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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 Lab. (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:
Journal Article: Accepted Manuscript
Journal Name:
Computational Geosciences (Amsterdam)
Additional Journal Information:
Journal Name: Computational Geosciences (Amsterdam); 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. doi:10.1007/s10596-015-9493-8.
Hyman, Jeffrey D., Guadagnini, Alberto, and Winter, C. Larrabee. 2015. "Statistical scaling of geometric characteristics in stochastically generated pore microstructures". United States. doi: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 (Amsterdam)},
number = 4,
volume = 19,
place = {United States},
year = 2015,
month = 5
}

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