基于多点地质统计的多孔介质重构方法及实现
|
摘要
随着渗流力学研究的不断深入,发现许多不符合达西定律的渗流现象,也提出多种达西定律修正公式,但这些修正仍然采用基于宏观统计层面的假设,并不能反映非达西渗流的机理。多孔介质孔隙空间的几何特性和拓扑结构决定着多孔介质中流体的传输特性,因此,只有开展多孔介质中的孔隙空间及连通性研究才能揭示渗流的内在机理。
由于多孔介质的孔隙空间及连通性异常复杂,很难用几个明确参数进行描述,因此如果能够借助真实的多孔介质孔隙数据,从中提取和复制孔隙的结构特征,才能较好地重构出与真实情况相似的孔隙空间。该研究是进行渗流力学微观机理研究的关键。
本文首先采用扫描电镜及同步辐射装置分别获取真实多孔介质的二维和三维数据,以这些数据为训练图像,采用多点地质统计法进行多孔介质重构。主要研究内容如下:
1.提出一种基于扫描电镜图像的二维多孔介质重构方法。该方法使用扫描电镜采集多孔介质二维数据,该二维数据作为训练图像。利用数据模板扫描训练图像,多孔介质的先验模型被明确而定量地引入到建模当中。先验模型包含了被研究的多孔介质中确信存在的样式,而训练图像则是该样式的定量化表达,可以说训练图像中的概率信息决定了最终的模拟结果。通过再现高阶统计量,多点地质统计法能够从训练图像中捕捉复杂的特征样式并把它们复制到重构图像中。比较二维变差函数在X和Y方向的变化趋势,可知重构的二维图像与真实的多孔介质二维图像结构特征相似。
2.采用二维图像进行多孔介质三维重构。如果从二维图像重构三维孔隙结构,需要考虑增加二维图像在Z方向的特征信息,因此提取训练图像的采样点作为条件数据,再利用多点地质统计法重构原始训练图像的下层图像,新得到的重构图像作为新的训练图像重构其下层图像,重构时也要提取采样点作为条件数据。重复该步骤若干次,得到一组二维孔隙图像。将这些图像依次叠加,可以得到多孔介质的三维结构。
3.开展两点和多点地质统计法的多孔介质重构对比研究。使用同步辐射装置获取多孔介质的体数据,以该体数据作为训练图像。利用多点地质统计法提取体数据的特征模式,然后将这些模式“复制”到重构区域。这些重构结果具有与真实体数据相似的结构特征。通过与两点地质统计法的比较发现,多点地质统计法的重构结果与真实情况更为接近。
4.在重构过程中使用servosystem控制目标图像概率。虽然多点地质统计法重构的多孔介质结构具有随机性,但是这些重构结果均具有相似的结构特征和孔隙度。
5.提出在多孔介质重构过程中使用多重数据模板的方法。在重构过程中,数据模板不能太小,否则无法获取训练图像中较大范围内的数据特征:而另一方面,较大的数据模板会包含较多节点,这样会大大增加计算机内存和CPU的负担,因此只能选择合适的数据模板尺寸。应用多重模板一方面可以反映更大尺度下的孔隙形态,另一方面也可以适当减小扫描模板的大小来减少CPU和内存的负担。实验证明多重模板的重构效果比较理想。
6.提出一种结合使用软硬数据的多孔介质重构方法。在许多领域里,由于受到客观条件或技术水平限制,所能得到的硬数据非常有限,但是可以获得相对比较丰富的软数据。与仅仅使用硬数据和无条件数据的情况相比,在多孔介质重构过程中加入软数据,可以提高重构精度,而CPU和内存负担不会大幅增加。
7.提出一种重构多孔介质连续型变量状态值的方法。针对多孔介质中例如孔隙度或渗透率等连续型变量,利用基于过滤器的filtersim进行重构。过滤器对训练图像进行降维处理,形成了“过滤器得分空间”,这可以提高重构效率。对过滤器获得的“过滤器得分空间”进行有效划分,从而对训练图像特征模式分类,形成了提取模式的“特征库”。比较“特征库”中的特征模式与当前数据事件,找到与数据事件最接近的特征模式,将其“粘贴”到待模拟节点位置,就完成了该节点的模拟。利用filtersim进行孔隙度模拟,取得了较好的重构效果。
The mechanism of fluid flow in porous media is widely involved in many engineering fields.Darcy's law,based on the macroscopic statistical theories,is of great importance in the mechanism of fluid flow in porous media.With the development of mechanism of fluid flow in porous media,many researchers found that a large amount of phenomena that did not according with Darcy's law.Then some corrections were made to them,which failed to reflect the rule of transportation in non-Darcy situation because those corrections also relied on the macroscopic statistical hypotheses.The object studied in the mechanism of fluid flow in porous media is the rules of fluid flow,which are not only dependent on the properties of fluid,but also associated with the characteristics of porous media.Fluid properties are determined by the transportation characteristics of porous media,which are also dependent on the geometrical and topological structure of pore space.Therefore,it is very important to describe the pore space and connectivity for the study of micro-scale mechanism of fluid flow in porous media.
It is impossible to use only several parameters to describe the porous media due to their high irregularity and complicated topology.Therefore,extracting and copying structural features from the real pore space can reconstruct better pore space similar to the real condition,which is also the key problem for the study of micro-scale mechanism of fluid flow in porous media.
The 2D and 3D data of porous media were respectively obtained by scanning electron microscopy microtomography and synchrotron microtomography. Reconstruction of porous media was made based on MPS(multiple-point geostatistics) and those data taken as training images.The detailed research is as follows:
1.A 2D reconstruction method of porous media based on images from scanning electron microscopy microtomography and MPS is proposed.2D data scanned by scanning electron microscopy microtomography are used as a training image which will be scanned by data templates.A training image is the numerical representation of a prior geological model that contains the patterns believed to exist in realistic porous media under study.By reproducing high-order statistics,MPS can capture complex features from the training image and regenerate them in reconstructed images.The reconstructed 2D image has the similar characteristics with the real porous media by comparing their variogram curves in the X and Y directons.
2.A 3D reconstruction method of porous media based on 2D images and MPS is proposed.The information in the Z direction should be added if 3D structure of pore space is reconstructed based on only 2D images.Sample points drawn from the training image are used as conditional data.MPS regenerate the next layer of original training image.New reconstructed images are used as new training images repeatedly to reconstruct their next layers.Also,sample points should be extracted from each new training image.At last,a group of 2D pore space images are obtained.Stack these images sequentially,and then the 3D pore structure can be achieved.
3.The reconstructed results from MPS and two-point geostatistics are compared.Volume data of porous media,obtained from synchrotron microtomography devices,are used as training image.Patterns existing in the training image are extracted and "copied" to the reconstructed region. These reconstructed results of porous media from MPS have similar structural characteristics with the real volume data.Compared with the results reconstructed by two-point geostatistics,the results from MPS are better.
4.Servosystem can control the target distribution well in reconstructed images. Although the reconstructed results of porous media are stochastic,they still have similar structural characteristics and close porosity.
5.A method using multiple grids in reconstruction is presented.During reconstruction,the data search neighborhood should not be taken too small; otherwise,large-scale structure of the training image cannot be reproduced. On the other hand,if the search neighborhood is too large,the associated data template will include a large number of grid nodes,which will increase the CPU-time and raise the memory demand.One solution to capture large-scale structure while considering a data template with a reasonably small number of grid nodes is provided by the multiple-grid method. Experimental results prove the method is practical.
6.A method integrating soft data with hard data in porous reconstruction is proposed.In many fields,there are two types of data:hard data and soft data. Soft data typically provide an extensive coverage of the field under study although with low resolution.Sometimes,the hard data we can obtain are quite little,but soft data are abundant.It is necessary to condition the reconstructed models to all these different types of data to improve the accuracy of reconstructed porous media,which will be better than the unconditional reconstruction and the reconstruction using hard data only,but the cost of CPU and memory won't increase largely.
7.A method to reconstruct the continuous variables in porous media is proposed.Filtersim,based on filters,can reconstruct the continuous categories in porous media,such as porosity and permeability.Filters can reduce the dimensions of training images to form "filter score" space,which enhances the efficiency of reconstruction."Filter score" space is partitioned to classify the patterns existing in training images and forms a "database" of patterns.The closet pattern will be found by comparing the patterns in that "database" and current data event.Then this pattern will be patched to the nodes to be simulated.The porosity simulation is made by using filtersim and matches the training image well.
由于多孔介质的孔隙空间及连通性异常复杂,很难用几个明确参数进行描述,因此如果能够借助真实的多孔介质孔隙数据,从中提取和复制孔隙的结构特征,才能较好地重构出与真实情况相似的孔隙空间。该研究是进行渗流力学微观机理研究的关键。
本文首先采用扫描电镜及同步辐射装置分别获取真实多孔介质的二维和三维数据,以这些数据为训练图像,采用多点地质统计法进行多孔介质重构。主要研究内容如下:
1.提出一种基于扫描电镜图像的二维多孔介质重构方法。该方法使用扫描电镜采集多孔介质二维数据,该二维数据作为训练图像。利用数据模板扫描训练图像,多孔介质的先验模型被明确而定量地引入到建模当中。先验模型包含了被研究的多孔介质中确信存在的样式,而训练图像则是该样式的定量化表达,可以说训练图像中的概率信息决定了最终的模拟结果。通过再现高阶统计量,多点地质统计法能够从训练图像中捕捉复杂的特征样式并把它们复制到重构图像中。比较二维变差函数在X和Y方向的变化趋势,可知重构的二维图像与真实的多孔介质二维图像结构特征相似。
2.采用二维图像进行多孔介质三维重构。如果从二维图像重构三维孔隙结构,需要考虑增加二维图像在Z方向的特征信息,因此提取训练图像的采样点作为条件数据,再利用多点地质统计法重构原始训练图像的下层图像,新得到的重构图像作为新的训练图像重构其下层图像,重构时也要提取采样点作为条件数据。重复该步骤若干次,得到一组二维孔隙图像。将这些图像依次叠加,可以得到多孔介质的三维结构。
3.开展两点和多点地质统计法的多孔介质重构对比研究。使用同步辐射装置获取多孔介质的体数据,以该体数据作为训练图像。利用多点地质统计法提取体数据的特征模式,然后将这些模式“复制”到重构区域。这些重构结果具有与真实体数据相似的结构特征。通过与两点地质统计法的比较发现,多点地质统计法的重构结果与真实情况更为接近。
4.在重构过程中使用servosystem控制目标图像概率。虽然多点地质统计法重构的多孔介质结构具有随机性,但是这些重构结果均具有相似的结构特征和孔隙度。
5.提出在多孔介质重构过程中使用多重数据模板的方法。在重构过程中,数据模板不能太小,否则无法获取训练图像中较大范围内的数据特征:而另一方面,较大的数据模板会包含较多节点,这样会大大增加计算机内存和CPU的负担,因此只能选择合适的数据模板尺寸。应用多重模板一方面可以反映更大尺度下的孔隙形态,另一方面也可以适当减小扫描模板的大小来减少CPU和内存的负担。实验证明多重模板的重构效果比较理想。
6.提出一种结合使用软硬数据的多孔介质重构方法。在许多领域里,由于受到客观条件或技术水平限制,所能得到的硬数据非常有限,但是可以获得相对比较丰富的软数据。与仅仅使用硬数据和无条件数据的情况相比,在多孔介质重构过程中加入软数据,可以提高重构精度,而CPU和内存负担不会大幅增加。
7.提出一种重构多孔介质连续型变量状态值的方法。针对多孔介质中例如孔隙度或渗透率等连续型变量,利用基于过滤器的filtersim进行重构。过滤器对训练图像进行降维处理,形成了“过滤器得分空间”,这可以提高重构效率。对过滤器获得的“过滤器得分空间”进行有效划分,从而对训练图像特征模式分类,形成了提取模式的“特征库”。比较“特征库”中的特征模式与当前数据事件,找到与数据事件最接近的特征模式,将其“粘贴”到待模拟节点位置,就完成了该节点的模拟。利用filtersim进行孔隙度模拟,取得了较好的重构效果。
The mechanism of fluid flow in porous media is widely involved in many engineering fields.Darcy's law,based on the macroscopic statistical theories,is of great importance in the mechanism of fluid flow in porous media.With the development of mechanism of fluid flow in porous media,many researchers found that a large amount of phenomena that did not according with Darcy's law.Then some corrections were made to them,which failed to reflect the rule of transportation in non-Darcy situation because those corrections also relied on the macroscopic statistical hypotheses.The object studied in the mechanism of fluid flow in porous media is the rules of fluid flow,which are not only dependent on the properties of fluid,but also associated with the characteristics of porous media.Fluid properties are determined by the transportation characteristics of porous media,which are also dependent on the geometrical and topological structure of pore space.Therefore,it is very important to describe the pore space and connectivity for the study of micro-scale mechanism of fluid flow in porous media.
It is impossible to use only several parameters to describe the porous media due to their high irregularity and complicated topology.Therefore,extracting and copying structural features from the real pore space can reconstruct better pore space similar to the real condition,which is also the key problem for the study of micro-scale mechanism of fluid flow in porous media.
The 2D and 3D data of porous media were respectively obtained by scanning electron microscopy microtomography and synchrotron microtomography. Reconstruction of porous media was made based on MPS(multiple-point geostatistics) and those data taken as training images.The detailed research is as follows:
1.A 2D reconstruction method of porous media based on images from scanning electron microscopy microtomography and MPS is proposed.2D data scanned by scanning electron microscopy microtomography are used as a training image which will be scanned by data templates.A training image is the numerical representation of a prior geological model that contains the patterns believed to exist in realistic porous media under study.By reproducing high-order statistics,MPS can capture complex features from the training image and regenerate them in reconstructed images.The reconstructed 2D image has the similar characteristics with the real porous media by comparing their variogram curves in the X and Y directons.
2.A 3D reconstruction method of porous media based on 2D images and MPS is proposed.The information in the Z direction should be added if 3D structure of pore space is reconstructed based on only 2D images.Sample points drawn from the training image are used as conditional data.MPS regenerate the next layer of original training image.New reconstructed images are used as new training images repeatedly to reconstruct their next layers.Also,sample points should be extracted from each new training image.At last,a group of 2D pore space images are obtained.Stack these images sequentially,and then the 3D pore structure can be achieved.
3.The reconstructed results from MPS and two-point geostatistics are compared.Volume data of porous media,obtained from synchrotron microtomography devices,are used as training image.Patterns existing in the training image are extracted and "copied" to the reconstructed region. These reconstructed results of porous media from MPS have similar structural characteristics with the real volume data.Compared with the results reconstructed by two-point geostatistics,the results from MPS are better.
4.Servosystem can control the target distribution well in reconstructed images. Although the reconstructed results of porous media are stochastic,they still have similar structural characteristics and close porosity.
5.A method using multiple grids in reconstruction is presented.During reconstruction,the data search neighborhood should not be taken too small; otherwise,large-scale structure of the training image cannot be reproduced. On the other hand,if the search neighborhood is too large,the associated data template will include a large number of grid nodes,which will increase the CPU-time and raise the memory demand.One solution to capture large-scale structure while considering a data template with a reasonably small number of grid nodes is provided by the multiple-grid method. Experimental results prove the method is practical.
6.A method integrating soft data with hard data in porous reconstruction is proposed.In many fields,there are two types of data:hard data and soft data. Soft data typically provide an extensive coverage of the field under study although with low resolution.Sometimes,the hard data we can obtain are quite little,but soft data are abundant.It is necessary to condition the reconstructed models to all these different types of data to improve the accuracy of reconstructed porous media,which will be better than the unconditional reconstruction and the reconstruction using hard data only,but the cost of CPU and memory won't increase largely.
7.A method to reconstruct the continuous variables in porous media is proposed.Filtersim,based on filters,can reconstruct the continuous categories in porous media,such as porosity and permeability.Filters can reduce the dimensions of training images to form "filter score" space,which enhances the efficiency of reconstruction."Filter score" space is partitioned to classify the patterns existing in training images and forms a "database" of patterns.The closet pattern will be found by comparing the patterns in that "database" and current data event.Then this pattern will be patched to the nodes to be simulated.The porosity simulation is made by using filtersim and matches the training image well.
引文
白鹤翔,葛咏,李德玉.2006.多点模拟算法与试验对比分析[J].地球信息科学,8(4):117-121.
蔡睿贤,刘启斌.2008.求解数理方程解析解的一种新方法——混合分离变量法.中国科学G辑:物理力学天文学[J],38(9):1236-1245.
陈群,任建勋,过增元.2008.流体流动场协同原理及其在减阻中的应用.科学通报[J]53(4):489-492.
杜宇健,萧德云.2004.Kriging算法在温度场计算中的应用分析[J].计算机辅助设计与图形学学报,16(8):1153-1158.
冯国庆,陈浩,张烈辉 等.利用多点地质统计学方法模拟岩相分布[J].西安石油大学学报(自然科学版),20(5):9-11.
高慧梅,姜汉桥,陈民锋.2007.多孔介质孔隙网络模型的应用现状[J].大庆石油地质与开发,26(2):74-79.
郭尚平,黄延章,周娟,等.1990.物理化学渗流微观机理[M].北京:科学出版社,6-18.
侯健,李振泉,张顺康,等.2008.岩石三维网络模型构建的实验和模拟研究[J].中国科学G 辑:物理力学天文学,38(11):1563-1575.
侯景儒.1998.实用地质统计学(空间信息统计学)[M].北京:地质出版社,1-10.
胡雪蛟,杜建华,刘翔,等.2001.多孔介质突破特性的尺度效应.科学通报[J],46(4):345-347.
黄丰.2007.多孔介质模型的三维重构研究[D]:[博士].合肥:中国科学技术大学.
黄丰,卢德唐,王磊等.2007.多孔介质3维孔隙空间的隐式曲面造型方法[J].中国图象图形学报:12(5):899-904.
金京男.2006.地质统计学在平坝山石灰石矿均化开采中的应用[D]:[硕士].北京:北京科技大学,8-16.
孔祥言.1999.高等渗流力学[M].合肥:中国科学技术大学出版社,1-20.
林茂松.2006.科学计算可视化的应用研究[D]:[博士].四川:西南交通大学,1-24.
牛文杰.2002a.贝叶斯同位置协同克里金估值法的研究[J].计算机辅助设计与图形学学报,14(4):343-347.
牛文杰.2002b.三维数据场可视化克里格建模及其算法的理论和应用研究[D]:[博士].北京:北京航空航天大学,1-24.
牛文杰.2004.基于先验信息的残余克里金法的研究[J].计算机工程与应用,35:80-83.
儒耐尔A G.1982.矿业地质统计学[M].侯景儒,黄竞先,译.北京:冶金工业出版社,66-69.
孙其诚,黄晋,王光谦.2008.液态泡沫强制渗流波叠加现象及其能量分析.科学通报[J], 53(13):1507-1510.
孙玉建.2007.非参数地质统计学进展[J].地质与勘探,43(4):79-82.
孙宪华.2000.硬数据和软数据[J].北京统计,124(6):35.
唐泽圣.1999.清华大学学术专著—三维数据场可视化[M].北京:清华大学出版社,1-21.
王达健,陈书荣,张雄飞等.2001.多孔介质孔隙模型及其应用——毛细管束模型[J].计算机与应用化学,18(5):429-432.
王文成.1998.三维数据场体绘制技术的研究和实现[D]:[博士].北京:中国科学院软件研究所.1-24.
王兴勇.2003.Lattice Boltzmann方法的理论及其在水力计算中应用的研究[D]:[博士].南京:河海大学,1.
吴胜和,李文克.2004.多点地质统计学:理论、应用与展望[J].古地理学报,7(1):137-144.
杨满平.2005.油气储层多孔介质的变形理论及应用研究[D]:[博士].成都:西南石油学院,10-11.
袁益让,韩玉笈.2008.三维油资源渗流力学运移聚集的大规模数值模拟和应用.中国科学G 辑:物理力学天文学[J],38(11):1582-1600.
张程远.2003.地质统计约束地震反演研究[D]:[博士].合肥:中国科学技术大学,14.
张洪武,秦建敏.2005.基于率相关模型的多孔介质应变局部化基本理论.科学通报[J],50(24):2713-2719.
张团峰.1997.试论克里金估计与随机模拟的本质区别[J].西安石油学院学报,12(2):52-55.
张勇.2004.三维非均质多孔介质渗透系数和孔隙度的上升尺度.科学通报[J],49(20):2113-2121.
周迪斌.2008.基于纹理的高质量矢量可视化研究[D]:[博士].浙江:浙江大学,11-14.
周宏伟,张亚衡,李爱民,等.2008.孔隙介质中流体渗流边界演化过程的实验研究.科学通报[J],53(3):351-358.
Arpat G.2005.Sequential simulation with patterns[D]:[Ph.D.].USA:Stanford University.Bakke S,φren P E.1997.3-D pore-scale modelling of sandstones and flow simulations in the pore networks[J].Journal of Petroleum Science and Engineering,2(2),136-149.
Blunt M J,Jackson M D,Piri M et al.2002.Detailed physics,predictive capabilities and macroscopic consequences for pore-network models of muitiphase flow.Adv Water Res[J],25:1069-1089.
Blunt M,King P.Macroscopic parameters from simulations of pore scale flow.Physical Review A,1990,42(8):4780-4787.
Blunt M,King P.1991.Relative permeability from two- and three-dimensional pore-scale modeling[J].Transport in Porous Media,6(8):407-433.
Bryant S L,King P R,Mellor D W.1993.Network model evaluation of permeability and spatial correlation in a real random sphere packing.Transport in Porous Media,11(1):53-70.
Bryant S,Blunt M.1992.Prediction of relative permeability in simple porous-media[J].PhysicalReview A,46(4),2004-2011.
Caers J.2001.Geostatistical reservoir modelling using statistical pattern recognition[J].Journal of Petroleum Science and Engineering,29(3-4),177-188.
Caers,J.2003.Efficient gradual deformation using a streamline-based proxy method[J],Journal of Petroleum Science and Engineering 39:57-83.
Caers,J.2002.History matching under a training image-based geological model constraints[M]//2002 SPE Annual Technical Conference and Exhibition,San Antonio,Texas.SPE paper #:77429.
Coker D A,Torquato S,Dunsmuir J H.1996.Morphology and physical properties of Fontainebleau sandstone via a tomographic analysis.J Geophys Res-Solid Earth[J],101:17497-17506.
Coker D A,Torquato S.1995.Extraction of morphological quantities from a digitized medium[J].Journal of Applied Physics,77(12):6087-6099.
Deutsch C V,Joumel A G.1998.GSLIB:Geostatistical Software Library and User's Guide[M].2nded.New York:Oxford Press.
Deutsch C,Wang L.1996.Quantifying object-based stochastic modeling of fluvial reservoir[J].Mathematical Geology 28(7),857-880.
Deutsch,C V,Tran T.2002.Fluvsim:a program for object-based stochasticmodeling of fluvial depositional system[J],Computers & Geosciences:525-535.
Dixit A B,Buckley J S,McDougall S R,et al.2000.Empirical measures of wettability in porous media and the relationship between them derived from pore-scale modeling.Transport Porous Med,40(1):27-54.
Dixit A B,McDougall S R,Sorbie K S,et al.1999.Pore-scale modeling of wettability effects and their influence on oil recovery[J].SPE Reservoir Evaluation Eng 2:25-36.
Dixit A B,McDougall S R,Sorbie K S.1998.A pore-level investigation of relative-permeability hysteresis in water-wet systems[J].SPE J.3:15-23.
Dullien F A L．2001．现代渗流物理学[M]．范玉平,赵东伟等译．北京：石油工业出版社,109-131．
Dunsmuir J H,Ferguson S R,D'Amico K L,et al.1991.X-ray microtomography.A new tool for the characterization of porous media[M].// SPE 22860.Proc.Annual Technical Conference.Dallas,Texas,October 6-9,423-430.
Fatt I.1956.The network model of porous media:I.capillary pressure characteristics.Transactions of AIME[J],207(1):144-159.
Fredrich J T.1999.3D imaging of porous media using laser scanning confocal microscopy with application to microscale transport processes[J].Physics and Chemistry of the Earth.Part A:Solid Earth and Geodesy,24(7):551-561.
Guardiano F,Srivastava R M.1993.Multivariate geostatistics:beyond bivariate moments.[M]//In Soares,A.,editor,Geostatistics-Troia.Dordrecht:Kluwer Academic Publication,volume 1,133-144.
Guo Z L,Zheng C G,Shi B C.2002.Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice boltzmann method[J].Chinese Phys,11(4):366-374.
Haldorsen H,Chang D.1986.Notes on stochastic shales:from outcrop to simulation model[M]//Lake L,Caroll H.Reservoir Characterization.London:Academic Press,445-485.
Haldorsen H,Damsleth E.1990.Stochastic modeling[J].Journal of Petroleum Technology:404-412.
Hazlett R D.1995.Simulation of capillary-dominated displacements in microtomographic images of reservoir rocks[J],Transport in Porous Media,20(1):21-35,1995.
He X,Zou Q,Luo L S.1997.Analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice boltzmann BGK model[J].J.Stat.Phys,87,115-136.
Herron G.1985.A Characterization of Certain C1 Discrete Triangular Interpolation[J].SIAM Journal of Numerical Analysis,22,811-819.
Hidajat I,Rastogi A,Singh M,et al.2002.Transport properties of porous media from thin-sections[J].SPE J,7(1):40-48.
Joshi M.1974.A class of stochastic models for porous media.[D]:[Ph.D.].USA:University of Kansas.
Journel A.1986.Constrained Interpolation and Qualitative Information---The Soft Krging Approach[J],Mathematical Geology,18(3):269-286.
Journel A.2002.Combining knowledge from diverse sources:an alternative to traditional data independence hypotheses[J].Mathematical Geology,34(5),573-596.
Journel A.1974.Geostatistics for conditional simulation of orebodies[J].Economic Geology,69:673-680.
Journel A,Deutsch C.1993.Entropy and spatial disorder[J],Mathematical Geology,25(3):329-355.
Levitz P.1998.Off-lattice reconstruction of porous media:critical evaluation,geometrical confinement and molecular transport[J].Advances in Colloid and Interface Science,77(4):71-106.
Liu Y H,Journel A.2004.Improving simulation with a structured path guided by information content[J].Mathematical Geology,36(8):945-964.
Liu Y H.2006.Using the Snesim program for multiple-point statistical simulation[J].Computers & Geosciences,32:1544-1563.
Lu B L,Torquato S.1992.Lineal-path function for random heterogeneous materials[J],Physical Review A,45(2):922-929.
Manwart C,Torquato S,Hilfer R.2000.Stochastic reconstruction of sandstones[J].Phys Rev E,62:893-899.
Marcote D,David M.1988.Trend Surface Analysis as a Special Case of IRF-k Krging[J].Mathematical Geology,20(7),821-824.
Nielson G M.1983.A Method for Interpolating Scattered Data Based Upon a Minimum Norm Network[J].Mathematics of Computation,40(161),253-271.
Okabe H,Blunt M J.2004.Prediction of permeability for porous media reconstructed using multiple-point statistics[J].Physical Review E,70.066135:1-10.
Okabe H.,Blunt M J.2005.Pore space reconstruction using multiple-point statistics[J].Journal of Petroleum Science and Engineering,46:121-137.
φren P E,Bakke S,Arntzen O J.Extending predictive capabilities to network models[M]//.In:Proceedings of the 1997 SPE Annual Technical Conference and Exhibition.Richardson:Society of Petroleum Engineers,1997.369-381.
φren P E,Bakke S.2002.Process based reconstruction of sandstones and predictions of transport properties[J].Transport in Porous Media,46(2):311-343.
φren P E,Bakke S.2003.Reconstruction of Berea sandstone and pore-scale modeling of wettability effects[J].J Pet Sci Eng,39:177—199.
Pilotti M.2000.Reconstruction of clastic porous media.Transport in Porous Media,41(3):359-364.
Poirier C,Tinaw R.1991.Finite Element Stress Tensor Fields Interpolation and Manipulation Using 3D Dual Kriging[J],Computer&Structures,40(2),211-222.
Quiblier J A.1984.A new three-dimensional modeling technique for studying porous media[J].Journal of Colloid and Interface Science,98(1):84-102.
Remy N.2004.Geostatistical Earth Modeling Software:User's Manual[EB/OL].CA:Stanford University,[2007-04-13].Http://sgems.sourceforge.net/
Remy N.Boucher A,Wu J B.2009.Applied Geostatistics with SGeMS:A Users' Guide[M],Cambridge University Press.
Robert S M,Robert S B,Daryl W G.1996.Boundary conditions for the lattice boltzmann method [J].Phys.Fluids,8(7):1788-1800.
Roberts A P,Torquato S.1999.Chord-distribution functions of three-dimensional random media:approximate first passage times of Gaussian processes[J].Physical Review E,59(5):4953-4963.
Sahimi M.1995.Flow and transport in porous media and fractured rock—from classical method to modern approaches[M].VCH Verlagsgesellschaft mbH:158-214.
Stoyan D.,Kendall W,Mecke J.1987.Stochastic Geometry and Its Applications[M].New York John Wiley & Sons.
Strebelle S,Payrazyan K,Caers J.2002a.Modeling of a deepwater turbidite reservoir conditional to seismic data using multiple-point geostatistics[M].// SPE 77425,presented at the 2002 Society of Petroleum Engineers Annual Technical Conference and Exhibition,San Antonio,TX.
Strebelle S.2000.Sequential simulation drawing structures from training images[D]:[Ph.D.].USA:Stanford University.
Strebelle S.2002b.Conditional simulation of complex geological structures using multiple-point statistics[J].Mathematical Geology,34(1):1-21.
Talukdar M S,Torsaeter O,Ioannidis M A.2002.Stochastic reconstruction of particulate media from two-dimensional images[J].Journal of Colloid and Interface Science,248(2):419-428.
Tomutsa L,Radmilovic V.2003.Focused ion beam assisted three-dimensional rock imaging at submicron-scaie[M].// International Symposium of the Society of Core Analysts,SCA2003-47.
Tomutsa L,Silin D.2004.Nanoscale Pore Imaging and Pore Scale Fluid Flow Modeling in Chalk[EB/OL].California:University of California,[2007-08-12].http:// repositories.cdlib.org/lbnl/LBNL-56266.
Tran T.1994.Improving variogram reproduction on dense simulation grids[J],Computers & Geosciences,20(7):1161-1168.
Wong P Z,KoPlik J,Tomanic J.1984.Conductivity and Permeability of rocks[J].Physical Review B,30(11):6606-6614.
Wu J B.2007.4D Seismic and Multiple-Point Pattern Data Integration Using Geostatistics[D]:[Ph.D.].USA:Stanford University.
Yeong C L Y,Torquato S.1998.Reconstructing random media[J].Physical Review E,57(1):495-506.
Zhang T F,Bombarde S,Strebelle S,et al.2005.3d porosity modeling of a carbonate reservoir using continuous multiple-point statistics simulation[J].SPE paper # 96308.
Zhang T F,Journel A.2002a.Merging prior structural interpretation and local data:the multiple-point geostatistics answer.[M]// Stanford Center for Reservoir Forecasting Annual Report 16.Stanford University,Stanford,CA.
Zhang T F.2002b.Multiple-point simulation of multiple reservoir facies.[D]:[M.S.].USA:Stanford University.
Zhang T F.2006.Filter-based training pattern classification for spatial pattern simulation[D]:[Ph.D.].USA:Stanford University.
Zhang T F.2008.Incorporating geological conceptual models and interpretations into reservoir modeling using multiple-point geostatistics[J].Earth Science Frontiers,15(1):26-35.
Zhang T,Lu D T,Li D L.2008.A Statistical Information Reconstruction Method of Images Based on Multiple-point Geostatistics Integrating Soft Data with Hard Data[M].// 2008 International Symposium on Computer Science and Computational Technology(ISCSCT 2008).Shanghai:573-578.
Zhang T,Lu D T,Li D L.2009a.Porous Media Reconstruction Using a Cross-section Image and Multiple-point Geostatistics[M].// 2009 International Conference on Advanced Computer Control(ICACC 2009).Singapore:24-29.
Zhang T,Lu D T,Li D L.2009b.An Improved Reconstruction Method for Porous Media Based on Multiple-point Geostatistics[M].// International Forum on Porous Flow and Applications,Wuhan:653-659.
蔡睿贤,刘启斌.2008.求解数理方程解析解的一种新方法——混合分离变量法.中国科学G辑:物理力学天文学[J],38(9):1236-1245.
陈群,任建勋,过增元.2008.流体流动场协同原理及其在减阻中的应用.科学通报[J]53(4):489-492.
杜宇健,萧德云.2004.Kriging算法在温度场计算中的应用分析[J].计算机辅助设计与图形学学报,16(8):1153-1158.
冯国庆,陈浩,张烈辉 等.利用多点地质统计学方法模拟岩相分布[J].西安石油大学学报(自然科学版),20(5):9-11.
高慧梅,姜汉桥,陈民锋.2007.多孔介质孔隙网络模型的应用现状[J].大庆石油地质与开发,26(2):74-79.
郭尚平,黄延章,周娟,等.1990.物理化学渗流微观机理[M].北京:科学出版社,6-18.
侯健,李振泉,张顺康,等.2008.岩石三维网络模型构建的实验和模拟研究[J].中国科学G 辑:物理力学天文学,38(11):1563-1575.
侯景儒.1998.实用地质统计学(空间信息统计学)[M].北京:地质出版社,1-10.
胡雪蛟,杜建华,刘翔,等.2001.多孔介质突破特性的尺度效应.科学通报[J],46(4):345-347.
黄丰.2007.多孔介质模型的三维重构研究[D]:[博士].合肥:中国科学技术大学.
黄丰,卢德唐,王磊等.2007.多孔介质3维孔隙空间的隐式曲面造型方法[J].中国图象图形学报:12(5):899-904.
金京男.2006.地质统计学在平坝山石灰石矿均化开采中的应用[D]:[硕士].北京:北京科技大学,8-16.
孔祥言.1999.高等渗流力学[M].合肥:中国科学技术大学出版社,1-20.
林茂松.2006.科学计算可视化的应用研究[D]:[博士].四川:西南交通大学,1-24.
牛文杰.2002a.贝叶斯同位置协同克里金估值法的研究[J].计算机辅助设计与图形学学报,14(4):343-347.
牛文杰.2002b.三维数据场可视化克里格建模及其算法的理论和应用研究[D]:[博士].北京:北京航空航天大学,1-24.
牛文杰.2004.基于先验信息的残余克里金法的研究[J].计算机工程与应用,35:80-83.
儒耐尔A G.1982.矿业地质统计学[M].侯景儒,黄竞先,译.北京:冶金工业出版社,66-69.
孙其诚,黄晋,王光谦.2008.液态泡沫强制渗流波叠加现象及其能量分析.科学通报[J], 53(13):1507-1510.
孙玉建.2007.非参数地质统计学进展[J].地质与勘探,43(4):79-82.
孙宪华.2000.硬数据和软数据[J].北京统计,124(6):35.
唐泽圣.1999.清华大学学术专著—三维数据场可视化[M].北京:清华大学出版社,1-21.
王达健,陈书荣,张雄飞等.2001.多孔介质孔隙模型及其应用——毛细管束模型[J].计算机与应用化学,18(5):429-432.
王文成.1998.三维数据场体绘制技术的研究和实现[D]:[博士].北京:中国科学院软件研究所.1-24.
王兴勇.2003.Lattice Boltzmann方法的理论及其在水力计算中应用的研究[D]:[博士].南京:河海大学,1.
吴胜和,李文克.2004.多点地质统计学:理论、应用与展望[J].古地理学报,7(1):137-144.
杨满平.2005.油气储层多孔介质的变形理论及应用研究[D]:[博士].成都:西南石油学院,10-11.
袁益让,韩玉笈.2008.三维油资源渗流力学运移聚集的大规模数值模拟和应用.中国科学G 辑:物理力学天文学[J],38(11):1582-1600.
张程远.2003.地质统计约束地震反演研究[D]:[博士].合肥:中国科学技术大学,14.
张洪武,秦建敏.2005.基于率相关模型的多孔介质应变局部化基本理论.科学通报[J],50(24):2713-2719.
张团峰.1997.试论克里金估计与随机模拟的本质区别[J].西安石油学院学报,12(2):52-55.
张勇.2004.三维非均质多孔介质渗透系数和孔隙度的上升尺度.科学通报[J],49(20):2113-2121.
周迪斌.2008.基于纹理的高质量矢量可视化研究[D]:[博士].浙江:浙江大学,11-14.
周宏伟,张亚衡,李爱民,等.2008.孔隙介质中流体渗流边界演化过程的实验研究.科学通报[J],53(3):351-358.
Arpat G.2005.Sequential simulation with patterns[D]:[Ph.D.].USA:Stanford University.Bakke S,φren P E.1997.3-D pore-scale modelling of sandstones and flow simulations in the pore networks[J].Journal of Petroleum Science and Engineering,2(2),136-149.
Blunt M J,Jackson M D,Piri M et al.2002.Detailed physics,predictive capabilities and macroscopic consequences for pore-network models of muitiphase flow.Adv Water Res[J],25:1069-1089.
Blunt M,King P.Macroscopic parameters from simulations of pore scale flow.Physical Review A,1990,42(8):4780-4787.
Blunt M,King P.1991.Relative permeability from two- and three-dimensional pore-scale modeling[J].Transport in Porous Media,6(8):407-433.
Bryant S L,King P R,Mellor D W.1993.Network model evaluation of permeability and spatial correlation in a real random sphere packing.Transport in Porous Media,11(1):53-70.
Bryant S,Blunt M.1992.Prediction of relative permeability in simple porous-media[J].PhysicalReview A,46(4),2004-2011.
Caers J.2001.Geostatistical reservoir modelling using statistical pattern recognition[J].Journal of Petroleum Science and Engineering,29(3-4),177-188.
Caers,J.2003.Efficient gradual deformation using a streamline-based proxy method[J],Journal of Petroleum Science and Engineering 39:57-83.
Caers,J.2002.History matching under a training image-based geological model constraints[M]//2002 SPE Annual Technical Conference and Exhibition,San Antonio,Texas.SPE paper #:77429.
Coker D A,Torquato S,Dunsmuir J H.1996.Morphology and physical properties of Fontainebleau sandstone via a tomographic analysis.J Geophys Res-Solid Earth[J],101:17497-17506.
Coker D A,Torquato S.1995.Extraction of morphological quantities from a digitized medium[J].Journal of Applied Physics,77(12):6087-6099.
Deutsch C V,Joumel A G.1998.GSLIB:Geostatistical Software Library and User's Guide[M].2nded.New York:Oxford Press.
Deutsch C,Wang L.1996.Quantifying object-based stochastic modeling of fluvial reservoir[J].Mathematical Geology 28(7),857-880.
Deutsch,C V,Tran T.2002.Fluvsim:a program for object-based stochasticmodeling of fluvial depositional system[J],Computers & Geosciences:525-535.
Dixit A B,Buckley J S,McDougall S R,et al.2000.Empirical measures of wettability in porous media and the relationship between them derived from pore-scale modeling.Transport Porous Med,40(1):27-54.
Dixit A B,McDougall S R,Sorbie K S,et al.1999.Pore-scale modeling of wettability effects and their influence on oil recovery[J].SPE Reservoir Evaluation Eng 2:25-36.
Dixit A B,McDougall S R,Sorbie K S.1998.A pore-level investigation of relative-permeability hysteresis in water-wet systems[J].SPE J.3:15-23.
Dullien F A L．2001．现代渗流物理学[M]．范玉平,赵东伟等译．北京：石油工业出版社,109-131．
Dunsmuir J H,Ferguson S R,D'Amico K L,et al.1991.X-ray microtomography.A new tool for the characterization of porous media[M].// SPE 22860.Proc.Annual Technical Conference.Dallas,Texas,October 6-9,423-430.
Fatt I.1956.The network model of porous media:I.capillary pressure characteristics.Transactions of AIME[J],207(1):144-159.
Fredrich J T.1999.3D imaging of porous media using laser scanning confocal microscopy with application to microscale transport processes[J].Physics and Chemistry of the Earth.Part A:Solid Earth and Geodesy,24(7):551-561.
Guardiano F,Srivastava R M.1993.Multivariate geostatistics:beyond bivariate moments.[M]//In Soares,A.,editor,Geostatistics-Troia.Dordrecht:Kluwer Academic Publication,volume 1,133-144.
Guo Z L,Zheng C G,Shi B C.2002.Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice boltzmann method[J].Chinese Phys,11(4):366-374.
Haldorsen H,Chang D.1986.Notes on stochastic shales:from outcrop to simulation model[M]//Lake L,Caroll H.Reservoir Characterization.London:Academic Press,445-485.
Haldorsen H,Damsleth E.1990.Stochastic modeling[J].Journal of Petroleum Technology:404-412.
Hazlett R D.1995.Simulation of capillary-dominated displacements in microtomographic images of reservoir rocks[J],Transport in Porous Media,20(1):21-35,1995.
He X,Zou Q,Luo L S.1997.Analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice boltzmann BGK model[J].J.Stat.Phys,87,115-136.
Herron G.1985.A Characterization of Certain C1 Discrete Triangular Interpolation[J].SIAM Journal of Numerical Analysis,22,811-819.
Hidajat I,Rastogi A,Singh M,et al.2002.Transport properties of porous media from thin-sections[J].SPE J,7(1):40-48.
Joshi M.1974.A class of stochastic models for porous media.[D]:[Ph.D.].USA:University of Kansas.
Journel A.1986.Constrained Interpolation and Qualitative Information---The Soft Krging Approach[J],Mathematical Geology,18(3):269-286.
Journel A.2002.Combining knowledge from diverse sources:an alternative to traditional data independence hypotheses[J].Mathematical Geology,34(5),573-596.
Journel A.1974.Geostatistics for conditional simulation of orebodies[J].Economic Geology,69:673-680.
Journel A,Deutsch C.1993.Entropy and spatial disorder[J],Mathematical Geology,25(3):329-355.
Levitz P.1998.Off-lattice reconstruction of porous media:critical evaluation,geometrical confinement and molecular transport[J].Advances in Colloid and Interface Science,77(4):71-106.
Liu Y H,Journel A.2004.Improving simulation with a structured path guided by information content[J].Mathematical Geology,36(8):945-964.
Liu Y H.2006.Using the Snesim program for multiple-point statistical simulation[J].Computers & Geosciences,32:1544-1563.
Lu B L,Torquato S.1992.Lineal-path function for random heterogeneous materials[J],Physical Review A,45(2):922-929.
Manwart C,Torquato S,Hilfer R.2000.Stochastic reconstruction of sandstones[J].Phys Rev E,62:893-899.
Marcote D,David M.1988.Trend Surface Analysis as a Special Case of IRF-k Krging[J].Mathematical Geology,20(7),821-824.
Nielson G M.1983.A Method for Interpolating Scattered Data Based Upon a Minimum Norm Network[J].Mathematics of Computation,40(161),253-271.
Okabe H,Blunt M J.2004.Prediction of permeability for porous media reconstructed using multiple-point statistics[J].Physical Review E,70.066135:1-10.
Okabe H.,Blunt M J.2005.Pore space reconstruction using multiple-point statistics[J].Journal of Petroleum Science and Engineering,46:121-137.
φren P E,Bakke S,Arntzen O J.Extending predictive capabilities to network models[M]//.In:Proceedings of the 1997 SPE Annual Technical Conference and Exhibition.Richardson:Society of Petroleum Engineers,1997.369-381.
φren P E,Bakke S.2002.Process based reconstruction of sandstones and predictions of transport properties[J].Transport in Porous Media,46(2):311-343.
φren P E,Bakke S.2003.Reconstruction of Berea sandstone and pore-scale modeling of wettability effects[J].J Pet Sci Eng,39:177—199.
Pilotti M.2000.Reconstruction of clastic porous media.Transport in Porous Media,41(3):359-364.
Poirier C,Tinaw R.1991.Finite Element Stress Tensor Fields Interpolation and Manipulation Using 3D Dual Kriging[J],Computer&Structures,40(2),211-222.
Quiblier J A.1984.A new three-dimensional modeling technique for studying porous media[J].Journal of Colloid and Interface Science,98(1):84-102.
Remy N.2004.Geostatistical Earth Modeling Software:User's Manual[EB/OL].CA:Stanford University,[2007-04-13].Http://sgems.sourceforge.net/
Remy N.Boucher A,Wu J B.2009.Applied Geostatistics with SGeMS:A Users' Guide[M],Cambridge University Press.
Robert S M,Robert S B,Daryl W G.1996.Boundary conditions for the lattice boltzmann method [J].Phys.Fluids,8(7):1788-1800.
Roberts A P,Torquato S.1999.Chord-distribution functions of three-dimensional random media:approximate first passage times of Gaussian processes[J].Physical Review E,59(5):4953-4963.
Sahimi M.1995.Flow and transport in porous media and fractured rock—from classical method to modern approaches[M].VCH Verlagsgesellschaft mbH:158-214.
Stoyan D.,Kendall W,Mecke J.1987.Stochastic Geometry and Its Applications[M].New York John Wiley & Sons.
Strebelle S,Payrazyan K,Caers J.2002a.Modeling of a deepwater turbidite reservoir conditional to seismic data using multiple-point geostatistics[M].// SPE 77425,presented at the 2002 Society of Petroleum Engineers Annual Technical Conference and Exhibition,San Antonio,TX.
Strebelle S.2000.Sequential simulation drawing structures from training images[D]:[Ph.D.].USA:Stanford University.
Strebelle S.2002b.Conditional simulation of complex geological structures using multiple-point statistics[J].Mathematical Geology,34(1):1-21.
Talukdar M S,Torsaeter O,Ioannidis M A.2002.Stochastic reconstruction of particulate media from two-dimensional images[J].Journal of Colloid and Interface Science,248(2):419-428.
Tomutsa L,Radmilovic V.2003.Focused ion beam assisted three-dimensional rock imaging at submicron-scaie[M].// International Symposium of the Society of Core Analysts,SCA2003-47.
Tomutsa L,Silin D.2004.Nanoscale Pore Imaging and Pore Scale Fluid Flow Modeling in Chalk[EB/OL].California:University of California,[2007-08-12].http:// repositories.cdlib.org/lbnl/LBNL-56266.
Tran T.1994.Improving variogram reproduction on dense simulation grids[J],Computers & Geosciences,20(7):1161-1168.
Wong P Z,KoPlik J,Tomanic J.1984.Conductivity and Permeability of rocks[J].Physical Review B,30(11):6606-6614.
Wu J B.2007.4D Seismic and Multiple-Point Pattern Data Integration Using Geostatistics[D]:[Ph.D.].USA:Stanford University.
Yeong C L Y,Torquato S.1998.Reconstructing random media[J].Physical Review E,57(1):495-506.
Zhang T F,Bombarde S,Strebelle S,et al.2005.3d porosity modeling of a carbonate reservoir using continuous multiple-point statistics simulation[J].SPE paper # 96308.
Zhang T F,Journel A.2002a.Merging prior structural interpretation and local data:the multiple-point geostatistics answer.[M]// Stanford Center for Reservoir Forecasting Annual Report 16.Stanford University,Stanford,CA.
Zhang T F.2002b.Multiple-point simulation of multiple reservoir facies.[D]:[M.S.].USA:Stanford University.
Zhang T F.2006.Filter-based training pattern classification for spatial pattern simulation[D]:[Ph.D.].USA:Stanford University.
Zhang T F.2008.Incorporating geological conceptual models and interpretations into reservoir modeling using multiple-point geostatistics[J].Earth Science Frontiers,15(1):26-35.
Zhang T,Lu D T,Li D L.2008.A Statistical Information Reconstruction Method of Images Based on Multiple-point Geostatistics Integrating Soft Data with Hard Data[M].// 2008 International Symposium on Computer Science and Computational Technology(ISCSCT 2008).Shanghai:573-578.
Zhang T,Lu D T,Li D L.2009a.Porous Media Reconstruction Using a Cross-section Image and Multiple-point Geostatistics[M].// 2009 International Conference on Advanced Computer Control(ICACC 2009).Singapore:24-29.
Zhang T,Lu D T,Li D L.2009b.An Improved Reconstruction Method for Porous Media Based on Multiple-point Geostatistics[M].// International Forum on Porous Flow and Applications,Wuhan:653-659.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |