Abstract
Permeability estimation has been extensively researched in diverse fields; however, methods that suitably consider varying geometries and changes within the flow region, for example, hydraulic fracture closing for several years, are yet to be developed. Therefore, in the present study a new permeability estimation method is presented based on the generalized Darcy’s friction flow relation, in particular, by examining frictional flow parameters and characteristics of their variations. For this examination, computational fluid dynamics (CFD) simulations of simple hydraulic fractures filled with five layers of structured microbeads and accompanied by geometry changes and flow transitions are performed. Consequently, it was checked whether the main structures and shapes of each flow path are preserved, even for geometry variations within porous media. However, the scarcity and discontinuity of streamlines increase dramatically in the transient- and turbulent-flow regions. The quantitative and analytic examinations of the frictional flow features were also performed. Accordingly, the modified frictional flow parameters were successfully presented as similarity parameters of porous flows. In conclusion, the generalized Darcy’s friction flow relation and friction equivalent permeability (FEP) equation were both modified using the similarity parameters. For verification, the FEP values of the other aperture models were estimated and then it was checked whether they agreed well with the original permeability values. Ultimately, the proposed and verified method is expected to efficiently estimate permeability variations in porous media with changing geometric factors and flow regions, including such instances as hydraulic fracture closings.
Highlights
Permeability estimation has been extensively researched in diverse fields such as atomic power, biomechanics, architecture and petroleum engineering
The averaged streamline velocity is the only available variable to describe the detouring and complex flow paths through tortuous pores, but it must be valid only in the laminar-flow region, as we investigated in the previous section
The present study mainly aimed to present a new method that may be used to estimate permeability values in cases where there may be varying geometrical and flow changes in porous media, within both laminar and turbulent flow regimes
Summary
Conditions (typically, turbulent to laminar) should be clarified for production forecasts (Cipolla, 2010). It was attempted to characterize the overall friction loss of whole pore networks originated from various flow loss elements, such as tortuosity, reduction, expansion, divergence, etc., using the friction factor–Reynolds number relationship from a macroscopic point of view instead of integrating all the microscopic features of each pore path individually This kind of theoretical approach based on f · Re has the advantage that it is applicable to turbulent-flow regions as well as laminar-flow regions (White, 2001). An attempt is made to examine the preservation characteristics of frictional flow parameters, which can be effectively used for permeability estimations of hydraulic fractures, regardless of variations in geometric features and flow conditions. The verified method is expected to efficiently estimate the permeability variations in porous media with constantly changing geometric factors and flow regions, such as hydraulic fracture closing
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