一种新的基于拓扑结构特征的微裂隙-孔隙空间描述方法
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摘要
微裂隙在多孔介质储层大量发育并与基质孔隙连通,是流体渗流特别是非常规储层油气渗流的重要通道.高精度无损成像技术以及数字岩心技术的快速发展,为孔裂隙空间描述、孔裂隙模型构建等研究提供了数据支撑.本文基于传统孔隙空间拓扑学,分析裂隙拓扑结构特征,充分考虑三维裂隙空间区别于普通孔隙的面状特征以及与基质孔隙之间的相互连通关系,提出"特征点化"的思路,将裂隙空间点进行分类,形成了适用于多种孔裂隙空间的描述以及结构特征分析方法.首先基于传统孔隙拓扑结构分析方法,提出"线面共存"的新骨架模型,提取裂隙中轴骨架面、中轴骨架线,精细刻画裂隙轮廓以及孔裂隙连通关系;其次,基于各类空间点的拓扑结构共性分别提取相应点集,分割孔隙、裂隙空间,构建微裂隙-孔隙骨架模型;第三,基于新的孔裂隙骨架模型提取孔裂隙空间的几何-拓扑结构特征参数,获取裂隙孔隙度、开度、倾角等重要裂隙几何参数,以及孔裂隙配位数、裂隙发育范围等拓扑参数;最后基于上述骨架提取描述方法,对理想与真实孔裂隙空间的数字岩心进行了骨架提取和分析.从微裂隙拓扑形态开展研究进而对裂隙-孔隙空间描述,可简化此类孔隙介质的建模过程,为后续气、液流动模拟提供准确数据基础,促进缝洞介质油气开发的进展.
Natural micro-fractures in ultra-tight formations, such as shales and coal seams, provide key information about pore structure and continuous channel in it. How to identify the geometrical and topological properties of micro-fractured structure and matrix pore space and the correlation between them are the major contributors which can lead to strong calculation results during the following seepage flow simulation. Through characterizing the pore space included micro-fractures(i.e., connectivity capability of pore space, extension of fracture, etc.), we can therefore describe and develop pore-fracture structure and the suitable models to gain better understanding of the roles of micro-fractures on the drainage of hydrocarbons from matrix pores. In this work, we proposed a new skeleton model to distinguish fractures from pore space via extraction of surface points set of fracture. In the procedure of points set extraction, we improved the classic "medial axis based" shrink method to "medial surface-based" method for new fracture description through introducing a new set of skeleton points(i.e., surface points and edge points of the fracture), one of which describes its aperture and the other is used for collecting connectivity information and determining the extension ranges of the fracture. The new skeleton model can show more comprehensible forms of the real connected junction instead of the former ideal model, voxel-thickness medial surface extracted can also satisfy demands of the classic skeleton extraction model and preserve the topology of the original pore space included micro-fractures in the meantime. New points set classification method mentioned above is determined by considering the difference of their topological properties. Through calculating and collecting their topological number one by one, we can obtain a new skeleton model formed with medial axis and surface. Among them, the simple points set was composed of values of topological number T6=T26=1 in the 3×3×3 direct neighborhood system as before and would be deleted in the process of shrinking pore space in the certain order of the distance values of the space. The surface points forming medial surface was composed of the points close to the center of the micro-fractures in all directions. An object point was defined as surface point if no background voxels continuously existed between any two neighbor voxel that shares a "face" in its 3×3×3 neighborhood system, which means its topological number T6>1. Edge points represented as the junction between fractures and matrix if they are always the one of the 26 neighbors of surface points. Moreover, in the process of obtaining new skeleton model, characteristic parameters and connectivity of micro-fractures can then be easily got via statistics and calculation. Through combining Euclidean distance maps and geometric transformation, we can easily calculated the parameters of width, thickness, orientation, and inclination angle of micro-fractures. Connectivity location information from edge points would play the part of following simulation of flow interaction between fractures and the matrix. As a contrast, ideal and real fracture models were used to verify feasibility of our new methods, all results showed good effectiveness and accuracy. The study will lead to more realistic pore space models and help to extend the applicability to a wider range of porous media especially for the study of multi-scale pore space representation. This work was inspired by challenges in developing a fast and accurate method for micro-scale modeling in micro-fractured porous media, and potentially applicable for flow simulations in the tight porosity samples. Overall, our new methods improved the level of micro-fracture characterization representation of the pore space including fractures for the following flow simulation.
Natural micro-fractures in ultra-tight formations, such as shales and coal seams, provide key information about pore structure and continuous channel in it. How to identify the geometrical and topological properties of micro-fractured structure and matrix pore space and the correlation between them are the major contributors which can lead to strong calculation results during the following seepage flow simulation. Through characterizing the pore space included micro-fractures(i.e., connectivity capability of pore space, extension of fracture, etc.), we can therefore describe and develop pore-fracture structure and the suitable models to gain better understanding of the roles of micro-fractures on the drainage of hydrocarbons from matrix pores. In this work, we proposed a new skeleton model to distinguish fractures from pore space via extraction of surface points set of fracture. In the procedure of points set extraction, we improved the classic "medial axis based" shrink method to "medial surface-based" method for new fracture description through introducing a new set of skeleton points(i.e., surface points and edge points of the fracture), one of which describes its aperture and the other is used for collecting connectivity information and determining the extension ranges of the fracture. The new skeleton model can show more comprehensible forms of the real connected junction instead of the former ideal model, voxel-thickness medial surface extracted can also satisfy demands of the classic skeleton extraction model and preserve the topology of the original pore space included micro-fractures in the meantime. New points set classification method mentioned above is determined by considering the difference of their topological properties. Through calculating and collecting their topological number one by one, we can obtain a new skeleton model formed with medial axis and surface. Among them, the simple points set was composed of values of topological number T6=T26=1 in the 3×3×3 direct neighborhood system as before and would be deleted in the process of shrinking pore space in the certain order of the distance values of the space. The surface points forming medial surface was composed of the points close to the center of the micro-fractures in all directions. An object point was defined as surface point if no background voxels continuously existed between any two neighbor voxel that shares a "face" in its 3×3×3 neighborhood system, which means its topological number T6>1. Edge points represented as the junction between fractures and matrix if they are always the one of the 26 neighbors of surface points. Moreover, in the process of obtaining new skeleton model, characteristic parameters and connectivity of micro-fractures can then be easily got via statistics and calculation. Through combining Euclidean distance maps and geometric transformation, we can easily calculated the parameters of width, thickness, orientation, and inclination angle of micro-fractures. Connectivity location information from edge points would play the part of following simulation of flow interaction between fractures and the matrix. As a contrast, ideal and real fracture models were used to verify feasibility of our new methods, all results showed good effectiveness and accuracy. The study will lead to more realistic pore space models and help to extend the applicability to a wider range of porous media especially for the study of multi-scale pore space representation. This work was inspired by challenges in developing a fast and accurate method for micro-scale modeling in micro-fractured porous media, and potentially applicable for flow simulations in the tight porosity samples. Overall, our new methods improved the level of micro-fracture characterization representation of the pore space including fractures for the following flow simulation.
引文
1 Karpyn Z T,Piri M.Prediction of fluid occupancy in fractures using network modeling and X-ray microtomography.I:Data conditioning and model description.Phys Rev E,2007,76:016315
2 Yao J,Sun H,Huang Z Q,et al.Key mechanics problems of unconventional shale gas reservoirs(in Chinese).Sci Sin-Phys Mech Astron,2013,43:1527–1547[姚军,孙海,黄朝琴,等.页岩气藏开发中的关键力学问题.中国科学:物理学力学天文学,2013,43:1527–1547]
3 Knackstedt M,Arns C,Ghous A,et al.3D imaging and flow characterization of the pore space of carbonate core samples.In:Proceedings of International Symposium of the Society of Core Analysts.Trondheim,2006
4 Madadi M,Sahimi M.Lattice Boltzmann simulation of fluid flow in fracture networks with rough,self-affine surfaces.Phys Rev E,2003,67:026309
5 Prodanovic M,Bryant S L,Karpyn Z T.Investigating matrix/fracture transfer via a level set method for drainage and imbibition.SPE J,2010,15:125–136
6 Yao J,Zhao J L,Zhang M,et al.Microscale shale gas flow simulation based on lattice Boltzmann method(in Chinese).Acta Petrol Sin,2015,36:1280–1289[姚军,赵建林,张敏,等.基于格子Boltzmann方法的页岩气微观流动模拟.石油学报,2015,36:1280–1289]
7 Hughes R G,Blunt M J.Network modeling of multiphase flow in fractures.Adv Water Resour,2001,24:409–421
8 Piri M,Karpyn Z T.Prediction of fluid occupancy in fractures using network modeling and X-ray microtomography.II:Results.Phys Rev E,2007,76:016316
9 Kranz R L.Microcracks in rocks:A review.Tectonophysics,1983,100:449–480
10 Cnudde V,Boone M N.High-resolution X-ray computed tomography in geosciences:A review of the current technology and applications.Earth-Sci Rev,2013,123:1–17
11 Wang L,Jin Y O,Butler I.Interpretation of particle breakage under compression using X-ray computed tomography and digital image correlation.Proced Eng,2015,102:240–248
12 Lee T C,Kashyap R L,Chu C N.Building skeleton models via 3-D medial surface axis thinning algorithms.Graph Model Im Proc,1994,56 :462–478
13 Lindquist W B,Venkatarangan A.Investigating 3D geometry of porous media from high resolution images.Phys Chem Earth A,1999,24 :593–599
14 Lindquist W B,Venkatarangan A,Dunsmuir J,et al.Pore and throat size distributions measured from synchrotron X-ray tomographic images of Fontainebleau sandstones.J Geophys Res Solid Earth,2000,105:21509–21527
15 Jiang Z.Quantitative characterisation of the geometry and topology of pore space in 3D rock images.Dissertation for Dcotoral Degree.Edinburgh:Heriot-Watt University,2008
16 Dhanalakshmi N,Latha Y M,Damodaram A.Skeletonization of Players in Dynamic Backgrounds Using Discrete Curve Evolution.New Delhi:Springer,2016.689–696
17 Lee J,Son H,Kim C,et al.Skeleton-based 3D reconstruction of as-built pipelines from laser-scan data.Autom Constr,2013,35:199 –207
18 Delerue J F,Perrier E.DXSoil,a library for 3D image analysis in soil science.Comput Geosci,2002,28:1041–1050
19 Sok R M,Knackstedt M A,Sheppard A P,et al.Direct and stochastic generation of network models from tomographic images:Effect of topology on residual saturations.Transport Porous Med,2002,46:345–371
20 Blunt M J.Flow in porous media—pore-network models and multiphase flow.Curr Opin Colloid Interface Sci,2001,6:197–207
21 Lopez X,Valvatne P H,Blunt M J.Predictive network modeling of single-phase non-Newtonian flow in porous media.J Colloid Interface Sci,2003,264:256–265
22 Blunt M J,Bijeljic B,Dong H,et al.Pore-scale imaging and modelling.Adv Water Resour,2013,51:197–216
23 Dong H,Blunt M J.Pore-network extraction from micro-computerized-tomography images.Phys Rev E,2009,80:036307
24 Bultreys T,De Boever W,Cnudde V.Imaging and image-based fluid transport modeling at the pore scale in geological materials:A practical introduction to the current state-of-the-art.Earth Sci Rev,2016,155:93–128
25 Wang W,Shahvali M,Su Y.A semi-analytical fractal model for production from tight oil reservoirs with hydraulically fractured horizontal wells.Fuel,2015,158:612–618
26 Wang W,Su Y,Sheng G,et al.A mathematical model considering complex fractures and fractal flow for pressure transient analysis of fractured horizontal wells in unconventional reservoirs.J Nat Gas Sci Eng,2015,23:139–147
27 Riasi M S,Palakurthi N K,Montemagno C,et al.A feasibility study of the pore topology method(PTM),a medial surface-based approach to multi-phase flow simulation in porous media.Transport Porous Med,2016,115:519–539
28 Jiang Z,Wu K,Couples G,et al.Efficient extraction of networks from three-dimensional porous media.Water Resour Res,2007,43:2578–2584
29 Corbett P,Hayashi F Y,Alves M S,et al.Microbial carbonates:A sampling and measurement challenge for petrophysics addressed by capturing the bioarchitectural components.Geol Soc London Spec Publ,2015,418:69–85
30 Wilson J,Chester J,Chester F.Microfracture analysis of fault growth and wear processes,Punchbowl Fault,San Andreas system,California.J Struct Geol,2003,25:1855–1873
31 Morgenthaler D G.Three-Dimensional Simple Points:Serial Erosion,Parallel Thinning,and Skeletonization.Maryland:University of Maryland,1981
32 Lindquist W B,Lee S M,Coker D A,et al.Medial axis analysis of void structure in three-dimensional tomographic images of porous media.J Geophys Res-Solid Earth,1996,101:8297–8310
33 Han X,Xu C,Prince J L.A topology preserving level set method for geometric deformable models.IEEE Trans Patt Anal Mach Intell,2003,25:755–768
34 Xie W,Thompson R P,Perucchio R.A topology-preserving parallel 3D thinning algorithm for extracting the curve skeleton.Pattern Recogn,2003,36:1529–1544
35 Lohou C,Bertrand G.A 3D 12-subiteration thinning algorithm based on P-simple points.Discrete Appl Math,2004,139:171–195
36 Zhou Q Y,Ju T,Hu S M.Topology repair of solid models using skeletons.IEEE Trans Vis Compo Graph,2007,13:675–685
37 Kong T Y,Rosenfeld A.Digital topology:Introduction and survey.Comput Vis Graph Image Process,1989,48:357–393
38 Bertrand G,Malandain G.A new characterization of three-dimensional simple points.Pattern Recogn Lett,1994,15:169–175
39 Borgefors G,Nystr?m I,Di Baja G S.Computing skeletons in three dimensions.Pattern Recogn,1999,32:1225–1236
40 Bertrand G.Simple points,topological numbers and geodesic neighborhoods in cubic grids.Pattern Recogn Lett,1994,15:1003–1011
41 Toriwaki J,Yoshida H.Fundamentals of Three-Dimensional Digital Image Processing.Berlin:Springer,2009
42 Palágyi K,Kuba A.A parallel 3D 12-subiteration thinning algorithm.Graph Models Image Process,1999,61:199–221
43 Ju T,Baker M L,Chiu W.Computing a family of skeletons of volumetric models for shape description.Comput Aided Des,2007,39:352 –360
44 Palágyi K.A 3D fully parallel surface-thinning algorithm.Theor Comput Sci,2008,406:119–135
45 Hadwiger H,Hadwiger H.Vorlesungenüber Inhalt,Oberfl?che Und Isoperimetrie.Berlin:Springer,1957
46 Wang X,Yao J,Jiang Z Y,et al.A new method of fast distance transform 3D image based on“neighborhood between voxels in space”theory(in Chinese).Chin Sci Bull,2017,62:1662–1669[王鑫,姚军,蒋泽云,等.一种新的三维欧式距离变换方法及在数字岩心中的应用.科学通报,2017,62:1662–1669]
2 Yao J,Sun H,Huang Z Q,et al.Key mechanics problems of unconventional shale gas reservoirs(in Chinese).Sci Sin-Phys Mech Astron,2013,43:1527–1547[姚军,孙海,黄朝琴,等.页岩气藏开发中的关键力学问题.中国科学:物理学力学天文学,2013,43:1527–1547]
3 Knackstedt M,Arns C,Ghous A,et al.3D imaging and flow characterization of the pore space of carbonate core samples.In:Proceedings of International Symposium of the Society of Core Analysts.Trondheim,2006
4 Madadi M,Sahimi M.Lattice Boltzmann simulation of fluid flow in fracture networks with rough,self-affine surfaces.Phys Rev E,2003,67:026309
5 Prodanovic M,Bryant S L,Karpyn Z T.Investigating matrix/fracture transfer via a level set method for drainage and imbibition.SPE J,2010,15:125–136
6 Yao J,Zhao J L,Zhang M,et al.Microscale shale gas flow simulation based on lattice Boltzmann method(in Chinese).Acta Petrol Sin,2015,36:1280–1289[姚军,赵建林,张敏,等.基于格子Boltzmann方法的页岩气微观流动模拟.石油学报,2015,36:1280–1289]
7 Hughes R G,Blunt M J.Network modeling of multiphase flow in fractures.Adv Water Resour,2001,24:409–421
8 Piri M,Karpyn Z T.Prediction of fluid occupancy in fractures using network modeling and X-ray microtomography.II:Results.Phys Rev E,2007,76:016316
9 Kranz R L.Microcracks in rocks:A review.Tectonophysics,1983,100:449–480
10 Cnudde V,Boone M N.High-resolution X-ray computed tomography in geosciences:A review of the current technology and applications.Earth-Sci Rev,2013,123:1–17
11 Wang L,Jin Y O,Butler I.Interpretation of particle breakage under compression using X-ray computed tomography and digital image correlation.Proced Eng,2015,102:240–248
12 Lee T C,Kashyap R L,Chu C N.Building skeleton models via 3-D medial surface axis thinning algorithms.Graph Model Im Proc,1994,56 :462–478
13 Lindquist W B,Venkatarangan A.Investigating 3D geometry of porous media from high resolution images.Phys Chem Earth A,1999,24 :593–599
14 Lindquist W B,Venkatarangan A,Dunsmuir J,et al.Pore and throat size distributions measured from synchrotron X-ray tomographic images of Fontainebleau sandstones.J Geophys Res Solid Earth,2000,105:21509–21527
15 Jiang Z.Quantitative characterisation of the geometry and topology of pore space in 3D rock images.Dissertation for Dcotoral Degree.Edinburgh:Heriot-Watt University,2008
16 Dhanalakshmi N,Latha Y M,Damodaram A.Skeletonization of Players in Dynamic Backgrounds Using Discrete Curve Evolution.New Delhi:Springer,2016.689–696
17 Lee J,Son H,Kim C,et al.Skeleton-based 3D reconstruction of as-built pipelines from laser-scan data.Autom Constr,2013,35:199 –207
18 Delerue J F,Perrier E.DXSoil,a library for 3D image analysis in soil science.Comput Geosci,2002,28:1041–1050
19 Sok R M,Knackstedt M A,Sheppard A P,et al.Direct and stochastic generation of network models from tomographic images:Effect of topology on residual saturations.Transport Porous Med,2002,46:345–371
20 Blunt M J.Flow in porous media—pore-network models and multiphase flow.Curr Opin Colloid Interface Sci,2001,6:197–207
21 Lopez X,Valvatne P H,Blunt M J.Predictive network modeling of single-phase non-Newtonian flow in porous media.J Colloid Interface Sci,2003,264:256–265
22 Blunt M J,Bijeljic B,Dong H,et al.Pore-scale imaging and modelling.Adv Water Resour,2013,51:197–216
23 Dong H,Blunt M J.Pore-network extraction from micro-computerized-tomography images.Phys Rev E,2009,80:036307
24 Bultreys T,De Boever W,Cnudde V.Imaging and image-based fluid transport modeling at the pore scale in geological materials:A practical introduction to the current state-of-the-art.Earth Sci Rev,2016,155:93–128
25 Wang W,Shahvali M,Su Y.A semi-analytical fractal model for production from tight oil reservoirs with hydraulically fractured horizontal wells.Fuel,2015,158:612–618
26 Wang W,Su Y,Sheng G,et al.A mathematical model considering complex fractures and fractal flow for pressure transient analysis of fractured horizontal wells in unconventional reservoirs.J Nat Gas Sci Eng,2015,23:139–147
27 Riasi M S,Palakurthi N K,Montemagno C,et al.A feasibility study of the pore topology method(PTM),a medial surface-based approach to multi-phase flow simulation in porous media.Transport Porous Med,2016,115:519–539
28 Jiang Z,Wu K,Couples G,et al.Efficient extraction of networks from three-dimensional porous media.Water Resour Res,2007,43:2578–2584
29 Corbett P,Hayashi F Y,Alves M S,et al.Microbial carbonates:A sampling and measurement challenge for petrophysics addressed by capturing the bioarchitectural components.Geol Soc London Spec Publ,2015,418:69–85
30 Wilson J,Chester J,Chester F.Microfracture analysis of fault growth and wear processes,Punchbowl Fault,San Andreas system,California.J Struct Geol,2003,25:1855–1873
31 Morgenthaler D G.Three-Dimensional Simple Points:Serial Erosion,Parallel Thinning,and Skeletonization.Maryland:University of Maryland,1981
32 Lindquist W B,Lee S M,Coker D A,et al.Medial axis analysis of void structure in three-dimensional tomographic images of porous media.J Geophys Res-Solid Earth,1996,101:8297–8310
33 Han X,Xu C,Prince J L.A topology preserving level set method for geometric deformable models.IEEE Trans Patt Anal Mach Intell,2003,25:755–768
34 Xie W,Thompson R P,Perucchio R.A topology-preserving parallel 3D thinning algorithm for extracting the curve skeleton.Pattern Recogn,2003,36:1529–1544
35 Lohou C,Bertrand G.A 3D 12-subiteration thinning algorithm based on P-simple points.Discrete Appl Math,2004,139:171–195
36 Zhou Q Y,Ju T,Hu S M.Topology repair of solid models using skeletons.IEEE Trans Vis Compo Graph,2007,13:675–685
37 Kong T Y,Rosenfeld A.Digital topology:Introduction and survey.Comput Vis Graph Image Process,1989,48:357–393
38 Bertrand G,Malandain G.A new characterization of three-dimensional simple points.Pattern Recogn Lett,1994,15:169–175
39 Borgefors G,Nystr?m I,Di Baja G S.Computing skeletons in three dimensions.Pattern Recogn,1999,32:1225–1236
40 Bertrand G.Simple points,topological numbers and geodesic neighborhoods in cubic grids.Pattern Recogn Lett,1994,15:1003–1011
41 Toriwaki J,Yoshida H.Fundamentals of Three-Dimensional Digital Image Processing.Berlin:Springer,2009
42 Palágyi K,Kuba A.A parallel 3D 12-subiteration thinning algorithm.Graph Models Image Process,1999,61:199–221
43 Ju T,Baker M L,Chiu W.Computing a family of skeletons of volumetric models for shape description.Comput Aided Des,2007,39:352 –360
44 Palágyi K.A 3D fully parallel surface-thinning algorithm.Theor Comput Sci,2008,406:119–135
45 Hadwiger H,Hadwiger H.Vorlesungenüber Inhalt,Oberfl?che Und Isoperimetrie.Berlin:Springer,1957
46 Wang X,Yao J,Jiang Z Y,et al.A new method of fast distance transform 3D image based on“neighborhood between voxels in space”theory(in Chinese).Chin Sci Bull,2017,62:1662–1669[王鑫,姚军,蒋泽云,等.一种新的三维欧式距离变换方法及在数字岩心中的应用.科学通报,2017,62:1662–1669]
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