Image‐based modeling of granular porous media

We propose a new method of modeling granular media that utilizes a single two- or three-dimensional image and is formulated based on a Markov process. The process is mapped onto one that minimizes the difference between the image and a stochastic realization of the granular medium and utilizes a novel approach to remove possible unphysical discontinuities in the realization. Quantitative comparison between the morphological properties of the realizations and representative examples indicates excellent agreement.

[1]  Gerd Sauermann,et al.  Minimal model for sand dunes. , 2002, Physical review letters.

[2]  Guilhem Mollon,et al.  Fourier–Voronoi-based generation of realistic samples for discrete modelling of granular materials , 2012, Granular Matter.

[3]  Hilfer,et al.  Stochastic reconstruction of sandstones , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  Hans J. Herrmann,et al.  Simulating deformations of granular solids under shear , 1995 .

[5]  Philippe Gotteland,et al.  Influence of relative density on granular materials behavior: DEM simulations of triaxial tests , 2009 .

[6]  H. J. Herrmann,et al.  Influence of particle shape on sheared dense granular media , 2006 .

[7]  Tang-Tat Ng,et al.  Particle shape effect on macro‐ and micro‐behaviors of monodisperse ellipsoids , 2009 .

[8]  A. Journel,et al.  The Necessity of a Multiple-Point Prior Model , 2007 .

[9]  T Aste,et al.  Geometrical structure of disordered sphere packings. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Guy T. Houlsby,et al.  A new algorithm for contact detection between convex polygonal and polyhedral particles in the discrete element method , 2012 .

[11]  Yannis F. Dafalias,et al.  Fabric evolution within shear bands of granular materials and its relation to critical state theory , 2011 .

[12]  S. Hall,et al.  Grain-scale experimental investigation of localised deformation in sand: a discrete particle tracking approach , 2012 .

[13]  Rudolf Hilfer,et al.  Local Porosity Theory and Stochastic Reconstruction for Porous Media , 2000 .

[14]  R. Hilfer,et al.  Quantitative analysis of experimental and synthetic microstructures for sedimentary rock , 1999, cond-mat/9908478.

[15]  G. McDowell,et al.  The importance of modelling ballast particle shape in the discrete element method , 2006 .

[16]  José E. Andrade,et al.  Granular element method for three‐dimensional discrete element calculations , 2014 .

[17]  Clayton V. Deutsch,et al.  GSLIB: Geostatistical Software Library and User's Guide , 1993 .

[18]  J. Sherwood,et al.  LETTER TO THE EDITOR: Packing of spheroids in three-dimensional space by random sequential addition , 1997 .

[19]  L. Santaló.  Integral geometry and geometric probability , 1976 .

[20]  Schwartz,et al.  Grain consolidation and electrical conductivity in porous media. , 1985, Physical review. B, Condensed matter.

[21]  Xuxin Tu,et al.  Multiscale framework for behavior prediction in granular media , 2009 .

[22]  T. Matsushima,et al.  Simple shear simulation of 3D irregularly-shaped particles by image-based DEM , 2010 .

[23]  Pejman Tahmasebi,et al.  Reconstruction of three-dimensional porous media using a single thin section. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  R. Hilfer.  Review on Scale Dependent Characterization of the Microstructure of Porous Media , 2001, cond-mat/0105458.

[25]  Y. Amarouchene,et al.  Dynamic sand dunes. , 2001, Physical review letters.

[26]  Olga Veksler,et al.  Fast Approximate Energy Minimization via Graph Cuts , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[27]  E. Garboczi.  Three-dimensional mathematical analysis of particle shape using X-ray tomography and spherical harmonics: Application to aggregates used in concrete , 2002 .

[28]  Alsidqi Hasan,et al.  Spatial variation of void ratio and shear band thickness in sand using X-ray computed tomography , 2008 .

[29]  Pierre M. Adler,et al.  Flow in simulated porous media , 1990 .

[30]  Pejman Tahmasebi,et al.  Multiscale and multiresolution modeling of shales and their flow and morphological properties , 2015, Scientific Reports.

[31]  VekslerOlga,et al.  Fast Approximate Energy Minimization via Graph Cuts , 2001 .

[32]  Aleksandar Donev,et al.  Experiments on random packings of ellipsoids. , 2005, Physical review letters.

[33]  Pejman Tahmasebi,et al.  Conditional reconstruction: An alternative strategy in digital rock physics , 2016 .

[34]  M. Sahimi,et al.  Three-Dimensional Stochastic Characterization of Shale SEM Images , 2015, Transport in Porous Media.

[35]  Jeffrey D. Hyman,et al.  Stochastic generation of explicit pore structures by thresholding Gaussian random fields , 2014, J. Comput. Phys..

[36]  G. Saussine,et al.  Quasistatic rheology, force transmission and fabric properties of a packing of irregular polyhedral particles , 2008, 0805.0178.

[37]  Pejman Tahmasebi,et al.  Multiscale study for stochastic characterization of shale samples , 2016 .

[38]  José E. Andrade,et al.  Granular Element Method for Computational Particle Mechanics , 2012 .

[39]  M. Sahimi,et al.  Microstructural characterization of random packings of cubic particles , 2016, Scientific Reports.

[40]  Pejman Tahmasebi,et al.  Enhancing multiple‐point geostatistical modeling: 1. Graph theory and pattern adjustment , 2016 .

[41]  D. Pedroso,et al.  Molecular dynamics simulations of complex-shaped particles using Voronoi-based spheropolyhedra. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  T. Liebling,et al.  Three-dimensional distinct element simulation of spherocylinder crystallization , 2005 .

[43]  Sebastien Strebelle,et al.  Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics , 2002 .

[44]  H. Konietzky,et al.  Discrete element simulation of ballast and gravel under special consideration of grain-shape, grain-size and relative density , 2011 .

[45]  Andrew J. Whittle,et al.  Pore shapes, volume distribution and orientations in monodisperse granular assemblies , 2015 .

[46]  M. Coop,et al.  The influence of particle characteristics on the behaviour of coarse grained soils , 2010 .

[47]  Pejman Tahmasebi,et al.  Enhancing multiple‐point geostatistical modeling: 2. Iterative simulation and multiple distance function , 2016 .

[48]  Gilles Saussine,et al.  Force transmission in a packing of pentagonal particles. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  J. Mecke.  Santaló, L. A., Integral Geometry and Geometric Probability, (Encyclopedia of Mathematics and Its Applications) 1. London‐Amsterdam‐Don Mills‐Sydney‐Tokyo, Addison‐Wesley Publishing Company 1976. XVII, 404 S., $ 17.50 , 1979 .

[50]  M. Sahimi,et al.  Cross-correlation function for accurate reconstruction of heterogeneous media. , 2013, Physical review letters.

[51]  Martin Vetterli,et al.  Fast Fourier transforms: a tutorial review and a state of the art , 1990 .

[52]  Pejman Tahmasebi,et al.  Pore-scale simulation of flow of CO2 and brine in reconstructed and actual 3D rock cores , 2017 .

[53]  R. Hilfer,et al.  Stochastic multiscale model for carbonate rocks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  T. Ensslin,et al.  Improving stochastic estimates with inference methods: calculating matrix diagonals. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[55]  M. Blunt,et al.  Pore space reconstruction of vuggy carbonates using microtomography and multiple‐point statistics , 2007 .

[56]  Mohammad Saadatfar,et al.  Computer Simulation of Granular Materials , 2009, Computing in Science & Engineering.

[57]  C. Pan,et al.  Lattice‐Boltzmann simulation of two‐phase flow in porous media , 2004 .

[58]  Reza Rahimi Tabar,et al.  Packing of nonoverlapping cubic particles: Computational algorithms and microstructural characteristics. , 2016, Physical review. E.