Computational Geosciences

, Volume 19, Issue 4, pp 845–854 | Cite as

Statistical scaling of geometric characteristics in stochastically generated pore microstructures

  • Jeffrey D. Hyman
  • Alberto Guadagnini
  • C. Larrabee Winter


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.


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


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Jeffrey D. Hyman
    • 1
  • Alberto Guadagnini
    • 2
    • 3
  • C. Larrabee Winter
    • 4
  1. 1.Computational Earth Sciences (EES-16) Earth and Enviromental Sciences Division and The Center for Nonlinear Studies, Theoretical DivisionLos Alamos National LaboratoryLos AlamosUSA
  2. 2.Dipartmento di Ingegneria Civile e AmbientalePolitecnico di MilanoMilanoItaly
  3. 3.Department of Hydrology and Water ResourcesUniversity of ArizonaTucsonUSA
  4. 4.Department of Hydrology and Water ResourcesProgram in Applied Mathematics, University of ArizonaTucsonUSA

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