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Parameter identification for fractional fractal diffusion model based on experimental data.

Xiu Yang1, Xiaoyun Jiang1, Jianhong Kang2

  • 1School of Mathematics, Shandong University, Jinan 250100, People's Republic of China.

Chaos (Woodbury, N.Y.)
|September 2, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces a fractional fractal diffusion model for gas transport in coal. It compares parameter estimation methods like BFGS, nonlinear conjugate gradient, and Bayesian approaches for accuracy.

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Area of Science:

  • Geosciences and Environmental Science
  • Chemical Engineering

Background:

  • Porous coal matrices exhibit complex structural characteristics influencing gas transport.
  • Understanding gas diffusion in heterogeneous coal is crucial for resource extraction and management.

Purpose of the Study:

  • To establish and numerically solve a fractional fractal diffusion model for gas transport in porous coal.
  • To compare the effectiveness of various parameter estimation techniques (BFGS, nonlinear conjugate gradient, Bayesian) for the model.

Main Methods:

  • A fractional fractal diffusion model was developed based on coal matrix properties.
  • Numerical solution employed a L1 finite difference method (temporal) and spectral collocation method (spatial).
  • Gas adsorption/desorption experiments were conducted on coal samples for parameter validation.

Main Results:

  • Physical parameters of the fractional fractal diffusion model were obtained using BFGS, nonlinear conjugate gradient, and Bayesian methods.
  • Comparative analysis revealed the advantages and limitations of each parameter estimation technique.
  • The study provides a framework for modeling gas transport in complex porous media.

Conclusions:

  • The fractional fractal diffusion model effectively describes gas transport in heterogeneous coal.
  • Different parameter estimation methods offer varying trade-offs between accuracy, computational cost, and robustness.
  • This research contributes to improved modeling of gas diffusion in porous materials.