多孔介质三维重建及流体动画模拟
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摘要
许多工业应用都涉及多孔介质内流体运动的问题,比如低渗透和特低渗透油气田开发、地下水的利用、煤气层的开采、以及金属材料的制备等等。建立一套软件,能够精确地对多孔介质进行三维重建,并在此基础上抽取介质内的孔隙网络,动画模拟流体在介质孔隙内的流动,不仅可以帮助人们通过计算机实验快速方便地确定多孔介质相关物理参数,而且对于研究多孔介质空间结构对孔隙流的影响也有非常大的帮助。无论从实际应用还是理论研究上来讲,该课题都有非常重要的研究价值。本文要做的工作就是基于一系列多孔介质的断层切片图像重建其三维空间结构并动画模拟多孔介质内流体流动。
本文主要的研究内容及成果如下:
1、介绍和分析多孔介质三维重建及流体动画模拟的研究现状。
2、采用三维图像法重建多孔介质空间结构。针对扫描仪器的成像特点,对获得的断层切片图像采用一系列的图像处理方法进行背景去除和噪声过滤,并结合多孔介质的相关知识,对断层切片图像内的轮廓线进行扩展容纳表面孔隙,识别固体骨架和孔隙空间,提取介质内有效孔隙网络。
3、断层切片的间距有可能大于断层切片内像素的间距,为了避免由此造成的压缩现象,本文在介绍已有插值算法基础上,采用基于灰度值和基于轮廓的插值方法获取夹层图像,并且针对轮廓提取的问题,结合多孔介质的断层切片图像特点,提出了基于双向扫描线的提取算法。
4、基于Marching cube(MC)算法对断层切片图像构成的三维数据场进行绘制。由于多孔介质的孔隙表面结构复杂,为了加快MC算法的运行速度,本文提出了基于区域划分技术对MC算法进行改进,获得了理想的运行速度。
5、介绍了SPH算法的基本理论,并针对其中邻居粒子查找问题,提出了基于坐标系变换的计算域划分方案,优化了查找效率,最后通过一个算例验证了新方案的有效性。
6、针对原有固壁边界处理方法不能够很好适应复杂边界条件的问题,本文提出了基于粒子和多边形边界交互的固壁边界面处理方法。通过模拟兔型复杂容器内的水流流动验证了方法的有效性,同时也模拟了经典溃坝流问题,经过与原有边界处理方法结果的数值比较,验证了新方法的数值正确性。
7、模拟了单个孔隙网络内的孔隙流和和多孔介质渗流,分析多孔介质空间结构对孔隙流和渗流的影响。
Many industrial applications involve fluid flow in porous media issues, such as low and lower permeable oil and gas field development, underground water mining, gas layer exploitation, metal materials production and so on. Establishing a set of software that can accurately reconstruct porous media’s three dimensional model, and based on this model, extracting the pore network of porous media, simulating fluid flow in media’s pore network through animation, not only can help people quickly and easily determine porous media’s relevant physical parameters by computer experiments, but also can provide a very big help for studying how the porous media’s spatial structure impacts on porosity flow. In terms of practical application and theoretical research, the subject has a very important research value. The work in this paper is to reconstruct porous media’s three dimension model based on a series of fault slice images, and to simulate fluid flow in porous media through animation.
In this paper, the research contents and results are as follows:
1. Descript and analyse the research status of reconstructing porous media and simulating fluid flow by animation.
2. Use three dimensional image reconstruction method to reconstruct porous media’s spatial structure. Based on the characteristics of scanning instrument, use a series of image processing methods to remove background and filter noises in fault slice images, and combined with the relevant porous media knowledge to extend the porous media’s contour in order to contain surface porosities, identify solid skeleton and pore space, extract valid pore network within the porous media.
3. The distance between fault slice images maybe greater than the distance among pixels within a fault slice image. To avoid the compression phenomenon, based on the introduced interpolation algorithms in this paper, use the gray interpolation and the contour interpolation algorithms to get sandwich images. For the problem of extracting porous media’s contour, combined with the porous media fault slice image characteristics, we propose an extraction algorithm based on double directional scanning.
4. Use Marching cube(MC) algorithm to draw the fault slice images’three dimensional data field. Since the surface structure of porous media pore is complex, in order to accelerate the MC algorithm’s running speed, we propose a modified MC algorithm based on region division technology, the running speed of this modified algorithm is faster than original MC algorithm.
5. Introduce the SPH algorithm’s basic theory and in order to promote the efficiency of looking for neighbor particles, we propose a region division method based on the coordinate transformation, through a numerical example we verify the new method’s effectiveness.
6. Original solid wall boundary treatments is not well adapted to the complex boundary conditions. To solve this problem, we propose a new treatment based on the interaction of particles and solid wall boundary. Through the simulation of water flow in rabbit complex container, we verify the validity of the new method, also through the simulation of classical dam break flow, after the comparison of numerical results between new method and original methods, we verify the numerical accuracy of the new method.
7. Based on the simulation of fluid flow in a single pore network and porous media seepage, we analyse porous media spatial structure’s impact on porosity flow and seepage.
本文主要的研究内容及成果如下:
1、介绍和分析多孔介质三维重建及流体动画模拟的研究现状。
2、采用三维图像法重建多孔介质空间结构。针对扫描仪器的成像特点,对获得的断层切片图像采用一系列的图像处理方法进行背景去除和噪声过滤,并结合多孔介质的相关知识,对断层切片图像内的轮廓线进行扩展容纳表面孔隙,识别固体骨架和孔隙空间,提取介质内有效孔隙网络。
3、断层切片的间距有可能大于断层切片内像素的间距,为了避免由此造成的压缩现象,本文在介绍已有插值算法基础上,采用基于灰度值和基于轮廓的插值方法获取夹层图像,并且针对轮廓提取的问题,结合多孔介质的断层切片图像特点,提出了基于双向扫描线的提取算法。
4、基于Marching cube(MC)算法对断层切片图像构成的三维数据场进行绘制。由于多孔介质的孔隙表面结构复杂,为了加快MC算法的运行速度,本文提出了基于区域划分技术对MC算法进行改进,获得了理想的运行速度。
5、介绍了SPH算法的基本理论,并针对其中邻居粒子查找问题,提出了基于坐标系变换的计算域划分方案,优化了查找效率,最后通过一个算例验证了新方案的有效性。
6、针对原有固壁边界处理方法不能够很好适应复杂边界条件的问题,本文提出了基于粒子和多边形边界交互的固壁边界面处理方法。通过模拟兔型复杂容器内的水流流动验证了方法的有效性,同时也模拟了经典溃坝流问题,经过与原有边界处理方法结果的数值比较,验证了新方法的数值正确性。
7、模拟了单个孔隙网络内的孔隙流和和多孔介质渗流,分析多孔介质空间结构对孔隙流和渗流的影响。
Many industrial applications involve fluid flow in porous media issues, such as low and lower permeable oil and gas field development, underground water mining, gas layer exploitation, metal materials production and so on. Establishing a set of software that can accurately reconstruct porous media’s three dimensional model, and based on this model, extracting the pore network of porous media, simulating fluid flow in media’s pore network through animation, not only can help people quickly and easily determine porous media’s relevant physical parameters by computer experiments, but also can provide a very big help for studying how the porous media’s spatial structure impacts on porosity flow. In terms of practical application and theoretical research, the subject has a very important research value. The work in this paper is to reconstruct porous media’s three dimension model based on a series of fault slice images, and to simulate fluid flow in porous media through animation.
In this paper, the research contents and results are as follows:
1. Descript and analyse the research status of reconstructing porous media and simulating fluid flow by animation.
2. Use three dimensional image reconstruction method to reconstruct porous media’s spatial structure. Based on the characteristics of scanning instrument, use a series of image processing methods to remove background and filter noises in fault slice images, and combined with the relevant porous media knowledge to extend the porous media’s contour in order to contain surface porosities, identify solid skeleton and pore space, extract valid pore network within the porous media.
3. The distance between fault slice images maybe greater than the distance among pixels within a fault slice image. To avoid the compression phenomenon, based on the introduced interpolation algorithms in this paper, use the gray interpolation and the contour interpolation algorithms to get sandwich images. For the problem of extracting porous media’s contour, combined with the porous media fault slice image characteristics, we propose an extraction algorithm based on double directional scanning.
4. Use Marching cube(MC) algorithm to draw the fault slice images’three dimensional data field. Since the surface structure of porous media pore is complex, in order to accelerate the MC algorithm’s running speed, we propose a modified MC algorithm based on region division technology, the running speed of this modified algorithm is faster than original MC algorithm.
5. Introduce the SPH algorithm’s basic theory and in order to promote the efficiency of looking for neighbor particles, we propose a region division method based on the coordinate transformation, through a numerical example we verify the new method’s effectiveness.
6. Original solid wall boundary treatments is not well adapted to the complex boundary conditions. To solve this problem, we propose a new treatment based on the interaction of particles and solid wall boundary. Through the simulation of water flow in rabbit complex container, we verify the validity of the new method, also through the simulation of classical dam break flow, after the comparison of numerical results between new method and original methods, we verify the numerical accuracy of the new method.
7. Based on the simulation of fluid flow in a single pore network and porous media seepage, we analyse porous media spatial structure’s impact on porosity flow and seepage.
引文
[1]叶仲斌. 2007.提高采收率原理[M].石油工业出版社,8-36.
[2]徐运亭. 2006.低渗透油藏渗流机理研究及应用[M].石油工业出版社,1-44.
[3]薛禹群. 2007.地下水数值模拟[M].科学出版社,30-35.
[4]陈建军. 2008.天然气开发新技术论文集[C],121-126
[5]赵浩峰. 2004.金属基复合材料及其浸渗制备的理论与实践.冶金工业出版社,359-394.
[6]FattⅠ. 1956. The network model of porous media:Ⅰ.capillary pressure characteristics[J]. Transactions of AIME, 207(1):144-159.
[7]J.F. Da?an, J. Saliba. 1991. Determination d'un reseau aléatoire de pores pour modéliser la sorption et la migration d'humidite dans un mortier de ciment[J]. Int. J. Heat Mass Transfer, 34: 2081–2096.
[8]Lenormand R, Touboul E, Zarcone C. 1988. Numerical models and experiments on immiscible displacements in porous media[J]. Fluid Mech, 1:165-187
[9]Coppens M O, Froment G F. 1995. Diffusion and reaction in a fractal catalyst pore-Ⅱdiffusion and first order reaction[J]. 50(6):1027-1039
[10]Leon C A. 1998. New perspectives in mercury porosimetry[J]. Advances in Colloid and Interface Science, 76-77:341-372.
[11]Friesen W I, Mikula R J. 1987. Fractal dimensions of coal particles[J]. Journal of Colloid and Interface Science, 120(1):263-271.
[12]Zhang Baoquan, Li Shaofen. 1995. Determination of the surface fractal dimension for porous media by mercury porosimetry[J]. Industrial & Engineering Chemistry Research,34(4):1383-1386.
[13]Rahman M S. 1997. Physical meaning and interpretation of fractal dimensions of fine particles measured by different methods[J]. Journal of Food Engineering, 32(4):447-456.
[14]刘永忠,陈三强,孙皓. 2004.冻干物料孔隙特性表征的分形模型与分形维数[J].农业工程学报,20(6):41-45.
[15]许丽敏,薛安. 2009.基于Delaunay三角网与Voronoi图联合提取等高线骨架的地形重建算法研究[J].北京大学学报,1:43-48.
[16]Joshi M. 1974. A class of stochastic models for porous media[D]. Lawrence Kansas University.
[17]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.
[18]Quiblier J A. 1984. A new three-dimensional modeling technique for studying porous-media[J]. Colloid Interface Sci,98(1):84-102.
[19]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.
[20]Okabe H, Blunt M J. 2005. Pore space reconstruction using multiple-point statistics[J]. Journal of Petroleum Science and Engineering, 46:121-137.
[21]Hazlett R D. 1997. Statistical characterization and stochastic modeling of pore networks in relation to fluid flow[J]. Mathematical Geology,29(4):801-822.
[22]王国栋. 2009.采用模拟退火算法的冠状动脉三维重建优化研究[J].工程图学学报,1:102-108.
[23]Holt R M, Fjaer E, Torsaeter O. et al. 1996. Petrophysical laboratory measurements for basin and reservoir evaluation[J]. Marine and Petroleum Geology, 13(4):383-391.
[24]Lin C, Cohen M H. 1982. Quantitative methods for microgeometric modeling[J]. Journal of Applied Physics, 53(6):4152-4165.
[25]Kass M, Miller G. 1990. Rapid, Stable Fluid Fynamics for Computer Graphics[J]. ACM Computer Graphics(SIGGRAPH 90),24:49-57.
[26]O’Brien J J, Hodgins J K. 1995. Dynamics Simulation of Splashing Fluids[J]. Computer Animation, 95:198-205.
[27] Chen, Vitoria Lobo. 1995. toward interactive-rate simulation of fluid with moving obstacles using navier-stokes equations,graphical models and image processing, 57(2):107-116.
[28]Foster N, Metaxas D. 1996. Realistic Animation of Liquids[J]. Graphical Models and Image Processing, 58(5):471-483.
[29]Stam J. 1999. Stable Fluids[C]. Proc.of SIGGRAPH. New York: ACM Press, 121-128.
[30]Foster N, Fedkiw R. 2001. Practical Animation of Liquids[C]. Proc.of SIGGRAPH. New York: ACM Press, 23-30.
[31]Fedkiw R, Stam J, Jensen H. Visual Simulation of Smoke[C]. Computer Graphics(SIGGRAPH 2001), New York: ACM, 15-22.
[32]Foster N, Fedkiw R. 2001. Practical animation of liquids[C]. Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques. New York: ACM Press, 23-30.
[33]Osher S, Fedkiw R. Level Set Methods: An Overview and Some Recent Results[J]. Comput Phys, 169:463-502.
[34]Reeves W T. 1983. Particle Systems-A Technique for Modeling a Class of Fuzzy Objects[C]. ACM Transactions on Graphics, 2(2):91-108.
[35]Gingold R, Monaghan J. 1977. Smoothed particle hydrodynamics: theory and application tonon-spherical stars[J]. Mon. Not. R. astr. Soc, 181:375-389.
[36]Lucy L B. 1977. A Numerical Approach to Testing the Fission Hypothesis[J]. Astron, 82(12):1013-1924.
[37]Stam J, Fiume E. 1995. Depicting fire and other gaseous phenomena using diffusion processes[C]. Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, Los Angeles, California, 129-136.
[38]Takeshita D, Ota S. Tamura M, et al. 2003. Particle-based visual simulation of explosive flames[C], Computer Graphics and Applications. Proceedings of the 11th Pacific Conference on Computer Graphics and Applications, Alberta, 482-486.
[39]Muller M, Charypar D, Gross M. 2003. Particle based fluid simulation for interactive applications[C]. Proceedings of ACM SIGGRAPH/Eurographics Symposium on Computer Animation, San Diego, California, 154-159.
[40]Premoze S, Tasdizen T, Bigler J, et al. 2003. Particle-based simulation of fluid[C]. Computer Graphics Forum, 22(3):401-410.
[41]Becker M, Teschner M. 2007. Weakly compressible SPH for free surface flows[C]. Proceedings of ACM SIGGRAPH/Eurographics Symposium on Computer Animation, San Diego, 1-8.
[42]Solenthaler B, Pajarola R. 2009. Predictive-Corrective Incompressible SPH[C]. Proceedings of ACM SIGGRAPH, New York, 28(3):248-254.
[43]Parshikov A N, Medin S A, Loukashenko I I, et al. 2000. Improvements in SPH Method by Means of Interparticle Contact Algorithm and Analysis of Perforation Tests at Moderate Projectile Velocities[J]. Int.J.Impact Eneng, 24:779-796.
[44]杨秀峰. 2010.溃坝流的光滑粒子法模拟[J].计算物理,27(2):173-180.
[2]徐运亭. 2006.低渗透油藏渗流机理研究及应用[M].石油工业出版社,1-44.
[3]薛禹群. 2007.地下水数值模拟[M].科学出版社,30-35.
[4]陈建军. 2008.天然气开发新技术论文集[C],121-126
[5]赵浩峰. 2004.金属基复合材料及其浸渗制备的理论与实践.冶金工业出版社,359-394.
[6]FattⅠ. 1956. The network model of porous media:Ⅰ.capillary pressure characteristics[J]. Transactions of AIME, 207(1):144-159.
[7]J.F. Da?an, J. Saliba. 1991. Determination d'un reseau aléatoire de pores pour modéliser la sorption et la migration d'humidite dans un mortier de ciment[J]. Int. J. Heat Mass Transfer, 34: 2081–2096.
[8]Lenormand R, Touboul E, Zarcone C. 1988. Numerical models and experiments on immiscible displacements in porous media[J]. Fluid Mech, 1:165-187
[9]Coppens M O, Froment G F. 1995. Diffusion and reaction in a fractal catalyst pore-Ⅱdiffusion and first order reaction[J]. 50(6):1027-1039
[10]Leon C A. 1998. New perspectives in mercury porosimetry[J]. Advances in Colloid and Interface Science, 76-77:341-372.
[11]Friesen W I, Mikula R J. 1987. Fractal dimensions of coal particles[J]. Journal of Colloid and Interface Science, 120(1):263-271.
[12]Zhang Baoquan, Li Shaofen. 1995. Determination of the surface fractal dimension for porous media by mercury porosimetry[J]. Industrial & Engineering Chemistry Research,34(4):1383-1386.
[13]Rahman M S. 1997. Physical meaning and interpretation of fractal dimensions of fine particles measured by different methods[J]. Journal of Food Engineering, 32(4):447-456.
[14]刘永忠,陈三强,孙皓. 2004.冻干物料孔隙特性表征的分形模型与分形维数[J].农业工程学报,20(6):41-45.
[15]许丽敏,薛安. 2009.基于Delaunay三角网与Voronoi图联合提取等高线骨架的地形重建算法研究[J].北京大学学报,1:43-48.
[16]Joshi M. 1974. A class of stochastic models for porous media[D]. Lawrence Kansas University.
[17]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.
[18]Quiblier J A. 1984. A new three-dimensional modeling technique for studying porous-media[J]. Colloid Interface Sci,98(1):84-102.
[19]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.
[20]Okabe H, Blunt M J. 2005. Pore space reconstruction using multiple-point statistics[J]. Journal of Petroleum Science and Engineering, 46:121-137.
[21]Hazlett R D. 1997. Statistical characterization and stochastic modeling of pore networks in relation to fluid flow[J]. Mathematical Geology,29(4):801-822.
[22]王国栋. 2009.采用模拟退火算法的冠状动脉三维重建优化研究[J].工程图学学报,1:102-108.
[23]Holt R M, Fjaer E, Torsaeter O. et al. 1996. Petrophysical laboratory measurements for basin and reservoir evaluation[J]. Marine and Petroleum Geology, 13(4):383-391.
[24]Lin C, Cohen M H. 1982. Quantitative methods for microgeometric modeling[J]. Journal of Applied Physics, 53(6):4152-4165.
[25]Kass M, Miller G. 1990. Rapid, Stable Fluid Fynamics for Computer Graphics[J]. ACM Computer Graphics(SIGGRAPH 90),24:49-57.
[26]O’Brien J J, Hodgins J K. 1995. Dynamics Simulation of Splashing Fluids[J]. Computer Animation, 95:198-205.
[27] Chen, Vitoria Lobo. 1995. toward interactive-rate simulation of fluid with moving obstacles using navier-stokes equations,graphical models and image processing, 57(2):107-116.
[28]Foster N, Metaxas D. 1996. Realistic Animation of Liquids[J]. Graphical Models and Image Processing, 58(5):471-483.
[29]Stam J. 1999. Stable Fluids[C]. Proc.of SIGGRAPH. New York: ACM Press, 121-128.
[30]Foster N, Fedkiw R. 2001. Practical Animation of Liquids[C]. Proc.of SIGGRAPH. New York: ACM Press, 23-30.
[31]Fedkiw R, Stam J, Jensen H. Visual Simulation of Smoke[C]. Computer Graphics(SIGGRAPH 2001), New York: ACM, 15-22.
[32]Foster N, Fedkiw R. 2001. Practical animation of liquids[C]. Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques. New York: ACM Press, 23-30.
[33]Osher S, Fedkiw R. Level Set Methods: An Overview and Some Recent Results[J]. Comput Phys, 169:463-502.
[34]Reeves W T. 1983. Particle Systems-A Technique for Modeling a Class of Fuzzy Objects[C]. ACM Transactions on Graphics, 2(2):91-108.
[35]Gingold R, Monaghan J. 1977. Smoothed particle hydrodynamics: theory and application tonon-spherical stars[J]. Mon. Not. R. astr. Soc, 181:375-389.
[36]Lucy L B. 1977. A Numerical Approach to Testing the Fission Hypothesis[J]. Astron, 82(12):1013-1924.
[37]Stam J, Fiume E. 1995. Depicting fire and other gaseous phenomena using diffusion processes[C]. Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, Los Angeles, California, 129-136.
[38]Takeshita D, Ota S. Tamura M, et al. 2003. Particle-based visual simulation of explosive flames[C], Computer Graphics and Applications. Proceedings of the 11th Pacific Conference on Computer Graphics and Applications, Alberta, 482-486.
[39]Muller M, Charypar D, Gross M. 2003. Particle based fluid simulation for interactive applications[C]. Proceedings of ACM SIGGRAPH/Eurographics Symposium on Computer Animation, San Diego, California, 154-159.
[40]Premoze S, Tasdizen T, Bigler J, et al. 2003. Particle-based simulation of fluid[C]. Computer Graphics Forum, 22(3):401-410.
[41]Becker M, Teschner M. 2007. Weakly compressible SPH for free surface flows[C]. Proceedings of ACM SIGGRAPH/Eurographics Symposium on Computer Animation, San Diego, 1-8.
[42]Solenthaler B, Pajarola R. 2009. Predictive-Corrective Incompressible SPH[C]. Proceedings of ACM SIGGRAPH, New York, 28(3):248-254.
[43]Parshikov A N, Medin S A, Loukashenko I I, et al. 2000. Improvements in SPH Method by Means of Interparticle Contact Algorithm and Analysis of Perforation Tests at Moderate Projectile Velocities[J]. Int.J.Impact Eneng, 24:779-796.
[44]杨秀峰. 2010.溃坝流的光滑粒子法模拟[J].计算物理,27(2):173-180.