• Transactions of the Korean Society of Mechanical Engineers B
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• v.41 no.4
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• pp.229-238
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• 2017

This study started to deduce a permeability relationship that can consider the geometric features of various porous media under different flow regimes. With reference to the previous works of Kozeny and Carman, the conventional Darcy-Weisbach relation (Darcy's friction flow equation) was reviewed and expanded for porous flow analysis. Based on the capillary model, this relation was transformed to the friction equivalent permeability (FEP) definition. The validity of the FEP definition was confirmed by means of comparison with the Kozeny-Carman equation. Hereby, it was shown that the FEP definition is the generalized form of the Kozeny-Carman equation, which is confined to laminar flow through a circular capillary. In conclusion, the FEP definition as a new permeability estimation method was successfully developed by expanding the Darcy-Weisbach relation for porous flow analyses.

• Journal of computational fluids engineering
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• v.21 no.4
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• pp.19-27
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• 2016

The flow analyses through a porous hydraulic fractures is among the most important tasks in recently developed shale reservoirs but is rendered difficult by non-Darcy effects and geometric changes in the hydraulic fractures during production. In this study, several Computational Fluid Dynamics(CFD) models of hydraulic fractures, with a simple shape such as that of parallel plates, filled with proppants were built. Direct Numerical Simulation(DNS) analyses were then carried out to examine the flow loss characteristics of the fractures. The hydraulic diameters for the simulation models were calculated using the DNS results, and then they were compared with the results from Kozeny's definition of hydraulic diameter which is most widely used in the flow analysis field. Also, the characteristic parameters based on both hydraulic diameters were estimated for the investigation of the flow loss variation features. Consequently, it was checked in this study that the hydraulic diameter based on Kozeny's definition is not accordant to the results from the DNS analyses, and the case using the CFD results exhibits f Re robustness like general pipe flows, whereas the other case using Kozeny's definition doesn't. Ultimately, it is expected that discoveries reported in this study would help further porous flow analyses such as hydraulic fracture flows.