N.Velocity and attenuation of seismic waves in two-phase media,Part 1:Theoretical formulations[J].Geophysics,1974,39(5):587-606.
[3] Xu S Y,White R E.A new velocity model for clay-sand mixtures[J].Geophysical Prospecting,1995,43(1):91-118.
[4] Robert G K,Xu S Y.An approximation for the Xu-White velocity model[J].Geophysics,2002,67(5):1406-1414.
[5] Wyllie M R J.Elastic wave velocities in heterogeneous and porous media[J].Geophysics,1956,21(1):41-70.
[6] 印兴耀,刘欣欣.储层地震岩石物理建模研究现状与进展[J].石油物探,2016,55(3):309-325.YIN Xingyao,LIU Xinxin.Research status and progress of the seismic rock-physics modeling methods[J].Geophysical Prospecting for Petroleum,2016,55(3):309-325.
[7] Yin X Y,Zong Z Y,Wu G C.Research on seismic fluid identification driven by rock physics[J].Science China:Earth Sciences,2015,58(2):159-171.
[8] 杨志芳,曹宏.地震岩石物理研究进展[J].地球物理学进展,2009,24(3):893-899.YANG Zhifang,CAO Hong.Review of progress in seismic rock physics[J].Progress in Geophysics,2009,24(3):893-899.
[9] 姜仁,曾庆才,黄家强,等.岩石物理分析在叠前储层预测中的应用[J].石油地球物理勘探,2014,49(2):322-328.JIANG Ren,ZENG Qingcai,HUANG Jiaqiang,et al.Application of rock physics analysis in pre-stack seismic reservoir prediction[J].Oil Geophysical Prospecting,2014,49(2):322-328.
[10] 方兴,孙夕平,张明,等.基于AVO流体反演的储层孔隙度预测技术[J].石油地球物理勘探,2012,47(3):469-472.FANG Xing,SUN Xiping,ZHANG Ming,et al.Re-servoir porosity prediction based on AVO fluid inversion[J].Oil Geophysical Prospecting,2012,47(3):469-472.
[11] 杨培杰.砂泥岩储层孔隙度和含水饱和度同步反演[J].地球物理学报,2018,61(2):673-682.YANG Peijie.Porosity and water saturation simultaneous inversion for sand-mudstone reservoir[J].Chinese Journal of Geophysics,2018,61(2):673-682.
[12] 李志勇,钱峰,胡光岷,等.储层弹性与物性参数地震叠前同步反演的确定性优化方法[J].地球物理学报,2015,58(5):1706-1716.LI Zhiyong,QIAN Feng,HU Guangmin,et al.Pre-stack seismic joint inversion of reservoir elastic and petrophysical parameters using deterministic optimization method[J].Chinese Journal of Geophysics,2015,58(5):1706-1716.
[13] Sen M K,Stoffa P L.Global Optimization Methods in Geophysical Inversion[M].Cambridge University Press,2013.
[14] Aster R C,Borchers B,Thurber C H.Parameter Estimation and Inverse Problems[M].Academic Press,2012.
[15] Grana D,Rossa E D.Probabilistic petrophysical pro-perties estimation integrating statistical rock physics with seismic inversion[J].Geophysics,2010,75(3):O21-O37.
[16] Larsen A L,Ulvmoen M,Omre H,et al.Bayesian lithology/fluid prediction and simulation on the basis of a Markov-chain prior model[J].Geophysics,2006,71(5):R69-R78.
[17] Grana D.Bayesian linearized rock-physics inversion[J].Geophysics,2016,81(6):D625-D641.
[18] 印兴耀,化世榜,宗兆云.基于线性近似的微分等效介质方程解耦方法[J].石油地球物理勘探,2016,51(2):281-287.YIN Xingyao,HUA Shibang,ZONG Zhaoyun.A decoupling approach for differential equivalent equations based on linear approximation[J].Oil Geophysical Prospecting,2016,51(2):281-287.
[19] Tian L,Hua S B,Yin X Y.A decoupling approach for differential equivalent equations based on linear approximation[C].Extended Abstracts of 78th EAGE Conference & Exhibition,2016,Tu13.
[20] Wu T T.The effect of inclusion shape on the elastic moduli of a two-phase material[J].International Journal of Solids and Structures,1966,2(1):1-8.
[21] 郑旭桢,王涛,刘钊,等.泥岩基质弹性参数对Xu-White模型横波速度估算的影响[J].石油地球物理勘探,2017,52(5):990-998.ZHENG Xuzhen,WANG Tao,LIU Zhao,et al.Influence of clay elastic parameters on S-wave velocity estimation based on Xu-White model[J].Oil Geophysical Prospecting,2017,52(5):990-998.
[22] 刘致水,孙赞东,董宁,等.一种修正的Kuster-Toks?z岩石物理模型及应用[J].石油地球物理勘探,2018,53(1):113-121.LIU Zhishui,SUN Zandong,DONG Ning,et al.A modified Kuster-Toks?z rock physics model and its application[J].Oil Geophysical Prospecting,2018,53(1):113-121.
[23] 贺锡雷,林凯,张祖豪,等.孔隙度和孔隙结构对储层特性影响的定量比较[J].石油物探,2018,57(2):179-184.HE Xilei,LIN Kai,ZHANG Zuhao,et al.Quantitative comparison of the influence of porosity and pore structure on reservoir characteristics[J].Geophysical Prospecting for Petroleum,2018,57(2):179-184.
[24] 韩如冰,刘强,江同文,等.钙质隔夹层特征、成因及分布——以塔里木盆地哈得油田东河砂岩为例[J].石油勘探与开发,2014,41(4):428-437.HAN Rubing,LIU Qiang,JIANG Tongwen,et al.Feature,origin and distribution of calcareous interlayers:A case of Carboniferous Donghe sandstone in Hade Oil Field,Tarim Basin,NW China[J].Petro-leum Exploration and Development,2014,41(4):428-437.
[25] 刘清俊,于炳松,周芳芳,等.阿克库勒凸起东河砂岩成岩作用与成岩相[J].西南石油大学学报(自然科学版),2011,33(5):54-62.LIU Qingjun,YU Bingsong,ZHOU Fangfang,et al.Diagenesis and diagenetic facies of Donghe sandstone of Akekule uplift in Tarim Basin[J].Journal of Southwest Petroleum University(Science & Techno-logy Edition),2011,33(5):54-62.
[26] Albert T.Inverse Problem Theory and Methods for Model Parameter Estimation[M].Society for Industrial and Applied Mathematics,Philadelphia,2005.
[27] 田军,吴国忱,宗兆云.鲁棒性AVO三参数反演方法及不确定性分析[J].石油地球物理勘探,2013,48(3):443-449.TIAN Jun,WU Guochen,ZONG Zhaoyun.Robust three-term AVO inversion and uncertainty analysis[J].Oil Geophysical Prospecting,2013,48(3):443-449.
[2] Kuster G T,Toks?z M N.Velocity and attenuation of seismic waves in two-phase media,Part 1:Theoretical formulations[J].Geophysics,1974,39(5):587-606.
[3] Xu S Y,White R E.A new velocity model for clay-sand mixtures[J].Geophysical Prospecting,1995,43(1):91-118.
[4] Robert G K,Xu S Y.An approximation for the Xu-White velocity model[J].Geophysics,2002,67(5):1406-1414.
[5] Wyllie M R J.Elastic wave velocities in heterogeneous and porous media[J].Geophysics,1956,21(1):41-70.
[6] 印兴耀,刘欣欣.储层地震岩石物理建模研究现状与进展[J].石油物探,2016,55(3):309-325.YIN Xingyao,LIU Xinxin.Research status and progress of the seismic rock-physics modeling methods[J].Geophysical Prospecting for Petroleum,2016,55(3):309-325.
[7] Yin X Y,Zong Z Y,Wu G C.Research on seismic fluid identification driven by rock physics[J].Science China:Earth Sciences,2015,58(2):159-171.
[8] 杨志芳,曹宏.地震岩石物理研究进展[J].地球物理学进展,2009,24(3):893-899.YANG Zhifang,CAO Hong.Review of progress in seismic rock physics[J].Progress in Geophysics,2009,24(3):893-899.
[9] 姜仁,曾庆才,黄家强,等.岩石物理分析在叠前储层预测中的应用[J].石油地球物理勘探,2014,49(2):322-328.JIANG Ren,ZENG Qingcai,HUANG Jiaqiang,et al.Application of rock physics analysis in pre-stack seismic reservoir prediction[J].Oil Geophysical Prospecting,2014,49(2):322-328.
[10] 方兴,孙夕平,张明,等.基于AVO流体反演的储层孔隙度预测技术[J].石油地球物理勘探,2012,47(3):469-472.FANG Xing,SUN Xiping,ZHANG Ming,et al.Re-servoir porosity prediction based on AVO fluid inversion[J].Oil Geophysical Prospecting,2012,47(3):469-472.
[11] 杨培杰.砂泥岩储层孔隙度和含水饱和度同步反演[J].地球物理学报,2018,61(2):673-682.YANG Peijie.Porosity and water saturation simultaneous inversion for sand-mudstone reservoir[J].Chinese Journal of Geophysics,2018,61(2):673-682.
[12] 李志勇,钱峰,胡光岷,等.储层弹性与物性参数地震叠前同步反演的确定性优化方法[J].地球物理学报,2015,58(5):1706-1716.LI Zhiyong,QIAN Feng,HU Guangmin,et al.Pre-stack seismic joint inversion of reservoir elastic and petrophysical parameters using deterministic optimization method[J].Chinese Journal of Geophysics,2015,58(5):1706-1716.
[13] Sen M K,Stoffa P L.Global Optimization Methods in Geophysical Inversion[M].Cambridge University Press,2013.
[14] Aster R C,Borchers B,Thurber C H.Parameter Estimation and Inverse Problems[M].Academic Press,2012.
[15] Grana D,Rossa E D.Probabilistic petrophysical pro-perties estimation integrating statistical rock physics with seismic inversion[J].Geophysics,2010,75(3):O21-O37.
[16] Larsen A L,Ulvmoen M,Omre H,et al.Bayesian lithology/fluid prediction and simulation on the basis of a Markov-chain prior model[J].Geophysics,2006,71(5):R69-R78.
[17] Grana D.Bayesian linearized rock-physics inversion[J].Geophysics,2016,81(6):D625-D641.
[18] 印兴耀,化世榜,宗兆云.基于线性近似的微分等效介质方程解耦方法[J].石油地球物理勘探,2016,51(2):281-287.YIN Xingyao,HUA Shibang,ZONG Zhaoyun.A decoupling approach for differential equivalent equations based on linear approximation[J].Oil Geophysical Prospecting,2016,51(2):281-287.
[19] Tian L,Hua S B,Yin X Y.A decoupling approach for differential equivalent equations based on linear approximation[C].Extended Abstracts of 78th EAGE Conference & Exhibition,2016,Tu13.
[20] Wu T T.The effect of inclusion shape on the elastic moduli of a two-phase material[J].International Journal of Solids and Structures,1966,2(1):1-8.
[21] 郑旭桢,王涛,刘钊,等.泥岩基质弹性参数对Xu-White模型横波速度估算的影响[J].石油地球物理勘探,2017,52(5):990-998.ZHENG Xuzhen,WANG Tao,LIU Zhao,et al.Influence of clay elastic parameters on S-wave velocity estimation based on Xu-White model[J].Oil Geophysical Prospecting,2017,52(5):990-998.
[22] 刘致水,孙赞东,董宁,等.一种修正的Kuster-Toks?z岩石物理模型及应用[J].石油地球物理勘探,2018,53(1):113-121.LIU Zhishui,SUN Zandong,DONG Ning,et al.A modified Kuster-Toks?z rock physics model and its application[J].Oil Geophysical Prospecting,2018,53(1):113-121.
[23] 贺锡雷,林凯,张祖豪,等.孔隙度和孔隙结构对储层特性影响的定量比较[J].石油物探,2018,57(2):179-184.HE Xilei,LIN Kai,ZHANG Zuhao,et al.Quantitative comparison of the influence of porosity and pore structure on reservoir characteristics[J].Geophysical Prospecting for Petroleum,2018,57(2):179-184.
[24] 韩如冰,刘强,江同文,等.钙质隔夹层特征、成因及分布——以塔里木盆地哈得油田东河砂岩为例[J].石油勘探与开发,2014,41(4):428-437.HAN Rubing,LIU Qiang,JIANG Tongwen,et al.Feature,origin and distribution of calcareous interlayers:A case of Carboniferous Donghe sandstone in Hade Oil Field,Tarim Basin,NW China[J].Petro-leum Exploration and Development,2014,41(4):428-437.
[25] 刘清俊,于炳松,周芳芳,等.阿克库勒凸起东河砂岩成岩作用与成岩相[J].西南石油大学学报(自然科学版),2011,33(5):54-62.LIU Qingjun,YU Bingsong,ZHOU Fangfang,et al.Diagenesis and diagenetic facies of Donghe sandstone of Akekule uplift in Tarim Basin[J].Journal of Southwest Petroleum University(Science & Techno-logy Edition),2011,33(5):54-62.
[26] Albert T.Inverse Problem Theory and Methods for Model Parameter Estimation[M].Society for Industrial and Applied Mathematics,Philadelphia,2005.
[27] 田军,吴国忱,宗兆云.鲁棒性AVO三参数反演方法及不确定性分析[J].石油地球物理勘探,2013,48(3):443-449.TIAN Jun,WU Guochen,ZONG Zhaoyun.Robust three-term AVO inversion and uncertainty analysis[J].Oil Geophysical Prospecting,2013,48(3):443-449.
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