The robustness of the permeability of constructal tree-shaped fissures

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© 2015 Elsevier Ltd. Here we develop analytically the formulas for effective permeability in several configurations using the closed-form description of tree networks designed to provide flow access. The objective was to find the relation between the permeability and porosity of tree-shaped fissures. We found the effect of the fracture size on the permeability for fixed number of bifurcation and the results showed that the permeability of the fracture network increased rapidly with the size of the fracture. Next, we found a relation between the Reservoir Quality Index (RQI) and the porosity of the fracture. The results in this paper have been validated by comparison with experimental and numerical results. We show that the permeability formulas do not vary much from one tree design to the next, suggesting that similar formulas may apply to naturally fissured porous media with unknown precise details, which occur in natural reservoirs.






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Alalaimi, M, S Lorente, W Wechsatol and A Bejan (2015). The robustness of the permeability of constructal tree-shaped fissures. International Journal of Heat and Mass Transfer, 90. pp. 259–265. 10.1016/j.ijheatmasstransfer.2015.06.042 Retrieved from

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Adrian Bejan

J.A. Jones Distinguished Professor of Mechanical Engineering

Professor Bejan was awarded the Benjamin Franklin Medal 2018 and the Humboldt Research Award 2019. His research covers engineering science and applied physics: thermodynamics, heat transfer, convection, design, and evolution in nature.

He is ranked among the top 0.01% of the most cited and impactful world scientists (and top 10 in Engineering world wide) in the 2019 citations impact database created by Stanford University’s John Ioannidis, in PLoS Biology.  He is the author of 30 books and 700 peer-referred articles. His h-index is 111 with 92,000 citations on Google Scholar. He received 18 honorary doctorates from universities in 11 countries.

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