The robustness of the permeability of constructal tree-shaped fissures

Abstract

a b s t r a c tHere 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.

Thermal analysis in a triple-layered skin structure with embedded vasculature, tumor, and gold nanoshells

“…Although the orthogonal structure of blood vessels ( Fig. 1) is a special design, the constructal-design literature has shown convincingly [41,42] that when the complexity of the tree is as high as in the present model, the volume averaged flow perfusion properties (such as the permeability) do not change if the details of the tree architecture change. The tree flow architecture is robust, and this is why the use of assumed structures in the numerical modeling of previously untractable 'complex' flow structure has a real opportunity for advances.…”

“…To determine the diameters of the blood vessels on each level, we follow the constructal theory of multi-scale tree-shaped heat exchangers [41][42][43][44] and assume that the diameters of arteries are decreasing by a constant ratio c between successive levels of branched vessels, given by [44], For the blood flow in the vascular countercurrent network, we assume that the blood temperature in the cross-section of a vessel is assumed to be uniform. We further assume that a steady-state energy balance in the blood vessel can be reached because the length of the considered blood vessel is relatively short and the blood velocity is relatively high.…”

Current trends in constructal law and evolutionary design

“…More progress was made by using the constructal approach as a way to describe the permeability of naturally fractured porous materials . The hierarchy in scales that is observed in a porous network was predicted by invoking a volumetric organization to facilitate the flow access.…”

The effect of Al 2 O 3 -water nanofluid on the heat transfer and entropy generation of laminar forced convection through isotropic porous media

“…This extensive research has led to the development of various porous media applications such as porous media receivers [2], heat exchangers [3], nanofluid flow in double pipe heat exchangers [4], geopolymers and Vycor glasses [5], treeshaped fissures [6], and metal honeycombs [7]. In addition, an extensive discussion on the applications of porous media in modern technology has been provided in the most recent version of handbook of porous media [8].…”

“…(6) and second law analysis is performed for an Al 2 O 3 -water nanofluid, flowing through an isotropic porous media, consisting of commonly applied arrangements of square pillars, namely staggered and in-line. In order to assure the best thermal performance for both arrangements, a longitudinal distance of 2H between the square pillars is considered [13].…”