A Stochastic Method for Modelling the Geometry of a Single Fracture: Spatially Controlled Distributions of Aperture, Roughness and Anisotropy

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Abstract

We describe a simple but effective stochastic method to model the void structure of a single fracture in a form of voxel representation. A fracture void is delineated by two bounding wall surfaces that are separated by some distance (i.e. the local aperture) at each location on the medial surface that lies within the fracture void and serves as a model reference frame. The three surface height fields are generated based on four parameters (mean, standard deviation and two spatial correlation lengths) for each field and two parameters (coefficient and synergistic length) for the spatial correlation between the fracture walls. Testing of generated models demonstrates that not only are the model fracture apertures spatially correlated and characterized as a Gaussian field, but also the two fracture walls are closely correlated, with a similar shape and/or height. With respect to fracture apertures, three quantities, i.e. the mean aperture, roughness and anisotropy, can be derived from the fracture models to describe fracture morphology. The effect of model fractures on fluid flow is investigated in order to establish the relationship between fracture permeability and the three morphological quantities, revealing a way to avoid the significant estimation error associated with the use of the cubic law.

Original languageEnglish
Pages (from-to)797–819
Number of pages23
JournalTransport in Porous Media
Volume128
Issue number2
Early online date20 Mar 2019
DOIs
Publication statusPublished - Jun 2019

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Anisotropy
Surface roughness
Geometry
Error analysis
Flow of fluids
Testing

Keywords

  • Anisotropy
  • Aperture
  • Fracture
  • Permeability
  • Semi-variogram

ASJC Scopus subject areas

  • Catalysis
  • Chemical Engineering(all)

Cite this

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title = "A Stochastic Method for Modelling the Geometry of a Single Fracture: Spatially Controlled Distributions of Aperture, Roughness and Anisotropy",
abstract = "We describe a simple but effective stochastic method to model the void structure of a single fracture in a form of voxel representation. A fracture void is delineated by two bounding wall surfaces that are separated by some distance (i.e. the local aperture) at each location on the medial surface that lies within the fracture void and serves as a model reference frame. The three surface height fields are generated based on four parameters (mean, standard deviation and two spatial correlation lengths) for each field and two parameters (coefficient and synergistic length) for the spatial correlation between the fracture walls. Testing of generated models demonstrates that not only are the model fracture apertures spatially correlated and characterized as a Gaussian field, but also the two fracture walls are closely correlated, with a similar shape and/or height. With respect to fracture apertures, three quantities, i.e. the mean aperture, roughness and anisotropy, can be derived from the fracture models to describe fracture morphology. The effect of model fractures on fluid flow is investigated in order to establish the relationship between fracture permeability and the three morphological quantities, revealing a way to avoid the significant estimation error associated with the use of the cubic law.",
keywords = "Anisotropy, Aperture, Fracture, Permeability, Semi-variogram",
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N2 - We describe a simple but effective stochastic method to model the void structure of a single fracture in a form of voxel representation. A fracture void is delineated by two bounding wall surfaces that are separated by some distance (i.e. the local aperture) at each location on the medial surface that lies within the fracture void and serves as a model reference frame. The three surface height fields are generated based on four parameters (mean, standard deviation and two spatial correlation lengths) for each field and two parameters (coefficient and synergistic length) for the spatial correlation between the fracture walls. Testing of generated models demonstrates that not only are the model fracture apertures spatially correlated and characterized as a Gaussian field, but also the two fracture walls are closely correlated, with a similar shape and/or height. With respect to fracture apertures, three quantities, i.e. the mean aperture, roughness and anisotropy, can be derived from the fracture models to describe fracture morphology. The effect of model fractures on fluid flow is investigated in order to establish the relationship between fracture permeability and the three morphological quantities, revealing a way to avoid the significant estimation error associated with the use of the cubic law.

AB - We describe a simple but effective stochastic method to model the void structure of a single fracture in a form of voxel representation. A fracture void is delineated by two bounding wall surfaces that are separated by some distance (i.e. the local aperture) at each location on the medial surface that lies within the fracture void and serves as a model reference frame. The three surface height fields are generated based on four parameters (mean, standard deviation and two spatial correlation lengths) for each field and two parameters (coefficient and synergistic length) for the spatial correlation between the fracture walls. Testing of generated models demonstrates that not only are the model fracture apertures spatially correlated and characterized as a Gaussian field, but also the two fracture walls are closely correlated, with a similar shape and/or height. With respect to fracture apertures, three quantities, i.e. the mean aperture, roughness and anisotropy, can be derived from the fracture models to describe fracture morphology. The effect of model fractures on fluid flow is investigated in order to establish the relationship between fracture permeability and the three morphological quantities, revealing a way to avoid the significant estimation error associated with the use of the cubic law.

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