Reconstruction of 3D porous media using multiple-point statistics based on a 3D training image

Abstract To date many methods of constructing porous media have been proposed. Among them, the multiple-point statistics (MPS) method has a unique advantage in reconstructing 3D pore space because it can reproduce pore space of long-range connectivity. The Single Normal Equation Simulation (SNESIM) is one of most commonly used algorithms of MPS. In the SNESIM algorithm, the selection of training image is vital because it contains the basic pore structure patterns. In the previous reconstructions of 3D porous media using SNESIM, a 2D slice was usually employed as the training image. However, it is difficult for a 2D slice to contain complex 3D pore space geometry and topology patterns. In this paper, a 3D training image is used in order to provide more realistic 3D pore structure features. Besides, a multi-grid search template is applied for the purpose of capturing the pore structures of different scales and speeding up the reconstruction process. Two sandstone cores are taken as test examples and the 3D porous media are reconstructed. The two-point correlation function, pore network structure parameters and absolute permeability are applied as the evaluation indexes to validate the accuracy of the reconstructed models. The comparison result shows that the reconstructed models are in good agreement with the real model obtained by X-ray computed tomography scanning in the pore throat geometry and topology and transport property, which justifies the reliability of the proposed method.

[1]  Mostafa Alizadeh,et al.  Mathematical and neural network prediction model of three-phase immiscible recovery process in porous media , 2014 .

[2]  Zhi Xu,et al.  Multiple-point statistics method based on array structure for 3D reconstruction of Fontainebleau sandstone , 2012 .

[3]  S. Paddock.  Principles and practices of laser scanning confocal microscopy , 2000, Molecular biotechnology.

[4]  Jie Liu,et al.  Computational challenges in the analyses of petrophysics using microtomography and upscaling: A review , 2016, Comput. Geosci..

[5]  Philippe Renard,et al.  3D multiple-point statistics simulation using 2D training images , 2012, Comput. Geosci..

[6]  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.

[7]  J. Quiblier.  A new three-dimensional modeling technique for studying porous media , 1984 .

[8]  Shiyi Chen,et al.  Mesoscopic predictions of the effective thermal conductivity for microscale random porous media. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  R. Arabjamaloei,et al.  Lattice Boltzmann based simulation of gas flow regimes in low permeability porous media: Klinkenberg’s region and beyond , 2016 .

[10]  Digitally Reconstructed Porous Media: Transport and Sorption Properties , 2005 .

[11]  Yang Ju,et al.  3D numerical reconstruction of well-connected porous structure of rock using fractal algorithms , 2014 .

[12]  M. Blunt,et al.  Pore space reconstruction using multiple-point statistics , 2005 .

[13]  D. Fullwood,et al.  Microstructure reconstructions from 2-point statistics using phase-recovery algorithms , 2008 .

[14]  Jianlin Zhao,et al.  The microscale analysis of reverse displacement based on digital core , 2017 .

[15]  Kejian Wu,et al.  Modelling the permeability evolution of carbonate rocks , 2013 .

[16]  M. Blunt,et al.  Prediction of permeability for porous media reconstructed using multiple-point statistics. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Yingfang Zhou,et al.  Applications of digital core analysis and hydraulic flow units in petrophysical characterization , 2017 .

[18]  S. Torquato,et al.  Reconstructing random media. II. Three-dimensional media from two-dimensional cuts , 1998 .

[19]  C. Arns,et al.  Characterization of reactive flow-induced evolution of carbonate rocks using digital core analysis- part 1: Assessment of pore-scale mineral dissolution and deposition. , 2016, Journal of contaminant hydrology.

[20]  J. Thovert,et al.  Grain reconstruction of porous media: application to a Bentheim sandstone. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[22]  Min Liu,et al.  Impact of mineralogical heterogeneity on reactive transport modelling , 2017, Comput. Geosci..

[23]  Guangqing Yao,et al.  An improved model for permeability estimation in low permeable porous media based on fractal geometry and modified Hagen-Poiseuille flow , 2017 .

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

[25]  Alexandre Boucher,et al.  Considering complex training images with search tree partitioning , 2009, Comput. Geosci..

[26]  Stig Bakke,et al.  Reconstruction of Berea sandstone and pore-scale modelling of wettability effects , 2003 .

[27]  Kenneth Stuart Sorbie,et al.  3D Stochastic Modelling of Heterogeneous Porous Media – Applications to Reservoir Rocks , 2006 .

[28]  Karen Abrinia,et al.  3D microstructural reconstruction of heterogeneous materials from 2D cross sections: A modified phase-recovery algorithm , 2016 .

[29]  J. Howard,et al.  Stochastic Reconstruction of Chalk Samples Containing Vuggy Porosity Using a Conditional Simulated Annealing Technique , 2004 .

[30]  Martin J. Blunt,et al.  Analytical and numerical investigations of spontaneous imbibition in porous media , 2016 .

[31]  M. Minsky.  Memoir on inventing the confocal scanning microscope , 1988 .

[32]  Y. Keehm,et al.  Permeability prediction from thin sections: 3D reconstruction and Lattice‐Boltzmann flow simulation , 2004 .

[33]  S. Bakke,et al.  Process Based Reconstruction of Sandstones and Prediction of Transport Properties , 2002 .

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

[35]  Jianchao Cai,et al.  Fractal and multifractal analysis of different hydraulic flow units based on micro-CT images , 2017 .

[36]  Lei Zhang,et al.  Influence of pore structure parameters on flow characteristics based on a digital rock and the pore network model , 2016 .

[37]  M. Blunt,et al.  Pore-scale imaging and modelling , 2013 .

[38]  Sung-hoon Ahn,et al.  Review: Developments in micro/nanoscale fabrication by focused ion beams , 2012 .

[39]  Clayton V. Deutsch,et al.  ANNEALING TECHNIQUES APPLIED TO RESERVOIR MODELING AND THE INTEGRATION OF GEOLOGICAL AND ENGINEERING (WELL TEST) DATA , 1992 .

[40]  Martin J Blunt,et al.  Pore-network extraction from micro-computerized-tomography images. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[42]  Liang,et al.  Geometric and Topological Analysis of Three-Dimensional Porous Media: Pore Space Partitioning Based on Morphological Skeletonization. , 2000, Journal of colloid and interface science.

[43]  Pejman Tahmasebi,et al.  Multiple-point geostatistical modeling based on the cross-correlation functions , 2012, Computational Geosciences.

[44]  Karen Abrinia,et al.  Efficient three‐phase reconstruction of heterogeneous material from 2D cross‐sections via phase‐recovery algorithm , 2016, Journal of microscopy.

[45]  Yuhong Liu,et al.  Using the Snesim program for multiple-point statistical simulation , 2006, Comput. Geosci..

[46]  Ioannis Chatzis,et al.  Electrical Conductivity and Percolation Aspects of Statistically Homogeneous Porous Media , 1997 .

[47]  Bryant,et al.  Prediction of relative permeability in simple porous media. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[48]  John W. Crawford,et al.  An Efficient Markov Chain Model for the Simulation of Heterogeneous Soil Structure , 2004 .

[49]  Moran Wang,et al.  Electroosmosis in homogeneously charged micro- and nanoscale random porous media. , 2007, Journal of colloid and interface science.

[50]  C. A. Baldwin,et al.  Determination and Characterization of the Structure of a Pore Space from 3D Volume Images , 1996 .

[51]  Pavel Bedrikovetsky,et al.  Characterisation of formation damage during reactive flows in porous media , 2016 .

[52]  A. Safekordi,et al.  A multiple-point statistics algorithm for 3D pore space reconstruction from 2D images , 2011 .

[53]  János Urai,et al.  Multi-scale characterization of porosity in Boom Clay (HADES-level, Mol, Belgium) using a combination of X-ray μ-CT, 2D BIB-SEM and FIB-SEM tomography , 2015 .

[54]  Ali Vatani,et al.  Cessation of Darcy regime in gas flow through porous media using LBM: Comparison of pressure gradient approaches , 2017 .

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

[56]  Tuanfeng Zhang,et al.  MPS-Driven Digital Rock Modeling and Upscaling , 2015, Mathematical Geosciences.

[57]  Maysam Pournik,et al.  Mathematical modeling and simulation of nanoparticles transport in heterogeneous porous media , 2017 .