Journal
CHAOS SOLITONS & FRACTALS
Volume 141, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2020.110335
Keywords
Atangana-Baleanu derivative; Non-Darcy flow; Swartzendruber model
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Funding
- State Key Laboratory for GeoMechanics and Deep Underground Engineering, China University of Mining and Technology, Beijing [SKLGDUEK2027]
- National Natural Science Foundation of China [11671181, 51674266]
- State Key Research Development Program of China [2016YFC0600704]
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Two fractional Swartzendruber models applying the Atangana-Baleanu (A-B) derivative are proposed to describe non-Darcy flow in porous media. The analytical solutions of models are obtained by using Laplace transform. Fitting curves with the experimental data display the proposed models are suitable to describe non-Darcy flow problems in low and high permeability media. In addition, sensitivity analysis is performed to clarify the influence of relevant parameters on the A-B Swartzendruber models. In the light of the two-scale thermodynamics, the physical explanations of A-B Swartzendruber model I and II are revealed. The proposed A-B Swartzendruber models connect fluid flow of different scales, and provide a unified description of non-Darcy flow in porous media with low and high permeability. (C) 2020 Elsevier Ltd. All rights reserved.
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