Abstract
In recent developments of shale reservoirs, it is important to estimate the permeabilities of hydraulic fractures accompanying the Non- Darcy effects and geometric changes. Accordingly, a new permeability estimation method that considers the varying geometric features under different flow regions is demanded. To this end, the present study introduces the generalized Darcy’s friction flow relation, especially for examining the friction factor-Reynolds number (f · Re) relationship of porous flow, which is originally used in general internal friction flow analyses. Moreover, simple hydraulic fractures comprising structured microbeads are simulated via computational fluid dynamics during fracture aperture variations under different flow conditions from laminar to turbulent. Frictional flow features, e.g., the preservation characteristics of f · Re values, are examined under different geometry and flow conditions, and the transient flow characteristics are investigated using streamline analyses. Consequently, it is verified that the f · Re values vary slightly in proportion to the geometric changes caused by aperture reduction in each medium. Even though the variations in the f · Re values are much smaller than the permeability variations, it seems to be contrary to our expectation. Otherwise, the almost linear-variation aspects of f · Re values were observed in both directional flow cases. The linear-variation aspect of f · Re values is expected to be useful in the permeability-variation estimations in porous media with changing basic geometric factors, such as hydraulic fracture closing. Moreover, it is demonstrated that regardless of aperture reduction in the same type of medium, each porous flow has a very similar power-law relation between f and Re values when the flow velocity changes from the laminar to the turbulent condition. This aspect can be effectively used for obtaining permeability estimations of the varied media, particularly under different flow conditions.
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