General fractal topography: an open mathematical framework to characterize and model mono-scale-invariances

Jin, Yi; Liu, Xianhe; Song, Huacan; Zheng, Junling; Pan, Jienan

doi:10.1007/s11071-019-04931-9

Cited by 36 publications

(23 citation statements)

References 75 publications

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“…in which n is the number of the representative units and x p = x p1 + x p2 , as aforementioned. (2) The subdivision amount (the number of sub-regions) in a representative unit is denoted by N sub , which (Jin et al, 2019). (3) The fracture aperture and pore size are ranged in…”

Section: Determination Of Modeling Parametersmentioning

confidence: 99%

“…Their common feature is to quantify the fractal behavior by D obtained directly or indirectly. In fact, a single D cannot determine the fractal behavior (i.e., an assembly of scaling behaviors) because of its one‐to‐many relationship (Jin et al, 2019; Jin, Wu, et al, 2017), as aforementioned. Therefore, either for the static purposes (volumetric) or the dynamic purposes (heat and mass transfer), the first and essential step is to clearly identify the control mechanism of scale‐invariance properties.…”

Section: Existing Models For Scale‐invariance Behaviors and Their Unimentioning

confidence: 99%

“…Therefore, G is extended to

boldG ((), G_{+}, G_{-})

. Together with scaling range L [ l min , l max ] and

normalΩ ((), P, boldF)

, an arbitrary scale invariance can thus be defined by a mathematical framework of

F_{3s} ((), normalΩ false(P, boldF false), boldG, boldL)

(Jin et al, 2019), as Figure 2 demonstrates.…”

Section: Mathematical Framework For Fractal Dual‐porosity Mediamentioning

confidence: 99%

“…The subdivision amount (the number of sub‐regions) in a representative unit is denoted by N sub , which satisfies

N_{sub} = ((), 1 - x_{normalp}) \times P_{λ}^{d}

(Jin et al, 2019).…”

Section: Mathematical Framework For Fractal Dual‐porosity Mediamentioning

confidence: 99%

“…Definitions of original and behavioral complexities and representation of their assembly pattern in some representative fractal porous media (modified afterJin et al, 2019)…”

mentioning

confidence: 99%

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Characterizing the Complexity Assembly of Pore Structure in a Coal Matrix: Principle, Methodology, and Modeling Application

et al. 2020

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The pore structure in a coal matrix is a dual-porosity system where fractures and pores coexist and feature scale-invariance properties, which would affect the occurrence and migration of coalbed methane (CBM) significantly. Therefore, it is of fundamental importance to well define complexity types and effectively characterize their assembly mechanism of pore structure in a coal matrix. Here we identify the pore structure in a coal matrix as a dual-complexity system consisting of original complexity and behavioral complexity independent to each other, where the former determines the scaling types of single-or dual-porosity structure, while the latter dominates the scale-invariance properties of self-similarity, self-affinity, and multifractality. Next we clarify the essentials of scale-invariance properties and unify the definition of behavioral complexity. By employing Voronoi diagrams, we develop a dual-porosity coupling algorithm to describe the original complexity and set up a mathematical framework to characterize the complexity assembly in fractal dual-porosity media. For modeling demonstration, we select some typical coal samples from different reservoirs in China, extract the scale-invariance parameters, and establish fractal topography based on mercury intrusion porosimetry (MIP) and N 2 adsorption data. Using experimental tests, mathematical derivation, and numerical simulations in combination, we reveal the principle and methodology for the characterization of the complexity assembly in a coal matrix.

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Section: Determination Of Modeling Parametersmentioning

confidence: 99%

Section: Existing Models For Scale‐invariance Behaviors and Their Unimentioning

confidence: 99%

“…Therefore, G is extended to

boldG ((), G_{+}, G_{-})

. Together with scaling range L [ l min , l max ] and

normalΩ ((), P, boldF)

, an arbitrary scale invariance can thus be defined by a mathematical framework of

F_{3s} ((), normalΩ false(P, boldF false), boldG, boldL)

(Jin et al, 2019), as Figure 2 demonstrates.…”

Section: Mathematical Framework For Fractal Dual‐porosity Mediamentioning

confidence: 99%

“…The subdivision amount (the number of sub‐regions) in a representative unit is denoted by N sub , which satisfies

N_{sub} = ((), 1 - x_{normalp}) \times P_{λ}^{d}

(Jin et al, 2019).…”

Section: Mathematical Framework For Fractal Dual‐porosity Mediamentioning

confidence: 99%

“…Definitions of original and behavioral complexities and representation of their assembly pattern in some representative fractal porous media (modified afterJin et al, 2019)…”

mentioning

confidence: 99%

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