DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Statistical scaling of geometric characteristics in stochastically generated pore microstructures

Abstract

In this study, we analyze the statistical scaling of structural attributes of virtual porous microstructures that are stochastically generated by thresholding Gaussian random fields. Characterization of the extent at which randomly generated pore spaces can be considered as representative of a particular rock sample depends on the metrics employed to compare the virtual sample against its physical counterpart. Typically, comparisons against features and/patterns of geometric observables, e.g., porosity and specific surface area, flow-related macroscopic parameters, e.g., permeability, or autocorrelation functions are used to assess the representativeness of a virtual sample, and thereby the quality of the generation method. Here, we rely on manifestations of statistical scaling of geometric observables which were recently observed in real millimeter scale rock samples [13] as additional relevant metrics by which to characterize a virtual sample. We explore the statistical scaling of two geometric observables, namely porosity (Φ) and specific surface area (SSA), of porous microstructures generated using the method of Smolarkiewicz and Winter [42] and Hyman and Winter [22]. Our results suggest that the method can produce virtual pore space samples displaying the symptoms of statistical scaling observed in real rock samples. Order q sample structure functions (statistical moments of absolute increments) of Φmore » and SSA scale as a power of the separation distance (lag) over a range of lags, and extended self-similarity (linear relationship between log structure functions of successive orders) appears to be an intrinsic property of the generated media. The width of the range of lags where power-law scaling is observed and the Hurst coefficient associated with the variables we consider can be controlled by the generation parameters of the method.« less

Authors:
 [1];  [2];  [2]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Univ. of Arizona, Tucson, AZ (United States)
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1227728
Report Number(s):
LA-UR-14-28257
Journal ID: ISSN 1420-0597; PII: 9493
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Computational Geosciences
Additional Journal Information:
Journal Volume: 19; Journal Issue: 4; Journal ID: ISSN 1420-0597
Country of Publication:
United States
Language:
English
Subject:
54 ENVIRONMENTAL SCIENCES; porous media; microstructure; scaling; extended self-similarity; structure functions; stochastic methods; pore scale characterization; porosity

Citation Formats

Hyman, Jeffrey D., Guadagnini, Alberto, and Winter, C. Larrabee. Statistical scaling of geometric characteristics in stochastically generated pore microstructures. United States: N. p., 2015. Web. doi:10.1007/s10596-015-9493-8.
Hyman, Jeffrey D., Guadagnini, Alberto, & Winter, C. Larrabee. Statistical scaling of geometric characteristics in stochastically generated pore microstructures. United States. https://doi.org/10.1007/s10596-015-9493-8
Hyman, Jeffrey D., Guadagnini, Alberto, and Winter, C. Larrabee. Thu . "Statistical scaling of geometric characteristics in stochastically generated pore microstructures". United States. https://doi.org/10.1007/s10596-015-9493-8. https://www.osti.gov/servlets/purl/1227728.
@article{osti_1227728,
title = {Statistical scaling of geometric characteristics in stochastically generated pore microstructures},
author = {Hyman, Jeffrey D. and Guadagnini, Alberto and Winter, C. Larrabee},
abstractNote = {In this study, we analyze the statistical scaling of structural attributes of virtual porous microstructures that are stochastically generated by thresholding Gaussian random fields. Characterization of the extent at which randomly generated pore spaces can be considered as representative of a particular rock sample depends on the metrics employed to compare the virtual sample against its physical counterpart. Typically, comparisons against features and/patterns of geometric observables, e.g., porosity and specific surface area, flow-related macroscopic parameters, e.g., permeability, or autocorrelation functions are used to assess the representativeness of a virtual sample, and thereby the quality of the generation method. Here, we rely on manifestations of statistical scaling of geometric observables which were recently observed in real millimeter scale rock samples [13] as additional relevant metrics by which to characterize a virtual sample. We explore the statistical scaling of two geometric observables, namely porosity (Φ) and specific surface area (SSA), of porous microstructures generated using the method of Smolarkiewicz and Winter [42] and Hyman and Winter [22]. Our results suggest that the method can produce virtual pore space samples displaying the symptoms of statistical scaling observed in real rock samples. Order q sample structure functions (statistical moments of absolute increments) of Φ and SSA scale as a power of the separation distance (lag) over a range of lags, and extended self-similarity (linear relationship between log structure functions of successive orders) appears to be an intrinsic property of the generated media. The width of the range of lags where power-law scaling is observed and the Hurst coefficient associated with the variables we consider can be controlled by the generation parameters of the method.},
doi = {10.1007/s10596-015-9493-8},
journal = {Computational Geosciences},
number = 4,
volume = 19,
place = {United States},
year = {Thu May 21 00:00:00 EDT 2015},
month = {Thu May 21 00:00:00 EDT 2015}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Hydraulic tortuosity in arbitrary porous media flow
text, January 2011


Integral Geometry in Statistical Physics
journal, April 1998


Extended power-law scaling of heavy-tailed random air-permeability fields in fractured and sedimentary rocks
journal, September 2012

  • Guadagnini, A.; Riva, M.; Neuman, S. P.
  • Hydrology and Earth System Sciences, Vol. 16, Issue 9
  • DOI: 10.5194/hess-16-3249-2012

Flow in simulated porous media
journal, July 1990

  • Adler, P. M.; Jacquin, C. G.; Quiblier, J. A.
  • International Journal of Multiphase Flow, Vol. 16, Issue 4
  • DOI: 10.1016/0301-9322(90)90025-E

Percolation and Minimal Spanning Forests in Infinite Graphs
journal, January 1995


Percolation of level sets for two-dimensional random fields with lattice symmetry
journal, November 1994

  • Alexander, Kenneth S.; Molchanov, Stanislav A.
  • Journal of Statistical Physics, Vol. 77, Issue 3-4
  • DOI: 10.1007/BF02179453

Mortar coupling and upscaling of pore-scale models
journal, September 2007

  • Balhoff, Matthew T.; Thomas, Sunil G.; Wheeler, Mary F.
  • Computational Geosciences, Vol. 12, Issue 1
  • DOI: 10.1007/s10596-007-9058-6

Extended Self-Similarity in the Dissipation Range of Fully Developed Turbulence
journal, November 1993


Extended self-similarity in turbulent flows
journal, July 1993


Modeling of Multiscale Porous Media
journal, May 2011

  • Biswal, Bibhu; Øren, Pål-Eric; Held, Rudolf J.
  • Image Analysis & Stereology, Vol. 27, Issue 1
  • DOI: 10.5566/ias.v28.p23-34

Pore-scale imaging and modelling
journal, January 2013


Extended self-similarity works for the Burgers equation and why
journal, April 2010

  • Chakraborty, Sagar; Frisch, Uriel; Ray, Samriddhi Sankar
  • Journal of Fluid Mechanics, Vol. 649
  • DOI: 10.1017/S0022112010000595

Extraction of morphological quantities from a digitized medium
journal, June 1995

  • Coker, David A.; Torquato, Salvatore
  • Journal of Applied Physics, Vol. 77, Issue 12
  • DOI: 10.1063/1.359134

Hydraulic tortuosity in arbitrary porous media flow
journal, September 2011


Statistical Scaling of Geometric Characteristics in Millimeter Scale Natural Porous Media
journal, February 2014


Numerical investigation of apparent multifractality of samples from processes subordinated to truncated fBm: NUMERICAL INVESTIGATION OF APPARENT MULTIFRACTALITY
journal, December 2011

  • Guadagnini, Alberto; Neuman, Shlomo P.; Riva, Monica
  • Hydrological Processes, Vol. 26, Issue 19
  • DOI: 10.1002/hyp.8358

Extended power-law scaling of heavy-tailed random air-permeability fields in fractured and sedimentary rocks
journal, September 2012

  • Guadagnini, A.; Riva, M.; Neuman, S. P.
  • Hydrology and Earth System Sciences, Vol. 16, Issue 9
  • DOI: 10.5194/hess-16-3249-2012

Local Porosity Theory and Stochastic Reconstruction for Porous Media
book, December 2000


High-precision synthetic computed tomography of reconstructed porous media
journal, December 2011


Heterogeneities of flow in stochastically generated porous media
journal, November 2012

  • Hyman, Jeffrey D.; Smolarkiewicz, Piotr K.; Winter, C. Larrabee
  • Physical Review E, Vol. 86, Issue 5
  • DOI: 10.1103/PhysRevE.86.056701

Pedotransfer functions for permeability: A computational study at pore scales: PEDOTRANSFER FUNCTIONS FOR PERMEABILITY
journal, April 2013

  • Hyman, Jeffrey D.; Smolarkiewicz, Piotr K.; Larrabee Winter, C.
  • Water Resources Research, Vol. 49, Issue 4
  • DOI: 10.1002/wrcr.20170

Hyperbolic regions in flows through three-dimensional pore structures
journal, December 2013


Stochastic generation of explicit pore structures by thresholding Gaussian random fields
journal, November 2014


Continuum reconstruction of the pore scale microstructure for Fontainebleau sandstone
journal, April 2010

  • Latief, F. D. E.; Biswal, B.; Fauzi, U.
  • Physica A: Statistical Mechanics and its Applications, Vol. 389, Issue 8
  • DOI: 10.1016/j.physa.2009.12.006

Fractal porous media IV: Three-dimensional stokes flow through random media and regular fractals
journal, August 1990

  • Lemaitre, R.; Adler, P. M.
  • Transport in Porous Media, Vol. 5, Issue 4
  • DOI: 10.1007/BF01141990

Fractional Brownian Motions, Fractional Noises and Applications
journal, October 1968

  • Mandelbrot, Benoit B.; Van Ness, John W.
  • SIAM Review, Vol. 10, Issue 4
  • DOI: 10.1137/1010093

Stochastic reconstruction of sandstones
journal, July 2000


Recent Advances in Statistical and Scaling Analysis of Earth and Environmental Variables
book, January 2013


Prediction of permeability for porous media reconstructed using multiple-point statistics
journal, December 2004


Pore-scale and continuum simulations of solute transport micromodel benchmark experiments
journal, June 2014


Image analysis algorithms for estimating porous media multiphase flow variables from computed microtomography data: a validation study
journal, February 2009


A new three-dimensional modeling technique for studying porous media
journal, March 1984


Sub-Gaussian model of processes with heavy-tailed distributions applied to air permeabilities of fractured tuff
journal, March 2012

  • Riva, Monica; Neuman, Shlomo P.; Guadagnini, Alberto
  • Stochastic Environmental Research and Risk Assessment, Vol. 27, Issue 1
  • DOI: 10.1007/s00477-012-0576-y

Anisotropic Scaling of Berea Sandstone Log Air Permeability Statistics
journal, January 2013

  • Riva, Monica; Neuman, Shlomo P.; Guadagnini, Alberto
  • Vadose Zone Journal, Vol. 12, Issue 3
  • DOI: 10.2136/vzj2012.0153

Applications of 2D-NMR maps and geometric pore scale modeling for petrophysical evaluation of a gas well
journal, September 2008

  • Romero, Pedro; Gladkikh, Mikhail; Azpiroz, Guillermo
  • Computational Geosciences, Vol. 13, Issue 2
  • DOI: 10.1007/s10596-008-9098-6

Extended power-law scaling of air permeabilities measured on a block of tuff
journal, January 2012

  • Siena, M.; Guadagnini, A.; Riva, M.
  • Hydrology and Earth System Sciences, Vol. 16, Issue 1
  • DOI: 10.5194/hess-16-29-2012

Pores resolving simulation of Darcy flows
journal, May 2010

  • Smolarkiewicz, Piotr K.; Larrabee Winter, C.
  • Journal of Computational Physics, Vol. 229, Issue 9
  • DOI: 10.1016/j.jcp.2009.12.031

Simulations of reactive transport and precipitation with smoothed particle hydrodynamics
journal, March 2007

  • Tartakovsky, Alexandre M.; Meakin, Paul; Scheibe, Timothy D.
  • Journal of Computational Physics, Vol. 222, Issue 2
  • DOI: 10.1016/j.jcp.2006.08.013

X-ray imaging and analysis techniques for quantifying pore-scale structure and processes in subsurface porous medium systems
journal, January 2013


High-Order Moments of the Phase Function for Real and Reconstructed Model Porous Media: A Comparison
journal, March 1993

  • Yao, J.; Frykman, P.; Kalaydjian, F.
  • Journal of Colloid and Interface Science, Vol. 156, Issue 2
  • DOI: 10.1006/jcis.1993.1141

Reconstructing random media
journal, January 1998