Statistical scaling of geometric characteristics in stochastically generated pore microstructures

Jeffrey D. Hyman, Alberto Guadagnini, C Larrabee Winter

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)845-854
Number of pages10
JournalComputational Geosciences
Volume19
Issue number4
DOIs
StatePublished - May 21 2015

Fingerprint

Specific surface area
Microstructure
microstructure
Rocks
Scaling
surface area
pore space
Porosity
Surface area
Scaling laws
porosity
rock
Autocorrelation
Structure-function
winter
autocorrelation
power law
Metric
permeability
Gaussian Random Field

Keywords

  • Extended self-similarity
  • Microstructure
  • Pore scale characterization
  • Porosity
  • Porous media
  • Scaling
  • Stochastic methods
  • Structure functions

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Computers in Earth Sciences
  • Computational Mathematics

Cite this

Statistical scaling of geometric characteristics in stochastically generated pore microstructures. / Hyman, Jeffrey D.; Guadagnini, Alberto; Winter, C Larrabee.

In: Computational Geosciences, Vol. 19, No. 4, 21.05.2015, p. 845-854.

Research output: Contribution to journalArticle

@article{1179052b41e3467f8867bec1644b417c,
title = "Statistical scaling of geometric characteristics in stochastically generated pore microstructures",
abstract = "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.",
keywords = "Extended self-similarity, Microstructure, Pore scale characterization, Porosity, Porous media, Scaling, Stochastic methods, Structure functions",
author = "Hyman, {Jeffrey D.} and Alberto Guadagnini and Winter, {C Larrabee}",
year = "2015",
month = "5",
day = "21",
doi = "10.1007/s10596-015-9493-8",
language = "English (US)",
volume = "19",
pages = "845--854",
journal = "Computational Geosciences",
issn = "1420-0597",
publisher = "Springer Netherlands",
number = "4",

}

TY - JOUR

T1 - Statistical scaling of geometric characteristics in stochastically generated pore microstructures

AU - Hyman, Jeffrey D.

AU - Guadagnini, Alberto

AU - Winter, C Larrabee

PY - 2015/5/21

Y1 - 2015/5/21

N2 - 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.

AB - 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.

KW - Extended self-similarity

KW - Microstructure

KW - Pore scale characterization

KW - Porosity

KW - Porous media

KW - Scaling

KW - Stochastic methods

KW - Structure functions

UR - http://www.scopus.com/inward/record.url?scp=84941879530&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84941879530&partnerID=8YFLogxK

U2 - 10.1007/s10596-015-9493-8

DO - 10.1007/s10596-015-9493-8

M3 - Article

AN - SCOPUS:84941879530

VL - 19

SP - 845

EP - 854

JO - Computational Geosciences

JF - Computational Geosciences

SN - 1420-0597

IS - 4

ER -